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arXiv:astro­ph/0406546
v1
24
Jun
2004
Draft version July 29, 2004
Preprint typeset using L A T E X style emulateapj v. 11/12/01
THE HUBBLE HIGHER-z SUPERNOVA SEARCH:
SUPERNOVAE TO z  1:6 AND CONSTRAINTS ON TYPE Ia PROGENITOR MODELS a
a BASED ON OBSERVATIONS WITH THE NASA/ESA HUBBLE SPACE TELESCOPE,
OBTAINED AT THE SPACE TELESCOPE SCIENCE INSTITUTE, WHICH IS OPERATED BY
AURA, INC., UNDER NASA CONTRACT NAS 5-26555
Louis-Gregory Strolger 2 , Adam G. Riess 2 , Tomas Dahlen 2 , Mario Livio 2 ,
Nino Panagia 2;3 , Peter Challis 4 , John L. Tonry 5 , Alexei V. Filippenko 6 ,
Ryan Chornock 6 , Henry Ferguson 2 , Anton Koekemoer 2 , Bahram Mobasher 2;3 ,
Mark Dickinson 2 , Mauro Giavalisco 2 , Stefano Casertano 2 , Richard Hook 7 ,
Stephane Blondin 8 , Bruno Leibundgut 8 , Mario Nonino 9 , Piero Rosati 8 , Hyron Spinrad 6 ,
Charles C. Steidel 10 , Daniel Stern 11 , Peter M. Garnavich 12 , Thomas Matheson 4 ,
Norman Grogin 13 , Ann Hornschemeier 13 , Claudia Kretchmer 13 , Victoria G. Laidler 14 ,
Kyoungsoo Lee 13 , Ray Lucas 2 , Duilia de Mello 13 , Leonidas A. Moustakas 2 ,
Swara Ravindranath 2 , Marin Richardson 2 , and Edward Taylor 15
2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (email: strolger@stsci.edu).
3 Aôliated with the Space Telescope Division of the European Space Agency, ESTEC, Noordwijk, the
Netherlands.
4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138.
5 University of Hawaii, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822.
6 Department of Astronomy, University of California, 601 Campbell Hall, Berkeley, CA 94720-3411.
7 Space Telescope - European Coordinating Facility, European Southern Observatory, Karl Schwarzschild
Str.-2, D-85748, Garching, Germany.
8 European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany.
9 INAF, Astronomical Observatory of Trieste, Via Tiepolo 11 34131 Trieste, Italy
10 Department of Astronomy, California Institute of Technology, MS 105-24, Pasadena, CA 91125.
11 Jet Propulsion Laboratory, MS 169-506, California Institute of Technology, Pasadena, CA 91109.
12 University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556
13 Johns Hopkins University, Dept. of Physics and Astronomy, 3400 N. Charles Street, Baltimore, MD 21218.
14 Computer Sciences Corporation at Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218.
15 University of Melbourne, School of Physics, Victoria 3010, Australia.
Draft version July 29, 2004
ABSTRACT
We present results from the Hubble Higher-z Supernova Search, the rst space-based open eld survey
for supernovae (SNe). In cooperation with the Great Observatories Origins Deep Survey, we have used
the Hubble Space Telescope with the Advanced Camera for Surveys to cover  300 square arcmin in the
area of the Chandra Deep Field South and the Hubble Deep Field North on ve separate search epochs
(separated by  45 day intervals) to a limiting magnitude of F850LP  26. These deep observations
have allowed us to discover 42 SNe in the redshift range 0:2 < z < 1:6. As these data span a large
range in redshift, they are ideal for testing the validity of Type Ia supernova progenitor models with the
distribution of expected \delay times," from progenitor star formation to SN Ia explosion, and the SN
rates these models predict. Through a Bayesian maximum likelihood test, we determine which delay-
time models best reproduce the redshift distribution of SNe Ia discovered in this survey. We nd that
models that require a large fraction of \prompt" (less than 2 Gyr) SNe Ia poorly reproduce the observed
redshift distribution and are rejected at > 95% condence. We nd that Gaussian models best t the
observed data for mean delay times in the range of 3 to 4 Gyr.
Subject headings: Surveys|supernovae: general
1. introduction
Type Ia supernovae (SNe Ia) have proven that they are
unequivocally suited as precise distance indicators, ideal
for probing the vast distances necessary to measure the ex-
pansion history of the Universe. The results of the High-z
Supernova Search Team (Riess et al. 1998) and the Su-
pernova Cosmology Project (Perlmutter et al. 1999) have
astonishingly shown that the Universe is not decelerating
(and therefore not matter dominated), but is apparently
accelerating, driven apart by a dominant negative pres-
sure, or \dark energy." Complementary results from the
cosmic microwave background by WMAP (Bennett et al.
2003) and large-scale structure from 2dF (Peacock et al.
2001; Percival et al. 2001; Efstathiou et al. 2002) congru-
ously show evidence for a low matter
density(
M = 0:3)
and a non-zero cosmological
constant(
 = 0:7), but nei-
ther directly require the presence of dark energy.
However, it is possible that there are astrophysical ef-
fects which allow SNe Ia to appear systematically fainter
1

2 L. -G. Strolger et al.
with distance and therefore mimic the most convincing ev-
idence for the existence of dark energy. A pervasive screen
of \gray dust" scattered within the intergalactic medium
could make SNe Ia seem dim, but show little corresponding
reddening (Aguirre 1999). Alternatively, the progenitor
systems of SNe Ia could be changing with time, resulting
in evolving populations of events, and possibly necessitat-
ing modications to the empirical correlations which are
currently used to make SNe Ia precise standard candles.
To date, the investigations of either eect have only pro-
vided contrary evidence, disfavoring popular intergalactic
dust models (Riess et al. 2000), and statistically showing
strong similarity in SN Ia characteristics at all age epochs,
locally and at hzi  0:5 (Riess et al. 1998; Perlmutter et al.
1999; Riess et al. 2000; Aldering, Knop, & Nugent 2000;
Sullivan et al. 2003), but neither has been conclusively
ruled out.
A simple test of the high-redshift survey results would be
to search for SNe Ia at even higher redshifts, beyond z  1.
In the range 1 < z < 2, we should observe SNe Ia explod-
ing in an epoch of cosmic deceleration, thus becoming rela-
tively brighter than at lower redshifts. This is expected to
be unmistakably distinguishable from simple astrophysical
challenges to the SN Ia conclusion. Indeed, results from 19
SNe Ia observed in the range 0:7 < z < 1:2 from the latest
High-z Supernova survey (Tonry et al. 2003) and in the IfA
survey (Barris et al. 2004) show indications of past decel-
eration, but these SNe represent the highest-redshift bin
attainable from the ground, in which condent identica-
tion and light-curve parameters are pushed to their limits.
To thoroughly and reliably survey SNe Ia at 1 < z < 2,
and to perform the follow-up observations necessary for
such a study, requires observing deeper than can be fea-
sibly done with the ground-based telescopes. However,
with the Hubble Space Telescope (HST) and the Advanced
Camera for Surveys (ACS), a higher-z SN survey is prac-
tical. Through careful planning, the Great Observatories
Origins Deep Survey (GOODS) has been designed to ac-
commodate a deep survey for SNe with a specic emphasis
on the discovery and follow-up of z & 1 SNe Ia.
We discovered 42 SNe over the 8-month duration of the
survey. We also measured redshifts, both spectroscopic
and photometric, for all but one of the SN host galaxies.
For the rst time, we have a signicant sample of SNe Ia
spanning a large range in redshift, from a complete survey
with well understood systematics and limitations. Cer-
tainly this has allowed for precise measurement of the SN
rates and the rate evolution with redshift (See Dahlen et al.
2004), but it also allows for a comparison of the observed
SN Ia rate history to the star-formation rate history, and
thus an analysis of SN Ia assembly time, or \delay time,"
relative to a single burst of star formation. By explor-
ing the range and distribution of the time from progenitor
formation to SN Ia explosion that is required by the data,
we can provide clues to the nature of the mechanism (or
mechanisms) which produce SNe Ia.
We describe the Hubble Higher-z Supernova Search
(HHZSS) project in x 2, along with image processing and
reduction, transient detection, and SN identication meth-
ods. In x 3 we show the results of the survey, including
discovery information on all SNe, and multi-epoch, multi-
band photometry of SNe over the search epochs of the
survey. In x 4 we report on observational constraints on
the inherent SN frequency distribution, or the distribu-
tion \delay times" for SN Ia progenitors, and discuss the
implied constraints on the model SN Ia progenitor sys-
tems. Elsewhere, we report on the rates of SNe Ia and
core-collapse SNe, the comparison of these measured rates
to those made by other surveys, and to the predicted SN
formation-rate history partly predicted from the analysis
in this paper (Dahlen et al. 2004). In another paper we
report on the constraints of cosmological parameters and
the nature of high-z SNe Ia (Riess et al. 2004b).
2. goods and the \piggyback" transient survey
GOODS was designed to combine extremely deep multi-
wavelength observations to trace the galaxy formation his-
tory and the nature and distribution of light from star for-
mation and active nuclei (Giavalisco et al. 2004a). Using
HST/ACS, it has probed the rest-frame ultraviolet (UV)
to optical portion of high-redshift galaxies through obser-
vations in the F435W , F606W , F775W , and F850LP
bandpasses, with a goal of achieving extended source sen-
sitivities only 0.5{0.8 mag shallower than the original Hub-
ble Deep Field observations (Williams et al. 1996). Images
were obtained in 15 overlapping \tiled" pointings, cover-
ing a total eective area of  150 square arcmin per eld.
Two elds with high ecliptic latitude were observed, the
Chandra Deep Field South (CDFS) and the Hubble Deep
Field North (HDFN), to provide complementary data from
missions in other wavelengths (Chandra X-ray Observa-
tory, XMM-Newton, Spitzer Space Telescope) and to al-
low ground-based observations from both hemispheres (see
Figures 1 and 2).
The GOODS observations in the F850LP band were
scheduled over 5 epochs separated by  45 days to accom-
modate a \piggybacking" transient survey. This baseline
is ideal for selecting SNe Ia near peak at z  1, and SNe Ia
on the rise at z > 1:3, as the risetime (from explosion to
maximum brightness) for SNe Ia is  20 days in the rest
frame (Riess et al. 1999). The baseline also insures that
no SN in the desired redshift range will have suôcient
time to rise within our detection threshold, and then fall
beyond detection before the eld is revisited, maximizing
the overall yield.
Intentionally, the GOODS lter selections were nearly
ideal for the detection, identication, and analysis of high-
redshift SNe Ia. For a SN Ia at z  1, the F850LP band
covers nearly the same part of the SED as the rest-frame B
band. The K-correction, or the correction of the observed
ux to some rest-frame bandpass (e.g., F850LP to B), is
thus relatively small.
Monte Carlo simulations of the survey, assuming de-
tection limits based on the  2100 s exposure times per
epoch (using the ACS Exposure Time Calculator) and the
desired baseline between epochs, implied that the distribu-
tion of SNe Ia would be centered at z  1, with  1=3 to
1=2 of the events occurring in the 1 < z < 2 range. Scal-
ing from other lower-z SN survey yields, it was expected
that a total of 30{50 SNe of all types would be discovered,
and that  1=2 of them would be SNe Ia. These numbers
implied that we could expect to nd  6 to 8 SNe Ia in
the range of 1:2 . z . 1:8, which could be suôcient for
an initial investigation of cosmology in the deceleration

