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THE ASTRONOMICAL JOURNAL, 118 : 2675 õ 2688, 1999 December
( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE RISE TIME OF NEARBY TYPE Ia SUPERNOVAE ADAM G. RIESS,1 ALEXEI V. FILIPPENKO,1 WEIDONG LI,1 RICHARD R. TREFFERS,1 BRIAN P. SCHMIDT,2 YULEI QIU,3 JINGYAO HU,3 MARK ARMSTRONG,4 CHUCK FARANDA,5 ERIC THOUVENOT,6 AND CHRISTIAN BUIL6
Received 1999 July 12 ; accepted 1999 August 24

ABSTRACT We present calibrated photometric measurements of the earliest detections of nearby Type Ia supernovae (SNe Ia). The set of D30 new, unïltered CCD observations delineate the early rise behavior of SNe Ia 18 to 10 days before maximum. Using simple empirical models, we demonstrate the strong correlation between the rise time (i.e., the time between explosion and maximum), the postrise light-curve shape, and the peak luminosity. Using a variety of light-curve shape methods, we ïnd the rise time to B maximum for an SN Ia with *m (B) \ 1.1 mag and peak M \[19.45 mag to be 19.5 ^ 0.2 days. We 15 V ïnd that the peak brightness of SNe Ia is correlated with their rise time ; SNe Ia that are 0.10 mag brighter at peak in the B band require 0.80 ^ 0.05 days longer to reach maximum light. We determine the eects of several possible sources of systematic errors, but none of these signiïcantly impacts the inferred rise time. We explore the degree to which comparisons between the observed and theoretically predicted rise times constrain SN Ia progenitor systems. Key words : cosmology : observations õ supernovae : general
1

. INTRODUCTION

A few weeks after explosion, the visual luminosity of a Type Ia supernova (SN Ia) increases a trillionfold, by which time its peak output can rival the glow of its host galaxy. Unfortunately, this dramatic rise to prominence is difficult to detect and therefore remains poorly documented (Vacca & Leibundgut 1996 ; Leibundgut et al. 1991a, 1991b). Enough of this rise occurs in the ïrst few hours after explosion that it is possible to detect low-redshift (z \ 0.02) SNe Ia that are less than 1 day old. Discovering SNe Ia in their youth requires great persistence and good fortune ; potential host galaxies must be monitored frequently to increase the odds of an early detection. Even when SNe Ia are detected early in their development, the observations are often recorded with a medium that does not easily lend itself to precise, quantitative analysis : naked-eye observations, photographic plate images, and unïltered CCD images. To facilitate comparisons with subsequent observations, early SN Ia observations need to be reliably calibrated on standard passband systems using linear detectors. To date, the earliest reliable and precisely quantiïable detection (i.e., employing a CCD and a standard passband) of a nearby SN Ia is D13 days before B-band maximum, but still D1 week after explosion (SN 1994D, Richmond et al. 1995). Detections of SNe Ia earlier than 10 days before B maximum have been reliably measured and reported for only four nearby SNe Ia (SN 1994ae, Riess et al. 1999b ; SN 1994D, Richmond et al. 1995 ; SN 1992bc, Hamuy et al. 1996a ; SN 1990N, Lira et al. 1998, Leibundgut et al. 1991a).
õõõõõõõõõõõõõõõ 1 Department of Astronomy, University of California, Berkeley, Berkeley, CA 94720-3411. 2 Mount Stromlo and Siding Spring Observatories, Australian National University, Private Bag, Weston Creek, ACT 2611, Australia. 3 Beijing Astronomical Observatory, Chinese Academy of Sciences, Beijing 100080, China. 4 UK Supernova Patrol, British Astronomical Association, Rolvenden, England, UK. 5 7860 NW 53 Court, Lauderhill, FL 33351. 6 Centre National dîEtudes Spatiale des Rayonnements, 18 Avenue Edouard Belin, Toulouse Cedex 4, F-31401, France.

