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THE ASTRONOMICAL JOURNAL, 116 : 1009 õ1038, 1998 September
( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

OBSERVATIONAL EVIDENCE FROM SUPERNOVAE FOR AN ACCELERATING UNIVERSE AND A COSMOLOGICAL CONSTANT ADAM G. RIESS,1 ALEXEI PETER M. GARNAVICH,2 B. LEIBUNDGUT,6 M. R. V. FILIPPENKO,1 PETER CHALLIS,2 ALEJANDRO CLOCCHIATTI,3 ALAN DIERCKS,4 RON L. GILLILAND,5 CRAIG J. HOGAN,4 SAURABH JHA,2 ROBERT P. KIRSHNER,2 M. PHILLIPS,7 DAVID REISS,4 BRIAN P. SCHMIDT,8,9 ROBERT A. SCHOMMER,7 CHRIS SMITH,7,10 J. SPYROMILIO,6 CHRISTOPHER STUBBS,4 NICHOLAS B. SUNTZEFF,7 AND JOHN TONRY11
Received 1998 March 13 ; revised 1998 May 6

ABSTRACT We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 ¹ z ¹ 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters : the Hubble constant (H ), the mass density () ), the cosmological constant (i.e., the 0 M vacuum energy density, ) ), the deceleration parameter (q ), and the dynamical age of the universe (t ). " 0 õ15% farther than expected in a low mass 0 The distances of the high-redshift SNe Ia are, on average, 10% density () \ 0.2) universe without a cosmological constant. Dierent light curve ïtting methods, SN Ia M subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant (i.e., ) [ 0) and a current acceleration of the expansion (i.e., q \ 0). With no prior " 0 constraint on mass density other than ) º 0, the spectroscopically conïrmed SNe Ia are statistically M p conïdence levels, and with ) [ 0 at the 3.0 p and 4.0 p consistent with q \ 0 at the 2.8 p and 3.9 " conïdence levels, 0for two dierent ïtting methods, respectively. Fixing a "" minimal îî mass density, ) \ M 0.2, results in the weakest detection, ) [ 0 at the 3.0 p conïdence level from one of the two methods. " the spectroscopically conïrmed SNe Ia require ) [ 0 at 7 p For a ÿat universe prior () ] ) \ 1), M " and 9 p formal statistical signiïcance for the two dierent ïtting methods. A universe closed"by ordinary matter (i.e., ) \ 1) is formally ruled out at the 7 p to 8 p conïdence level for the two dierent ïtting M methods. We estimate the dynamical age of the universe to be 14.2 ^ 1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely eect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these eects appear to reconcile the data with ) \ 0 and q º 0. " 0 Key words : cosmology : observations õ supernovae : general

õõõõõõõõõõõõõõõ 1 Department of Astronomy, University of California at Berkeley, Berkeley, CA 94720-3411. 2 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138. 3 Departamento de Astronom·a y Astrof ·sica, Pontiïcia Universidad Catolica, Casilla 104, Santiago 22, Chile. 4 Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195. 5 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei Munchen, Germany. 7 Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatories, Casilla 603, La Serena, Chile. NOAO is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 8 Mount Stromlo and Siding Spring Observatories, Private Bag, Weston Creek, ACT 2611, Australia. 9 Visiting Astronomer, Cerro Tololo Inter-American Observatory. 10 Department of Astronomy, University of Michigan, 834 Dennison Building, Ann Arbor, MI 48109. 11 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822.

1

. INTRODUCTION

This paper reports observations of 10 new high-redshift Type Ia supernovae (SNe Ia) and the values of the cosmological parameters derived from them. Together with the four high-redshift supernovae previously reported by our High-z Supernova Search Team (Schmidt et al. 1998 ; Garnavich et al. 1998a) and two others (Riess et al. 1998b), the sample of 16 is now large enough to yield interesting cosmological results of high statistical signiïcance. Conïdence in these results depends not on increasing the sample size but on improving our understanding of systematic uncertainties. The time evolution of the cosmic scale factor depends on the composition of mass-energy in the universe. While the universe is known to contain a signiïcant amount of ordinary matter, ) , which decelerates the expansion, its M dynamics may also be signiïcantly aected by more exotic forms of energy. Preeminent among these is a possible energy of the vacuum () ), Einsteinîs "" cosmological con" 1009


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RIESS ET AL.

Vol. 116 1.2. A Brief History of Supernova Cosmology

stant,îî whose negative pressure would do work to accelerate the expansion (Carroll, Press, & Turner 1992 ; Schmidt et al. 1998). Measurements of the redshift and apparent brightness of SNe Ia of known intrinsic brightness can constrain these cosmological parameters. 1.1. T he High-z Program Measurement of the elusive cosmic parameters ) and ) through the redshift-distance relation depends onMcom" paring the apparent magnitudes of low-redshift SNe Ia with those of their high-redshift cousins. This requires great care to assure uniform treatment of both the nearby and distant samples. The High-z Supernova Search Team has embarked on a program to measure supernovae at high redshift and to develop the comprehensive understanding of their properties required for their reliable use in cosmological work. Our team pioneered the use of supernova light curve shapes to reduce the scatter about the Hubble line from pB 0.4 mag to pB 0.15 mag (Hamuy et al. 1996a, 1996c, 1995 ; Riess, Press, & Kirshner 1995, 1996a). This dramatic improvement in the precision of SNe Ia as distance indicators increases the power of statistical inference for each object by an order of magnitude and sharply reduces their susceptibility to selection bias. Our team has also pioneered methods for using multicolor observations to estimate the reddening to each individual supernova, near and far, with the aim of minimizing the confusion between eects of cosmology and dust (Riess et al. 1996a ; Phillips et al. 1998). Because the remaining scatter about the Hubble line is so small, the discussion of the Hubble constant from lowredshift SNe Ia has already passed into a discussion of the best use of Cepheid distances to galaxies that have hosted SNe Ia (Saha et al. 1997 ; Kochanek 1997 ; Madore & Freedman 1998 ; Riess et al. 1996a ; Hamuy et al. 1996c ; Branch 1998). As the use of SNe Ia for measuring ) and ) proM " gresses from its infancy into childhood, we can expect a similar shift in the discussion from results limited principally by statistical errors to those limited by our depth of understanding of SNe Ia. Published high-redshift SN Ia data are a small fraction of the data in hand both for our team and for the Supernova Cosmology Project (Perlmutter et al. 1995, 1997, 1998). Now is an opportune time to spell out details of the analysis, since further increasing the sample size without scrupulous attention to photometric calibration, uniform treatment of nearby and distant samples, and an eective way to deal with reddening will not be proïtable. Besides presenting results for four high-z supernovae, we have published details of our photometric system (Schmidt et al. 1998) and stated precisely how we used ground-based photometry to calibrate our Hubble Space T elescope (HST ) light curves (Garnavich et al. 1998b). In this paper, we spell out details of newly observed light curves for 10 objects, explain the recalibration of the relation of light curve shape and luminosity for a large low-redshift sample, and combine all the data from our teamîs work to constrain cosmological parameters. We also evaluate how systematic eects could alter the conclusions. While some comparison with the stated results of the Supernova Cosmology Project (Perlmutter et al. 1995, 1997, 1998) is possible, an informed combination of the data will have to await a similarly detailed description of their measurements.

While this paper emphasizes new data and constraints for cosmology, a brief summary of the subject may help readers connect work on supernovae with other approaches to measuring cosmological parameters. Empirical evidence for SNe I presented by Kowal (1968) showed that these events had a well-deïned Hubble diagram whose intercept could provide a good measurement of the Hubble constant. Subsequent evidence showed that the original spectroscopic class of Type I should be split (Doggett & Branch 1985 ; Uomoto & Kirshner 1985 ; Wheeler & Levreault 1985 ; Wheeler & Harkness 1990 ; Porter & Filippenko 1987). The remainder of the original group, now called Type Ia, had peak brightness dispersions of 0.4 mag to 0.6 mag (Tammann & Leibundgut 1990 ; Branch & Miller 1993 ; Miller & Branch 1990 ; Della Valle & Panagia 1992 ; Rood 1994 ; Sandage & Tammann 1993 ; Sandage et al. 1994). Theoretical models suggested that these "" standard candles îî arise from the thermonuclear explosion of a carbon-oxygen white dwarf that has grown to the Chandrasekhar mass (Hoyle & Fowler 1960 ; Arnett 1969 ; Colgate & McKee 1969). Because SNe Ia are so luminous (M B [19.5 mag), Colgate (1979) suggested that B observations of SNe Ia at z B 1 with the forthcoming Space Telescope could measure the deceleration parameter, q . From a methodical CCD-based supernova search0 that spaced observations across a lunation and employed prescient use of image-subtraction techniques to reveal new objects, Hansen, Jòrgensen, & Nòrgaard-Nielsen (1987) detected SN 1988U, a SN Ia at z \ 0.31 (Nòrgaard-Nielsen et al. 1989). At this redshift and distance precision (pB 0.4 to 0.6 mag), D100 SNe Ia would have been needed to distinguish between an open and a closed universe. Since the Danish group had already spent 2 years to ïnd one object, it was clear that larger detectors and faster telescopes needed to be applied to this problem. Evidence of systematic problems also lurked in supernova photometry, so that merely increasing the sample would not be adequate. Attempts to correct supernova magnitudes for reddening by dust (Branch & Tammann 1992) based on the plausible (but incorrect) assumption that all SNe Ia have the same intrinsic color had the unfortunate eect of increasing the scatter about the Hubble line or alternately attributing bizarre properties to the dust absorbing SN Ia light in other galaxies. In addition, wellobserved supernovae such as SN 1986G (Phillips et al. 1987 ; Cristiani et al. 1992), SN 1991T (Filippenko et al. 1992a ; Phillips et al. 1992 ; Ruiz-Lapuente et al. 1992), and SN 1991bg (Filippenko et al. 1992b ; Leibundgut et al. 1993 ; Turatto et al. 1996) indicated that large and real inhomogeneity was buried in the scatter about the Hubble line. Deeper understanding of low-redshift supernovae greatly improved their cosmological utility. Phillips (1993) reported that the observed peak luminosity of SNe Ia varied by a factor of 3. But he also showed that the decrease in B brightness in the 15 days after peak [*m (B)] was a good predictor of the SN Ia luminosity,15with slowly declining supernovae more luminous than those which fade rapidly. A more extensive database of carefully and uniformly observed SNe Ia was needed to reïne the understanding of SN Ia light curves. The Calan/Tololo survey (Hamuy et al. 1993a) made a systematic photographic search for supernovae between cycles of the full Moon. This search was


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EVIDENCE FOR AN ACCELERATING UNIVERSE

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extensive enough to guarantee the need for scheduled follow-up observations, which were supplemented by the cooperation of visiting observers, to collect well-sampled light curves. Analysis of the Calan/Tololo results generated a broad understanding of SNe Ia and demonstrated their remarkable distance precision (after template ïtting) of pB 0.15 mag (Hamuy et al. 1995, 1996a, 1996b, 1996c, 1996d ; Tripp 1997, 1998). A parallel eort employed data from the Calan/Tololo survey and from the Harvard Smithsonian Center for Astrophysics (CfA) to develop detailed empirical models of SN Ia light curves (Riess et al. 1995 ; Riess 1996). This work was extended into the multicolor light curve shape (MLCS) method, which employs up to four colors of SN Ia photometry to yield excellent distance precision (B0.15 mag) and a statistically valid estimate of the uncertainty for each object with a measurement of the reddening by dust for each event (Riess et al. 1996a ; see Appendix of this paper). This work has also placed useful constraints on the nature of dust in other galaxies (Riess et al. 1996b ; but see Tripp 1998). The complete sample of nearby SNe Ia light curves from the Calan/Tololo and CfA samples provides a solid founda tion from which to extend the redshift-distance relation to explore cosmological parameters. The low-redshift sample used here has 34 SNe Ia with z \ 0.15. Since the high-redshift observations reported here consumed large amounts of observing time at the worldîs ïnest telescopes, we have a strong incentive to ïnd efficient ways to use the minimum set of observations to derive the distance to each supernova. A recent exploration of this by Riess et al. (1998b) is the "" snapshot îî method, which uses only a single spectrum and a single set of photometric measurements to infer the luminosity distance to a SN Ia with D10% precision. In this paper, we employ the snapshot method for six SNe Ia with sparse data, but a shrewdly designed program that was intended to use the snapshot approach could be even more eective in extracting useful results from slim slices of observing time. Application of large-format CCDs and sophisticated image analysis techniques by the Supernova Cosmology Project (Perlmutter et al. 1995) led to the discovery of SN 1992bi (z \ 0.46), followed by six more SNe Ia at z B 0.4 (Perlmutter et al. 1997). Employing a correction for the luminosity/light curve shape relation (but none for host galaxy extinction), comparison of these SNe Ia to the Calan/Tololo sample gave an initial indication of "" low îî ) " and "" high îî ) : ) \ 0.06`0.28 for a ÿat universe and Mfor a universe without a cosmological con" ~0.34 ) \ 0.88`0.69 M ~0.60 stant () 4 0). The addition of one very high redshift " SN Ia observed with HST had a signiïcant eect (z \ 0.83) on the results : ) \ 0.4 ^ 0.2 for a ÿat universe, and ) \ M 0.2 ^ 0.4 for a " universe with ) 4 0. (Perlmutter et al. " volatile the subject is 1998). This illustrates how young and at present. 1.3. T his Paper Our own High-z Supernova Search Team has been assiduously discovering high-redshift supernovae, obtaining their spectra, and measuring their light curves since 1995 (Schmidt et al. 1998). The goal is to provide an independent set of measurements that uses our own techniques and compares our data at high and low redshifts to constrain the cosmological parameters. Early results from four SNe Ia (three observed with HST ) hinted at a non-negligible cosmological constant and "" low îî ) but were limited by M

statistical errors : ) \ 0.65 ^ 0.3 for a ÿat universe, ) \ " M [0.1 ^ 0.5 when ) 4 0 (Garnavich et al. 1998a). Our aim " in this paper is to move the discussion forward by increasing the data set from four high-redshift SNe to 16, to spell out exactly how we have made the measurement, and to consider various possible systematic eects. In ° 2 we describe the observations of the SNe Ia including their discovery, spectral identiïcation, photometric calibration, and light curves. We determine the luminosity distances (including K-corrections) via two methods, MLCS and a template-ïtting method [*m (B)], as 15 explained in ° 3. Statistical inference of the cosmological parameters including H , ) , ) , q , t , and the fate of the 0 M "00 universe is contained in ° 4. Section 5 presents a quantitative discussion of systematic uncertainties that could aect our results : evolution, absorption, selection bias, a local void, weak lensing, and sample contamination. Our conclusions are summarized in ° 6.
2

. OBSERVATIONS

2.1. Discovery We have designed a search program to ïnd supernovae in the redshift range 0.3 \ z \ 0.6 with the purpose of measuring luminosity distances to constrain cosmological parameters (Schmidt et al. 1998). Distances are measured with the highest precision from SNe Ia observed before maximum brightness and in the redshift range of 0.35 \ z \ 0.55, where our set of custom passbands measures the supernova light emitted in rest-frame B and V . By imaging ïelds near the end of a dark run, and then again at the beginning of the next dark run, we ensure that the newly discovered supernovae are young (Nòrgaard-Nielsen et al. 1989 ; Hamuy et al. 1993a ; Perlmutter et al. 1995). Observing a large area and achieving a limiting magnitude of m B 23 mag yields many SN Ia candidates in the desired R redshift range (Schmidt et al. 1998). By obtaining spectra of these candidates with 4 m to 10 m telescopes, we can identify the SNe Ia and conïrm their youth using the spectral feature aging technique of Riess et al. (1997). The 10 new SNe Ia presented in this paper (SN 1995ao, SN 1995ap, SN 1996E, SN 1996H, SN 1996I, SN 1996J, SN 1996K, SN 1996R, SN 1996T, and SN 1996U) were discovered using the CTIO 4 m Blanco Telescope with the facility prime-focus CCD camera as part of a three-night program in 1995 OctoberõNovember and a six-night program in 1996 FebruaryõMarch. This instrument has a pixel scale of 0A43, and the Tek 2048 ] 2048 pixel CCD . frame covers 0.06 deg2. In each of the search programs, multiple images were combined after removing cosmic rays, dierenced with "" template îî images, and searched for new objects using the prescription of Schmidt et al. (1998). The data on 1995 October 27 and November 17 were gathered under mediocre conditions, with most images having seeing worse than 1A . The resulting dierenced images were suffi.5 cient to ïnd new objects brighter than m \ 22.5 mag. The R data acquired in 1996 had better image quality (D1A5), and . the dierenced images were sufficient to uncover new objects brighter than m \ 23 mag. R In total, 19 objects were identiïed as possible supernovaeõtwo new objects were detected on each of 1995 November 17 and 1995 November 29, ïve new objects on 1996 February 14 õ15, two on 1996 February 20 õ21, and eight on 1996 March 15 õ16 (Kirshner et al. 1995 ; Garnavich et al. 1996a, 1996b).