The Hubble Higher-z Supernova Search Project 3
epoch.
2.1. Image Processing and Search Method
The success of this survey has been due, in large part,
to the rapid processing and delivery of data, and the rapid
post-processing by a reliable pipeline. The exposures con-
stituting a single tile in a single passband arrived from
HST within 6 to 18 hours after observation (with an aver-
age of  10 hours), and fully processed (dierenced with
previous epochs) within a few hours after arrival. In gen-
eral, the complete multi-wavelength data for a single tile
were fully searched for candidate SNe within a day after
observation.
The individual exposures of a tile in a given epoch were
reduced (bias-subtracted and at-eld corrected) through
the calacs standard ACS calibration pipeline. The well-
dithered subexposures (or CR splits; see below) were then
corrected for geometric distortions and combined using
the multidrizzle pipeline (Koekemoer et al. 2002). For
the survey, we maintained the physical pixel size of 0:05 00
pixel 1 for the discovery of transients.
A key feature of this pipeline is its identication and
removal of cosmic rays (CRs) and hot pixels. Each 2100 s
exposure in F850LP consisted of 4 individual 520 s CR
splits, each dithered by small osets. In each of the CR
splits, the CR contamination, at the time of the survey,
was as high as  1% of all pixels, and hot pixels accounted
for an additional  1% (Riess 2002). With such a high in-
cidence of CRs and hot pixels, averaging (or taking the
median) over the few CR splits would not adequately re-
move these potential confusion sources. Instead, we used
the minmed algorithm described in Mack et al. (2003). Ba-
sically, of the pixels in each CR split covering the same area
of sky, the highest-value pixel was rejected. The median
of the remaining three pixels was then compared to the
minimum-value pixel. If the minimum pixel was within
6 of the median, then the median value was kept, oth-
erwise the minimum value was used. A second pass was
performed, repeating the minmed rejection on pixels neigh-
boring those which had been previously replaced with min-
imum values (indicating CR or hotpixel impact), but at
a lower threshold to remove \halos" around bright CRs.
The result was that each pixel of the output combined im-
age was either the median or the minimum of the input
values. Admittedly, the combined result was less sensi-
tive than can be obtained in a straight median, but the
multidrizzle algorithm (with minmed) did successfully
reject > 99% of CRs and hot pixels after combination.
The search was conducted in 8 campaigns (4 campaigns
for each of the HDFN and the CDFS surveys) by dier-
encing images from contiguous epochs. For a given tile
in a eld, images covering the same area from the previ-
ous epoch were aligned (registered) using the sources in
the tiles. Catalogs of the pixel centroids and instrumen-
tal magnitudes of sources on each image were made using
SExtractor (Bertin & Arnouts 1996) and fed into a trian-
gle matching routine (starmatch, courtesy of B. Schmidt)
which determined the linear registration transformation
from one epoch to the next. The typical precision of the
registrations was 0.2{0.3 pixels root-mean square (RMS),
and the point-spread function (PSF) in each epoch of ob-
servation remained nominally at 0.10{0:13 00 FWHM. The
combination of precise registration and nearly constant
PSF allowed for images to be subtracted directly, with-
out the need for image convolution.
Several examples of the image subtraction quality are
shown in Figures 3, 4, and 5. In ideal situations, only
transient sources remain in the residual image on a nearly
zero-level background. However, in practice there were
many situations which produced non-transient residuals.
Although extensive care was taken to remove many CRs
and hot pixels in the image processing, these artifacts did
occasionally slip past the rejection algorithms, specically
when multiple eects were coincident on the same area of
sky. For example, for a given pixel in each of the four CR
splits covering the same area of sky, the probability that
the pixels were impacted by a CR in 3 of the 4 exposures
is approximately 1 in 10 6 . Roughly 20 pixels in the com-
bined 20 million pixel array would show CR residuals after
passing through the multidrizzle algorithm. In addition,
\breathing" in the optical path, focus drift, and the slight
change in the pixel scale across the image plane have all
led to small yet detectable variations in the PSF. Some-
times bright compact objects were over-subtracted in the
wings of their radial proles and under-subtracted in the
inner 1{2 pixels. Other instrumental sources of confusion
include diraction spikes, correlated noise from multiple
image resampling, and slight registration errors due to the
lack of sources over a large registration area.
The non-trivial abundance of false positives required rig-
orous residual inspection methods. We therefore searched
the subtracted images redundantly to minimize false detec-
tion biases and to maximize recovery of elusive, faint tran-
sients. An automated routine was performed to identify
PSF-like residuals which were well separated ( 2 pixels)
from known saturated pixels, and above  4 5 of the sky
background. The inherent nature of this routine prohibits
the detection of nonstellar residuals, faint residuals, resid-
uals near bright stars or nuclei (which may be saturated),
or residuals in areas where the RMS of the background
could not be easily determined by the automated routine.
Therefore, so that no potential SNe were lost, several hu-
man searchers visually inspected each subtracted image.
At least two pairs of searchers independently scoured a
few residual tiles. Visual searching of only a few tiles in-
sured that it was done thoroughly, and helped to alleviate
monotony and fatigue.
Candidate SNe found by the software and the searchers
were then scrutinized based on the following set of criteria
to select SNe and further reject instrumental (and astro-
nomical) false positives:
(1) Misregistration: Areas with . 10 detectable sources
per arcmin 2 are typically poorly registered (& 0:5 pixel
RMS). Sources in these areas of the subtracted images are
under-subtracted on one side, and over-subtracted on the
other. If the total ux in an aperture encompassing the
source was not signicantly greater than a few times the
background RMS, it was assumed that the residual was an
artifact of misregistration.
(2) Cosmic ray residuals: The number of pixels in
 2100 s combined images that still contain CRs due to
impacts on the same regions of sky on one or more individ-
ual  520 s exposures is roughly 4500 2  (0:01) N , where
N is the number of impacted exposures (out of 4). This