This is unfortunate, as the SN Ia rise to glory during the time interval between explosion and maximum brightness (hereafter referred to as the "" rise time îî) holds signiïcant clues for understanding the progenitors and physics of SNe Ia (Leibundgut & Pinto 1992) and ultimately their utility for the determination of cosmological parameters. 1.1. A Constraint on SN Ia Progenitors Precise knowledge of the SN Ia rise time could provide valuable constraints on models of SN Ia progenitors. Although the ways the explosion characteristics inÿuence the SN Ia rise behavior are complex, requiring detailed simulations to understand, some general dependences can be understood. The rise behavior of an SN Ia is determined by the rate at which energy in the interior is released and subsequently diuses to the surface of the supernova. Although the energy deposition rate is always decreasing, homologous expansion of material continually increases the rate at which energy diuses to the surface during the rising phase. At this epoch, the photosphere grows in radius while receding through the expanding ejecta. The available energy source is the radioactive 56Ni (followed by radioactive 56Co), which is synthesized in the explosive burning of carbon and oxygen to nuclear statistical equilibrium (Hoyle & Fowler 1960 ; Arnett 1969 ; Colgate & McKee 1969 ; Arnett 1982 ; Hoÿich, Khokhlov, & Muller 1992 ; Leibundgut & Pinto 1992 ; Pinto & Eastman 2000). The initial progenitor mass plays an important role, providing both the source of fuel and the obstruction to energy diusion. The rate of diusion to the surface depends on the proximity of the radioactive material to the photosphere, the temperature, and the density of the homologously expanding envelope, factors that determine the opacity of the supernova. Detailed modeling of the explosion yields predictions of the dependence of the progenitor initial conditions and explosion mechanism on the SN Ia rise time (Hoÿich & Khokhlov 1996 ; Hoÿich, Wheeler, & Thielemann 1998). In general, single white dwarf progenitor systems seem to produce the shortest rise times. The rise time of double degenerate systems is extended by the additional barrier to 2675


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Vol. 118

diusion presented by the thick disk of the tidally disrupted companion. Among single degenerate systems with a mixture of deÿagration and detonation burning fronts, explosions with larger fractions of supersonic burning produce shorter rise times (Hoÿich & Khokhlov 1996). 1.2. A T heoretical Calibration of SN Ia L uminosity Knowledge of the SN Ia rise time also provides the means to calibrate the peak luminosity of SNe Ia independent of the Cepheid distance scale. One method is to use the rise time to indicate the instantaneous rate of energy deposition from the radioactive decay of 56Ni and 56Co. This method still relies on theoretical modeling to indicate the likely mass of decaying nickel and the relation at maximum between the energy deposited and that radiated (once known as Arnettîs law ; Arnett 1982 ; Arnett, Branch, & Wheeler 1985). An alternate route is to use the rise time to calibrate the luminosity of the expanding SN Ia photosphere at peak. This method also has theoretical input in the form of a spectral synthesis model. A comparison of the model and observed spectrum at peak luminosity yields the velocity of the photosphere and its model temperature. Together with the rise time, this information yields the size of the photosphere and hence the luminosity of the supernova at maximum. Although both methods are only semiempirical, each is essentially independent, relying on a dierent aspect of SN Ia theoretical modeling. To be consistent, the two methods require a rise time to bolometric peak of 14 to 22 days (Nugent et al. 1995). Because measurements of the rise time provide a new window into the physics of SNe Ia, a comparison of the rise time for high-redshift and low-redshift SNe Ia could be a valuable test of evolution. Such a comparison is performed by Riess et al. (1999a). Here we report calibrated measurements of the earliest detections of low-redshift SNe Ia and the rise time inferred from them. These observations, beginning fewer than 2 days after the explosion, provide new constraints on SN Ia evolution, progenitors, and luminosity. As discussed in ° 2, we have collected the earliest CCD images of SNe Ia. These images are usually unïltered, and we have transformed them to standard passbands. We analyze the SN Ia rise behavior in ° 3. In ° 4, we explore and analyze possible systematic errors and biases in our measurements. We discuss the implications for SN Ia physics and progenitors in ° 5.
2

. OBSERVATIONS

2.1. Sample Selection To measure the SN Ia rise behavior, we have collected the earliest available CCD images of SNe Ia. To compile our sample of observations of young SNe Ia the following selection criteria were used : 1. SNe Ia with well-sampled CCD light curves ; 2. SNe Ia whose hosts were observed with CCDs between 10 and 25 days before B maximum ; 3. Spectroscopically normal SNe Ia (Branch, Fisher, & Nugent 1993) ; 4. SNe Ia with redshift z ¹ 0.02. We limited our analysis to CCD observations because of their well-known advantages : they are highly linear detectors over a large dynamic range and their digital output allows us to accurately subtract contamination from underlying host-galaxy light. Criterion 1 was necessary to be able