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RIESS ET AL. were SNe Ia, one was a SN II, and two were active galactic nuclei or SNe II (Kirshner et al. 1995 ; Garnavich et al. 1996a, 1996b). The remaining six candidates were observed, but the spectra did not have sufficient signal to allow an unambiguous classiïcation. The identiïcation spectra for the 10 new SNe Ia are summarized in Table 1 and shown in Figure 1. In addition we include the spectral data for three previously analyzed SNe : SN 1997ce, SN 1997cj, and SN 1997ck (Garnavich et al. 1998a). The spectral data for SN 1995K are given by Schmidt et al. (1998). The spectrum of SN 1997ck shows only an [O II] emission line at 7328.9 ñ in four separate exposures (Garnavich et al. 1998a). The equivalent R-band magnitude of the exposure was 26.5, which is more than 1.5 mag dimmer than the supernova would have been in R, suggesting that the SN was not in the slit when the host galaxy was observed. Most of the host galaxies showed emission lines of [O II], [O III], or Ha in the spectrum, and the redshift was easily measured for these. For the remainder, the redshift was found by matching the broad features in the high-redshift supernovae to those in local supernova spectra. The intrinsic dispersion in the expansion velocities of SNe Ia (Branch et al. 1988 ; Branch & van den Bergh 1993) limits the precision of this method to 1 pB 2500 km s~1 independent of the signal-to-noise ratio of the SN spectrum. The method used to determine the redshift for each SN is given in Table 1. Following the discovery and identiïcation of the SNe Ia, photometry of these objects was obtained from observatories scheduled around the world. The SNe were primarily observed through custom passbands designed to match the wavelength range closest to rest-frame Johnson B and V passbands. Our "" B45,îî "" V45,îî "" B35,îî and "" V35 îî ïlters are speciïcally designed to match Johnson B and V redshifted by z \ 0.45 and z \ 0.35, respectively. The characteristics of these ïlters are described by Schmidt et al. (1998). A few observations were obtained through standard bandpasses as noted in Table 2, where we list the photometric observations for each SN Ia. Photometry of local standard stars in the supernova ïelds in the B35, V35, B45, V45 (or "" supernova îî) photometric system were derived from data taken on three photometric nights. The method has been described in Schmidt et

2.2. Data Spectra of the supernova candidates were obtained to classify the SNe and obtain redshifts of their host galaxies. For this purpose, the Keck Telescope, Multiple Mirror Telescope (MMT), and the European Southern Observatory 3.6 m (ESO 3.6 m) were utilized following the fall of 1995 and spring of 1996 search campaigns. Some galaxy redshifts were obtained with the Keck Telescope in the spring of 1998. The Keck spectra were taken with the Low Resolution Imaging Spectrograph (LRIS ; Oke et al. 1995), providing a resolution of 6 ñ full width at half-maximum (FWHM). Exposure times were between 3 ] 900 and 5 ] 900 s, depending on the candidate brightness. The MMT spectra were obtained with the Blue Channel Spectrograph and 500 line mm~1 grating, giving a resolution of 3.5 ñ FWHM. Exposure times were 1200 s and repeated ïve to seven times. The MMT targets were placed on the slit using an oset from a nearby bright star. The ESO 3.6 m data were collected with the ESO Faint Object Spectrograph Camera (EFOSC1) at a nominal resolution of 18 ñ FWHM. Single 2700 s exposures were made of each target. Using standard reduction packages in IRAF, the CCD images were bias-subtracted and divided by a ÿat-ïeld frame created from a continuum lamp exposure. Multiple images of the same object were shifted where necessary and combined using a median algorithm to remove cosmic-ray events. For single exposures, cosmic rays were removed by hand using the IRAF/IMEDIT routine. Sky emission lines were problematic, especially longward of 8000 ñ. The spectra were averaged perpendicular to the dispersion direction, and that average was subtracted from each line along the dispersion. However, residual noise from the sky lines remains. The one-dimensional spectra were then extracted using the IRAF/APSUM routine and wavelength-calibrated either from a comparison lamp exposure or the sky emission lines. The ÿux was calibrated using observations of standard stars and the IRAF/ONEDSTDS database. The candidates were classiïed from visual inspection of their spectra and comparison with the spectra of wellobserved supernovae (see ° 5.7). In all, 10 of the candidates

TABLE 1 HIGH-z SUPERNOVA SPECTROSCOPY SN 1995ao ...... 1995ap ...... 1996E ....... 1996H ...... 1996I ....... 1996J ....... 1996K ...... 1996R ...... 1996T ....... 1996U ...... 1997ce ...... 1997cj ...... 1997cj ...... 1997ck ...... UT Date 1995 1995 1996 1996 1996 1996 1996 1996 1996 1996 1997 1997 1997 1997 Nov 23 Nov 23 Feb 23 Feb 23 Feb 23 Feb 23 Feb 23 Mar 18 Mar 18 Mar 18 May 4 May 2 May 4 May 4 Telescope Keck I Keck I ESO 3.6 ESO 3.6 ESO 3.6 ESO 3.6 ESO 3.6 MMT MMT MMT Keck II MMT Keck II Keck II Spectral Range (nm) 510 510 600 600 600 600 600 400 400 400 570 400 570 570 õ1000 õ1000 õ990 õ990 õ990 õ990 õ990 õ900 õ900 õ900 õ940 õ900 õ940 õ940 Redshift 0.24b 0.30c 0.43b 0.62b 0.57c 0.30b 0.38c 0.16b 0.24b 0.43b 0.44c 0.50b 0.50c 0.97b Comparison a 1996X([4) 1996X([4) 1989B(]9) 1996X(]5) 1996X(]5) 1995D(]0) 1995D(]0) 1989B(]12) 1996X([4) 1995D(]0) 1995D(]0) ... 1995D(]0) ...

m m m m m

a Supernova and its age (relative to B maximum) used for comparison spectrum in Fig. 1. b Derived from emission lines in host galaxy. c Derived from broad features in SN spectrum.


FIG. 1.õIdentiïcation spectra (in f ) of high-redshift SNe Ia. The spectra obtained for the 10 new SNe of the high-redshift sample are shown in the rest j frame. The data are compared to nearby SN Ia spectra of the same age as determined by the light curves (see Table 1). The spectra of the three objects from Garnavich et al. (1998a) are also displayed.


TABLE 2 SN Ia IMAGING JDa UT Date B45 V45 SN 1996E 127.6 128.6 132.1 134.6 135.5 138.7 139.6 157.6 163.7 ...... ...... ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 1996 1996 Feb Feb Feb Feb Feb Feb Feb Mar Mar 14 15 19 21 22 25 26 15 21 22.30(0.09) 22.27(0.04) 22.46R(0.11) 22.66(0.10) 22.68(0.13) 23.04(0.12) 22.89(0.15) 24.32(0.18) ... ... 21.86(0.08) ... 21.99(0.26) 22.09(0.06) 22.29(0.15) 22.72(0.33) 23.51(0.77) 22.87(0.50) SN 1996H 127.6 128.6 132.1 134.6 135.5 136.6 138.7 139.6 140.6 141.6 142.6 157.6 161.6 164.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 Feb Feb Feb Feb Feb Feb Feb Feb Feb Feb Feb Mar Mar Mar 14 15 19 21 22 23 25 26 27 28 29 15 19 22 22.78(0.13) 22.81(0.06) 22.71R(0.29) 22.85(0.08) 22.83(0.18) 22.84(0.13) 22.85(0.09) 22.88(0.15) 22.96(0.16) 23.05(0.08) 23.21(0.20) 23.98(0.22) 24.16(0.22) ... ... 22.25(0.14) 22.40I(0.37) 22.48(0.19) 22.28(0.10) ... 22.58(0.15) 22.52(0.25) 23.10(0.10) ... 22.69(0.16) 23.18(0.28) ... 24.01(0.30) SN 1996I 128.6 132.1 134.6 135.5 136.6 138.7 140.6 142.6 157.6 161.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 Feb Feb Feb Feb Feb Feb Feb Feb Mar Mar 15 19 21 22 23 25 27 29 15 19 22.77(0.05) 22.95(0.22) 22.95(0.05) 22.92(0.05) 22.88(0.09) 23.12(0.13) 23.64(0.36) 23.48(0.10) 24.83(0.17) 24.70(0.31) ... 22.30(0.22) 22.65(0.15) 22.64(0.20) 22.74(0.28) 22.86(0.17) 22.67(0.36) 23.06(0.22) 23.66(0.30) ... SN 1996J 127.6 128.6 134.6 135.6 135.6 139.7 140.7 157.6 161.8 166.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 Feb Feb Feb Feb Feb Feb Feb Mar Mar Mar 14 15 21 22 22 26 27 15 19 24 22.01(0.02) 21.95(0.03) 21.57(0.03) 21.62(0.04) ... 21.63(0.04) ... 22.77(0.05) ... ... ... 21.95(0.07) 21.59(0.05) 21.61(0.04) ... 21.46(0.07) ... 22.06(0.12) ... ... SN 1996K 128.5 135.5 135.5 135.7 136.6 138.6 138.7 139.6 140.8 157.5 157.5 161.7 162.6 165.6 168.5 169.7 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 1996 Feb Feb Feb Feb Feb Feb Feb Feb Feb Mar Mar Mar Mar Mar Mar Mar 15 22 22 22 23 25 25 26 27 15 15 19 20 23 26 27 23.74(0.04) 22.49(0.07) 22.52(0.07) 22.56(0.03) 22.48(0.05) 22.15(0.10) 22.18(0.07) 22.37(0.05) ... 22.83(0.07) 22.81(0.09) 23.20(0.16) 23.17(0.06) ... ... 24.05(0.26) ... ... ... 22.48(0.06) 22.26(0.16) 22.47(0.11) ... 22.42(0.13) ... ... ... 22.45(0.13) 22.79(0.12) ... ... ... ... ... ... ... ... ... ... ... 22.23(0.10) 22.93(0.12) 22.86(0.10) 23.17(0.17) ... 23.58(0.16) ... 24.42(0.25) ... ... ... ... ... ... ... ... 22.06(0.11) 22.61(0.19) 22.45(0.10) 22.69(0.15) ... 23.17(0.14) 23.20(0.19) ... CTIO 4 m ESO 3.6 m ESO 3.6 m ESO 3.6 m ESO 1.5 m ESO 1.5 m ESO 1.5 m ESO 1.5 m ESO 1.5 m CTIO 4 m CTIO 4 m CTIO 4 m WIYN CTIO 1.m CTIO 1.m MDM ... ... ... 21.84(0.03) 21.89(0.04) ... 21.90(0.07) 23.69(0.07) 24.34(0.19) ... ... ... ... 21.46(0.06) 21.47(0.02) ... 21.77(0.05) 21.83(0.04) 22.05(0.05) 22.76(0.07) CTIO 4 m CTIO 4 m CTIO 4 m ESO 3.6 m ESO 3.6 m ESO 1.5 m ESO 1.5 m CTIO 4 m CTIO 4 m CTIO 1.5 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CTIO 4 m ESO NTT CTIO 4 m ESO 3.6 m ESO 3.6 m ESO 1.5 m ESO 1.5 m WIYN CTIO 4 m CTIO 4 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CTIO 4 m CTIO 4 m ESO NTT CTIO 4 m ESO 3.6 m ESO 3.6 m ESO 1.5 m ESO 1.5 m ESO 1.5 m WIYN WIYN CTIO 4 m CTIO 4 m WIYN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CTIO 4 m CTIO 4 m ESO NTT CTIO 4 m CTIO 4 m ESO 1.5 m ESO 1.5 m CTIO 4 m WIYN B35 V35 Telescope


EVIDENCE FOR AN ACCELERATING UNIVERSE
TABLE 2õContinued JDa UT Date B45 V45 SN 1996R 157.7 158.7 167.7 191.7 ...... ...... ...... ...... 1996 1996 1996 1996 Mar Mar Mar Apr 15 16 25 18 20.48(0.01) 20.59(0.03) ... 22.41(0.09) ... 20.70(0.03) ... ... SN 1996T 161.7 167.6 191.7 212.6 ...... ...... ...... ...... 1996 1996 1996 1996 Mar 19 Mar 25 Apr 18 May 9 20.83R(0.03) 20.95R(0.04) ... 22.52R(0.08) . . . . . . . . . . . . 20.86V(0.02) 20.96V(0.03) 22.37V(0.17) 22.99V(0.31) . . . . . . . . . . . . CTIO 4 m CTIO 1.5 m ESO 1.5 m WIYN . . . . . . . . . . . . . . 21.62 . . . V . . . (0.04) . CTIO 4 m CTIO 4 m CTIO 1.5 m ESO 1.5 m B35 V35 Telescope

1015

SN 1996U 158.7 160.7 161.7 165.7 167.7 186.7 188.7 ...... ...... ...... ...... ...... ...... ...... 1996 1996 1996 1996 1996 1996 1996 Mar Mar Mar Mar Mar Apr Apr 16 18 19 23 25 13 15 22.16(0.04) 22.00(0.11) 22.04(0.05) ... 22.19(0.10) 23.33R(0.17) 23.51(0.17) ... 22.03(0.18) 22.23(0.26) 22.35(0.28) ... 22.64I(0.28) 22.96(0.36) SN 1995ao 39.6 ....... 46.6 ....... 51.6 ....... 1995 Nov 18 1995 Nov 25 1995 Nov 30 21.42(0.05) 21.30(0.03) 21.24(0.05) ... 21.10(0.13) ... SN 1995ap 39.6 46.6 48.6 51.6 ....... ....... ....... ....... 1995 1995 1995 1995 Nov Nov Nov Nov 18 25 27 30 22.41(0.14) 21.13(0.08) 21.04(0.11) 21.04(0.11) ... 21.40(0.10) ... ... ... ... ... 21.65(0.09) ... ... ... 20.92(0.07) CTIO 4 m WIYN WIYN CTIO 4 m ... ... 21.52(0.05) ... ... 21.12(0.03) CTIO 4 m WIYN CTIO 4 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CTIO 4 m MDM CTIO 4 m CTIO 1.5 m CTIO 1.5 m Las Campanas WIYN

NOTE.õUncertainties in magnitudes are listed in parentheses. a Actually JD [ 2,450,000.

al. (1998) but we summarize it here. The supernova photometric system has been deïned by integrating the ÿuxes of spectrophotometric standards from Hamuy et al. (1994) through the supernova bandpass response functions (based on the ïlter transmissions and a typical CCD quantum efficiency function) and solving for the photometric coefficients that would yield zero color for these stars and monochromatic magnitudes of 0.03 for Vega. This theoretically deïned photometric system also provides transformations between the Johnson/Kron-Cousins system and the supernova system. We use theoretically derived transformations to convert the known V , R, and I magnitudes of Landolt (1992) standard ïelds into B35, V35, B45, V45 photometry. On nights that are photometric, we observe Landolt standard ïelds with the B35, V35, B45, V45 ïlters and measure the starsî instrumental magnitudes from apertures large enough to collect all the stellar light. We then derive the transformation from the supernova system to the instrumental system as a function of the instrumental magnitudes, supernova system colors, and observed air mass. Because our theoretical response functions are very similar to the instrumental response functions, our measured color coefficients were small, typically less than 0.02 mag per mag of B45 [ V45 or B35 [ V35. These long-wavelength ïlters also reduced the eect of atmospheric extinction (compared to B and V ). Typical extinction coefficients were 0.11, 0.09, 0.07, and 0.06 mag per air mass for B35, B45, V35, and V45, respectively. Isolated stars on each supernova frame were selected as

local standards. The magnitudes of the local standards were determined from the transformation of their instrumental magnitudes, measured from similarly large apertures. The ïnal transformed magnitudes of these local standards, averaged over three photometric nights, are given in Table 3. The locations of the local standards and the SNe are shown in Figure 2. The uncertainties in the local standardsî magnitudes are the quadrature sum of the uncertainty (dispersion) of the instrumental transformations (typically 0.02 mag) and the individual uncertainties from photon (Poisson) statistics. The dispersion in the instrumental transformation quantiïes the errors due to imperfect ÿat-ïelding, small changes in the atmospheric transparency, incomplete empirical modeling of the response function, and seeing variations. This uncertainty is valid for any single observation of the local standards. To measure the brightness of the supernovae free from host galaxy contamination, we obtained deep images of the hosts a year after, or months before, the discovery of the SNe. These images were used to subtract digitally a hostîs light from the supernovaîs light, leaving only the stellar point-spread function (PSF). The algorithms employed to match the resolution, intensity, and coordinate frames of images prior to subtraction are described in Schmidt et al. (1998). The brightness of the SNe in these uncrowded ïelds was then measured relative to the calibrated local standard stars in the ïeld by ïtting a model of a PSF to the stars and supernova using the DoPHOT algorithm (Schmidt et al. 1998 ; Mateo & Schechter 1989 ; Schechter, Mateo, & Saha 1993).


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TABLE 3 SN Ia FIELD LOCAL STANDARD STARS Star B45 V45 SN 1996E 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 20.84(0.02) 20.07(0.03) 19.60(0.03) 19.76(0.03) 19.16(0.03) 20.85(0.02) 20.71(0.02) 18.69(0.03) 19.22(0.03) 18.35(0.03) 18.29(0.03) 20.52(0.02) SN 1996H 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 18.16(0.02) 19.96(0.02) 21.13(0.02) 20.76(0.02) 19.62(0.02) 20.02(0.02) 17.84(0.02) 18.50(0.02) 19.41(0.02) 19.21(0.02) 19.23(0.02) 19.69(0.02) SN 1996I 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 19.59(0.02) 22.35(0.02) 20.62(0.02) 20.22(0.02) 17.46(0.02) 18.02(0.02) 18.67(0.02) 20.72(0.02) 18.93(0.02) 18.97(0.02) 17.18(0.02) 17.55(0.02) SN 1996J 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 18.59(0.02) 20.27(0.02) 20.20(0.02) 19.63(0.02) 21.12(0.02) 20.27(0.02) 17.38(0.02) 19.49(0.02) 19.45(0.02) 18.67(0.02) 19.63(0.02) 20.00(0.02) SN 1996K 1 2 3 4 5 6 7 ...... ...... ...... ...... ...... ...... ...... 19.06(0.02) 19.76(0.03) 19.41(0.03) 19.84(0.03) 19.30(0.02) 19.04(0.02) 18.05(0.02) 18.81(0.02) 19.43(0.03) 18.17(0.02) 18.64(0.02) 17.70(0.02) 18.06(0.02) 17.17(0.02) SN 1996R 1 2 3 4 5 ...... ...... ...... ...... ...... 17.29(0.03) 18.15(0.03) 19.05(0.03) 19.20(0.03) 18.06(0.03) 16.61(0.02) 17.78(0.03) 18.67(0.03) 18.22(0.03) 17.64(0.03) SN 1996T 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 18.29(0.02) 19.77(0.02) 20.43(0.02) 21.28(0.02) 21.28(0.02) 21.34(0.02) V V V V V V 18.01(0.02) 18.57(0.02) 19.31(0.02) 20.57(0.02) 20.27(0.02) 20.37(0.02) R R R R R R ... ... ... ... ... ... 18.01 18.48 19.51 20.02 18.54 V V V V V (0.03) (0.03) (0.03) (0.03) (0.03) . . . . . . . . . . 19.22(0.02) 19.94(0.03) 19.90(0.03) 20.28(0.03) 19.84(0.02) 19.45(0.02) 18.47(0.02) 19.09(0.02) 20.74(0.02) 20.70(0.02) 20.09(0.02) 21.69(0.02) 20.57(0.02) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B35

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TABLE 3õContinued V35 Star B45 V45 SN 1995ap . . . . . . 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 19.49(0.03) 19.19(0.03) 18.97(0.03) 19.67(0.03) 20.51(0.03) 20.90(0.03) 18.21(0.03) 18.76(0.03) 18.24(0.03) 18.61(0.03) 19.44(0.03) 20.31(0.03) 20.28(0.03) 19.54(0.03) 19.43(0.03) 20.31(0.02) 21.16(0.02) 21.53(0.02) 18.69(0.02) 18.88(0.02) 18.47(0.02) 18.98(0.02) 19.81(0.02) 20.50(0.02) B35 V35

NOTE.õUncertainties in magnitudes are listed in parentheses. . . . . . .

. . . . . .