4 L. -G. Strolger et al.
number can grow slightly when considering hot pixels and
bright pixels with CRs. To further reject these artifacts,
we required that candidates have no more than one con-
stituent exposure aected by CRs or hot pixels.
(3) Stellar prole: Residuals in the subtracted images
were required to show a radial prole consistent with the
PSF ( 2 pixels FWHM). Narrower proles were consid-
ered to be stacked noise (if not residual CRs) and wider
proles were typically poor subtractions from misregistra-
tions, breathing, or focus drift.
(4) Multiple epochs of detection: It was required that
each candidate be detected (to within 5) on each of
the CR split exposures that were not impacted by CRs
or hot pixels at the relevant location. Additional weight
was given to candidates that were clearly detected in the
F775W band, or additionally in the F606W band. How-
ever, this was not a strict criterion as it was expected that
SNe Ia at higher redshifts would become less detectable in
the bluer wavelengths (see Section 2.2).
(5) Variable galactic nuclei: Sources that were . 1 pixel
from their host nuclei were considered potential active
galactic nuclei (AGNs) and typically not included in the
target of opportunity follow-up program (see x2.3). How-
ever, these residuals were followed over subsequent search
epochs, and in all but one case, suôcient photometric evi-
dence (see x2.2) was found to classify them as SNe. Bright
residuals that were coincident with the nuclei of galax-
ies were also compared with known X-ray sources from
the Chandra Deep Field South and Chandra Deep Field
North 1 Megasecond catalogs (Brandt et al. 2001; Giacconi
et al. 2002). Indeed, the only variable source unidentied
by spectroscopic or photometric means was identied as
known X-ray source, and therefore rejected as the only
conrmed optically variable AGN in the survey.
(6) Solar-system objects and slow-moving stars: We re-
quired that our candidates show no proper motion. As-
suming we were sensitive to 1/2-pixel shifts, the proper
motion of any candidate could not be more than 0:025 00
over the  2100 s combined exposure, or ! < 0:043 00 hr 1
(0.1 deg yr 1 ). Hypothetically, if a source was bound to
the Sun (with tangential velocity  30 km hr 1 ), then
its distance would have to be D > [(30 km s 1 )/(0.043"
hr 1 )], or greater than 3; 400 AU. In addition, if the object
was illuminated by re ected sunlight, then its apparent
magnitude (m) would be related to its angular diameter
() by
m = m + 5 log(=2D); (1)
where m is the apparent magnitude of the Sun. Since
 must be consistent with the PSF ( 0:1 00 ), the source
would have to be  4 times larger than Jupiter (at the
distance assumed from the limits on proper motion), and
the apparent magnitude of the source would have to be
m  55 mag! Alternatively, using the limiting magnitude
for the survey, m lim  26 (see x 4.2), the source would
have to have an angular size of  > 18 ô in order to have
been lit by the Sun at its assumed distance.
A similar argument can be made for slow-moving stars.
Since ! = 0:043 00 hr 1 is the fastest a source could move
without being detected, in the  45 days since the eld was
last observed the source could have moved < 1000 pixels.
Our survey was clearly sensitive to negative residuals as
well as positive ones (a fact indicated by the frequent dis-
covery of SNe declining in brightness since the previous
epoch). We saw no negative candidates which were de-
tected within 1000 pixels of a positive source on the same
epoch of observation.
Most of these SNe have been observed on more than
one epoch, and all but two were detected within 3:5 00 of a
galaxy (presumably the host). It would be highly unlikely
for any of these to be objects moving within the Solar
System or the Galaxy.
2.2. Identication of SNe and Redshift Determination
SNe are generally classied by the presence or absence
of particular features in their optical spectra (see Filip-
penko 1997 for a review). Historically, the primary divi-
sion in type has been by the absence (SNe I) or presence
(SNe II) of hydrogen in their spectra, but the classica-
tion currently extends to at least 7 distinct subtypes (SN
IIL, IIP, IIn, IIb, Ia, Ib, and Ic). It is now generally ac-
cepted that the explosion mechanism is a more physical
basis by which to separate SNe. SNe Ia probably arise
from the thermonuclear explosion of carbon-oxygen white
dwarf stars, while all other types of SNe are produced by
the core collapse of massive stars (& 10M ).
There can be considerable challenges in the ground-
based spectroscopic identication of high-redshift SNe. As
the principal goal of this survey has been to acquire many
SNe Ia at z > 1, a fundamental prerequisite was that we
could make condent identications of at least this SN
type. Much to our benet, HST with the ACS G800L
grism provides superb spectra with signicantly higher
signal-to-noise ratio (S/N) than can currently be achieved
from the ground. Its limitation is the low spectral res-
olution (R  =
  200 per pixel, in rst order) and
the overlap of multiple spectral orders from other nearby
sources. Spectral resolution of  1500 km s 1 is not prob-
lematic for SNe with ejecta velocities of & 10; 000 km s 1 .
However, because of the spectral-order confusion and the
lack of a slit mask, the G800L grism could only be used for
SNe with substantial angular separation from their hosts
and from other nearby sources.
It was expected that SN candidates would generally be
either too faint to be spectroscopically observed from the
ground, or too close to their host galaxies or other nearby
sources to be identied with the ACS grism. We there-
fore had to rely on some secondary method by which to
identify SNe, specically to select likely SNe Ia from the
sample. The inherent dierences in the ejecta composi-
tions of SNe Ia and SNe II leads to an observable dierence
in their intrinsic early-time UV ux. As optical observa-
tions shift to the rest-frame UV for z & 1 SNe, the \UV
decit" in SNe Ia can be a useful tool for discriminat-
ing SNe Ia from SNe II, the most common types of core-
collapse (CC) SNe. Using a method pioneered by Panagia
(2003) and fully developed in Riess et al. (2004b), we use
the F850LP apparent magnitude, the F775W F850LP
and F606W F850LP colors, the measured redshift or
photometric redshift estimates (see below), and age con-
straints provided by the baseline between search epochs
to grossly identify SNe as either SNe Ia or SNe CC. This
method is only useful for z & 1 SNe near maximum light,
and is not foolproof in its identication. There are SNe CC
(e.g., luminous SNe Ib and Ic) which can occupy nearly the