to accurately determine the date of B maximum and therefore the age of all observations. Criterion 2 targets the observations of SNe Ia that will yield the most useful constraints on the rise behavior. The period earlier than 10 days before B maximum was chosen because this is the epoch where exceedingly few SNe Ia have been observed and where new data are needed (see ° 1). Criterion 3 was chosen so that the inferred rise behavior will be representative of prototypical SNe Ia. Peculiar SNe Ia have been shown to deviate substantially from linear relations derived from typical SNe Ia. This requirement can and should be relaxed in the future when a sizeable sample of very early observations of peculiar SNe Ia has been collected. Criterion 4, that the SNe Ia be nearby, is important so that observations at very early times can yield signiïcant constraints. For example, at z \ 0.02 an SN Ia at D15 days before B maximum will have an apparent brightness of D18.5 mag in B. This also results in a measured rise behavior that is representative of SNe Ia at low redshifts, a desirable characteristic for the comparison with the rise behavior of SNe Ia at high redshift (Goldhaber 1998 ; Groom 1998 ; Goldhaber et al. 1999 ; Nugent 1998). Very early detections of supernovae are most common in supernova searches that monitor potential host galaxies with high frequency. An additional requirement is that past observations are catalogued and stored so that images of host galaxies obtained before SN discoveries can be retrieved for later analysis. In most cases, SN light in very early images is not recognized until later, when the SN brightens. Two proliïc discoverers of supernovae are the Beijing Astronomical Observatory (BAO) Supernova Search, employing a 0.6 m telescope (Li et al. 1996), and the Lick Observatory Supernova Search (LOSS), with the 0.75 m Katzman Automatic Imaging Telescope (KAIT ; Treers et al. 1997 ; see also Richmond, Treers, & Filippenko 1993). The BAO search has been operating since 1996 April and to date has discovered 13 SNe Ia. LOSS has been underway since the end of 1997 and to date has discovered 14 SNe Ia. For all SNe Ia known to pass criteria 1, 3, and 4, we queried the BAO and LOSS databases and obtained all host-galaxy images expected to be between 10 and 25 days before the observed B maxima. These observations are listed in Table 1 and include SNe 1996bo, 1996bv, 1996by, 1997bq, 1998bu, 1998dh, and 1998ef. We also combed the IAU Circulars and an amateur supernova ïndersî network, VSNET,7 for reports of very early observations of SNe Ia that also passed criteria 1, 3, and 4. This search yielded two valuable additions : SN 1998aq and SN 1990N. In addition, a prediscovery detection of SN 1998bu in NGC 3368 (M96) was reported on VSNET by amateur astronomer C. Faranda, using an unïltered CCD and 0.25 m telescope, from his backyard in Lauderhill, Florida. This nearby SN Ia was discovered approximately 9 days before B maximum, but the image by Faranda was obtained 16 to 17 days before B maximum (Meikle & Hernandez 1999). NGC 3368 was also observed by LOSS 4 days earlier (i.e., 20 to 21 days before B maximum), though SN 1998bu was not detected. SN 1998aq was discovered by M. Armstrong (Armstrong et al. 1998), with a 0.26 m reÿector and an unïltered CCD in the
õõõõõõõõõõõõõõõ 7 Accessible at http ://www.kusastro.kyoto-u.ac.jp/vsnet/SNe/SNe.html.


No. 6, 1999

THE RISE TIME OF NEARBY TYPE Ia SUPERNOVAE
TABLE 1 SN Ia EARLY DETECTIONS JULIAN DATE (2,440,000 ])a SN Ia 1990Na ...... 1994D ...... 1996bo ...... 1996bv ...... 1996by ...... 1997bq ...... 1998aq ...... 1998bu ...... 1998dh ...... 1998ef ....... z 0.003 0.001 0.017 0.017 0.014 0.009 0.004 0.003 0.009 0.018 Discovery 8,065 9,419 10,379b 10,400c 10,432 10,546 10,916 10,943 11,018 11,104 max 8,082 9,432 10,386 10,404 10,441 10,556 10,931 10,952 11,028 11,114 B Observed 8,065õ8,072 9,420, 9,421 10,375 10,390 10,432, 10,429 10,541 10,910, 10,916 10,932, 10,936 11,010, 11,014, 11,018 11,096, 111,00, 11,104 FILTER Unïltered B, V V Unïltered Unïltered Unïltered Unïltered Unïltered Unïltered Unïltered SOURCE E. Thouvenot Richmond et al. 1995 BAO BAO BAO BAO M. Armstrong LOSS, C. Faranda LOSS LOSS