17.85(0.02) 19.78(0.02) 19.79(0.02) 19.06(0.02) 20.20(0.02) 20.06(0.02)

18.88(0.02) 19.53(0.03) 18.62(0.02) 19.06(0.02) 18.25(0.02) 18.40(0.02) 17.49(0.02)

. . . . .

... ... ... ... ... ...

SN 1995ao 1 2 3 4 5 6 ...... ...... ...... ...... ...... ...... 20.36(0.03) ... 20.09(0.03) 20.10(0.03) 16.37(0.03) ... 20.15(0.03) ... 19.50(0.03) 19.75(0.03) 15.47(0.03) ... 20.59(0.03) 17.89(0.03) 20.50(0.03) 20.39(0.03) 16.62(0.03) 17.32(0.03) 20.19(0.03) 17.50(0.03) 19.79(0.03) 19.86(0.03) 15.73(0.03) 16.81(0.03)

Systematic and statistical components of error were evaluated by measuring the brightness of artiïcial stars added to the subtracted frames. These artiïcial stars had the same brightness and background as the measured SNe (Schmidt et al. 1998). The "" systematic îî error was measured from the dierence in the mean magnitude of the artiïcial stars before and after the image processing (i.e., alignment, scaling, "" blurring,îî and subtracting). The systematic errors were always less than 0.1 mag and were of either sign. Any signiïcant systematic error is likely the result of a mismatch in the global properties of the template image and SN image based on only examining a local region of the two images. A correction based on the systematic error determined from the artiïcial stars was applied to the measured SN magnitude to yield an unbiased estimate of the SN magnitude. The dispersion of the recovered artiïcial magnitudes about their mean was assigned to the statistical uncertainty of the SN magnitude. The supernova PSF magnitudes were transformed to the B35, V35, B45, V45 system using the local standard magnitudes and the color coefficients derived from observations of the Landolt standards. The ïnal SN light curves are the average of the results derived from ïve or six local standards, weighted by the uncertainty of each local standard star. The light curves are listed in Table 4 and displayed in Figure 3. The SN magnitude errors are derived from the artiïcial star measurements as described above. The small color and atmospheric extinction coefficients give us conïdence that the supernova photometry accurately transformed to the B35, V35, B45, V45 system. However, it is well known that a nonstellar ÿux distribution can produce substantial systematic errors in supernova photometry (Menzies 1989). We have anticipated this problem by using identical ïlter sets at the various observatories and by deïning our photometric system with actual instrumental response functions. To measure the size of this eect on our SN photometry, we have calculated the systematic error incurred from the dierences in the instrumental response functions of dierent observatories we employed. Spectrophotometric calculations from SN Ia spectra using various instrumental response functions show that the expected dierences are less than 0.01 mag and can safely be ignored.
3

. ANALYSIS

3.1. K-Corrections A strong empirical understanding of SN Ia light curves has been garnered from intensive monitoring of SNe Ia at z ¹ 0.1 through B and V passbands (Hamuy et al. 1996a ; Riess 1996 ; Riess et al. 1998c ; Ford et al. 1993 ; Branch 1998 and references therein). We use this understanding to


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE

1017

FIG. 2.õLocal standard stars in the ïelds of SNe Ia. The stars are listed in Table 2, and the locations of the stars and SNe are indicated in the ïgure. The orientation of each ïeld is east to the right and north at the top. The width and length of each ïeld is 96E \ 4@ 96H \ 4@ 96I \ 4@9, 96J \ 4@ 96K \ 4@ .9, .9, . .9, .9, 96R \ 5@ 96T \ 4@ 96U \ 4@ 95ao \ 4@ 95ap \ 4@ .0, .9, .9, .8, .8.

compare the light curves of the high-redshift and lowredshift samples at the same rest wavelength. By a judicious choice of ïlters, we minimize the dierences between B and V rest-frame light observed for distant SNe and their nearby counterparts. Nevertheless, the range of redshifts involved makes it difficult to eliminate all such dierences. We therefore employ "" K-corrections îî to convert the observed magnitudes to rest-frame B and V (Oke &

Sandage 1968 ; Hamuy et al. 1993b ; Kim, Goobar, & Perlmutter 1996 ; Schmidt et al. 1998). The cross-band K-correction for SNe Ia has been described as a function of the observed and rest-frame ïlter transmissions, the redshift of the supernova, and the age of the supernova (see eq. [1] of Kim et al. 1996). Such a K-correction assumes that the spectral energy distribution of all SNe Ia of a given age is homogeneous, yet it has been


1018
TABLE 4 TYPE Ia SUPERNOVA LIGHT CURVES CORRECTED TO THE REST FRAME JDa B V SN 1996E 127.6 128.6 132.1 134.6 135.5 138.7 139.6 157.6 163.7 ...... ...... ...... ...... ...... ...... ...... ...... ...... 23.04(0.09) 23.02(0.05) 23.23(0.11) 23.39(0.10) 23.41(0.13) 23.80(0.12) 23.65(0.15) 25.14(0.18) ... ... 22.72(0.08) ... 22.84(0.26) 22.95(0.06) 23.14(0.15) 23.57(0.33) 24.42(0.77) 23.78(0.50) SN 1996H 127.6 128.6 132.1 134.6 135.5 136.6 138.7 139.6 140.6 141.6 142.6 157.6 161.6 164.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 23.32(0.13) 23.39(0.09) 23.27(0.30) 23.48(0.11) 23.29(0.18) 23.29(0.14) 23.47(0.10) 23.55(0.18) 23.58(0.18) 23.62(0.12) 23.74(0.21) 24.44(0.22) 24.60(0.22) ... ... 23.42(0.14) 23.56(0.37) 23.58(0.19) 23.40(0.10) ... 23.64(0.15) 23.56(0.25) 24.13(0.11) ... 23.72(0.16) 23.86(0.28) ... 24.62(0.30) SN 1996I 128.6 132.1 134.6 135.5 136.6 138.7 140.6 142.6 157.6 161.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 23.45(0.08) 23.62(0.22) 23.57(0.06) 23.54(0.06) 23.58(0.10) 23.81(0.14) 24.28(0.36) 24.13(0.10) 25.38(0.17) 25.25(0.31) ... 23.25(0.22) 23.66(0.15) 23.65(0.20) 23.74(0.28) 23.82(0.17) 23.66(0.36) 24.02(0.22) 24.39(0.30) ... SN 1996J 127.6 128.6 134.6 135.6 135.6 135.6 139.7 140.7 157.6 157.6 161.8 168.7 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 22.58(0.03) 22.52(0.04) 22.22(0.03) 22.34(0.03) 22.39(0.04) 22.27(0.05) 22.31(0.06) 22.41(0.07) 24.17(0.15) 23.86(0.06) ... ... ... 22.72(0.07) 22.27(0.06) 22.08(0.06) 22.08(0.06) 22.08(0.06) 22.15(0.09) 22.39(0.05) 22.52(0.04) 22.52(0.04) 22.76(0.05) 23.48(0.07) SN 1996K 128.5 135.5 135.5 135.7 136.6 138.6 138.6 139.6 140.8 157.5 157.5 157.5 157.5 161.7 161.7 162.6 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... 24.24(0.05) 23.02(0.07) 23.04(0.07) 23.09(0.03) 23.01(0.05) 22.68(0.10) 22.71(0.07) 22.90(0.05) 22.76(0.10) 23.43(0.12) 23.35(0.10) 23.61(0.07) 23.59(0.09) 23.96(0.16) 23.68(0.17) 23.95(0.07) ... ... ... 23.19(0.06) 22.98(0.16) 23.20(0.11) 23.20(0.11) 23.15(0.13) 22.77(0.11) 23.29(0.19) 23.29(0.19) 23.29(0.19) 23.29(0.19) 23.23(0.13) 23.23(0.13) 23.57(0.12) [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ 0.50 0.53 0.53 0.53 0.53 0.53 0.53 0.54 0.53 0.50 0.50 0.79 0.79 0.77 0.51 0.79 [0.57 [0.57 [0.64 [0.50 [0.50 [0.65 [0.68 [0.51 [0.62 [1.09 ... ... [ [ [ [ [ [ [ [ [ [ 0.68 0.67 0.62 0.62 0.70 0.69 0.64 0.65 0.55 0.55 [0.54 [0.58 [0.56 [0.63 [0.47 [0.45 [0.62 [0.67 [0.62 [0.56 [0.53 [0.47 [0.44 ... [0.74 [0.74 [0.77 [0.73 [0.74 [0.76 [0.76 [0.82 ... K B K V

RIESS ET AL.
TABLE 4õContinued JDa 165.6 168.5 169.6 169.7 ...... ...... ...... ...... B 24.09(0.16) ... 24.92(0.25) 24.91(0.26) V 23.80(0.14) 23.73(0.19) ... ... SN 1996R 157.7 158.7 167.7 191.7 ...... ...... ...... ...... ... ... 22.24(0.03) ... 20.81(0.02) 20.92(0.03) ... 22.76(0.09) SN 1996T 161.7 167.6 191.7 212.6 ...... ...... ...... ...... 21.24(0.02) 21.34(0.03) 22.73(0.20) 23.35(0.35) 21.27(0.03) 21.35(0.04) ... 22.81(0.09) SN 1996U 158.7 160.7 161.7 165.7 167.7 186.7 188.7 ...... ...... ...... ...... ...... ...... ...... 22.89(0.05) 22.73(0.11) 22.78(0.05) ... 22.94(0.10) 24.23(0.17) 24.34(0.17) ... 22.88(0.18) 23.09(0.26) 23.21(0.28) ... 23.49(0.28) 23.85(0.36) SN 1995ao 46.6 ....... 51.6 ....... 21.85R(0.13) 21.95(0.05) ... 21.70(0.03) [0.75 [0.43 [0.73 [0.73 [0.74 ... [0.75 [0.90 [0.83 [ [ [ [ 0.38 0.38 0.37 0.36 ... ... [0.63 ... B [0.50 ... [0.50 [0.86 K

Vol. 116

V [0.62 [0.63 ... ...

K

... [0.86 ... [0.85 [0.85 [0.84 [0.84 [0.91 [0.91

[0.33 [0.33 ... [0.35

... [1.17 [1.15 [1.10 [1.12 ... [1.06 [1.04 [1.03 ... [1.04 [0.69 ... [0.61

[0.44 [0.40 ... [0.29

... [0.85 [0.85 [0.86 ... [0.86 [0.89

... [0.58

... [0.96 [1.02 [1.01 [1.00 [0.97 [1.00 [0.97 [0.73 ...

SN 1995ap 39.6 46.6 48.6 51.6 ....... ....... ....... ....... ... 21.96R(0.10) ... 21.84(0.09) 22.85(0.14) 21.57(0.08) 21.49(0.11) 21.40(0.08) ... [0.56 ... [0.20 [0.44 [0.45 [0.45 [0.89

NOTE.õUncertainties in magnitudes are listed in parentheses. a Actually JD [ 2,450,000.

... [0.78 [0.68 [0.62 [0.62 [0.62 [0.69 [0.62 [0.69 [0.69 [0.71 [0.73

... ... ... [0.71 [0.72 [0.72 [0.72 [0.73 [0.71 [0.67 [0.67 [0.67 [0.67 [0.78 [0.78 [0.78

shown (Pskovskii 1984 ; Phillips et al. 1987 ; Phillips 1993 ; Leibundgut et al. 1993 ; Nugent et al. 1995 ; Riess et al. 1996a ; Phillips et al. 1998 ; Lira 1995 ; see Appendix of this paper) that at a given age, the colors of SNe Ia exhibit real variation related to the absolute magnitude of the supernova. A variation in SN Ia color, at a ïxed phase, could have dire consequences for determining accurate K-corrections. An appropriate K-correction quantiïes the dierence between the supernova light that falls into a standard passband (e.g., B) at z \ 0 and that which falls into the ïlters we employ to observe a redshifted SN Ia. Dierences in SN Ia color, at a ïxed phase, would alter the appropriate K-correction. We need to know the color of each supernova to determine its K-correction precisely. Dierences in SN Ia color can arise from interstellar extinction or intrinsic properties of the supernova such as a variation in photospheric temperature (Nugent et al. 1995). Nugent et al. (1998b) have shown that, to within 0.01 mag, the eects of both extinction and intrinsic variations on the SN Ia spectral energy distribution near rest-frame B and V , and hence on the K-correction, can be reproduced by application of a Galactic reddening law (Cardelli, Clayton, & Mathis 1989) to the spectra. The dierence in color, at a given age, between an individual SN Ia and a ïducial SN Ia is quantiïed by a color excess, E , and B~ determines the eects of either extinction or intrinsicVvaria-


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE

1019

FIG. 3.õLight curves of high-redshift SNe Ia. B ( ïlled symbols) and V (open symbols) photometry in the rest frame of 10 well-observed SNe Ia is shown with B increased by 1 mag for ease of view. The lines are the empirical MLCS model ïts to the data. Supernova age is shown relative to B maximum.

tion on the spectra and observed colors of the SNe. For most epochs, ïlter combinations, and redshifts, the variation of the K-correction with the observed variations of color excess is only 0.01 to 0.05 mag. For redshifts that poorly match the rest-frame wavelengths to the observed wavelengths, the custom K-correction for very red or very blue SNe Ia can dier from the standard K-correction by 0.1 to 0.2 mag. This prescription requires the age and observed color for each observation to be known before its K-correction can be calculated. The age is best determined from ïtting the light curveîs time of maximum. Yet we must use the Kcorrection to determine the time of maximum and the true color of each epoch. This conundrum can be solved by iteratively converging to a solution by repeated cycles of

K-correcting and empirical ïtting of the light curves. Table 4 lists the ïnal cross-band K-corrections we used to convert the observations to the rest-frame passbands. We have also corrected the light curves in Figure 3 and our light curve ïts for a 1 ] z time dilation, expected in an expanding universe (Riess et al. 1997). 3.2. L ight Curve Fitting As described in ° 1, empirical models for SNe Ia light curves that employ the observed correlation between light curve shape, luminosity, and color have led to signiïcant improvements in the precision of distance estimates derived from SNe Ia (Hamuy et al. 1995, 1996c ; Riess et al. 1995, 1996a ; Tripp 1997, 1998). Here we employ the MLCS method prescribed by Riess et al. (1996a) as reanalyzed in


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the Appendix, and the template-ïtting method of Hamuy et al. (1995, 1996d) to ït the light curves in Table 4. The growing sample of well-observed SN Ia light curves (Hamuy et al. 1996a ; Riess 1996 ; Riess et al. 1998c ; Ford et al. 1993) justiïes reïnements in the MLCS method that are described in the Appendix. These include a new derivation of the relation between light curve shape, luminosity, and color from SNe Ia in the Hubble ÿow using redshift as the distance indicator. In addition, this empirical description has been extended to a second-order (i.e., quadratic) relation between SN Ia luminosity and light curve shape. A more realistic a priori probability distribution for extinction has been utilized from the calculations of Hatano, Branch, & Deaton (1998). Further, we now quantify the residual correlations between observations of dissimilar time, passband, or both. The empirical model for a SN Ia light and color curve is still described by four parameters : a date of maximum (t), a luminosity dierence (*), an apparent distance (k ), and an extinction (A ). Because of the redshifts of the SN B host galaxies, we ïrst Bcorrect the supernova light curves for Galactic extinction (Burstein & Heiles 1982) and then determine host galaxy extinction. To treat the high- and low-redshift SNe Ia consistently, we restricted the MLCS ïts to the nearby SNe Ia observations in B and V within 40 days after maximum brightness in the rest frame. This is the age by which all high-redshift light curve observations ended. Because of this restriction, we also limited our consideration of nearby SNe Ia to those with light curves which began no later than D5 days after B maximum. Although more precise distance estimates could be obtained for the nearby sample by including later data and additional colors, the nearby sample is large enough to determine the nearby expansion rate to sufficient precision. The parameters of the MLCS ïts to 27 SNe Ia in the nearby Hubble ÿow (0.01 \ z \ 0.13 ; Hamuy et al. 1996a ; Riess et al. 1998c) are given in Table 10 below. In Table 5 we list the parameters of the MLCS ïts to six SN Ia light curves presented here (SNe 1996E, 1996H, 1996I, 1996J, 1996K, 1996U) and for three SNe Ia from our previous work (SNe 1995K, 1997ce, 1997cj ; Garnavich et al. 1998a ; Schmidt et al. 1998). We have placed all MLCS distances on the Cepheid distance scale using Cepheid distances to galaxies hosting photoelectrically observed SNe Ia : SN 1981B, SN 1990N, and SN 1972E (Saha et al. 1994, 1997 ; Riess et al. 1996a). However, conclusions about the values of the cosmological parameters ) , ) , and q are M" 0 independent of the distance scale. An additional supernova, SN 1997ck, was studied by Garnavich et al. (1998a) in a galaxy with z \ 0.97. Its restframe B light curve was measured with the HST (see Fig. 3).

Although this object lacks a spectroscopic classiïcation and useful color information, its light curve shape and peak luminosity are consistent with those of a typical SN Ia. Owing to the uncertainty in this objectîs extinction and classiïcation, we will analyze the SNe Ia distances both with and without this most distant object. We have also determined the distances to the same 27 nearby SNe Ia and the 10 well-observed high-redshift events using a template-ïtting approach (Hamuy et al. 1995, 1996d). The maximum-light magnitudes and the initial decline rate parameter *m (B) for a given SN Ia are 15 derived by comparing the goodness of ïts of the photometric data to a set of six template SN Ia light curves selected to cover the full range of observed decline rates. The intrinsic luminosity of the SN is then corrected to a standard value of the decline rate [*m (B) \ 1.1] using a linear 15 relation between *m (B) and the luminosities for a set of 15ÿow (Phillips et al. 1998). An extincSNe Ia in the Hubble tion correction has been applied to these distances based on the measured color excess at maximum light using the relation between *m (B) and the unreddened SN Ia color at 15 maximum light (Phillips et al. 1998). These extinction measurements employ the same Bayesian ïlter (in the Appendix) used for the MLCS ïts. The ïnal distance moduli are also on the Cepheid distance scale as described by Hamuy et al. (1996c) and Phillips et al. (1998). Parameters of these ïts to the nearby and high-redshift SNe Ia are provided in Table 10 and Table 6, respectively. For both the MLCS and template-ïtting methods, the ït to the data determines the light curve parameters and their uncertainties. The "" goodness îî of the ïts was within the expected statistical range with the exception of SN 1996J. This supernova is at a measured redshift of z \ 0.30, but some of the observations were obtained through a set of ïlters optimized for z \ 0.45. The uncertainty from this mismatch and the additional uncertainty from separate calibrations of the local standardsî magnitudes in two sets of ïlters may be the source of the poor result for this object. Four remaining SNe Ia presented here (SNe 1995ao, 1995ap, 1996T, and 1996R) are too sparsely sampled to provide meaningful light curves ïtted by either of the light curve ïtting methods. However, Riess et al. (1998b) describe a technique to measure the distance to sparsely observed SNe that lack well-sampled light curves. This "" snapshot îî method measures the age and the luminosity/light curve shape parameter from a SN Ia spectrum using techniques from Riess et al. (1997) and Nugent et al. (1995). An additional photometric epoch in two passbands (with host galaxy templates if needed) provides enough information to determine the extinction-free distance. For the four sparsely

TABLE 5 HIGH-z MLCS SN Ia LIGHT CURVE PARAMETERS SN 1996E ...... 1996H ...... 1996I ....... 1996J ....... 1996K ...... 1996U ...... 1997ce ...... 1997cj ...... 1997ck ...... 1995K ...... z 0.43 0.62 0.57 0.30 0.38 0.43 0.44 0.50 0.97 0.48 mmax B 22.81(0.21) 23.23(0.19) 23.35(0.28) 22.23(0.12) 22.64(0.12) 22.78(0.22) 22.85(0.09) 23.19(0.11) 24.78(0.25) 22.91(0.13) mmax V 22.72(0.23) 23.56(0.18) 23.59(0.26) 22.21(0.11) 22.84(0.14) 22.98(0.30) 22.95(0.09) 23.29(0.12) ... 23.08(0.20) * [0.08(0.19) [0.42(0.16) [0.06(0.26) [0.22(0.10) 0.29(0.06) [0.52(0.29) 0.07(0.08) [0.04(0.11) [0.19(0.23) [0.33(0.26) B 0.31 0.00 0.00 0.24 0.00 0.00 0.00 0.00 ... 0.00 A k (p ) 0 k0 41.74(0.28) 42.98(0.17) 42.76(0.19) 41.38(0.24) 41.63(0.20) 42.55(0.25) 41.95(0.17) 42.40(0.17) 44.39(0.30) 42.45(0.17)

NOTE.õUncertainties in magnitudes are listed in parentheses.