The Hubble Higher-z Supernova Search Project 5
same magnitude-color space as SNe Ia. However, these
bright SN Ib/c make up only  20% of all SNe Ib/c,
which as a group are only  1=3 as plentiful as other
SNe CC (Cappellaro, Evans, & Turatto 1999).
From the ground, we have obtained spectroscopic iden-
tication of 6 SNe Ia and 1 SN CC in the redshift range
0.2{1.1 using Keck + LRIS (see Table 1). With HST/ACS
and the G800L grism, we have obtained excellent spectra
of 6 SNe Ia at z = 0:8{1.4, the most distant sample of
spectroscopically conrmed SNe; see Riess et al. (2004a).
These spectra cover only the 2500{5000  A range in the
rest frame, but they are of excellent S/N, unattainable for
such high-z SNe from the ground. These identications
also serve as an excellent proof of concept in the color-
magnitude selection.
Using Keck, the VLT, and the ACS grism, we have ob-
tained spectroscopic redshifts for 29 of the 42 SNe in our
sample. To our benet, part of the GOODS endeavor in-
volved obtaining extensive multi-wavelength photometry
spanning the U to the near-IR passbands to estimate the
photometric redshifts (\phot-z") of galaxies in the HDFN
and CDFS elds (Mobasher et al. 2004). The precision
of the phot-z from GOODS with respect to known spec-
troscopic redshifts has been within  0:1 RMS, with the
occasional instance ( 10% of a tested sample) where the
phot-z method misestimates the actual redshift by more
than 20%. In order to improve on the accuracy of the phot-
z measurements for the host galaxies, we remeasured the
multi-wavelength photometry by visually determining the
centroid of the host galaxies, and manually determining an
annulus in which the sky background is determined. This
allowed better photometric precision than was generally
achieved in the SExtractor-based automated cataloging.
Comparing the sample of 26 SN host galaxy spectroscopic
redshifts to the phot-z estimates from the improved pho-
tometry 16 resulted in a precision of 0.05 RMS (after re-
jecting two > 7 outliers), and only  5% of the sample
was misestimated by more than 10% (see Figure 6). The
redshifts of the remainder of the SN hosts (without spec-
troscopic redshifts) were determined in this way, with the
exception of SN 2002fv, whose host was not identied due
to the magnitude limits of the survey.
We t template light curves to grossly identify SNe
which were not spectroscopically identied, and were not
at z & 1 nor constrained near maximum light. Using
the light curves of SNe 1994D, 1999em, 1998S, and 1994I
as models for SNe Ia, IIP, IIL, and Ib/c (respectively),
we transformed these model SNe to the redshifts of the
observed SNe, correcting for the eects of time dilation,
and applying K-corrections to the rest-frame bandpasses
to produce light curves as they would have been seen
through the F850LP , F775W , and F606W bandpasses
at the desired redshifts. The K-corrections were deter-
mined from model spectra (Nugent, Kim, & Perlmutter
2002) for SNe Ia, and from color-age light-curve interpola-
tions for SNe CC. We have also made use of the web tool
provided by Poznanski et al. (2002) to check the derived
colors for the SNe CC. We visually determined the best-t
model light curve to the observed light curves, allowing
shifting along the time axis, magnitude osets, and ex-
tinction/reddening (assuming the Galactic extinction law)
along the magnitude axis. Best ts required consistency in
the light-curve shape and peak color (to within magnitude
limits) and in peak luminosity in that the derived absolute
magnitude in the rest-frame B band had to be consistent
with the observed distribution of absolute B-band magni-
tudes shown in Richardson et al. (2002).
Each discovered SN was given an identity rank (gold,
silver, or bronze) re ecting our condence in the identi-
cation. A gold rank indicated the highest condence that
the SN was the stated type, and it was not likely that the
SN could have been some other SN type. A silver rank in-
dicated the identity was quite condent, but the SN lacked
suôcient corroborating evidence to be considered gold. A
bronze rank indicated that there was evidence the SN type
was correct, but there was a signicant possibility that the
SN type was incorrect.
We were clearly condent of the SN type in cases where
a high S/N (& 20) spectrum conclusively revealed its type;
these SNe were gold, by denition. However, the majority
of SNe were without suôcient spectra to unambiguously
determine a type. We then used additional information on
the SN redshift, photometric data, and host-galaxy mor-
phology, seeking a consistent picture for a specic SN type.
We rst considered the possibility that a candidate was
a SN Ia. We required that the light-curve shape was at
least consistent with a SN Ia at its redshift, and that the
observed colors and derived absolute magnitude could be
made consistent with the template light-curve colors with
< 1 mag of extinction (assuming the Galactic extinction
law). If the SN was at z & 1, and its peak colors were
F775W F850LP & 0:5 mag and F606W F850LP & 1
mag, we considered it highly likely to be a SN Ia.
The study of Hamuy et al. (2000) has shown that at
low redshifts, early-type galaxies (ellipticals) only pro-
duce SNe Ia, and have not as yet been shown to produce
SNe CC. Hence, we regard SNe found in red elliptical hosts
to have been most likely SNe Ia and unlikely SNe CC.
Based on the above information, any SN in our survey at
z > 1, in a red elliptical host, and having light curves and
peak colors consistent with a SN Ia, were most condently
considered SNe Ia and ranked \gold SNe Ia." SNe hav-
ing photometric data consistent with SNe Ia, and either
at z > 1 (identiable by their peak color) or in early-type
host galaxies, were considered SNe Ia with a high con-
dence, and therefore ranked \silver SNe Ia." SNe having
light curves consistent with SNe Ia, but without any other
information to conrm their type, were ranked as \bronze
SNe Ia."
If the light curves for a SN seemed inconsistent with a
SN Ia, we compared them to the model light curves for
SNe CC. If the SN showed a slow rate of decline from
peak (consistent with SNe IIP and some SNe IIn), then it
was considered a SN CC with high condence, or a \silver
SN CC." All other SNe, inconsistent with SNe Ia, SNe IIP,
or slowly declining SNe IIn, were placed into the \bronze
SN CC" category. For clarity, we include a ow chart
showing the conditions used to determine the identica-
tion condence rank (Figure 7).
2.3. Follow-up HST Observations
16 Only 26 SN host galaxies have both measured spectroscopic and photometric redshifts.

6 L. -G. Strolger et al.
An intensive target of opportunity (ToO) follow-up pro-
gram with HST (GO 9352; Riess, PI) was conducted for
candidate SNe Ia in the range of z & 1. The decision
to trigger the ToO was based on the prior certainty of
SN Ia type and redshift range. These observations are in-
tended to support multi-wavelength light-curve shape t-
ting (Riess et al. 1996) with multiple observations in pass-
bands as close to the rest-frame U , B, and V bands as
possible. The ToO program consisted of supplementary
observations with ACS (in F775W and F850LP bands),
NICMOS (in the F110W and F160W bands), and ACS
G800L grism spectra when feasible. These observations
were rapidly initiated (within  1 week of SN detection) so
that identication and color measurements could be made
as near to maximum light as possible, and so that the light-
curve sampling could be optimized. Using an updated ver-
sion of the multicolor light-curve shape algorithm (Jha,
Riess, & Kirshner 2004, in preparation), we estimate key
parameters of the rest-frame optical light curves, particu-
larly the B-band magnitude at maximum, the rest-frame
U B and B V colors at maximum, and the rate of
decline from maximum light in the B band. Further de-
tails on the ToO program, including the photometric and
spectroscopic data, can be found in Riess et al. (2004b).
3. results of the survey
Over the course of 8 search campaigns from 2002 August
to 2003 May, we successfully discovered 42 SNe of both
physical types over a wide range of redshifts. The SNe
are shown in their discovery-epoch images in Figures 3, 4,
and 5. They are listed in Table 1 with their U. T. date of
discovery, coordinates, physical SN type, type condence,
redshift, source of measured redshift, and oset from host
galaxies, if detected.
The optical HST/ACS photometry for most of the SNe
is given in Table 2. This photometry consists of discovery
epoch apparent magnitudes, and data on the SN (when
detected) from subsequent search epochs. The optical
and infrared photometry for the 16 SNe Ia which were
used in the cosmological analysis (speccally SNe 2002fw,
2002fx, 2002hp, 2002hr, 2002kc, 2002kd, 2002ki, 2003ak,
2003az, 2003bd, 2003be, 2003dy, 2003eb, 2003eq, 2003es,
and 2003lv) are shown in Riess et al. (2004b). The data
listed in Tables 1 and 2, and in Riess et al. (2004b), super-
sede preliminary data announced in IAU Circulars 7981,
8012, 8038, 8052, 8069, 8081, 8083, 8125, 8140, and 8141.
For each SN, images from all survey epochs in which
the SN was not detected (to within a 10 limit) were
combined to create a template image. Images from each
epoch in which the SN was detected had the template
image subtracted from it to remove the host galaxy and
other background light. The apparent magnitude in each
passband was measured through a narrow aperture (0:15 00
radius) centered on the SN. The residual sky brightness
(and noise) were determined in larger aperture annuli (0.6{
1 00 ). Aperture corrections determined by Gilliland & Riess
(2002) were applied to correct from the encircled ux in
the narrow aperture to what would be expected in a nearly
innite aperture. We then measured the apparent magni-
tudes relative to the 1 count per second zero points deter-
mined by Sirianni et al. (2003). Photometric errors were
approximated using the ACS Exposure Time Calculator.
4. delay time functions and models for sne ia
progenitor systems
The current consensus on SNe Ia is that they are ther-
monuclear explosions of white dwarf (WD) stars as they
accrete matter to reach the Chandrasekhar mass (Livio
2001). The two most likely scenarios are single degener-
ate (SD) systems (a single WD accreting material from
a normal companion star), and double degenerate (DD)
systems (the merger of two WDs). It is not yet fully un-
derstood which scenario represents the preferred mecha-
nism or channel for the production of these events, or if
more than one channel is used by progenitors to make
SNe Ia. To that end, there is some uncertainty concerning
the characteristic time scale from the formation of these
progenitors to the occurrence of the events, and concern-
ing the distribution of these delay times. Nevertheless,
there is some consensus that the delay time in the SD
scenario is chie y governed by the main-sequence lifetime
of the companion star which is on the order of 10 9 yr,
and in DD by the time necessary to gravitationally radi-
ate away the angular momentum (Iben & Tutukov 1984;
Tutukov & Yungelson 1994) which is on the order of 10 8
yr. Chemical evolution in the solar neighborhood (Yoshii,
Tsujimoto, & Nomoto 1996), and additional SD/DD mod-
eling (Ruiz-Lapuente & Canal 1998; Hachisu et al. 1999),
suggest 0.5{3 Gyr mean delay times should be plausible
for SD, and a mean of  0:3 Gyr in DD.
Even within the SD scenario, there is quite a diversity
of specic models. In addition to the substantial mass
accretion [ _
M acc  (5 10)  10 8 M yr 1 ], there can
be signicant winds ( _
Mwind  0:5 _
M acc ), and possibly
companion-mass stripping ( _
M strip  0:1 _
M acc ) to accom-
modate a larger range in companion star masses (Hachisu
et al. 1999). Indeed, there are a variety of SD models
which can reproduce a satisfactory set of SN Ia character-
istics, but none as yet which have thoroughly accounted
for the SN Ia diversity (see Livio 2001 for a review). It
is possible, in light of this diversity, that there are several
channels by which SNe Ia are produced. For example, it
is possible to imagine a scenario in which SD channels ac-
count for the majority of SN Ia events, perhaps & 80%,
and the other  20% would come from DD systems. This
would be consistent with the observed luminosity diversity
at z  0, and, assuming some simple evolutionary argu-
ments, could account for the apparent lack of diversity at
higher redshifts (Livio 2001; Li et al. 2001). Ultimately,
it is this uncertainty in the progenitor systems that in-
evitably makes it diôcult to quantify the intrinsic distri-
bution of delay times, which would allow a comparison of
the observed SN Ia rate to the star formation rate.
We therefore attempt to constrain the apparent distri-
bution of delay times through the observed SN rates and
measurements of the star formation history. The frequency
distribution, or number distribution [N Ia (z)], of SNe in
our survey can be given by
N Ia (z) = SNR Ia (z)t c (z)(1+z) 1  
4