2677

a Also on JD 2,448,071 and 2,448,072 with B,V by Lira et al. 1998. b Date of independent discovery by Armstrong et al. 1998. c Date of discovery (W. D. Li 1998, private communication).

course of the UK Supernova Patrol, approximately 15 days before B maximum, and the host galaxy was also imaged D21 days before B maximum. SN 1990N was discovered by E. Thouvenot (Maury et al. 1990), using a 0.6 m telescope and an unïltered CCD, about 17 days before B maximum and was subsequently observed with the same equipment for the next 7 days. In all cases, the observers furnished us with their unïltered CCD images (see Table 1). We have included SN 1994D, using the observations by Richmond et al. (1995) in B and V commencing D13 days before B maximum. Although SN 1994ae was observed in R about 13 days before B maximum by the Leuschner Observatory Supernova Search (the predecessor to the Lick search ; Van Dyk et al. 1994), Ho et al. (1999) have found that the Leuschner R passband is a poor match to JohnsonCousins R, and its transmission function has not been adequately quantiïed. Hence we have not included SN 1994ae in the present analysis. In ° 4, we address possible biases on the rise-time measurements attributable to our sample selection. A remarkably early detection of SN 1989B was reported by Marvin & Perlmutter (1989) on behalf of the Berkeley Automated Supernova Search 17 to 18 days before B maximum at approximately mag 17. Unfortunately, the high surface brightness of the knotty spiral arm (R \ 15.6 in a 7A aperture at the position of the SN ; Wells et al. 1994) .4 makes it extremely difficult to evaluate the brightness of a D17 mag stellar object without the aid of sophisticated galaxy subtraction procedures. Our inability to obtain this CCD image forces us to regard this early detection as merely anecdotal. We note that several very early photographic SN Ia detections have also been reported. One detection in this category was presented by Barbon et al. (1982) for SN 1979B in NGC 3913. A prediscovery photographic plate revealed the supernova at 4.5 to 5.5 mag below peak about 14 to 18 days before maximum. The precision of this measurement is limited by the poor sampling of the light curve and the difficulty in evaluating the accuracy of the photographic magnitudes. In the course of monitoring SN 1980N in NGC 1316, Hamuy et al. (1991) obtained prediscovery photographic images of SN 1981D at 15 to 16 days before maximum. Although they report the SN to have been 5 to 6 mag below peak at this epoch, their inability to

reliably subtract the galaxy background (D3 mag brighter than the SN) makes this measurement difficult to interpret. These data (and others like it) fail our selection criteria and have not been included in our analysis. 2.2. Photometric Calibrations Several amateur and professional supernova searches use unïltered CCDs to increase their efficiency : an unïltered CCD image can reach fainter magnitudes in less time than a ïltered CCD. Of the D30 observations made approximately 10 or more days before B maximum, over 80% of the unique temporal samplings of the early rise are recorded with unïltered CCDs. The images that employed standard ïlters were obtained at the oldest ages of our sample (10 to 13 days before B maximum) and yield the weakest constraints on the rise behavior. If we wish to quantify the behavior of SNe Ia at the earliest observed times we need to make use of the available unïltered CCD observations of young SNe Ia. By either empirically characterizing a CCDîs sensitivity or with explicit knowledge of its response function, it is possible to accurately transform an unïltered SN Ia magnitude to a standard passband for comparison with subsequent ïltered observations. The same method has been used by Schmidt et al. (1998) to transform supernova magnitudes observed with nonstandard ïlters to a standard system. Here we will review the steps in the transformation. In what follows, we will consider the standard passband to be Johnson V , but this transformation process is general and valid for other passbands. We ïrst measured the dierences in the unïltered magnitudes between the SNe and individual local standard (LS) stars in the SN ïelds. In cases with signiïcant host-galaxy light at the position of the SN, we initially subtracted template images of the host galaxy and then ïtted point-spread functions to the SN and LS stars (Schmidt et al. 1998). Referring to an individual, unïltered CCD system as a nonstandard passband system called "" W îî (for white light), the result is the measured quantity *W \ W [W , (1) SN LS or the magnitude dierence between the SN and any LS star in the W passband.