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE
TABLE 6 HIGH-z TEMPLATE-FITTING SN Ia LIGHT CURVE PARAMETERS SN 1996E ...... 1996H ...... 1996I ....... 1996J ....... 1996K ...... 1996U ...... 1997ce ...... 1997cj ...... 1997ck ...... 1995K ...... z 0.43 0.62 0.57 0.30 0.38 0.43 0.44 0.50 0.97 0.48 mmax B 22.72(0.19) 23.31(0.06) 23.42(0.08) 22.28(0.05) 22.80(0.05) 22.77(0.05) 22.83(0.05) 23.29(0.05) 24.78(0.16) 22.92(0.08) mmax V 22.60(0.12) 23.57(0.06) 23.61(0.08) 22.06(0.05) 22.86(0.08) 22.96(0.11) 22.92(0.05) 23.29(0.05) ... 23.07(0.07) *M (B) 15 1.18(0.13) 0.87(0.05) 1.39(0.17) 1.27(0.27) 1.31(0.14) 1.18(0.10) 1.30(0.06) 1.16(0.03) 1.00(0.17) 1.16(0.18) B 0.10 0.00 0.00 0.64 0.00 0.00 0.00 0.09 ... 0.00 A k (p ) 0 k0 42.03(0.22) 43.01(0.15) 42.83(0.21) 40.99(0.25) 42.21(0.18) 42.34(0.17) 42.26(0.16) 42.70(0.16) 44.30(0.19) 42.49(0.17)

1021

NOTE.õUncertainties in magnitudes are listed in parentheses.

observed SNe Ia in our sample, we have measured the SN parameters with this method and list them in Table 7. This sample of sparsely observed, high-redshift SNe Ia is augmented by distances for SN 1997I (z \ 0.17) and SN 1997ap (z \ 0.83) given by Riess et al. (1998b). For all SN Ia distance measurements, the dominant source of statistical uncertainty is the extinction measurement. The precision of our determination of the true extinction is improved using our prior understanding of its magnitude and direction (Riess et al. 1996a ; see Appendix).
4

parsecs, the predicted distance modulus is k \ 5 log D ] 25 . (3) p L Using the data described in ° 2 and the ïtting methods of ° 3, we have derived a set of distances, l , for SNe with 0 0.01 ¹ z ¹ 0.97. The available set of high-redshift SNe includes nine well-observed SNe Ia, six sparsely observed SNe Ia, and SN 1997ck (z \ 0.97), whose light curve was well observed but lacks spectroscopic classiïcation and color measurements. The Hubble diagrams for the nine well-observed SNe Ia plus SN 1997ck, with light curve distances calculated from the MLCS method and the template approach, are shown in Figures 4 and 5. The likelihood for the cosmological parameters can be determined from a s2 statistic, where [k (z ; H , ) , ) ) [ k ]2 0m" 0, i (4) s2(H , ) , ) ) \ ; p, i i 0M" p2 ] p2 v i k0, i and p is the dispersion in galaxy redshift (in units of distance vmoduli) due to peculiar velocities. This term also includes the uncertainty in galaxy redshift. We have calculated this s2 statistic for a wide range of the parameters H , 0 ) , and ) . We do not consider the unphysical region of M " parameter space where ) \ 0 ; equation (2) describes the eect of massive particles Mn the luminosity distance. There o is no reason to expect that the evaluation of equation (2) for ) \ 0 has any correspondence to physical reality. We also M neglect the region of () , ) ) parameter space, which gives M îî rise to so-called "" bouncing " or rebounding universes that do not monotonically expand from a "" big bang îî and for which equation (2) is not solvable (see Figs. 6 and 7) (Carroll et al. 1992). Because of the large redshifts of our distant sample and the abundance of objects in the nearby sample, our analysis is insensitive to p within its likely range of 100 km s~1 ¹ p ¹ 400 km s~1 vMarzke et al. 1995 ; Lin et al. 1996). For ( v our analysis we adopt p \ 200 km s~1. For high-redshift SNe Ia whose redshifts vwere determined from the broad features in the SN spectrum (see Table 1), we add 2500 km s~1 in quadrature to p . v Separating the eects of matter density and vacuum energy density on the observed redshift-distance relation could in principle be accomplished with measurements of SNe Ia over a signiïcant range of high redshifts (Goobar & Perlmutter 1995). Because the matter density decreases with time in an expanding universe, while the vacuum energy density remains constant, the relative inÿuence of ) to ) M " on the redshift-distance relation is a function of redshift.

. COSMOLOGICAL IMPLICATIONS OF TYPE Ia SUPERNOVAE

4.1. Cosmological Parameters Distance estimates from SN Ia light curves are derived from the luminosity distance, L 1@2 , D\ L 4nF

AB

(1)

where L and F are the SNîs intrinsic luminosity and observed ÿux, respectively. In Friedmann-RobertsonWalker cosmologies, the luminosity distance at a given redshift, z, is a function of the cosmological parameters. Limiting our consideration of these parameters to the Hubble constant, H , the mass density, ) , and the vacuum energy 0 density (i.e., the cosmological Mconstant), ) (but see " Caldwell, Dave, & Steinhardt 1998 ; Garnavich et al. 1998a, 1998b for other energy densities), the luminosity distance is D \ cH~1(1 ] z) o ) o~1@2 sinn L 0 k ]

G

(2) 0 where ) \ 1 [ ) [ ) and sinn is sinh for ) º 0 and M k sin for )k ¹ 0 (Carroll et " 1992). For D in units of megaal. k L
TABLE 7 HIGH-z SN Ia SNAPSHOT PARAMETERS SN 1995ao ...... 1995ap ...... 1996R ....... 1996T........ 1997Ia ....... 1997apa ...... z 0.30 0.23 0.16 0.24 0.17 0.83 t spec [2.8 [2.9 8.6 [4.5 0.1 [2.0 * 0.35 0.69 0.28 [0.12 [0.39 0.00 V 0.00 0.00 0.10 0.10 0.00 0.00 A k (p ) 0 k0 40.74(0.60) 40.33(0.46) 39.08(0.40) 40.68(0.43) 39.95(0.24) 43.67(0.35)

P

o ) o1@2 k

z

dz[(1 ] z)2(1 ] ) z) [ z(2 ] z)) ]~1@2 , M "

H

a See Perlmutter et al. 1998 ; Riess et al. 1998b.


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RIESS ET AL.

Vol. 116

44 42

MLCS
m-M (mag)

44 42 40 38 36 34

m15(B)

m-M (mag)

40 38 36 34
M=0.24, =0.76 M=0.20, =0.00 M=1.00, =0.00

M=0.20, =0.80 M=0.20, =0.00 M=1.00, =0.00

(m-M) (mag)

(m-M) (mag)

0.5

0.5

0.0

0.0

-0.5

-0.5

0.01

0.10 z

1.00

0.01

0.10 z

1.00

FIG. 4.õMLCS SNe Ia Hubble diagram. The upper panel shows the Hubble diagram for the low-redshift and high-redshift SNe Ia samples with distances measured from the MLCS method (Riess et al. 1995, 1996a ; Appendix of this paper). Overplotted are three cosmologies : "" low îî and "" high îî ) with ) \ 0 and the best ït for a ÿat cosmology, ) \ 0.24, M " M ) \ 0.76. The bottom panel shows the dierence between data and " models with ) \ 0.20, ) \ 0. The open symbol is SN 1997ck (z \ 0.97), M " which lacks spectroscopic classiïcation and a color measurement. The average dierence between the data and the ) \ 0.20, ) \ 0 prediction M " is 0.25 mag.

FIG. 5.õ*m (B) SN Ia Hubble diagram. The upper panel shows the 15 Hubble diagram for the low-redshift and high-redshift SNe Ia samples with distances measured from the template-ïtting method parameterized by *m (B) (Hamuy et al. 1995, 1996d). Overplotted are three cosmologies : 15 "" low îî and "" high îî ) with ) \ 0 and the best ït for a ÿat cosmology, M " ) \ 0.20, ) \ 0.80. The bottom panel shows the dierence between M and models from the ) \ 0.20, ) \ 0 prediction. The open symbol " data M is SN 1997ck (z \ 0.97), which lacks " spectroscopic classiïcation and a color measurement. The average dierence between the data and the ) \ 0.20, ) \ 0 prediction is 0.28 mag. M "

The present data set has only a modest range of redshifts, so we can only constrain speciïc cosmological models or regions of () , ) ) parameter space to useful precision. M The s2 statistic"of equation (4) is well suited for determining the most likely values for the cosmological parameters H , ) , and ) as well as the conïdence intervals sur0M rounding them." For constraining regions of parameter space not bounded by contours of uniform conïdence (i.e., constant s2), we need to deïne the probability density function (PDF) for the cosmological parameters. The PDF (p)of these parameters given our distance moduli is derived from the PDF of the distance moduli given our data from Bayesîs theorem, p(H , ) , ) o l ) \ 0m"0 p(l o H , ) , ) )p(H , ) , ) ) 00m" 0 m ", p(l ) 0 (5) where l is our set of distance moduli (Lupton 1993). Since we have0 no prior constraints on the cosmological parameters (besides the excluded regions) or on the data, we take p(H , ) , ) ) and p(l ) to be constants. Thus, we have for 0m" 0 the allowed region of (H , ) , ) ) 0m" p(H , ) , ) o l ) P p(l o H , ) , ) ) . (6) 0m"0 00m"

We assume each distance modulus is independent (aside from systematic errors discussed in ° 5) and normally distributed, so the PDF for the set of distance moduli given the parameters is a product of Gaussians : 1 p(l o H , ) , ) ) \ < 00m" i J2n(p20, i ] p2) v k [k (z ; H , ) , ) )[k ]2 0, i . (7) ] exp [ p, i i 0 m " 2(p2 ] p2) k0, i v Rewriting the product as a summation of the exponents and combining with equation (4), we have

G

H

1 s2 exp [ . p(l o H , ) , ) ) \ < 00m" 2 i J2n(p20, i ] p2) v k (8) The product in front is a constant, so combining with equation (6) the PDF for the cosmological parameters yields the standard expression (Lupton 1993) s2 . p(H , ) , ) o l ) P exp [ 0m"0 2

C

DAB

AB

(9)


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE

1023

3
No Big Bang

2

95.4%

q 0=-0.5

q 0=0 Accelerating Decelerating



1
q 0=0.5

99.7% 95.4% 68.3%

Expands to Infinity
Closed Open
tot

0

Recollapses

=0

^

distance scale adds an uncertainty of D10% to the derived Hubble constant (Feast & Walker 1987 ; Kochanek 1997 ; Madore & Freedman 1998). A realistic determination of the Hubble constant from SNe Ia would give 65 ^ 7 km s~1 Mpc~1, with the uncertainty dominated by the systematic uncertainties in the calibration of the SN Ia absolute magnitude. These determinations of the Hubble constant employ the Cepheid distance scale of Madore & Freedman (1991), which uses a distance modulus to the Large Magellanic Cloud (LMC) of 18.50 mag. Parallax measurements by the Hipparcos satellite indicate that the LMC distance could be greater, and hence our inferred Hubble constant smaller, by 5% to 10% (Reid 1997), though not all agree with the interpretation of these parallaxes (Madore & Freedman 1998). All subsequent indications in this paper for the cosmological parameters ) and ) are independent of the value M " for the Hubble constant or the calibration of the SN Ia absolute magnitude. Indications for ) and ) , independent from H , can be " found by reducingM our three-dimensional PDF0 to two dimensions. A joint conïdence region for ) and ) is " derived from our three-dimensional likelihood M space p() , ) o l ) \ M"0



99.7%

99.7%

P

=

=1

MLCS

~=

p() , ) , H o l )dH . M" 00 0

(11)

-1 0.0

0.5

1.0

The normalized PDF comes from dividing this relative PDF by its sum over all possible states, p(H , ) , ) o l ) 0m"0 exp ([s2/2) \ , (10) /= dH /= d) /= exp ([s2/2)d) ~= 0 ~= "0 M neglecting the unphysical regions. The most likely values for the cosmological parameters and preferred regions of parameter space are located where equation (4) is minimized or, alternately, equation (10) is maximized. The Hubble constants as derived from the MLCS method, 65.2 ^ 1.3 km s~1 Mpc~1, and from the templateïtting approach, 63.8 ^ 1.3 km s~1 Mpc~1, are extremely robust and attest to the consistency of the methods. These determinations include only the statistical component of error resulting from the point-to-point variance of the measured Hubble ÿow and do not include any uncertainty in the absolute magnitude of SN Ia. From three photoelectrically observed SNe Ia, SN 1972E, SN 1981B, and SN 1990N (Saha et al. 1994, 1997), the SN Ia absolute magnitude was calibrated from observations of Cepheids in the host galaxies. The calibration of the SN Ia magnitude from only three objects adds an additional 5% uncertainty to the Hubble constant, independent of the uncertainty in the zero point of the distance scale. The uncertainty in the Cepheid


99.7%

FIG. 6.õJoint conïdence intervals for () , ) ) from SNe Ia. The solid contours are results from the MLCS methodM " to well-observed SNe applied Ia light curves together with the snapshot method (Riess et al. 1998b) applied to incomplete SNe Ia light curves. The dotted contours are for the same objects excluding the unclassiïed SN 1997ck (z \ 0.97). Regions representing speciïc cosmological scenarios are illustrated. Contours are closed by their intersection with the line ) \ 0. M

No

Big

Bang



1.5
M

2.0

2.5

3

95.4%

2

99.7%

q 0=-0.5

q 0=0



1
68.3%
Accelerating Decelerating q 0=0.5

95.4%

0

99.7%
Closed Open

Expands to Infinity Recollapses

=0

^



tot

m15(B)

=1

-1 0.0

0.5

1.0



1.5
M

2.0

2.5

FIG. 7.õJoint conïdence intervals for () , ) ) from SNe Ia. The solid M method applied to wellcontours are results from the template-ïtting " observed SNe Ia light curves together with the snapshot method (Riess et al. 1998b) applied to incomplete SNe Ia light curves. The dotted contours are for the same objects excluding the unclassiïed SN 1997ck (z \ 0.97). Regions representing speciïc cosmological scenarios are illustrated. Contours are closed by their intersection with the line ) \ 0. M


1024

RIESS ET AL. ) \[0.38 ^ 0.22 and ) \[0.52 ^ 0.20 for the MLCS M M and template-ïtting approaches, respectively (see Table 8). This result emphasizes the need for a positive cosmological constant for a plausible ït. For the four sparsely observed SNe Ia (SN 1996R, SN 1996T, SN 1995ao, and SN 1995ap), we employed the snapshot distance method (Riess et al. 1998b) to determine the luminosity distances. Unfortunately, the low priority given to these objects resulted in observations not only limited in frequency but in signal-to-noise ratio as well. Consequently, these four distances are individually uncertain at the 0.4 õ 0.6 mag level. We have compared these distances directly to a set of nine SNe Ia distances measured by the same snapshot method with 0.01 ¹ z ¹ 0.83 from Riess et al. (1998b) and reprinted here in Tables 7 and 9. This approach avoids the requirement that distances calculated from light curves and the snapshot method be on the same distance scale, although this has been shown to be true (Riess et al. 1998b). The complete but sparse set of 13 snapshot distances now including six SNe Ia with z º 0.16 yields conclusions that are less precise but fully consistent with the statistically independent results from the well-sampled SN Ia light curves (see Table 8). Having derived the two PDFs, p() , ) ), for the D40 M" SNe Ia light curves and the 13 incomplete ("" snapshot îî) SNe Ia light curves independently, we can multiply the two PDFs to yield the PDF for all D50 SNe Ia, which includes 15 SNe with 0.16 ¹ z ¹ 0.62. Contours of constant PDF from the MLCS method and the template-ïtting method, each combined with the snapshot PDF, are shown in Figures 6 and 7. These contours are closed by their intersection with the line ) \ 0 and labeled by the total probabilM ity contained within. Including the snapshot distances modestly strengthens all of the previous conclusions about the detection of a nonnegligible, positive cosmological constant (see Table 8). This set of 15 high-redshift SNe Ia favors ) º 0 and an eternally expanding universe at 99.7% (3.0 "p) and more than 99.9% (4.0 p) conïdence for the MLCS and template-ïtting methods, respectively. This complete set of spectroscopic SNe Ia represents the full strength of the high-redshift sample and provides the most reliable results. A remarkably high-redshift supernova (z \ 0.97), SN 1997ck, was excluded from all these analyses owing to its uncertain extinction and the absence of a spectroscopic identiïcation. Nevertheless, if we assume a negligible extinction of A \ 0.0 ^ 0.1 for SN 1997ck as inferred for most of B our high-redshift sample and further assume it is of Type Ia, as its well-observed B rest-frame light curve suggests (see Fig. 3), we could include this object in our previous analysis (see Table 8). As seen in Figures 6 and 7, SN 1997ck constrains speciïc values of ) and ) by eectively closing M our conïdence contours because of" the increased redshift range of this augmented sample. The values implied using SN 1997ck and the rest of the spectroscopic SNe Ia, under the previous assumptions, are ) \ 0.24`0.56 , ) \ 0.72`0.72 from the MLCS method M and ) ~0.24 `0.40 , \ 0.80 " ~0.48 `0.52 from the template-ïtting M ) \ 1.56 method.~0.48 The " ~0.70 a non-negligible, positive cosmological preference for constant remains strong (see Table 8). As seen in Table 8, the values of the s2 for the cosmological ïts are reassuringly close to unity. l This statement is more meaningful for the MLCS distances, which are accompanied by statistically reliable estimates of the distance