V (z); (2)
where SNR Ia (z) is the intrinsic SN volume rate (number
per unit time per unit comoving volume). The survey's
eôciency with redshift is represented as a \control time,"

The Hubble Higher-z Supernova Search Project 7
t c (z), or the amount of time in which a SN Ia at a given
redshift could have been observed by our survey (see x 4.2).
 is the solid angle of the survey area ( 300 sq. arcmin,
or 2:54  10 5 steradians).
V is the volume comoving
element contained in a shell about z and is dened by

V (z)  V (z +
z) V (z), with
V (z) =4H 3
0(2
k ) 1


H 0

DL (z)
1 + z

1
+
k H 2
0

DL (z)
1 + z
 2  1=2
j
k j 1=2 sinn 1 (H o

DL (z)
1 + z

j
k j 1=2 )

;
(3)
where H 0 is the Hubble constant at the present epoch
t 0 , and DL is the luminosity distance. Here \sinn"
and
k are terms which describe the curvature of space,
where sinn = sinh
when
k > 0 (open Universe), and
sinn = sin
when
k < 0 (closed Universe) 17
.
k is de-
ned by
1
k
=
M
+
 .
We assume that the intrinsic SN Ia rate would be a re-
ection of the star formation rate, SFR(z), distorted and
shifted to lower redshifts by the convolved delay time dis-
tribution function, (t d ):
SNR Ia (t) = 
Z t
t F
SFR(t 0 )  (t t 0 ) dt 0 ; (4)
where
R
SNR Ia (z) dz 
R
SNR Ia (t) dt. Here, t is the
age of the Universe at redshift z, t F is the time when
the rst stars were formed, and for computational conve-
nience, we set z F = 10. We dene  as the number of
SNe Ia per formed solar mass. Therefore, (t d ) is the fre-
quency distribution of SNe Ia (yr 1 ), and represents the
relative number that explode at a time t d since a single
burst of star formation.
As the HHZSS GOODS data span a vast range in red-
shift extending to z  1:6, they are well suited to prob-
ing SNR Ia (z), and to determining (t d ). In this analysis,
we attempt to determine constraints on (t d ) by testing
a few model distributions in their ability to recover the
observed redshift distribution of SNe Ia from this survey.
Overall normalization factors, such as the number of SNe
per unit formed stellar mass, are largely ignored in this
analysis. The actual rates of SNe Ia (including normaliza-
tion) are calculated and analyzed in Dahlen et al. (2004).
We use the gold, silver, and bronze SNe Ia together (a to-
tal of 25 SNe Ia) throughout this analysis, and we assume

M =
0:30,
 = 0:70, and H 0 = 70 km s 1 Mpc 1 .
4.1. The Star Formation Rate Model
Various observations of galaxies in the rest-frame pass-
bands have given information on SFR(z), now extend-
ing to z & 5 (Giavalisco et al. 2004b). This current
model broadly supports the ndings of Madau, Pozzetti,
& Dickinson (1998) in suggesting that SFR(z) is peaked
at 1 < z < 2, but it is substantially atter in its decline
at z > 2. There is, however, some uncertainty in the
amount of correction for extinction in the galaxies them-
selves (see Giavalisco et al. 2004b for a discussion). Indeed,
without the extinction correction, the deduced SFR(z)
would be similar to the Madau, Pozzetti, & Dickinson
(1998) function, but extending to higher redshifts.
We therefore chose to include an analysis for two SFR
models. Using a modied version of the parametric form
suggested by Madau, Della Valle, & Panagia (1998), we
assume SFR(t) evolves as
SFR(t) = a(t b e t=c + d e d(t t o )=c ); (5)
where t is given in Gyr. By tting the measurements
of SFR(z) from several surveys (see Giavalisco et al.
2004b), we determined the coeôcients of the function to
be a = 0:182; b = 1:26; c = 1:865; and d = 0:071 for
the extinction-corrected model (M1), and a = 0:021; b =
2:12; c = 1:69; and d = 0:207 for the uncorrected model
(M2; see Figure 8). Here t is the age of the Universe at
redshift z, and t o = 13:47 corresponds to z = 0 for both
models.
4.2. The Control Time: The Eôciency of the Survey
In comparing predicted yields to what was observed, it
is imperative that corrections are made based on various
conditions of the survey. This includes observational ef-
fects such as the magnitude limits, eective sky coverage,
and time over which the survey was conducted, as well as
SN type parameters such as the intrinsic luminosity range,
light-curve shapes, and extinction environments. We com-
bine all of these systematic eects to a single parameter,
the \control time" [t c (z)], which is in eect the amount of
time a SN at a given redshift could have been observed.
We dene t c (z) as
t c (z) =
Z
t
Z
M
Z
A
P (tjM ; A ; z)P (M )P (A  ) dA  dM dt;
(6)
which is a product of probabilities for observing a SN
of specic absolute magnitude (M  , at rest-frame central
wavelength ) with specic host-galaxy extinction (A  ) at
specic times (t), summed over all viable absolute mag-
nitudes, extinction values, and time. All parameters in
the equation are dimensionless, except for dt with units of
time.
We determined the sensitivity of our survey in a real-
time method, by placing false SNe of random magni-
tudes (in the range 23{27 mag) in search-epoch images.
The modied search images passed through our image-
subtraction pipeline, on to the visual inspection, unbe-
knownst to the search team. In doing so, we were able
to determine the combination of the intrinsic sensitivity
limits and the search team's eôciency. Only a moder-
ate number ( 40) of false SNe were added to the survey
data so that searchers would not become desensitized to
real transients by an overwhelming number of bogus de-
tections. To add some realism to the test, the majority
of false SNe were added to known galaxies in a Gaussian
radial distribution (0:50 00  0:25 00 , 10  5 pixels) truncated
at zero radius. It has also been documented that in inter-
mediate and high redshift surveys, a few SNe have been
discovered without host galaxies, to within the detection
limits of these surveys (Strolger et al. 2002; Gal-Yam et al.
2003; Germany et al. 2004; Germany & Strolger 2004).
17 In the case
of
k = 0, eq. 3 becomes V (z) = (4=3)D 3
L (1 + z) 3 .