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BAO C. Faranda E. Thouvenot M. Armstrong KAIT

On photometric nights at each of the telescopes, Landolt (1992) standard ïelds were observed to derive transformations between instrumental and expected magnitudes. These transformations were used to calibrate Johnson B and V passband magnitudes and colors of the LS stars. Now we seek a transformation of the LS stars from the standard passband, in this case V , to the nonstandard, W . This transformation is simply the pseudocolor V [W for any LS star. If we know the spectral energy distribution (SED) of a LS star, this pseudocolor is / S (j)F (j)dj / S (j)dj V j W / S (j)F (j)dj / S (j)dj) W j V ] ZP [ ZP , (2) V W where F (j) is the spectrum of a LS star in units of power per unit jarea per unit wavelength, ZP and ZP are the V W zero points of the V and W ïlter systems,8 and S (j) and V S (j) are the dimensionless sensitivity functions of the V W W systems. We refer to V [W , as deïned by equation and (2), as a "" pseudocolor îî because the sensitivity functions of the V and W bands generally have much more overlap than do the passbands in most standard systems. For each observatoryîs S (j), we used the manufacturerîs speciïed CCD response W function (or equivalently the quantum efficiency divided by the wavelength) and multiplied by the atmospheric transmission (Stone & Baldwin 1983). In addition, we have taken care to include the eects of materials in the light paths of the telescopes. The most important changes in the true response function are in the near ultraviolet (i.e., 3000 to 4000 A); at these wavelengths, layers of glass in the camera lens or covering the CCD window can aect the throughput of the telescope. In addition, aluminum and other mirror coatings can aect the ultimate transmission. Among the observatories in Table 1, these eects are only signiïcant for KAIT (LOSS), which boasts a strong UV CCD response. Figure 1 displays the eective CCD response functions for the observatories listed in Table 1. In Table 2, response characteristics for these CCDs are listed. Column (3) contains the wavelengths of peak efficiency (j ), column (4) gives the wavelength 0 range within which the CCDs efficiency is more than 10% of the peak (j ), and column (5) lists the full width at half 10 maximum sensitivity (*j). For each unïltered system in Table 2, we have numerically integrated equation (2) using a set of 175 spectrophotometric standard stars from Gunn & Stryker (1983). In V [W \[2.5 log
õõõõõõõõõõõõõõõ 8 Zero points are commonly deïned to yield V (Vega) \ W (Vega) \ 0.03, though this criterion is arbitrary here, since, as will be seen, the transformations are independent of the choice of passband zero points.

1.0 0.8 0.6 0.4

Relative Response

C

D

0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 4000 6000 8000 Wavelength (angstroms) 10000
SN

B

V

R

1990N (age=-14 days)

FIG. 1.õWavelength response functions. For each observer or observatory listed in Table 1, we show the CCD manufacturerîs stated response function multiplied by the atmospheric transmission, including eects of glass and mirror transmission. Overplotted for comparison are the Johnson-Cousins B and V response functions. Also shown is the spectrum of SN 1990N at 14 days before B-band maximum light. By accounting for the dierences between the SN Ia SED observed by a standard passband and an unïltered CCD, it is possible to transform an unïltered CCD observation of an SN Ia to a standard passband.

Figure 2, we show the synthetic values of V [W for these stars versus the standard colors B[V , where the W system illustrated is from BAO. The stellar SEDs result in a simple linear relation between the standard color B[V and the pseudocolors. These theoretically derived relations demonstrate that such transformations are highly linear and have a dispersion of less than 0.05 mag for stars with a color of [0.2 \ B[V \ 1.5. By measuring a starîs B[V color, we can use these relations to determine its pseudocolor and, equivalently, its transformation to the W system.

TABLE 2 STELLAR UNFILTERED TRANSFORMATIONS j 0 (A) (3) 6800 5000 7500 5500 5500 j 10 (A) (4) 3500õ10000 3000õ10000 4000õ10000 3700õ9000 4000õ10000 *j (A) (5) 4000 5500 3500 3500 3700

Observer (1) BAO ................ KAIT (LOSS) ...... E. Thouvenot ...... M. Armstrong ...... C. Faranda .........