The likelihood that the cosmological constant is greater than zero is given by summing the likelihood for this region of parameter space : = = d) p() , ) o l )d) . (12) " M"0 M 0 0 This integral was evaluated numerically over a wide and ïnely spaced grid of cosmological parameters for which equation (11) is nontrivial. From the nine spectroscopic high-redshift SNe Ia with well-observed light and color curves, a non-negligible positive cosmological constant is strongly preferred at the 99.6% (2.9 p) and greater than 99.9% (3.9 p) conïdence levels for the MLCS and template-ïtting methods, respectively (see Table 8). This region of parameter space is nearly identical to the one that results in an eternally expanding universe. Boundless expansion occurs for a cosmological constant of P() [ 0 o l ) \ " 0 0, 1 1[) 4n )º M] " cos~1 4) cos M 3 3 ) M

P

P

7

GC

A

B DH

0¹) ¹1 , M 3 , ) [1 M (13)

P

(Carroll, Press, & Turner 1992), and its likelihood is 1 d) M

P

0

4)M(cos K1@3 cos~1 *(1~)M)@)M+`(4n@3)L)3 p() , ) o l )d) . (14) M"0 " The preference for eternal expansion is numerically equivalent to the conïdence levels cited for a non-negligible, positive cosmological constant. We can include external constraints on ) , ) , or their M" sum to further reïne our determination of the cosmological parameters. For a spatially ÿat universe (i.e., ) ] ) 4 M ) 4 1), we ïnd ) \ 0.68 ^ 0.10 () \ 0.32 ^ 0.10) " and tot\ 0.84 ^ 0.09 ") \ 0.16 ^ 0.09)M for MLCS and ) ( " M template ïtting, respectively (see Table 8). The hypothesis that matter provides the closure density (i.e., ) \ 1) is M ruled out at the 7 p to 9 p level by either method. Again, ) [ 0 and an eternally expanding universe are strongly " preferred, at this same conïdence level. We emphasize that these constraints reÿect statistical errors only ; systematic uncertainties are confronted in ° 5. Other measurements based on the mass, light, X-ray emission, numbers, and motions of clusters of galaxies provide constraints on the mass density that have yielded typical values of ) B 0.2õ 0.3 (Carlberg et al. 1996 ; M Bahcall, Fan, & Cen 1997 ; Lin et al. 1996 ; Strauss & Willick 1995). Using the constraint that ) 4 0.2 provides a signiïcant indication for a cosmologicalMconstant : ) \ 0.65 ^ 0.22 and ) \ 0.88 ^ 0.19 for the MLCS " and " template-ïtting methods, respectively (see Table 8). For ) 4 0.3 we ïnd ) \ 0.80 ^ 0.22 and ) \ 0.96 ^ 0.20 " M for the MLCS and template-ïtting methods," respectively. If we instead demand that ) 4 0, we are forced to relax " the requirement that ) º 0 to locate a global minimum in M so yields an unphysical value of our s2 statistic. Doing

= p() , ) M 0 = d) ] M 1

P

"

P

o l )d) 0" =


TABLE 8 COSMOLOGICAL RESULTS NO CONSTRAINTa 0 0.2 H ) )

METHOD (HIGH-z SNe)

MLCS ] Snapshot (15) b ......... *M ] Snapshot (15)b .......... 15 MLCS ] Snap. ] 97ck (16) ...... *M ] Snap. ] 97ck (16) ....... 15 MLCS (9) .......................... *M (9) ........................... 15 MLCS ] 97ck (10) ................ *M ] 97ck (10) ................. 15 Snapshot (6) ....................... 65.2 63.8 65.2 63.7 63.4 1.3 1.3 1.3 1.3 2.7 c c c c c p) p) p) p) p) p) p) p) p) p) p) p) p) p) p) p) p) p)

0 ... ... ... ... ^ ^ ^ ^ ^

M ... ... 0.24`0.56 ~0.24 0.80`0.40 ~0.48 ... ... 0.00`0.60 ~0.00 0.72`0.44 ~0.56 ...

" ... ... 0.72`0.72 ~0.48 1.56`0.52 ~0.70 ... ... 0.48`0.72 ~0.24 1.48`0.56 ~0.68 ...

s2 l 1.19 1.03 1.17 1.04 1.19 1.05 1.17 1.04 1.30 t 0 ... ... ... ... 13.6`1.0 ~0.8 14.8`1.0 ~0.8 14.2`1.3 ~1.0 15.1`1.1 ~0.9 ... p() º 0) " 99.7% (3.0 [99.9% (4.0 99.5% (2.8 [99.9% (3.9 99.6% (2.9 [99.9% (3.9 99.5% (2.8 [99.9% (3.8 89.1% (1.6 p(q ¹ 0) 0 99.5% (2.8 [99.9% (3.9 99.3% (2.7 [99.9% (3.8 99.4% (2.4 [99.9% (3.8 99.3% (2.7 [99.9% (3.7 78.9% (1.3

q 0 [0.98 ^ [1.34 ^ [0.75 ^ [1.14 ^ [0.92 ^ [1.38 ^ [0.74 ^ [1.11 ^ [0.70 ^

0.40 0.40 0.32 0.30 0.42 0.46 0.32 0.32 0.80

) 41 tot ) M 0.28 ^ 0.10 0.17 ^ 0.09 0.24 ^ 0.10 0.21 ^ 0.09 0.28 ^ 0.10 0.16 ^ 0.09 0.24 ^ 0.10 0.20 ^ 0.09 0.40 ^ 0.50

)4 " ) M [0.34 ^ [0.48 ^ [0.35 ^ [0.41 ^ [0.38 ^ [0.52 ^ [0.38 ^ [0.44 ^ 0.06 ^

0.21 0.19 0.18 0.17 0.22 0.20 0.19 0.18 0.70

)4 M) " 0.65 ^ 0.84 ^ 0.66 ^ 0.80 ^ 0.68 ^ 0.88 ^ 0.68 ^ 0.84 ^ 0.44 ^

0.22 0.18 0.21 0.19 0.24 0.19 0.22 0.20 0.60

a ) º 0. M b Complete set of spectroscopic SNe Ia. c This uncertainty reÿects only the statistical error from the variance of SNe Ia in the Hubble ÿow. It does not include any contribution from the (much larger) SN Ia absolute magnitude error.


1026
TABLE 9 NEARBY SN Ia SNAPSHOT PARAMETERSa SN 1994U ...... 1997bp ...... 1996V ....... 1994C ....... 1995M ...... 1995ae ...... 1994B ....... log cz 3.111 3.363 3.870 4.189 4.202 4.308 4.431 * 0.03 [0.26 0.26 0.81 [0.15 0.38 [0.02 A Fit V 0.70 0.62 0.00 0.00 0.46 0.00 0.38

RIESS ET AL.

Vol. 116

k (p ) 0 k0 31.72(0.10) 32.81(0.10) 35.35(0.17) 36.72(0.15) 37.12(0.15) 37.58(0.21) 38.51(0.10)

a As given in Riess et al. 1998b.

uncertainty (Riess et al. 1996a). The values for s2 indicate a l good agreement between the expected distance uncertainties and the observed distance dispersions around the best-ït model. They leave little room for sources of additional variance, as might be introduced by a signiïcant difference between the properties of SNe Ia at high and low redshift. 4.2. Deceleration Parameter An alternate approach to exploring the expansion history of the universe is to measure the current (z \ 0) deceleration parameter, q 4 [a (t )a(t )/a5 2(t ), where a is the cosmic 0 scale factor. 0Because 0the 0 deceleration is deïned at the current epoch and the supernovae in our sample cover a wide range in redshift, we can only determine the value of q 0 within the context of a model for its origin. Nevertheless, for moderate values of deceleration (or acceleration) the determination of q from our SNe, all of which are at z \ 1, 0 provides a valuable description of the current deceleration parameter valid for most equations of state of the universe. We have derived estimates of q within a two-component model where q \ () /2) [ ) .0 This deïnition assumes 0 " that the only sources M the current deceleration are mass of density and the cosmological constant. A more complete deïnition for q would include all possible forms of energy 0 density (see Caldwell, Dave, & Steinhardt 1998) but is beyond the scope of this paper. From our working deïnition of q , negative values for the current deceleration (i.e., 0 accelerations) are generated only by a positive cosmological constant and not from unphysical, negative mass density. Current acceleration of the expansion occurs for a cosmological constant of ) ) º M, " 2 and its likelihood is P(q \ 0 o l ) \ 0 0 (15)

the sum of the likelihoods of the combinations of ) and M ) which produce that value of q . Values for q and their " 0 0 uncertainties for the dierent methods and sample cuts are summarized in Table 8. With the current sample we ïnd a robust indication for the sign of q and a more uncertain 0 estimate for its value, q \[1.0 ^ 0.4. Because lines of 0 constant q are skewed with respect to the major axis of our 0 uncertainty contours, more SNe Ia at redshifts greater than z \ 0.5 will be needed to yield a more robust indication for the value of q . 0 4.3. Dynamical Age of the Universe The dynamical age of the universe can be calculated from the cosmological parameters. In an empty universe with no cosmological constant, the dynamical age is simply the inverse of the Hubble constant ; there is no deceleration. SNe Ia have been used to map the nearby Hubble ÿow, resulting in a precise determination of the Hubble constant (Hamuy et al. 1995, 1996c ; Riess et al. 1995, 1996a). For a more complex cosmology, integrating the velocity of the expansion from the current epoch (z \ 0) to the beginning (z \ O) yields an expression for the dynamical age t (H , ) , ) ) \ H~1 00M" 0

P

=

[ z(2 ] z)) ]~1@2 dz (18) " (Carroll et al. 1992). Combining a PDF for the cosmological parameters, p(H , ) , ) ), with the above expression we 0M" can derive the PDF for the age of the universe : = dH d) 0 M ~= 0 = p(H , ) , ) o t , l )d) . (19) ] 0 M "00 " ~= Equation (19) expresses the likelihood for a given age, t , as the sum of the likelihoods of all combinations of H , 0 , ) 0M and ) that result in the given age. The peak of this func" tion provides our maximum likelihood estimate for the dynamical age, t . Without SN 1997ck, the peak is at 13.6`1.0 Gyr from0the MLCS PDF. For the template-ïtting ~0.8 approach the peak occurs at 14.8`1.0 Gyr. A naive com~0.8 bination of the two distributions yields an estimate of 14.2`1.0 Gyr adopting either methodîs uncertainty (see Fig. ~0.8 8). Again, these errors include only the statistical uncertainties of the measurement. Including the systematic uncertainty of the Cepheid distance scale, which may be as much as 10%, a reasonable estimate of the dynamical age would be 14.2 ^ 1.7 Gyr. An illuminating way to characterize the dynamical age independent of the Hubble constant is to measure the product H t . For the MLCS method, the template-ïtting 0 the method, and 0 combination of the two, we ïnd H t to be 0a 0.90, 0.96, and 0.93, respectively. These values imply 0 substantially older universe for a given value of H , in better 0 accordance with globular cluster ages than the canonical value of H t \ 2 for ) \ 1 and ) \ 0. Our determi0 3 " nation of the0 dynamical M of the universe is consistent age with the rather wide range of values of the ages using stellar theory or radioactive dating. Oswalt et al. (1996) have shown that the Galactic disk has a lower age limit of 9.5 Gyr measured from the cooling sequence of the white dwarfs. The radioactive dating of stars via the thorium and europium abundances gives a value of 15.2 ^ 3.7 Gyr p(t o l ) \ 00

0

(1 ] z)~1[(1 ] z)2(1 ] ) z) M

P

=

P

P

= = d) p() , ) o l )d) (16) M M"0 " 0 )M@2 considering only ) º 0. Figures 6 and 7 show the boundM ary between current acceleration and deceleration as well as lines of constant q . For the complete set of supernova 0 distances (excluding SN 1997ck), current acceleration is strongly preferred at the 99.5% (2.8 p) conïdence level for the MLCS method and a level of more than 99.9% (3.9 p) for the template-ïtting approach. The most likely value for q is given by the peak of the distribution : 0 = = d) p() , ) o q , l )d) . (17) p(q o l ) \ M M"00 " 00 0 ~= This expression determines the likelihood of a given q from 0

P

P

P

P


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE

1027

H0t0=

0.93 0.90 0.96

MLCS M15(B) combined

10

12

14 16 18 Dynamical Age (Gyr)

20

FIG. 8.õPDF for the dynamical age of the universe from SNe Ia (eq. [19]). The PDF for the dynamical age derived from the PDFs for H , ) , 0M ) is shown for the two dierent distance methods without the unclassiïed " 1997ck. A naive average (see ° 4.2) yields an estimate of 14.2`1.0 Gyr, SN not including the systematic uncertainties in the Cepheid distance~0.8 scale.

(Cowan et al. 1997). We can expect these ages to become more precise as more objects are observed. Perhaps the most widely quoted ages of the universe come from the age estimates of globular cluster stars. These are dependent on the distance scale used and the stellar

3
No Big Bang

19 17 16 15 18

14

13

12

11

19 17 18 16

15

14

13

12





0
12

10

11

1

9

8

9

10

2

models employed. VandenBerg, Stetson, & Bolte (1996) note that these two eects generally work in opposite directions : for instance, if one increases the distance to the LMC, the dynamical age of the universe increases, while the age based on the cluster ages decreases (the main-sequence turno is brighter, implying a younger population). This means that there is only a limited range in cosmological and stellar models that can bring the two ages into concordance. Prior to Hipparcos, typical age estimates based on the subdwarf distance scale were greater than 15 Gyr for cluster ages. Bolte & Hogan (1995) ïnd 15.8 ^ 2.1 Gyr for the ages of the oldest clusters, while Chaboyer, Demarque, & Sarajedini (1996) ïnd a typical age of 18 Gyr for the oldest clusters. Chaboyer (1995) also estimates the full range of viable ages to be 11õ21 Gyr with the dominant error due to uncertainties in the theory of convection. An independent distance scale based on parallaxes of white dwarfs provides an age estimate for the globular cluster M4 of 14.5 õ15.5 Gyr (Renzini et al. 1996). However, the Hipparcos parallaxes suggest an increased distance to the LMC and the globular clusters (Feast & Catchpole 1997 ; Reid 1997 ; but see Madore & Freedman 1998). With this new distance scale, the ages of the clusters have decreased to about 11.5 Gyr with an uncertainty of 2 Gyr (Gratton et al. 1997 ; Chaboyer et al. 1998). Given the large range in ages from the theoretical models of cluster turnos and the inconsistency of the subdwarf and white dwarf distance scales applied to the ages of globular clusters, a robust estimate for the ages of the globular clusters remains elusive. Even with these uncertainties, the dynamical age of the universe derived here is consistent with the ages based on stellar theory or radioactive dating. Evidently, it is no longer a problem that the age of the oldest stars is greater than the dynamical age of the universe. Despite our inability to place strong constraints on the values for ) and ) independently, our experiment is senM " sitive to the dierence of these parameters. Because the dynamical age also varies approximately as the dierence in ) and ) , our leverage on the determination of the M " dynamical age is substantial. This point can be illustrated with a display of lines of constant dynamical age as a function of ) and ) ; comparing Figure 9 to Figures 6 and 7, M " we see that the semimajor axes of our error ellipses are roughly parallel to the lines of constant dynamical age. Figure 9 also indicates why the most likely value for the dynamical age diers from the dynamical age derived for the most likely values of H , ) , and ) . For a ïxed value 0M " of the Hubble constant, younger dynamical ages span a larger region of the () , ) ) parameter space than older M ages. This shifts the most "likely value for t toward a 0 younger age and results in a "" tail îî in the distribution, p(t o l ), extending toward older ages. 00
5.

Relative Probability (%)

DISCUSSION

-1 0.0

0.5

1.0



1.5
M

2.0

2.5

FIG. 9.õLines of constant dynamical age in Gyr in the () , ) )-plane. Comparing these lines with the error ellipses in Figs. 5 and M reveals the 7" leverage this experiment has on measuring the dynamical age. This plot assumes H \ 65 km s~1 Mpc~1 as determined from nearby SNe Ia and is 0 subject to the zero point of the Cepheid distance scale.

The results of ° 4 suggest an eternally expanding universe that is accelerated by energy in the vacuum. Although these data do not provide independent constraints on ) and ) " to high precision without ancillary assumptions M incluor sion of a supernova with uncertain classiïcation, speciïc cosmological scenarios can still be tested without these requirements. High-redshift SNe Ia are observed to be dimmer than expected in an empty universe (i.e., ) \ 0) with no cosmoM logical constant. A cosmological explanation for this obser-


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RIESS ET AL.