8 L. -G. Strolger et al.
We therefore placed a few SNe in completely random lo-
cations, so that searchers would not bias their discoveries
based on the requirement of a host galaxy. Astonishingly,
100% of test SNe were recovered to mF850LP  25 mag, a
testament to the eôcacy of the search team and the unpar-
alleled stability of observing conditions with HST. Beyond
mF850LP  25 mag, the recovery eôciency drops rapidly,
reaching zero at mF850LP & 26:5 mag.
The limitation of the of this real-time method was that
there were few fake SNe, and therefore only a gross range
in detection eôciency could be assessed. This test can-
not appropriately test both rate of decline in eôciency,
and the eects of host galaxy light contamination on the
eôciency. We therefore independently tested the sensitiv-
ity of the survey through a more thorough Monte Carlo
simulation.
500 random host galaxies with phot-z in the range of 1.5
to 2.0 were selected from the GOODS data, and combined
to produce light prole of galaxies in this redshift range. A
function was t to the combined light prole using galfit:
Bulge = s e  exp

7:688
 r
r e
1=4
1

(7)
Disk = s o  exp
 r
r o
+ r 1
r
3

(8)
T otal = Bulge + Disk + Background; (9)
where the total light prole is well t by s e = 0:01; r e =
0:055; s o = 0:02; r o = 3:0; r 1 = 0:0; and Background  0.
A set galaxies with phot-z from 1.5 to 2.0 (183 total) were
selected in two test tiles, and one fake SN with a ran-
dom magnitude in the range 25.5{27.5 was added to each
of these galaxies with a radial distribution which follows
the derived cumulative light prole. A second distribution
of faint SNe (24 { 26.5 mag) were also added to selected
bright galaxies with phot-z < 0:5 using the same radial
distribution as was used for the faint population of galax-
ies (181 SN total, one per galaxy). These test images were
then run through the processing pipeline, and recovered
using the automated residual detection algorith. The re-
sults of both eôciency tests were combined to produce a
histogram of recovered fake SNe as a fraction of the num-
ber added (shown in Figure 9).
We t an analytical function to the eôciency distribu-
tion following
"(
m) = T
1 + e (
m m c )=S ; (10)
where
m is the magnitude corresponding to the ux dif-
ference between two consecutive epochs in the F850LP
band, determined by
m 1 = ZP 2:5  log(F 1 ) ) F 1 = 10 2
5 (m1 ZP )
m 2 = ZP 2:5  log(F 2 ) ) F 2 = 10 2
5 (m2 ZP )

m = ZP 2:5  log(F 2 F 1 ):
(11)
Here ZP is the photometric zero point, T is the maximum
eôciency, m c represents a cuto magnitude where "(
m)
drops below 50% of T , and S controls the shape of the
roll-o. As seen in Figure 9, the real-time tests show a
maximum eôciency which remains at 100% (T = 1) until
 25:5 mag, where background noise begins to play an im-
portant role. "(
m) drops with S = 0:4, reaches the cuto
at
m c = 25:85  0:1, and is essentially zero at
m  27.
A weighted least-squares t to the Monte Carlo data show
T = 1:030:09, m c = 25:910:12, and S = 0:390:08. As
the maximum eôciency cannot be > 100%, we set T=1 as
a prior, and found m c = 25:94 0:05 and S = 0:38  0:06.
It is important to note that m c represents only a  5 cut-
o. Our simulations show we could detect SNe to within
 3, but only a small fraction of the time (depending on
the local background light).
As with other supernova surveys, it was expected that
the eôciency would not only depend on the brightness of
the SN, but also the brightness of the host galaxy and the
local gradient of light (or synonymously the distance from
the host nucleus). Most modern surveys use image sub-
traction methods to nd SNe, and therefore generally do
not lose SNe because of overall light contamination from
the SN environment, as was the case with the original
\Shaw Eect" (Shaw 1979). However, faint SNe are lost
in the Poisson noise of the host galaxies (cf. Hardin et al.
2000), or in the residual remaining from an imperfect sub-
traction of the host galaxy. To account for the possibility
of this pseudo-Shaw Eect, we separated the fake SNe into
two distributions based on their proximity to the center
of the host nuclei, and drew recovery eôciency histograms
from the samples (see Figure 10). The eôciency histogram
drawn from the fake SNe which were nearly coincident with
their host nuclei, with radial distances of less than 5 pixels,
showed no substantial dierence from the histogram drawn
from well-separated SNe, indicating that the Shaw Eect
was likely insignicant to this survey. In fact, there was a
slight tendency to nd more SNe at small radial distances
than at larger radial distances. This was an attributed
to the automated residual detection algorithm, which also
identied the residuals of galaxies due to breathing or fo-
cus drift as potential SNe. An important distinction be-
tween the real-time method and the Monte Carlo test was
that human searchers were capable of distinguishing and
rejecting a poor subtraction due to a change in the PSF
from a SN candidate, whereas the automated method was
not. In reality, regions which showed such PSF residuals
were deemed \unsearchable" and rejected.
To asses what fraction of SNe could be lost by rejecting
these unsearchable regions (and therefore a potential loss
in eôciency), we convolved a test image with a narrow
Gaussian lter to produce an image with PSF  3 pixels
FWHM, which is 5{10% larger than the PSFs recorded
under the worst conditions of the survey. This convolved
image was subtracted from the original image (without the
convolution) to produce galaxy residuals which are under-
subtracted in the cores. A histogram was drawn from the 2
pixel aperture magnitudes of these residuals, which is well
represented by a Gaussian with h
mi = 28:42;  = 0:707.
SNe with magnitudes equal to or less than that of a galaxy
residual cannot be distinguished from the residual itself,
and therefore the ux contained in the narrow region of
the core would be unsearchable for SNe of those magni-
tudes. Accordingly, this ux cannot be included in the
total of galaxy light surveyed. As the SN rate is expected
to follow the galaxy light, the rejected ux would result in
a loss in the overall number of SNe discovered, which we

The Hubble Higher-z Supernova Search Project 9
represent as a reduction in eôciency.
For example, a galaxy core which produced a 22 mag
residual would be unsearchable for SNe > 22 mag. There-
fore, the eôciency for SNe > 22 mag would drop by a frac-
tion proportional to the fraction of all galaxy light that is
contained in the cores of galaxies which could produce 22
mag residuals. Fainter galaxy residuals only reduce the
eôciency for fainter SNe. These faint galaxy residuals are
more numerous, but the ux within the cores of the galax-
ies which produced them is a considerably smaller fraction
of the total ux in the image, and therefore their rejection
would result in only a small contribution to the eôciency
loss.
We nd that only 8% of the total light in an image was
contained in the cores of galaxies, nearly half of which
resided in bright galaxies. The galaxies which produced
residuals > 23 mag accounted for approximately 4% of
the ux in the image, and therefore an overall 4% eô-
ciency reduction for all SNe. Increasingly fainter galaxies
further reduced the eôciency for fainter SNe, leading to a
6% eôciency drop by
m = m c , and a 8% reduction by

m = 27:5. As can be seen in Figure 9, the pseudo-Shaw
Eect does not signicantly reduce the eôciency. As this
test involved the worst possible conditions of the survey,
it serves only as an upper limit to the impact on the eô-
ciency.
The survey eôciency was used to determine the prob-
ability of detecting SNe Ia of all redshifts at any given
time [P (t) in eq. 6]. To do so, it was important to use
a SN Ia light-curve model that has well observed multi-
wavelength data extending to the rest-frame U band. We
used SN 1994D (R. C. Smith 2003, private communica-
tion), a luminous yet \normal" (cf. Branch, Fisher, &
Nugent 1993) SN Ia with UBV RI observed light curves.
Studies have shown that this SN was relatively blue in
U B (by as much as 0.3 mag) compared to normal SNe Ia
at early epochs (Poznanski et al. 2002). We therefore at-
tempt to correct for this color excess in the template by
applying a linear color correction which is 0.3 mag when
the central wavelength of the F850LP lter matches, or
is blueward of the rest-frame central wavelength of the
U band lter, and gradually decreases to 0.0 mag when
the F850LP band matches or is redward of the rest-frame
B band. The light curves of SN 1994D were adjusted to
the rest frame, and relative to maximum light.
The apparent brightness of a SN Ia depends on a its
luminosity, the age of the SN, the lter in which it is
observed, its local host extinction, and the distance of
the event. For a SN Ia of a given absolute magnitude
(M peak ), redshift [or luminosity distance, DL (z)], and ex-
tinction (A ), we chose intrinsic light curve, M  (t 0
a ), of
the SN Ia model in the rest-frame passband which most
closely matches the observed F850LP band. The apparent
F850LP magnitude at any point in the model light-curve
was determined by
mF850LP (t 0
a ; z) = M peak +M [t 0
a  (1 + z) 1 ] + (U B) 94D
+ K 
F850LP [z; t 0
a  (1 + z) 1 ] +A  + 5 log(DL (z)) + 25:
(12)
We assumed that SNe Ia are nearly homogeneous events,
with a luminosity at peak of M peak;B = 19:5 
M peak .
The (U B) 94D parameter corrects for the for the U-B
color of the template (as described above), and K 
F850LP
is the K-correction from the rest-frame bandpass to the
F850LP band. t 0
a is the modied age of a SN Ia relative
to the epoch of maximum light in the B band (see below).
We further assumed the intrinsic B V color of SNe Ia at
peak is 0.0 (Lira 1995).
It has been shown that there is a dispersion in peak abso-
lute magnitudes of SNe Ia, and that the relative peak lumi-
nosity of the events relates to the rate in which their light
curves evolve from maximum light. Luminous SN 1991T-
like SNe Ia decline in brightness more slowly than more
normal SNe Ia, and under-luminous SN 1991bg-like SNe Ia
fade more rapidly from peak brightness. Several meth-
ods have been developed to account for this relation,
e. g. the
M 15 (B) method (Phillips 1993), the \stretch"
method (Perlmutter et al. 1997), and the multicolor light-
curve shape algorithm (Riess et al. 1996). To account for
the heterogeneity of SN Ia peak luminosity, and the cor-
responding eect on the light-curve evolution, we used a
combination of the most recent adaptation of
M 15 (B)
method (Phillips et al. 1999) and the stretch method (Perl-
mutter et al. 1997). The
M 15 (B) parameter is related to
the peak luminosity by the Phillips et al. (1999) relation,