CCD (2) Texas Instruments TC211 SITe UV2AR Thomson TH7863 Sony ICX027BL SBIG ST6

C

VW (6)

(p)

C (p) BW (7) 1.40 1.33 1.40 1.31 1.51 (0.07) (0.10) (0.11) (0.07) (0.09)

0.40 0.33 0.40 0.31 0.51

(0.07) (0.10) (0.11) (0.07) (0.09)


No. 6, 1999
1.0 0.8 V-unfiltered 0.6 0.4 0.2 0.0 -0.2 0.0 0.5

THE RISE TIME OF NEARBY TYPE Ia SUPERNOVAE
Synthetic Local Standards

2679

1.0 B-V

1.5

FIG. 2.õFor a set of 175 spectrophotometric stars given by Gunn & Stryker (1983), we have calculated synthetic unïltered CCD magnitudes for the BAO response function of Fig. 1. A comparison of the synthetic B[V colors and the dierence between the V and unïltered magnitudes (open circles) shows a well-deïned correlation. A similar relation is seen ( ïlled circles) by comparing the observed photometry of local standard stars in the ïelds of SNe. The slope of this correlation deïnes a transformation between unïltered and standard passband magnitudes as a function of B[V color.

We can now approximate equation (2) with a simpler expression valid for stars : V [W \ C (B[V ) , (3) VW where C is the slope of the linear relation between the standardVW color and the pseudocolor and we impose the condition that V [W \ 0 when B[V \ 0. While in principle we can derive the values of C from the theoretical VW sensitivity functions of the W passbands and spectrophotometry of stars, the most reliable way to solve for these values is to empirically measure them from the observed magnitudes of LS stars. This method has the advantage that it reduces our reliance on accurately assessing the sensitivity functions of the W systems. For all the LS stars in the ïelds of the SNe, we empirically ïtted the values of C with equation (3) using the VW instrumental W system magnitudes of the LS stars. In some cases we were able to obtain the W system magnitudes of Landolt (1992) ïelds. These C are given in Table 2 (col. VW [6]), as are transformation coefficients to B, C (col. [7]). BW Some empirical insight into the response functions of the unïltered CCD systems can be gained by comparing the values of the coefficients, C , with the correlation coeffiVW cients between two standard colors. The relations between the standard color B[V and other standard colors calculated from the Gunn & Stryker (1983) spectrophotometric standards are V [I \ 0.94(B[V ) , V [R \ 0.51(B[V ) , V [V 4 0.0(B[V ) , V [B 4 [1.0(B[V ) , (4) (5) (6) (7)

where the ïrst two relations hold for stars with B[V \ 1.3 mag. As seen in Table 2, the values of C range from 0.3 to VW 0.5. Comparing equation (3) with equations (4)õ(7), we note that the unïltered CCD response functions have peak effi-

ciency between V and R, although the wavelength regions between B and I are also sampled, as seen in Figure 1 and Table 2. As shown in Figure 2, the theoretical and empirical determinations of C are in good agreement. This was VW true for all W systems in Table 2. By use of equation (3) (the empirical version of eq. [2]), we have transformed the magnitudes of the LS stars in V (i.e., the standard system) to the W system. Adding these transformed magnitudes to equation (1) yields the magnitude of an SN on the W system. Unfortunately, early SN magnitudes in these nonstandard systems cannot readily be compared with subsequent observations through standard passbands. Therefore, we seek a transformation of the SN magnitude from the W system to a standard passband system. (An alternative is to transform subsequent SN magnitudes calibrated on standard systems to the W system, but the results would be difficult to evaluate.) The transformation we need is the inverse (i.e., the negative) of equation (2), except F (j) is now the SED of an j infant SN Ia. This pseudocolor is equivalent to a cross-ïlter K-correction between the W and V systems, as expressed by Kim, Goobar, & Perlmutter (1996), except no redshifting of the spectrum is involved (i.e., z \ 0). The appropriate SN Ia spectrum for this calculation is one at a similar age and color as the SN Ia to be transformed. We employed the earliest spectrum of SN 1990N shown in Figure 1 (Leibundgut et al. 1991a) and the earliest spectrum of SN 1994D (Filippenko 1997), both obtained D14 days before B maximum. These spectra should provide an accurate model of the SED, because their age coincides with the median age of our sample of SNe when they were observed. Because a few of the unïltered CCD response functions have some minor sensitivity redward of 8200 A and blueward of 3600 A, spectra of SN 1994U (Riess et al. 1998b) and SN 1990N (Leibundgut et al. 1991a) at 8 days before maximum were used to augment our description of the early SN Ia SED. This augmentation was included for completeness but has very little eect on the evaluation of equation (2). Nugent et al. (2000) have found that, to within 0.01 mag, the eects of both extinction and intrinsic color variation on the SN Ia SED can be reproduced by application of a Galactic reddening law (Cardelli, Clayton, & Mathis 1989). The augmented spectra of SN 1990N and SN 1994D were reddened and dereddened using a Galactic reddening law to match the earliest B[V color measurement of each SN Ia listed in Table 3 (col. [2]). In all cases, the earliest color measurement occurred 8 to 12 days before maximum light. Analysis of the early colors of SNe 1990N (Leibundgut et al. 1991a), 1994ae (Riess et al. 1999b), 1994D (Richmond et al. 1995), 1992bc (Hamuy et al. 1996a), 1997br (Li et al. 1999), 1995bd (Riess et al. 1999b), and 1998aq demonstrates that SNe Ia evolve, on average, by less than 0.05 mag in B[V between 10 to 14 days before B maximum. We conservatively adopt a statistical uncertainty of 1 p \ 0.10 mag for the individual B[V color of a young SN Ia. If the SED of an SN Ia undergoes a dramatic (and unexpected) change between 16õ18 days and 14 days before B maximum, a larger error could occur. However, in ° 4.2 we demonstrate that this potential systematic error does not aect our analysis. The uncertainties resulting from intrinsic variation in the early SN Ia SEDs are calculated from the dispersion of a set of 12 SN Ia spectra in the range of 8 to 14 days before B maximum.