Vol. 116

vation is that a positive vacuum energy density accelerates the expansion. Mass density in the universe exacerbates this problem, requiring even more vacuum energy. For a universe with ) \ 0.2, the MLCS and template-ïtting disM tances to the well-observed SNe are 0.25 and 0.28 mag farther on average than the prediction from ) \ 0. The " average MLCS and template-ïtting distances are still 0.18 and 0.23 mag farther than required for a 68.3% (1 p) consistency for a universe with ) \ 0.2 and without a cosmoM logical constant. Depending on the method used to measure all the spectroscopically conïrmed SN Ia distances, we ïnd ) to be " inconsistent with zero at conïdence levels from 99.7% (3.0 p) to more than 99.9% (4.0 p). Current acceleration of the expansion is preferred at the 99.5% (2.8 p) to greater than 99.9% (3.9 p) conïdence level. The ultimate fate of the universe is sealed by a positive cosmological constant. Without a restoring force provided by a surprisingly large mass density (i.e., ) [ 1) the universe will continue to expand M forever. How reliable is this conclusion ? Although the statistical inference is strong, here we explore systematic uncertainties in our results with special attention to those which can lead to overestimates of the SNe Ia distances. 5.1. Evolution The local sample of SNe Ia displays a weak correlation between light curve shape (or luminosity) and host galaxy type. The sense of the correlation is that the most luminous SNe Ia with the broadest light curves only occur in latetype galaxies. Both early-type and late-type galaxies provide hosts for dimmer SNe Ia with narrower light curves (Hamuy et al. 1996b). The mean luminosity dierence for SNe Ia in late-type and early-type galaxies is D0.3 mag (Hamuy et al. 1996b). In addition, the SN Ia rate per unit luminosity is almost twice as high in late-type galaxies as in early-type galaxies at the present epoch (Cappellaro et al. 1997). This suggests that a population of progenitors may exist in late-type galaxies that is younger and gives rise to brighter SNe Ia (with broader light curves) than those contained in early-type galaxies or within pockets of an older stellar population in the late-type galaxies. Such observations could indicate an evolution of SNe Ia with progenitor age. Hoÿich, Wheeler, & Thielemann (1998) calculate dier ences in the light curve shape, luminosity, and spectral characteristics of SNe Ia as a function of the initial composition and metallicity of the white dwarf progenitor. As we observe more distant samples, we expect the progenitors of SN Ia to come from a younger and more metal-poor population of stars. Hoÿich et al. (1998) have shown that a reduction in progenitor metallicity by a factor of 3 has little eect on the SN Ia bolometric luminosity at maximum. For their models, such a change in metallicity can alter the peak luminosity by small amounts (D0.05 mag) in rest-frame B and V , accompanied by detectable spectral signatures. These spectral indicators of evolution are expected to be most discernible in the rest-frame U passband, where line blanketing is prevalent. Future detailed spectral analyses at these short wavelengths might provide a constraint on a variation in progenitor metallicity. The eect of a decrease in SN Ia progenitor age at high redshift is predicted to be more signiïcant than metallicity (Hoÿich et al. 1998). Younger white dwarfs are expected to

evolve from more massive stars with a lower ratio of C/O in their cores. The lower C/O ratio of the white dwarf reduces the amount of 56Ni synthesized in the explosion, but an anticipated slower rise to maximum conserves more energy for an increased maximum brightness. By reducing the C/O ratio from 1 : 1 to 2 : 3, the B[V color at maximum is expected to become redder by 0.02 mag and the postmaximum decline would become steeper. This prediction of a brighter SN Ia exhibiting a faster postmaximum decline is opposite to what is seen in the nearby sample (Phillips 1993 ; Hamuy et al. 1995 1996a, 1996b, 1996c, 1996d ; Riess et al. 1996a ; Appendix) and will be readily testable for an enlarged high-redshift sample. Speciïcally, a larger sample of distant SNe Ia (currently being compiled) would allow us to determine the light curve shape relations at high redshift and test whether these evolve with look-back time. Presently, our sample is too small to make such a test meaningful. We expect that the relation between light curve shape and luminosity that applies to the range of stellar populations and progenitor ages encountered in the late-type and early-type hosts in our nearby sample should also be applicable to the range we encounter in our distant sample. In fact, the range of age for SN Ia progenitors in the nearby sample is likely to be larger than the change in mean progenitor age over the 4 õ 6 Gyr look-back time to the highredshift sample. Thus, to ïrst order at least, our local sample should correct our distances for progenitor or age eects. We can place empirical constraints on the eect that a change in the progenitor age would have on our SN Ia distances by comparing subsamples of low-redshift SNe Ia believed to arise from old and young progenitors. In the nearby sample, the mean dierence between the distances for the early-type (eight SNe Ia) and late-type hosts (19 SNe Ia), at a given redshift, is 0.04 ^ 0.07 mag from the MLCS method. This dierence is consistent with zero. Even if the SN Ia progenitors evolved from one population at low redshift to the other at high redshift, we still would not explain the surplus in mean distance of 0.25 mag over the ) \ 0 " prediction. For the template-ïtting approach, the mean difference in distance for SNe Ia in early-type and late-type hosts is 0.05 ^ 0.07 mag. Again, evolution provides an inadequate explanation for the 0.28 mag dierence in the template-ïtting SNe Ia distances and the ) \ 0 prediction. " However, the low-redshift sample is dominated by latetype hosts, and these may contain a number of older progenitors. It is therefore difficult to assess the precise eect of a decrease in progenitor age at high redshift from the consistency of distances to early-type and late-type hosts (see Schmidt et al. 1998). If, however, we believed that young progenitors give rise to brighter SNe Ia with broader light curves (Hamuy et al. 1996b) as discussed above, we could more directly determine the eect on distance determinations of drawing our high-redshift sample from an increasingly youthful population of progenitors. The mean dierence in the Hubble line deïned by the full nearby sample and the subsample of SNe Ia with broader than typical light curves (*\ 0) is 0.02 ^ 0.07 for the MLCS method. For the template-ïtting method, the dierence between the full sample and those with broader light curves [*m (B) \ 1.1] is 0.07 ^ 0.07. Again, we ïnd no indication of a15 systematic change in our distance estimates with a property that may correspond to a decrease in progenitor age. Another valuable test would be to compare low-


No. 3, 1998

EVIDENCE FOR AN ACCELERATING UNIVERSE

1029

redshift distances to starburst and irregular-type galaxies, which presumably are hosts to progenitors that are young and metal poor. Such a nearby sample may yield the closest approximation to the SNe Ia observed at high redshift. Future work will be needed to gather this informative sample, which would be composed of objects such as SN 1972E in NGC 5253 (which we does ït the luminosity light curve shape relations ; Hamuy et al. 1996a). Another check on evolutionary eects is to test whether the distribution of light curve decline rates is similar between the nearby sample of supernovae and the highredshift sample. Figure 10 shows the observed distribution of the MLCS light curve shape parameters, *, and the template-ïtting parameters, *m (B), with redshift. A Kolmogorov-Smirnov test shows 15 signiïcant dierence no in the distributions of the low- and high-redshift samples, but the sample is too small to be statistically signiïcant. The actual dierence in mean luminosity between the lowredshift and high-redshift samples implied by the light curve shapes is 0.02 mag by either method. We conclude that there is no obvious dierence between the shapes of SNe Ia light curves at z B 0 and at z B 0.5. It is reassuring that initial comparisons of high-redshift SN Ia spectra appear remarkably similar to those observed at low-redshift. This can be seen in the high signal-to-noise

SN 1992a (z=0.01)

SN 1994B (z=0.09)

Relative Flux

SN 1995E (z=0.01)

SN 1998ai (z=0.49)

SN 1989B (z=0.01)

3500

4000

4500 5000 5500 6000 Rest Wavelength (Angstroms)

6500

FIG. 11.õSpectral comparison (in f ) of SN 1998ai (z \ 0.49) with lowj redshift (z \ 0.1) SNe Ia at a similar age. Within the narrow range of SN Ia spectral features, SN 1998ai is indistinguishable from the low-redshift SNe Ia. The spectra from top to bottom are SN 1992A, SN 1994B, SN 1995E, SN 1998ai, and SN 1989B D5 days before maximum light. The spectra of the low-redshift SNe Ia were resampled and convolved with Gaussian noise to match the quality of the spectrum of SN 1998ai.

FIG. 10.õDistributions of MLCS light curve shape parameters, *, and template-ïtting parameters, *m (B), for the high- and low-redshift 15 samples of SNe Ia. Positive values for * and *m (B) [ 1.1 correspond to intrinsically dim SNe Ia, negative values for * 15 *m (B) \ 1.1 correand 15 spond to luminous SNe Ia. Histograms of the low-redshift (solid line) and high-redshift (dotted line) light curve shape parameters are mutually consistent with no indication that these samples are drawn from dierent populations of SNe Ia. Filled and open circles show the distribution of log (cz) for the low- and high-redshift samples, respectively.

ratio spectra of SN 1995ao (z \ 0.30) and SN 1995ap (z \ 0.23) in Figure 1. Another demonstration of this similarity at even higher redshift is shown in Figure 11 for SN 1998ai (z \ 0.49 ; Garnavich et al. 1996c), whose light curve was not used in this work. The spectrum of SN 1998ai was obtained at the Keck Telescope with a 5 ] 1800 s exposure using LRIS and was reduced as described in ° 2.2 (Filippenko et al. 1998). The spectral characteristics of this SN Ia appear to be indistinguishable from the range of characteristics at low redshift to good precision. In addition, a time sequence of spectra of SN Ia 1997ex (z \ 0.36 ; Nugent et al. 1998c) compared with those of local SNe Ia reveals no signiïcant spectral dierences (Filippenko et al. 1998). We expect that our local calibration will work well at eliminating any pernicious drift in the supernova distances between the local and distant samples. Until we know more about the stellar ancestors of SNe Ia, we need to be vigilant for changes in the properties of the supernovae at signiïcant look-back times. Our distance measurements could be particularly sensitive to changes in the colors of SNe Ia for a given light curve shape. Although our current observations reveal no indication of evolution of SNe Ia at z B 0.5, evolution remains a serious concern that can only be eased and perhaps understood by future studies. 5.2. Extinction Our SNe Ia distances have the important advantage of including corrections for interstellar extinction occurring in


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the host galaxy and the Milky Way. The uncertainty in the extinctions is a signiïcant component of error in our distance uncertainties. Extinction corrections based on the relation between SN Ia colors and luminosity improve distance precision for a sample of SNe Ia that includes objects with substantial extinction (Riess et al. 1996a). Yet, in practice, we have found negligible extinction to the high-redshift SNe Ia. The mean B[V color at maximum is [0.13 ^ 0.05 from the MLCS method and [0.07 ^ 0.05 from the template-ïtting approach, consistent with an unreddened B[V color of [0.10 to [0.05 expected for slowly declining light curves as observed in the high-redshift sample (Riess et al. 1996a ; Appendix). Further, the consistency of the measured Hubble ÿow from SNe Ia with late-type and early-type hosts (° 5.1) shows that the extinction corrections applied to dusty SNe Ia at low redshift do not alter the expansion rate from its value measured from SNe Ia in low dust environments. The conclusions reached in ° 4 would not alter if low- and highredshift SNe with signiïcant extinction were discarded rather than included after a correction for extinction. The results of ° 4 do not depend on the value of the ratios between color excess and selective absorption used to determine the extinctions of the high-redshift sample, because the mean observed reddening is negligible. Some modest departures from the Galactic reddening ratios have been observed in the Small and Large Magellanic Clouds, M31, and the Galaxy, and they have been linked to metallicity variations (Walterbos 1986 ; Hodge & Kennicutt 1982 ; Bouchet et al. 1985 ; Savage & Mathis 1979). Although our current understanding of the reddening ratios of interstellar dust at high redshift is limited, the lack of any signiïcant color excess observed in the high-redshift sample indicates that the type of interstellar dust that reddens optical light is not obscuring our view of these objects. Riess et al. (1996b) found indications that the Galactic ratios between selective absorption and color excess are similar for host galaxies in the nearby (z ¹ 0.1) Hubble ÿow. Yet, what if these ratios changed with look-back time ? Could an evolution in dust grain size descending from ancestral interstellar "" pebbles îî at higher redshifts cause us to underestimate the extinction ? Large dust grains would not imprint the reddening signature of typical interstellar extinction upon which our corrections rely. However, viewing our SNe through such gray interstellar grains would also induce a dispersion in the derived distances. To estimate the size of the dispersion, we assume that the gray extinction is distributed in galaxies in the same way as typical interstellar extinction. Hatano et al. (1998) have calculated the expected distribution of SN Ia extinction along random lines of sight in the host galaxies. A gray extinction distribution similar to theirs could yield diering amounts of mean gray extinction depending on the likelihood assigned to observing an extinction of A \ 0.0 mag. In the following calculations we vary only the Blikelihood of A \ 0.0 mag to derive new B extinction distributions with varying means. These dierent distributions also have diering dispersions of extinction. A mean gray extinction of 0.25 mag would be required to explain the measured MLCS distances without a cosmological constant. Yet the dispersion of individual extinctions for a distribution with a mean of 0.25 mag would be p \ AB 0.40 mag, signiïcantly larger than the 0.21 mag dispersion observed in the high-redshift MLCS distances. Gray extinc-

tion is an even less likely culprit with the template-ïtting approach ; a distribution with a mean gray extinction of 0.28 mag, needed to replace a cosmological constant, would yield a dispersion of 0.42 mag, signiïcantly higher than the distance dispersion of 0.17 mag observed in the highredshift template-ïtting distances. Furthermore, most of the observed scatter is already consistent with the estimated statistical errors as evidenced by the s2 (Table 8), leaving little to be caused by gray extincl tion. Nevertheless, if we assumed that all of the observed scatter were due to gray extinction, the mean shift in the SNe Ia distances would only be 0.05 mag. With the observations presented here, we cannot rule out this modest amount of gray interstellar extinction. This argument applies not only to exotic gray extinction but to any interstellar extinction not accounted for which obscures SNe Ia. Any spotty interstellar extinction that varies with line of sight in a way similar to the Hatano et al. (1998) model of galaxies will add dispersion to the SN Ia distances. The low dispersion measured for the high-redshift sample places a strong limit on any mean spotty interstellar extinction. Gray intergalactic extinction could dim the SNe without either telltale reddening or dispersion, if all lines of sight to a given redshift had a similar column density of absorbing material. The component of the intergalactic medium with such uniform coverage corresponds to the gas clouds producing Lya forest absorption at low redshifts. These clouds have individual H I column densities less than about 1015 cm~2 (Bahcall et al. 1996). However, these clouds display low metallicities, typically less than 10% of solar. Gray extinction would require larger dust grains, which would need a larger mass in heavy elements than typical interstellar grain size distributions to achieve a given extinction. Furthermore, these clouds reside in hard radiation environments hostile to the survival of dust grains. Finally, the existence of gray intergalactic extinction would only augment the already surprising excess of galaxies in highredshift galaxy surveys (Huang et al. 1997). We conclude that gray extinction does not seem to provide an observationally or physically plausible explanation for the observed faintness of high-redshift SNe Ia. 5.3. Selection Bias Sample selection has the potential to distort the comparison of nearby and distant supernovae. Most of our nearby (z \ 0.1) sample of SNe Ia was gathered from the Calan/ Tololo survey (Hamuy et al. 1993a), which employed the blinking of photographic plates obtained at dierent epochs with Schmidt telescopes and from less well deïned searches (Riess et al. 1998c). Our distant (z [ 0.16) sample was obtained by subtracting digital CCD images at dierent epochs with the same instrument setup. If they were limited by the ÿux of the detected events, both nearby and distant SN Ia searches would preferentially select intrinsically luminous objects because of the larger volume of space in which these objects can be detected. This well-understood selection eect could be further complicated by the properties of SNe Ia ; more luminous supernovae have broader light curves (Phillips 1993 ; Hamuy et al. 1995, 1996b ; Riess et al. 1995, 1996a). The brighter supernovae remain above a detection limit longer than their fainter siblings, but also can fail to rise above the detection limit in the time interval between successive


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search epochs. The complex process by which SNe Ia are selected in low- and high-redshift searches can be best understood with simulations (Hamuy & Pinto 1998). Although selection eects could alter the ratio of intrinsically dim to bright SNe Ia in our samples relative to the true population, our use of the light curve shape to determine the supernovaîs luminosity should correct most of this selection bias on our distance estimates. However, even after our light curve shape correction, SNe Ia still have a small dispersion as distance indicators (pB 0.15 mag), and any search program would still preferentially select objects that are brighter than average for a particular light curve shape and possibly select objects whose light curve shapes aid detection. To investigate the consequence of sample selection eects, we used a Monte Carlo simulation to understand how SNe Ia in our nearby and distant samples were chosen. For the purpose of this simulation, we ïrst assumed that the SN Ia rate is constant with look-back time. We assembled a population of SNe Ia with luminosities described by a Gaussian random variable p \ 0.4 mag and light curve MB shapes, which correspond to these luminosities as described by the MLCS vectors (see the Appendix). A Gaussian random uncertainty of p \ 0.15 mag is assumed in the determination of absolute magnitude from the shape of a supernovaîs light curve. The time interval between successive search epochs, the search epochîs limiting magnitudes, and the apparent light curve shapes were used to determine which SNe Ia were "" discovered îî and included in the simulation sample. A separate simulation was used to select nearby objects, with the appropriate time interval between epochs and estimates of limiting magnitudes. The results are extremely encouraging, with recovered values exceeding the simulated value of ) or ) by only 0.02 for M " these two parameters considered separately. Smoothly increasing the SN Ia rate by a factor of 10 by z \ 1 doubles this bias to 0.04 for either parameter. There are two reasons we ïnd such a small selection bias in the recovered cosmological parameters. First, the small dispersion of our distance indicator results in only a modest selection bias. Second, both nearby and distant samples include an excess of brighter than average SNe, so the dierence in their individual selection biases remains small. As discussed by Schmidt et al. (1998), obtaining accurate limiting magnitudes is complex for the CCD-based searches, and essentially impossible for the photographic searches. Limiting magnitudes vary from frame to frame, night to night, and ïlm to ïlm, so it is difficult to use the actual detection limits in our simulation. Nevertheless, we have run simulations varying the limiting magnitude, and this does not change the results signiïcantly. We have also tried increasing the dispersion in the SN Ia light curve shape versus absolute magnitude correlation at wavelengths shorter than 5000 ñ. Even doubling the distance dispersion of SNe Ia (as may be the case for rest-frame U) does not signiïcantly change the simulation results. Although these simulations bode well for using SNe Ia to measure cosmological parameters, there are other dierences between the way nearby and distant supernova samples are selected that are more difficult to model and are not included in our present simulations. Von Hippel, Bothun, & Schommer (1997) have shown that the selection function of the nearby searches is not consistent with that of a strict magnitude-limited search. It is unclear whether a

photographic search selects SNe Ia with dierent parameters or environments than a CCD search or how this could aect a comparison of samples. Future work on quantifying the selection criteria of the samples is needed. A CCD search for SNe Ia in Abell clusters by Reiss et al. (1998a) will soon provide a nearby SN Ia sample with better understood selection criteria. Although indications from the distributions of SN Ia parameters suggest that both our searches have sampled the same underlying population (see Fig. 10), we must continue to be wary of subtle selection eects that might bias the comparison of SNe Ia near and far. 5.4. Eect of a L ocal V oid It has been noted by Zehavi et al. (1998) that the SNe Ia out to 7000 km s~1 exhibit an expansion rate that is 6% greater than that measured for the more distant objects. The signiïcance of this peculiar monopole is at the 2 p to 3 p conïdence level ; it is not inconsistent with the upper limit of D10% for the dierence between the local and global values of H found by Kim et al. (1997). The implication is 0 that the volume out to this distance is underdense relative to the global mean density. This eect appears as an excess redshift for a given distance modulus (within 7000 km s~1) and can be seen with both the MLCS method and the template-ïtting method in Figures 4 and 5. If true, what eect would this result have on our conclusions ? In principle, a local void would increase the expansion rate measured for our low-redshift sample relative to the true, global expansion rate. Mistaking this inÿated rate for the global value would give the false impression of an increase in the low-redshift expansion rate relative to the high-redshift expansion rate. This outcome could be incorrectly attributed to the inÿuence of a positive cosmological constant. In practice, only a small fraction of our nearby sample is within this local void, reducing its eect on the determination of the low-redshift expansion rate. As a test of the eect of a local void on our constraints for the cosmological parameters, we reanalyzed the data discarding the seven SNe Ia within 7000 km s~1 (108 Mpc for H \ 65). The result was a reduction in the conïdence that ) 0 [ 0 from 99.7% (3.0 p) to 98.3% (2.4 p) for the MLCS " method and from more than 99.9% (4.0 p) to 99.8% (3.1 p) for the template-ïtting approach. The tests for both methods excluded the unclassiïed SN 1997ck and included the snapshot sample, the latter without two SNe Ia within 7000 km s~1. As expected, the inÿuence of a possible local void on our cosmological conclusions is relatively small. 5.5. W eak Gravitational L ensing The magniïcation and demagniïcation of light by largescale structure can alter the observed magnitudes of highredshift supernovae (Kantowski, Vaughan, & Branch 1995). The eect of weak gravitational lensing on our analysis has been quantiïed by Wambsganss et al. (1997) and summarized by Schmidt et al. (1998). SN Ia light will, on average, be demagniïed by 0.5% at z \ 0.5 and 1% at z \ 1 in a universe with a non-negligible cosmological constant. Although the sign of the eect is the same as the inÿuence of a cosmological constant, the size of the eect is negligible. Holz & Wald (1998) have calculated the weak lensing eects on supernova light from ordinary matter, which is not smoothly distributed in galaxies but rather clumped into stars (i.e., dark matter contained in MACHOs). With this scenario, microlensing by compact masses becomes a