M peak = 0:786(
m 15 (B) 1:1)+0:633(
m 15 (B) 1:1) 2 ;
(13)
which is well suited for SNe Ia in the range of 0:7 <

M 15 (B) < 1:7, extending from the most luminous and
slowly declining, to the less luminous, yet normal SNe Ia.
However, it does not appropriately account for the SNe Ia
similar to SN 1991bg, which evolve very rapidly and are
intrinsically several magnitudes fainter than SNe Ia in
the normal range. Indeed, the Phillips et al. (1999) re-
lation is  1:5 magnitudes brighter in the B band than
has been observed for SN 1991bg-like SNe in the range
1:7 <
M 15 (B) < 2:2. We therefore applied a correction
to the relation for SNe Ia in this range of
M 15 (B),

M peak = 1:35+0:786(
m 15 (B) 1:1)+0:633(
m 15 (B) 1:1) 2 :
(14)
Li et al. (2001) have found that the distribution of
SNe Ia favors normal events, with only  20% of events
in the range 0:7 <
m 15 (B) < 0:9 (SN 1991T-like SNe),
about 20% in the 1:7 <
m 15 (B) < 2:2 range (SN 1991bg-
like SNe), and the remaining 60% in the 0:9 <
m 15 (B) <
1:7 range. We attempted to characterize this observed dis-
tribution by assuming the intrinsic dispersion in
M 15 (B)
is Gaussian, centered at
M 15 (B) = 1:1  0:35 and trun-
cated at
M 15 (B) < 0:7 and
M 15 (B) > 2:2. The im-
plied distribution in peak luminosity is in agreement with
the observed distribution from Richardson et al. (2002),
and was used as the probability of observing a SN Ia of a
given luminosity [P (M  ) ) P(
M 15 (B))].
A simple way to quantify the eect on the light-curve
evolution is by the stretch parameter, which eectively
scales the time axis of light curve. Perlmutter et al. (1997)
give a relation for the stretch parameter to the
M 15 (B)
parameter,
stretch =
 1:96

M 15 (B) 1:1 + 1:96

: (15)

10 L. -G. Strolger et al.
The modied age of the SN Ia relative to maximum light
was then, t 0
a = t a  stretch, where the actual age, t a ,
is scaled by the stretch factor. We further adopted t 0
a
as the epoch in which the rst image was taken, and
t 0
a + 45 d to be when the second-epoch image was ob-
served. We stepped through viable values of t 0
a (from
 300 d before to  200 d after maximum light), each
time determining mF850LP (t 0
a ; z), mF850LP (t 0
a + 45; z),

m, and "(
m; t 0
a ; z). The function "(
m; t 0
a ; z) serves
as a normalized probability function for detecting a SN
at z at time t 0
a relative to peak in the observer's frame
[P (t 0
a )  "(
m; t 0
a ; z)].
The distribution of intrinsic extinction of SNe Ia due
to host galaxies has been well studied at low redshift.
Jha et al. (1999) has shown for 42 SNe (and 4 calibra-
tors) that the extinction distribution is fairly exponential,
with the form (AV ) / e AV . Assuming the wavelength-
dependent cross-sections of scattering dust to be propor-
tional to  1 , and that A /  1 , we adopt,
P (A ) / e A : (16)
As both of our survey elds were outside of the Galac-
tic plane (jbj > 54 ô ), it was assumed that the Galactic
extinction is negligible.
The total probability for SNe Ia at redshift z was the
sum of the above probabilities for all viable SN ages. We
dene the probability as an eective time in which a SN
at z can be detected in our survey by multiplying by the
step in t 0
a :
t c (z) =
Z
t 0
d
Z
A
Z

M15 (B)
"(
m; t 0
a ; z)  e (
M15 (B) 1:1) 2 =0:245
 e A=0:347 d[
M 15 (B)] dA  dt 0
a +Const:
(17)
As a nal note on the eôciency of the survey, one
might notice from Figure 1 that the distribution of SNe
in the HDFN survey eld appears conspicuously asym-
metric, possibly indicating an eect (physical or observa-
tional) that is unaccounted for in the calculation of the
control time. However, the astrometry and redshifts from
the GOODS photometric redshift catalog (Mobasher et al.
2004) shows no signicant large scale voids or \pockets"
in regions which have produced few SNe. It is always diô-
cult to determine the signicance of an apparent asymme-
try after the fact, but we have attempted to do so using
Monte Carlo simulations. From randomly placing 23 SNe
in an area the size of the HDFN, and bisecting the area
in several dierent ways, we nd that asymmetries similar
to the observed one can be drawn from random distribu-
tions a fair fraction of the time (> 20% K-S probability),
although the observed distribution is not the most proba-
ble one. Therefore, we treat this apparent asymmetry as
a small-number statistical coincidence, and do not make
attempts to correct for it.
4.3. The Delay Time Models
Tutukov & Yungelson (1994) suggest a general delay
time distribution model that can be represented by an ex-
ponential function. This e-folding distribution has been
often used (e.g., Madau, Della Valle, & Panagia 1998,
Gal-Yam & Maoz 2004) to explore progenitor constraints
and predict SN rates at high z. In this model, it is as-
sumed that the SNe Ia are SD systems in which the main-
sequence lifetimes of 0.3{3 M companion stars are chie y
responsible for the delay from formation to explosion. This
model also generally accounts for some additional lagtime
to allow the 3{8 M progenitor to rst become a WD.
Although this model is used more so for its mathemati-
cal convenience than for its physical basis, it is not entirely
devoid of the latter. Kobayashi et al. (1998) assume two
SD scenarios for companion stars, one involving a red-giant
companion with MRG;0  1M , and one with a main-
sequence star with MMS;0  2 3 M . Observations of
binary systems (Duquennoy & Mayor 1991) show that the
initial mass distribution function for companion stars can
be approximated by N (M c ) / M 0:35
c . Using this infor-
mation, and the assumption that delay times are primar-
ily dependent on the companion star's main-sequence life-
time, one can derive the delay time distribution for this SD
model as being (t d ) / (t d =10) 0:14 , where ht d;RG i  7:01
Gyr and ht d;MS i  1:46 Gyr. When considering both
SD scenarios, assuming the same mass distribution func-
tion, the mean delay time for both RG + MS companions
is ht d;RG+MS i  3:60 Gyr. This is fairly similar to an
e-folding distribution for  . 3. More detailed models
that involve population synthesis give broadly similar re-
sults (Yungelson & Livio 2000).
In this analysis, we assume an e-folding delay time dis-
tribution of the form
(t d ;  ) = e t d =
 ; (18)
where  is the characteristic delay time. We do not at-
tempt to separate the distribution into constituent parts
a priori (i.e., the progenitor or companion star lifetimes);
rather, we investigate the entire time lag distribution as
a whole. However, it should be noted that models which
do include time for WD development tend to require that
this lag time be  0:5 Gyr, not contributing signicantly
to the overall delay time distribution.
Although there is some physical basis in the above e-
folding model, it is not reasonable to expect that the delay
time distribution is intrinsically exponential (see Yungel-
son & Livio 2000). It is possible that SNe Ia progenitors
actually prefer a specic channel to the production events
(marked by a specic delay time) and that there is some
scatter in this channel which leads to a dispersion of delay
times, and ultimately a dispersion in SN Ia characteristics.
An example of using a simple model with a preferred delay
time was used by Dahlen & Fransson (1999). To account
for this possibility, we chose to further consider Gaussian
functions of two characteristic widths:
(t d ;  ) = 1
q
2 2
t d
e (t d ) 2 =(2 2
t d
) ; (19)
where our \wide" and \narrow" Gaussian models have
 t d
= 0:5 and  t d
= 0:2 , respectively. The (t d ;  )
models are shown in Figure 11 for several values of  .