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TABLE 3 SN Ia TRANSFORMATIONS THEORETICAL SN Ia (1) SN SN SN SN SN SN SN SN 1996by ...... 1996bv ...... 1997bq ...... 1998dh ...... 1998ef ....... 1998bu ...... 1998aq ...... 1990N ...... EARLY B[V (p) (2) 0.46 0.20 0.04 0.18 0.10 0.28 [0.18 0.05 (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) W [V (p) (3) [0.13 [0.02 0.00 0.07 0.06 [0.02 0.02 0.05 (0.11) (0.09) (0.08) (0.07) (0.07) (0.09) (0.05) (0.10) W [B (p) (4) [0.58 [0.21 0.04 [0.11 [0.04 [0.21 0.20 0.00 (0.11) (0.10) (0.11) (0.10) (0.12) (0.11) (0.11) (0.11) EMPIRICAL W [V (p) (5) [0.18 [0.08 [0.02 [0.06 [0.03 [0.14 0.06 [0.03 (0.04) (0.04) (0.02) (0.04) (0.03) (0.04) (0.03) (0.04) W [B (p) (6) [0.64 [0.28 [0.06 [0.25 [0.13 [0.42 0.24 [0.08 (0.11) (0.10) (0.10) (0.11) (0.11) (0.11) (0.11) (0.10)

Vol. 118

Because of the breadth of the unïltered response functions, we can reasonably transform the data to either the B, V , or R passband systems. The better the match between the ïltered and unïltered response functions, the less we must rely on the accuracy of the transformation. If there is little overlap between the ïltered and unïltered response functions, the pseudocolor becomes similar to a "" conventional îî color. As seen in Figure 1, the V and R passbands are the closest match to most of the unïltered response functions. Yet there is a strong historical precedent for measuring rise times relative to B maximum. In addition, for comparison with the rise time measured at high redshift, transforming to the B passband is desirable
Filtered

13.5
SN 1990N

Unfiltered

14.0 V mag 14.5 15.0

SN 1997bq

(Goldhaber et al. 1999 ; Goldhaber 1998 ; Groom 1998 ; Nugent 1998 ; Riess et al. 1999b). For these reasons, we have chosen to transform the data to both B and V . The greater uncertainty in the B transformation is included in the individual photometric uncertainties. The values and uncertainties in the theoretical pseudocolors W [V and W [B are listed in Table 3 (cols. [3] and [4], respectively). Combining these with equation (1) yields the SNe magnitudes on the standard system. We note that the B and V rise-time measurements will not be independent. An alternate method to transform the unïltered SN Ia magnitudes to a standard system is to employ the same empirical transformation previously used for stellar SEDs, equation (3), which only depends on the B[V color of the SED. It is well known that the SED of an SN Ia is extremely nonstellar over the vast majority of its observed lifetime (see Filippenko 1997 for a review). However, at very early times the SED of an SN Ia can be photometrically approximated by a thermal continuum (see Fig. 1), making the use of a transformation derived for stars plausible. (It is likely that this thermal continuum is even more dominant when the SNe Ia are younger than the earliest spectral observati