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more important eect, further decreasing the observed supernova brightnesses at z \ 0.5 by 0.02 mag for ) \ 0.2 (D. E. Holz 1998, private communication). Even M most if ordinary matter were contained in compact objects, this eect would not be large enough to reconcile the SNe Ia distances with the inÿuence of ordinary matter alone. 5.6. L ight Curve Fitting Method As described in ° 3.2, two dierent light curve ïtting methods, MLCS (Riess et al. 1996a ; Appendix) and a template-ïtting approach (Hamuy et al. 1995, 1996d), were employed to determine the distances to the nearby and high-redshift samples. Both methods use relations between light curve shape and luminosity as determined from SNe Ia in the nearby Hubble ÿow. Both methods employ an extinction correction from the measured color excess using relations between intrinsic color and light curve shape. In addition, both the MLCS and template-ïtting methods yield highly consistent measurements for the Hubble constant of H \ 65.2 ^ 1.3 and H \ 63.8 ^ 1.3, respectively 0 0 not including any uncertainty in the determination of the SN Ia absolute magnitude, which is the dominant uncertainty. It is also worth noting that both methods yield SN Ia distance dispersions of D0.15 mag when complete light curves in B, V , R, and I are employed. For the purpose of comparing the same data at high and low redshifts, the use of SN Ia observations at low redshift were restricted to only B and V within 40 days of maximum light. Although the conclusions reached by the two methods when applied to the high-redshift SNe are highly consistent, some dierences are worth noting. There are small dierences in the distance predictions at high redshift. For the distant sample, the template-ïtting distances exhibit a scatter of 0.17 mag around the best-ït model as compared with 0.21 mag for the MLCS method. In addition, the template-ïtting distances to the high-redshift SNe Ia are on (weighted) average 0.03 mag farther than the MLCS distances relative to the low-redshift sample. These dierences together result in slightly dierent conïdence intervals for the two methods (see Figs. 6, 7, and 8 and Table 8). For the set of 10 well-observed SNe Ia, a sample with scatter 0.17 mag or less is drawn from a population of scatter 0.21 mag 25% of the time. The chance that 10 objects could be drawn from this same population with a mean dierence of 0.03 mag is 66%. Future samples of SNe Ia will reveal if the observed dierences are explained by chance. Until then, we must consider the dierence between the cosmological constraints reached from the two ïtting methods to be a systematic uncertainty. Yet, for the data considered here, both distance ïtting methods unanimously favor the existence of a non-negligible, positive cosmological constant and an accelerating universe. 5.7. Sample Contamination The mean brightness of SNe Ia is typically 4 õ 40 times greater than that of any other type of supernova, favoring their detection in the volume of space searched at high redshift. Yet in the course of our high-redshift supernova search (and that of the Supernova Cosmology Project ; Perlmutter et al. 1995) a small minority of other supernova types have been found, and we must be careful not to include such objects in our SN Ia sample. The classiïcation of a supernova is determined from the presence or absence of speciïc features in the spectrum (Wheeler & Harkness 1990 ;

Branch, Fisher, & Nugent 1993 ; Filippenko 1997). The spectra of Type Ia supernovae show broad Si II absorption near 6150 ñ, Ca II (H and K) absorption near 3800 ñ, an S II absorption doublet near 5300 and 5500 ñ, and numerous other absorption features, with ionized Fe a major contributor (Filippenko 1997). For supernovae at high redshift, some of these characteristic features shift out of the observerîs frequency range as other, shorter wavelength features become visible. Classiïcation is further complicated by low signal-to-noise ratio in the spectra of distant objects. The spectra of SNe Ia evolve with time along a remarkably reliable sequence (Riess et al. 1997). Final spectral classiïcation is optimized by comparing the observed spectrum to well-observed spectra of SNe Ia at the same age as determined from the light curves. For most of the spectra in Figure 1, the identiïcation as a SN Ia is unambiguous. However, in three of the lowest signal-to-noise ratio casesõ1996E, 1996H, and 1996Iõthe wavelengths near Si II absorption (rest frame 6150 ñ) were poorly observed, and their classiïcation warrants closer scrutiny. These spectra are inconsistent with Type II spectra, which show Hb (4861 ñ) in emission and absorption and lack Fe II features shortly after maximum. These spectra are also inconsistent with Type Ib spectra, which would display He I j5876 absorption at a rest wavelength of D5700 ñ. The most likely supernova type to be misconstrued as a Type Ia is a Type Ic, as this type comes closest to matching the SN Ia spectral characteristics. Although SN Ic spectra lack Si II and S II absorption, the maximum-light spectra at blue wavelengths can resemble those of SNe Ia D2 weeks past maximum, when both are dominated by absorption lines of Fe II with P Cygni proïles. Type Ic events are rare and one luminous enough to be found in our search would be rare indeed, but not without precedent. An example of such an object is SN 1992ar (Clocchiatti et al. 1998), which was discovered in the course of the Calan/Tololo SN survey and which reached an absolute magnitude, uncorrected for host galaxy dust extinction, of M \[19.3 (H \ 65 km 0 s~1 Mpc~1). For both SN 1996H V and SN 1996I, the spectral match with a Type Ia at rest wavelengths less than 4500 ñ is superior to the ït to a Type Ic spectrum (see Fig. 1). In both cases the spectra rise from deep troughs at the 3800 ñ Ca II break (rest frame) to strong peaks at 3900 õ 4100 ñ (rest frame) as observed in SNe Ia. Type Ic spectra, by comparison, tend to exhibit a much weaker transition from trough to peak redward of the Ca II break (see Fig. 12). For SN 1996E, the spectral coverage does not extend blueward of a rest wavelength of 4225 ñ, rendering this diagnostic unusable. The absence of premaximum observations of SN 1996E makes it difficult to determine the age of the spectrum and that of the appropriate comparison spectra. As shown in Figure 12, the spectroscopic and photometric data for SN 1996E are consistent with a SN Ia caught D1 week after maximum light, or a luminous SN Ic discovered at maximum. There is a weak indication of S II absorption at D5375 ñ, which favors classiïcation as a Type Ia (see Figs. 1 and 12), but this alone does not provide a secure classiïcation. Note that the K-corrections for a SN Ia or SN Ic at this redshift (z \ 0.43) would be nearly identical due to the excellent match of the observed ïlters (B45 and V45) to the rest-frame (B and V ) ïlters. We have reanalyzed the cosmological parameters discarding SN 1996E as a safeguard against the possible con-


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2.0
96E 89B (Type Ia +13 days) 96E 92ar (Type Ic +3 days)

1.5 Relative F

1.0

0.5

0.0 22 23 Magnitude 24 25 26 27

4000

5000

6000

4000

5000

6000

V

V

B (+1 mag)

B (+1 mag)

0

10 20 Age (days)

30

0

10 20 Age (days)

30

FIG. 12.õComparison of the spectral and photometric observations of SN 1996E to those of Type Ia and Type Ic supernovae. The low signal-to-noise ratio of the spectrum of SN 1996E and the absence of data blueward of 4500 ñ makes it difficult to distinguish between a Type Ia and Ic classiïcation. The light and color curves of SN 1996E are also consistent with either supernova type. The spectrum was taken 6 days (rest frame) after the ïrst photometric observation.

tamination of our high-redshift sample. We also excluded SN 1997ck, which, for lack of a deïnitive spectral classiïcation, is an additional threat to contamination of our sample. With the remaining "" high-conïdence îî sample of 14 SNe Ia we ïnd the statistical likelihood of a positive cosmological constant to be 99.8% (3.1 p) from the MLCS method, a modest increase from 99.7% (3.0 p) conïdence when SN 1996E is included. For the template-ïtting approach, the statistical conïdence in a positive cosmological constant remains high at more than 99.9% (4.0 p), the same result as with SN 1996E. We conclude that for this sample our results are robust against sample contamination, but the possible contamination of future samples remains a concern. Even given existing detector technology, more secure supernova classiïcations can be achieved with greater signal-to-noise ratios for observed spectra, with optimally timed search epochs that increase the likelihood of premaximum discovery, and with an improved empirical understanding of the dierences among the spectra of supernova types. 5.8. Comparisons The results reported here are consistent with other reported observations of high-redshift SNe Ia from the

High-z Supernova Search Team (Garnavich et al. 1998a ; Schmidt et al. 1998), and the improved statistics of this larger sample reveal the potential inÿuence of a positive cosmological constant. These results are inconsistent at the D2 p conïdence level with those of Perlmutter et al. (1997), who found ) \ 0.94 ^ 0.3 () \ 0.06) for a ÿat universe and ) \ M " M 0.88 ^ 0.64 for ) 4 0. They are marginally consistent with " et al. (1998), who, with the addition of those of Perlmutter one very high redshift SN Ia (z \ 0.83), found ) \ 0.6 M ^ 0.2 () \ 0.4) for a ÿat universe and ) \ 0.2 ^ 0.4 for " M ) 4 0. " Although the experiment reported here is very similar to that performed by Perlmutter et al. (1997, 1998), there are some dierences worth noting. Schmidt et al. (1998), Garnavich et al. (1998a), and this paper explicitly correct for the eects of extinction evidenced by reddening of the SNe Ia colors. Not correcting for extinction in the nearby and distant sample could aect the cosmological results in either direction since we do not know the sign of the dierence of the mean extinction. In practice we have found few of the high-redshift SNe Ia to suer measurable reddening. A number of objects in the nearby sample display moderate


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extinction, for which we make individual corrections. We also include the Hubble constant as a free parameter in each of our ïts to the other cosmological parameters. Treating the nearby sample in the same way as the distant sample is a crucial requirement of this work. Our experience observing the nearby sample aids our ability to accomplish this goal. The statistics of gravitational lenses provide an alternate method for constraining the cosmological constant (Turner 1990 ; Fukugita, Futamase, & Kasai 1990). Although current gravitational-lensing limits for the cosmological constant in a ÿat universe () ¹ 0.66 at 95% conïdence ; " Kochanek 1996) are not inconsistent with these results, they are uncomfortably close. Future analysis that seeks to limit systematic uncertainties aecting both experiments should yield meaningful comparisons. The most incisive independent test may come from measurements of the ÿuctuation spectrum of the cosmic microwave background. While the supernova measurements provide a good constraint on ) [ ) , the CMB measurements of the angular scale for M the ïrst " Doppler peak, referring to much earlier epochs, are good measures of ) ] ) (White & Scott 1996). Since these constraints are M nearly" orthogonal in the coordinates of Figures 6 and 7, the region of intersection could be well deïned. Ongoing experiments from balloons and the South Pole may provide the ïrst clues to the location of that intersection. Our detection of a cosmological constant is limited not by statistical errors but by systematic ones. Further intensive study of SNe Ia at low (z \ 0.1), intermediate (0.1 ¹ z ¹ 0.3), and high (z [ 0.3) redshifts is needed to uncover and quantify lingering systematic uncertainties in this striking result.
6

3. The data favor eternal expansion as the fate of the universe at the 99.7% (3.0 p) to more than 99.9% (4.0 p) conïdence level from the spectroscopic SN Ia sample and the prior that ) º 0. M 4. We estimate the dynamical age of the universe to be 14.2 ^ 1.7 Gyr including systematic uncertainties in the zero point of the current Cepheid distance scale used for the host galaxies of three nearby SNe Ia (Saha et al. 1994, 1997). 5. These conclusions do not depend on inclusion of SN 1997ck (z \ 0.97), whose spectroscopic classiïcation remains uncertain, nor do they depend on which of two light curve ïtting methods is used to determine the SN Ia distances. 6. The systematic uncertainties presented by gray extinction, sample selection bias, evolution, a local void, weak gravitational lensing, and sample contamination currently do not provide a convincing substitute for a positive cosmological constant. Further studies are needed to determine the possible inÿuence of any remaining systematic uncertainties.

. CONCLUSIONS

1. We ïnd the luminosity distances to well-observed SNe with 0.16 ¹ z ¹ 0.97 measured by two methods to be in excess of the prediction of a low mass density () B 0.2) M universe by 0.25 to 0.28 mag. A cosmological explanation is provided by a positive cosmological constant with 99.7% (3.0 p) to more than 99.9% (4.0 p) conïdence using the complete spectroscopic SN Ia sample and the prior belief that ) º 0. M 2. The distances to the spectroscopic sample of SNe Ia measured by two methods are consistent with a currently accelerating expansion (q ¹ 0) at conïdence levels from 0 99.5% (2.8 p) to more than 99.9% (3.9 p) for q 4 () /2) 0 M [ ) using the prior that ) º 0. " M

We wish to thank Alex Athey and S. Elizabeth Turner for their help in the supernova search at CTIO. We have beneïted from helpful discussions with Peter Nugent, Alex Kim, Gordon Squires, and Marc Davis and from the eorts of Alan Dressler, Aaron Barth, Doug Leonard, Tom Matheson, Ed Moran, and Di Harmer. The work at U. C. Berkeley was supported by the Miller Institute for Basic Research in Science, by NSF grant AST 94-17213, and by grant GO-7505 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 5-26555. Support for A. C. was provided by the National Science Foundation through grant GF-1001-95 from AURA, Inc., under NSF cooperative agreement AST 8947990 and AST 96-17036, and from Fundacion Antorchas Argentina under project A-13313. This work was supported at Harvard University through NSF grants AST 92-21648, AST 95-28899, and an NSF Graduate Research Fellowship. C. S. acknowledges the generous support of the Packard Foundation and the Seaver Institute. This research was based in part on spectroscopic observations obtained with the Multiple Mirror Telescope, a facility operated jointly by the Smithsonian Institution and the University of Arizona.

APPENDIX THE MULTICOLOR LIGHT CURVE SHAPE METHOD Following the success of Phillips (1993), Riess et al. (1995) employed a linear estimation algorithm (Rybicki & Press 1992) to determine the relationship between the shape of a SN Ia light curve and its peak luminosity. This method was extended (Riess et al. 1996a) to utilize the SN Ia color curves to quantify the amount of reddening by interstellar extinction. In this appendix we describe further reïnements and optimization of the MLCS method for the application to high-redshift SNe Ia. Previously, the MLCS relations were derived from a set similar to the nearby (cz ¹ 2000 km s~1) sample of Phillips (1993) (Riess et al. 1995, 1996a). The relative luminosities of this "" training set îî of SNe Ia were calibrated with independent distance indicators (Tonry 1991 ; Pierce 1994). The absolute SN Ia luminosities were measured from Cepheid variables populating the host galaxies (Saha et al. 1994, 1997). Yet at moderate distances, the most reliable distance indicator available in nature is the redshift. The recent harvest of SN Ia samples (Hamuy et al. 1996a ; Riess et al. 1998c) with cz º 2500 km s~1 provides a homogeneous training set of objects for MLCS with well-understood relative luminosities. Here we employ a set (see Table 10) of B and V light curves with cz º 2500 km s~1 to determine the MLCS relations.


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TABLE 10 NEARBY MLCS AND TEMPLATE-FITTING SN Ia PARAMETERSa MLCS SN 1992bo ...... 1992bc ...... 1992aq ...... 1992ae ...... 1992P ....... 1990af ...... 1994M ...... 1994S ....... 1994T ....... 1995D ...... 1995E ....... 1995ac ...... 1995ak ...... 1995bd ...... 1996C ....... 1996ab ...... 1992ag ...... 1992al ...... 1992bg ...... 1992bh ...... 1992bl ...... 1992bp ...... 1992br ...... 1992bs ...... 1993H ...... 1993O ...... 1993ag ...... log cz 3.734 3.779 4.481 4.350 3.896 4.178 3.859 3.685 4.030 3.398 3.547 4.166 3.820 3.679 3.924 4.572 3.891 3.625 4.024 4.130 4.111 4.379 4.418 4.283 3.871 4.189 4.177 * 0.31 [0.50 0.05 [0.05 [0.19 0.09 0.04 [0.44 0.11 [0.42 [0.61 [0.47 0.15 [0.29 [0.07 [0.13 [0.50 [0.35 [0.06 [0.16 [0.06 [0.26 0.40 0.00 0.16 0.03 [0.19 B 0.00 0.00 0.00 0.00 0.00 0.18 0.08 0.00 0.22 0.00 2.67 0.00 0.00 2.52 0.24 0.00 0.77 0.00 0.50 0.28 0.00 0.04 0.00 0.00 0.67 0.00 0.64 A k (p) 0 34.72(0.16) 34.87(0.11) 38.41(0.15) 37.80(0.17) 35.76(0.13) 36.53(0.15) 35.39(0.18) 34.27(0.12) 36.19(0.21) 33.01(0.13) 33.60(0.17) 36.85(0.13) 35.15(0.16) 34.15(0.19) 35.98(0.20) 39.01(0.13) 35.37(0.23) 33.92(0.11) 36.26(0.21) 36.91(0.17) 36.26(0.15) 37.65(0.13) 38.21(0.19) 37.61(0.14) 35.20(0.26) 37.03(0.12) 36.80(0.17) TEMPLATE FITTING *m (B) 15 1.59 0.88 1.12 1.21 0.94 1.66 1.47 1.02 1.35 0.96 1.03 0.99 1.28 0.87 0.97 1.10 1.12 1.13 1.14 1.05 1.50 1.27 1.77 1.10 1.59 1.18 1.29 B 0.01 0.00 0.18 0.28 0.14 0.16 0.06 0.03 0.19 0.23 2.47 0.22 0.06 2.67 0.42 0.09 0.09 0.00 0.44 0.34 0.00 0.03 0.02 0.24 0.72 0.00 0.55 A k (p) 0 34.88(0.21) 34.77(0.15) 38.33(0.23) 37.77(0.19) 35.59(0.16) 36.67(0.25) 35.49(0.20) 34.34(0.14) 36.50(0.20) 32.79(0.16) 33.73(0.17) 36.60(0.16) 35.43(0.18) 34.00(0.18) 35.82(0.20) 39.10(0.17) 35.53(0.20) 34.13(0.14) 36.49(0.21) 36.87(0.17) 36.53(0.20) 37.96(0.15) 38.09(0.36) 37.63(0.18) 35.23(0.25) 37.31(0.14) 37.11(0.19) HOST TYPEb E L L E L L E L L E L L L L L L L L L L L E E L L E E

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a Light curves restricted to B and V data within 40 days of B maximum. b E \ early-type host, L \ late-type host.

The signiïcant increase in the size of the available training set of SNe Ia since Riess et al. (1996a) supports an expansion of our description of the MLCS relations. Riess et al. (1996a) described SNe Ia light curves as a linear family of the peak luminosity : m \M ]R *]k , (A1) V V V V m \M ]R *]E , (A2) B~V B~V B~V B~V where m and m are the observed light and color curves, * 4 M [ M (standard) is the dierence in maximum luminosity B~V v v between V ïducial template SN Ia and any other SN Ia, R and R the are vectors of correlation coefficients between * and V and EB~V is the color excess. All symbols in boldface denote the light curve shape, k is the apparent distance modulus, V B~V vectors that are functions of SN Ia age, with t \ 0 taken by convention as the epoch of B maximum. By adding a second-order term in the expansion, our empirical model becomes (A3) m \ M ] R * ] Q *2] k , V V V V V m \M ]R *]Q *2] E , (A4) B~V B~V B~V B~V B~V where Q , Q are the correlation coefficients of the quadratic relationship between *2 and the light curve shape. The V B~V vectors of coefficients (R , R ,Q ,Q ), as well as the ïducial templates (M , M ), are determined from the training V B~ V B~V V B in set of SNe Ia listed in Table 10.VThe empirical light and color curve families are shown~V Figure 13. As before, these MLCS relations show that the more luminous SNe Ia have broader light curves and are bluer until day D35, by which time all SNe Ia have the same color. The primary dierence from the previous MLCS relations is that near maximum, the color range spanned by the same range of SN Ia luminosities is much reduced. Further, the quadratic MLCS relations reveal that SNe Ia that are brighter or dimmer (than the ïducial value) by equal amounts do not show equal changes in their colors. Faint SNe Ia are far redder than the amount by which luminous SNe Ia are blue. Fitting of this quadratic model (eqs. [A3]õ[A4]) to a SN Ia still requires the determination of four "" free îî parameters : *, k , V E , and t . The parameters are determined by minimizing the expected deviations between data and model : B~V max s2\ r C~1rT , (A5) x x where r \ m [ M [ R * [ Q *2[ k x x x x x x (A6)


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FIG. 13.õMLCS empirical SN Ia light curve families in M , M , and (B[V ) . The derived light curves are given as a function of the luminosity V 0 dierence, *, between the peak visual luminosity of a SN Ia and B ïducial (* \ 0) SN Ia. Properties of the SN Ia families are indicated in the ïgure and the a Appendix. The light and color curves of SN 1995ac (open symbols) and SN 1996X ( ïlled symbols) are overplotted as examples of luminous and dim SNe Ia, respectively.

for any band x.Here C is the correlation matrix of the model and the measurements. Correlations of the data from the model were determined from the SNe Ia of Table 10. These correlations result from our still imperfect (but improving) description of the light curve shape behavior. Future expansion of the model will reduce these correlations further until they become constraints on the unpredictable, turbulent behavior of the SN Ia atmosphere. Riess et al. (1996a) quantiïed the autocorrelation (diagonal matrix elements) of the linear model. Here we have determined, in addition, the covariance (o-diagonal matrix elements) between two measurements of diering SN Ia age, passband, or both. The correlation matrix of the measurements, commonly called the "" noise,îî is, as always, provided by the conscientious observer. The a priori values for * used to determine the vectors R , R ,Q ,Q , M , and M are the dierences between the V B~ galaxy B~V B~V measured peak magnitudes and those predicted by the SN Ia host V V redshift. V These values for * must be corrected for the extinction, A . Because the values of A are not known a priori, we use an initial guess derived from the color excess measured V from the uniform color range of SNe IaVafter day 35 (Riess et al. 1996a ; Lira 1995). Initial guesses for *, k , E , and t yield estimates for R , R ,Q ,Q , M , and M by minimizing equation V BV max VB V B~V B~V (A5) with respect to the latter.~These estimates for R , R , Q , Q ~V , M , and M V yield improved estimates of *, k , V B~V V B~V V B~V V E , and t also determined by minimizing equation (A5) with respect to the latter. This iterative determination of these B~V and max vectors parameters is repeated until convergence is reached. Subsequent determination of the parameters *, k , E , V ~V and t for SNe Ia not listed in Table 10 (such as those reported here) is done by using the ïxed vectors derived fromBthis max training process. We also employ a reïned estimate of the selective absorption to color excess ratio, R \ A /E , which has been V V BV calculated explicitly as a function of SN Ia age from accurate spectrophotometry of SNe Ia (Nugent,~Kim, & Perlmutter 1998a). This work shows that although R is the canonical value of D3.1 for SNe Ia at maximum light or before, over the ïrst 10 days after maximum R slowly rises toVabout 3.4. For highly reddened SNe Ia, this change in R over time can appreciably V aect the shape of the SN V light curve (Leibundgut 1989). Ia Finally, we have reïned our a priori understanding of the likelihood for SN Ia interstellar extinction from host galaxies. The previous incarnation of MLCS (Riess et al. 1996a) employed a "" Bayesian ïlter îî to combine our measurement of extinction with our prior knowledge of its one-directional eect. In addition, it is less probable to observe a very large amount of extinction due to the ïnite column density of a spiral disk as well as a reduced likelihood for detection of SNe with large extinctions. To quantify this a priori likelihood for extinction we have adopted the calculations of Hatano et al. (1998), who determined the extinction distribution for SNe Ia in the bulge and disk of late-type galaxies. The primary dierence between our previous a priori distribution and the results of Hatano et al. (1998) are that nontrivial quantities of extinction are even


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less probable than assumed. In particular, Hatano et al. (1998) show that two-thirds of SNe Ia suer less than 0.3 to 0.5 mag of extinction, which is approximately half the amount of extinction previously assumed. Despite our use of an externally derived Bayesian prior for probable SN Ia extinction, it is important to continue testing that the a posteriori extinction distribution matches the expected one. A statistically signiïcant departure could imply an important deïciency in the SN Ia luminosity, light curve shape, and color relations. Speciïcally, excessively blue SNe Ia such as SN 1994D (E B [0.10 ^ 0.04), if B~V common, would reveal a shortcoming of these MLCS relations. However, using the current MLCS relations, the best estimate we can make for such blue SNe Ia is that their extinctions are negligible. (We note, however, that as the high- and low-redshift sample size increases, a better estimator of the extinction is the mean and not the mode of the extinction). If the a priori distributions of Hatano et al. (1998) are not signiïcantly in error, this practice is statistically sensible and does not introduce a signiïcant distance bias.

REFERENCES Arnett, W. D. 1969, Ap&SS, 5, 280 Bahcall, J. N., et al. 1996, ApJ, 457, 19 Bahcall, N. A., Fan, X., & Cen, R. 1997, ApJ, 485, 53 Bolte, M., & Hogan, C. J. 1995, Nature, 376, 399 Bouchet, P., Lequeux, J., Maurice, E., Prevot, L., & Prevot-Burnichon, M. L. 1985, A&A, 149, 300 Branch, D. 1998, ARA&A, in press Branch, D., Fisher, A., & Nugent, P. 1993, AJ, 106, 2383 Branch, D., & Miller, D. 1993, ApJ, 405, L5 Branch, D., & Tammann, G. A. 1992, ARA&A, 30, 359 Branch, D., & van den Bergh, S. 1993, AJ, 105, 2251 Branch, D., et al. 1988, ApJ, 330, 117 Burstein, D., & Heiles, C. 1982, AJ, 87, 1165 Caldwell, R. R., Dave, R., & Steinhardt, P. J. 1998, Phys. Rep. Lett., 80, 1582 Cappellaro, E., et al. 1997, A&A, 322, 431 Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245 Carlberg, R. G., Yee, H. K. C., Ellingson, E., Abraham, R., Gravel, P., Morris, S., & Pritchet, C. J. 1996, ApJ, 462, 32 Carroll, S. M., Press, W. H., & Turner, E. L. 1992, ARA&A, 30, 499 Chaboyer, B. 1995, ApJ, 444, L9 Chaboyer, B., Demarque, P., Kernan, P. J., & Krauss, L. M. 1998, ApJ, 494, 96 Chaboyer, B., Demarque, P., & Sarajedini, A. 1996, ApJ, 459, 558 Clocchiatti, A., et al. 1998, in preparation Colgate, S. 1979, ApJ, 232, 404 Colgate, S., & McKee, C. 1969, ApJ, 157, 623 Cowan, J. J., McWilliam, A., Sneden, C., & Burris, D. L. 1997, ApJ, 480, 246 Cristiani, S., et al. 1992, A&A, 259, 63 Della Valle, M., & Panagia, N. 1992, AJ, 104, 696 Doggett, J. B., & Branch, D. 1985, AJ, 90, 2303 Feast, M. W., & Catchpole, R. M. 1997, MNRAS, 286, 1P Feast, M. W., & Walker, A. R. 1987, ARA&A, 25, 345 Filippenko, A. V. 1997, ARA&A, 35, 309 Filippenko, A. V., et al. 1992a, ApJ, 384, 15 õõõ. 1992b, AJ, 104, 1543 õõõ. 1998, ApJ, in press Ford, C., et al. 1993, AJ, 106, 1101 Fukugita, M., Futamase, T., & Kasai, M. 1990, MNRAS, 246, 24 Garnavich, P., et al. 1996a, IAU Circ. 6332 õõõ. 1996b, IAU Circ. 6358 õõõ. 1996c, IAU Circ. 6861 õõõ. 1998a, ApJ, 493, 53 õõõ. 1998b, ApJ, in press Goobar, A., & Perlmutter, S. 1995, ApJ, 450, 14 Gratton, R. G., Fusi Pecci, F., Carretta, E., Clementini, G., Corsi, C. E., & Lattanzi, M. 1997, ApJ, 491, 749 Hamuy, M., et al. 1994, AJ, 108, 2226 õõõ. 1993a, AJ, 106, 2392 õõõ. 1996a, AJ, 112, 2408 Hamuy, M., Phillips, M. M., Maza, J., Suntze, N. B., Schommer, R. A., & Aviles, R. 1995, AJ, 109, 1 Hamuy, M., Phillips, M. M., Schommer, R. A., Suntze, N. B., Maza, J., & Aviles, R. 1996b, AJ, 112, 2391 Hamuy, M., Phillips, M. M., Suntze, N. B., Schommer, R. A., Maza, J., & Aviles, R. 1996c, AJ, 112, 2398 Hamuy, M., Phillips, M. M., Suntze, N. B., Schommer, R. A., Maza, J., Smith, R. C., Lira, P., & Aviles, R. 1996d, AJ, 112, 2438 Hamuy, M., Phillips, M. M., Wells, L. A., & Maza, J. 1993b, PASP, 105, 787 Hamuy, M., & Pinto, P. 1998, in preparation Hansen, L., Jòrgensen, H. E., & Nòrgaard-Nielsen, H. U. 1987, Messenger, 47, 46 Hatano, K., Branch, D., & Deaton, J. 1998, ApJ, 502, 177 Hodge, P. W., & Kennicutt, R. C. 1982, AJ, 87, 264 Hoÿich, P., Wheeler, J. C., & Thielemann, F. K. 1998, ApJ, 495, 617 Holz, D. E., & Wald, R. M. 1998, Phys. Rev. D, in press Hoyle, F., & Fowler, W. A. 1960, ApJ, 132, 565 Huang, J. S., Cowie, L. L., Gardner, J. P., Hu, E. M., Songaila, A., & Wainscoat, R. J. 1997, ApJ, 476, 12 Kantowski, R., Vaughan, T., & Branch, D. 1995, ApJ, 447, 35 Kim, A., Goobar, A., & Perlmutter, S. 1996, PASP, 108, 190 Kim, A., et al. 1997, ApJ, 476, 63 Kirshner, R. P., et al. 1995, IAU Circ. 6267 Kochanek, C. S. 1996, ApJ, 466, 638 õõõ. 1997, ApJ, 491, 13 Kowal, C. T. 1968, AJ, 73, 1021 Landolt, A. U. 1992, AJ, 104, 340 Leibundgut, B. 1989, Ph.D. thesis, Basel Univ. Leibundgut, B., et al. 1993, AJ, 105, 301 Lin, H., et al. 1996, ApJ, 471, 617 Lira, P. 1995, Masterîs thesis, Univ. Chile Lupton, R. 1993, Statistics in Theory and Practice (Princeton : Princeton Univ. Press) Mateo, M., & Schechter, P. L. 1989, in Proc. First ESO/ST-ECF Workshop on Data Analysis, ed. P. J. Grosbòl, F. Murtaugh, & R. H. Warmels (Garching : ESO), 127 Madore, B. F., & Freedman, W. L. 1991, PASP, 103, 933 õõõ. 1998, ApJ, 492, 110 Marzke, R. O., Geller, M. J., da Costa, L. N., & Huchra, J. P. 1995, AJ, 110, 477 Menzies, J. W. 1989, MNRAS, 237, 21 Miller, D., & Branch, D. 1990, AJ, 100, 530 Nòrgaard-Nielsen, H., et al. 1989, Nature, 339, 523 Nugent, P., Kim, A., & Perlmutter, S. 1998a, in preparation õõõ. 1998b, in preparation õõõ. 1998c, IAU Circ. 6804 Nugent, P., Phillips, M., Baron, E., Branch, D., & Hauschildt, P. 1995, ApJ, 455, L147 Oke, J. B., & Sandage, A. 1968, ApJ, 154, 21 Oke, J. B., et al. 1995, PASP, 107, 375 Oswalt, T. D., Smith, J. A., Wood, M. A., & Hintzen, P. 1996, Nature, 382, 692 Perlmutter, S., et al. 1995, ApJ, 440, 41 õõõ. 1997, ApJ, 483, 565 õõõ. 1998, Nature, 391, 51 Phillips, M. M. 1993, ApJ, L105, 413 Phillips, M. M., et al. 1987, PASP, 99, 592 õõõ. 1998, in preparation Phillips, M. M., Wells, L., Suntze, N., Hamuy, M., Leibundgut, B., Kirshner, R. P., & Foltz, C. 1992, AJ, 103, 1632 Pierce, M. J. 1994, ApJ, 430, 53 Porter, A. C., & Filippenko, A. V. 1987, AJ, 93, 1372 Pskovskii, Y. 1984, Soviet Astron., 28, 658 Reid, I. N. 1997, AJ, 114, 161 Renzini, A., et al. 1996, ApJ, 465, L23 Reiss, D. J., Germany, L. M., Schmidt, B. P., & Stubbs, C. W. 1998a, AJ, 115, 26 Riess, A. G. 1996, Ph.D. thesis, Harvard Univ. Riess, A. G., et al. 1997, AJ, 114, 722 Riess, A. G., Nugent, P. E., Filippenko, A. V., Kirshner, R. P., & Perlmutter, S. 1998b, ApJ, 504, 935 Riess, A. G., et al. 1998c, in preparation Riess, A. G., Press, W. H., & Kirshner, R. P. 1995, ApJ, 438, L17 õõõ. 1996a, ApJ, 473, 88 õõõ. 1996b, ApJ, 473, 588 Rood, H. J. 1994, PASP, 106, 170 Ruiz-Lapuente, P., Cappellaro, E., Turatto, M., Gouies, C., Danziger, I. J., Della Valle, M., & Lucy, L. B. 1992, ApJ, 387, L33 Rybicki, G. B., & Press, W. H. 1992, ApJ, 398, 169 Saha, A., et al. 1994, ApJ, 425, 14 õõõ. 1997, ApJ, 486, 1 Sandage, A., & Tammann, G. A. 1993, ApJ, 415, 1 Sandage, A., et al. 1994, ApJ, 423, L13 Savage, B. D., & Mathis, J. S. 1979, ARA&A, 17, 73 Schechter, P. L., Mateo, M., & Saha, A. 1993, PASP, 105, 1342 Schmidt, B. P., et al. 1998, ApJ, in press


1038

RIESS ET AL.
von Hippel, T., Bothun, G. D., & Schommer, R. A. 1997, AJ, 114, 1154 Walterbos, R. 1986, Ph.D. thesis, Leiden Univ. Wambsganss, J., Cen, R., Xu, G., & Ostriker, J. 1997, ApJ, 475, L81 Wheeler, J. C., & Harkness, R. P. 1990, Rep. Prog. Phys., 53, 1467 Wheeler, J. C., Harkness, R. P., Barkat, Z., & Swartz, D. 1986, PASP, 98, 1018 Wheeler, J. C., & Levreault, R. 1985, ApJ, 294, L17 White, M., & Scott, D. 1996, ApJ, 459, 415 Zehavi, I., Riess, A. G., Kirshner, R. P., & Dekel, A. 1998, ApJ, 503, 483

Strauss, M. A., & Willick, J. A. 1995, Phys. Rep., 261, 271 Tammann, G. A., & Leibundgut, B. 1990, A&A, 236, 9 Tonry, J. L. 1991, ApJ, 373, L1 Tripp, R. 1997, A&A, 325, 871 õõõ. 1998, A&A, 331, 815 Turatto, M., Benetti, S., Cappellaro, E., Danziger, I. J., Della Valle, M., Gouies, C., Mazzali, P. A., & Patat, F. 1996, MNRAS, 283, 1 Turner, E. L. 1990, ApJ, 365, 43 Uomoto, A., & Kirshner, R. P. 1985, A&A, 149, L7 VandenBerg, D. A., Stetson, P. B., & Bolte, M. 1996, ARA&A, 34, 461