The Hubble Higher-z Supernova Search Project 11
4.4. The Likelihood Test
With assumed SFR(z) and (t d ;  ) models, we have
used eqs. 2 and 4 to predict the expected number distri-
bution of SNe Ia for the survey. This was compared to the
observed distribution of SNe Ia to produce a conditional
probability test in an application of Bayes' method:
P[DatajSFR(z);(t d ;  );  ]
 P[SFR(z); (t d ;  );  jData]; (20)
where it was assumed that the SFR(z) model and all other
dependencies
(e.g.,
M
,
 , H 0 , and survey parameters)
are suôciently well determined that their uncertainties do
not signicantly contribute to the overall probability. The
predicted number distribution, given the assumptions on
the models, then served as a probability function for nd-
ing SNe Ia at the specic redshifts where we have found
them:
P[DatajSFR(z); (t d ;  );  ] =
25
Y
i=1
N Ia (z i )
=
25
Y
i=1
SNR Ia (z i )  t c (z i )  (1 + z i ) 1  
4 
V (z i ):
(21)
We normalized the probability distributions to serve as
a relative likelihood statistic. Changes in the input model
parameters will allow changes in the likelihood with red-
shift. Through assuming one of two SFR(z) models (M1
or M2), one of three (t d ;  ) models (e-folding, wide Gaus-
sian, or narrow Gaussian), and several values of  , we at-
tempted to determine the most likely distribution of delay
times. This will provide important clues to the distribu-
tion of channels for SN Ia production.
The P[DatajSFR(z); (t d ;  );  ] as a function of  is
shown in Figure 12 for the dierent (t d ) and SFR(z)
models. The maximum likelihood  values are listed in
Table 3 for each tested model. The 95% condence inter-
vals for each model are also tabulated in Table 3.
Although the Bayesian likelihood test gives the most
likely values of  within a given model, and to some ex-
tent, which models are preferred by the data (as the num-
ber of free parameters per model are the same), it does not
give a very good estimation of which models are inconsis-
tent with the data, and therefore can be rejected at some
condence interval. We attempt to assess how improbable
it would be to derive the observed sample from a given
model by a Monte Carlo simulation. For each model, an
articial sample of 25 redshifts were drawn from the model
distribution 10,000 times, and the likelihood of the test dis-
tribution was determined for each run. We then recorded
the success fraction, or the fraction of runs which produced
likelihood values less than or equal to the likelihood deter-
mined from the observed redshift distribution for the given
model. Models which produced redshift distributions sim-
ilar to the observed distribution less than 50 60% of the
time were considered improbable models for the data. The
success fractions as a function of  for the dierent (t d )
and SFR(z) models are shown in Figure 13.
In general, we nd that the 50 60% success fraction
interval in  was consistent with the 95% condence in-
tervals determined from the Bayesian likelihood test for
each model. However, the selection of the acceptable range
in success fraction is somewhat arbitrary. More stringent
cuts which seek to either isolate only those models which
well reproduce the data, or those which cannot reproduce
them at all, will constrict or expand the acceptable range
accordingly. We therefore chose to adopt the 95% interval
as our acceptable range in  for a given delay time and
SFR(z) model, acknowledging that there may be models
in slightly dierent ranges which could be considered ac-
ceptable depending on the selected tolerance level.
4.5. Results
The e-folding model showed a preference for large values
of  , with the likelihood of  increasing with the value of
 . As the probability distribution remained unbounded at
 = 10 Gyr (the limit of our testing region), we chose to
consider the 95% condence region for   10 Gyr. This
rejected  < 2:6 and < 2:2 Gyr to > 95% condence for
M1 and M2, respectively. The trend with increasing  can
be better exemplied by comparing the N (z) models to
the observed N (z). In Figure 14 the predicted number
distribution function of each model for selected values of
 is compared to the observed N (z), arbitrarily binned
with
z = 0:2. For values of  . 2, the e-folding models
require that nearly all SNe Ia explode within  2 Gyr of
progenitor star formation. These \prompt" SNe Ia result
in an overestimate of the number of SNe Ia at z > 1:5, and
do not allow for suôcient development of SNe Ia at lower
redshifts. Increasing the value of  increases the fraction
of SNe Ia with delay times over 2 Gyr, and therefore pro-
duces higher numbers of lower-z SNe. This alleviates a lot
of the skewness in the distribution. However the fraction
of prompt SNe Ia is never less than 10% of all SNe with
delay times below 10 Gyrs, thus the predicted number of
SNe Ia at z > 1:5 will always be overestimated for this
model. The overall result for large  was a distribution
which was too wide, overestimating the observed distri-
bution at high and low redshift, and underestimating the
vertex of the distribution. We nd that this trend existed
regardless which SFR model is used.
An expected behavior of the e-folding model is that, at
some value of  , short delay times like t d = 0:1 Gyr become
as probable as delay times as long as the age of the Uni-
verse. The supernova rate then becomes a re ection of the
cumulative SFR(z), and changes little with an increase in
 . This saturation appears to have been reached for  > 7
Gyr and > 5 Gyr for the M1 and M2 SFR models, re-
spectively. Therefore, the maximum likelihood values for
 in the e-folding model shown in Table 3 are likely a cir-
cumstance of the noise in the saturated region. Within our
range of modeling, we nd that there were only weak max-
imum likelihood values for  in the e-folding model using
either tested SFR model, and none adequately reproduced
the observed frequency distribution with redshift.
The SD progenitor models of Kobayashi et al. (1998)
suggest that a signicant wind emanating from the accret-
ing WD is required to allow a steady accretion onto the
WD, and to extend the range of companion-star masses.
However, in order for this wind to be adequate, the aver-
age galactic metallicity of the Universe must reach [Fe/H]
 1. In this original analysis, Kobayashi et al. (1998)

12 L. -G. Strolger et al.
predict this metallicity requirement imposes a redshift cut-
o, beyond which the Universe stops producing SNe Ia, at
z & 1:4. It is unlikely that this metallicity cuto could
exist at such a low redshift, as detections of SN 1997 at
z  1:7 and SN 2003ak at z = 1:55 (from this survey)
would be an obvious contradiction. However, in Nomoto
et al. (2000) a renement was made to allow the distribu-
tion of SNe Ia to continue to z  2, then rapidly decrease
in spiral galaxies, followed by a rapid decrease in ellipti-
cal galaxies at z  2:5. In this model, SNe Ia would not
be produced at all beyond z & 3:5. To account for the
possibility of a metallicity cuto (MCO), we executed an-
other test involving the e-folding model where in which
the cuto function as described by Nomoto et al. (2000) is
applied to the SFR(z). The outcome was very similar to
the results for the e-folding model without the MCO, with
95% condence intervals of  > 2:8 and > 2:0 Gyr for M1
and M2, respectively. This is not surprising, considering
that the applied MCO would not have a great impact until
z  2:5, and the survey was only sensitive to SNe Ia at
z < 2:0.
The Gaussian models did, however, show a clear peak in
the likelihood functions, indicating a value of  which, for
the model, is preferred by the data. For the wide Gaussian
model, the tests show a maximum likelihood at  = 4:0
Gyr for M1 (3.2 Gyr for M2). Again, as the probability
distribution was unbounded at  = 10, we consider  < 2:8
and < 2:0 to be rejected with 95% condence. Although
there appeared to be a statistically preferred value for 
for the wide Gaussian model, the predicted distribution
shown in Figure 14 in the range of the best-t model was
still wide, more skewed toward lower redshifts than the
observed distribution, and seemingly underestimated the
number observed in the 1:2 < z < 1:4 range. However,
this predicted redshift distribution was much better than
the best-ts obtained in the e-folding test, which was re-
ected in the factor of  2 increase in Bayesian likelihood
value.
In contrast to the previously tested models, the width in
the range of t d for the narrow Gaussian model grew weakly
with increasing  , allowing for tests of models without a
signicant fraction of prompt SNe Ia and a much more nar-
row distribution. The results of our test show a Bayesian
maximum likelihood value at  = 4:0 for M1 (3.2 for M2)
which was more than twice as likely as the best-t model
from the wide Gaussian model, and more than four times
more likely than the best-t e folding model. The prob-
ability distribution for this model was well bounded by
 = 10, indicating that the model was unsupported by the
data for large values of  . We therefore dened the 95%
condence interval centered on the maximum likelihood
value, with 3:6 <  < 4:6 for M1, and 2:4 <  < 3:8 for
M2. Visually, the predicted N (z) for the narrow Gaus-
sian show a much more convincing match to the observed
distributions at the maximum likelihood value than was
produced from either of the other tested models, as can
be seen in the panel labeled \BEST FIT" in Figure 14.
It appears that the mean (or characteristic) delay time
for SNe Ia can be well constrained and, at least for the
narrow Gaussian model, a convincing number distribution
with redshift can be drawn.
5. conclusions
Our tests have shown a strong preference by the ob-
served frequency distribution for delay time distributions
in which the majority of SNe Ia occur more than 2 Gyr
from the formation of the progenitor star. All (t d ;  )
models which implied that most SNe Ia explode within
 2 Gyr of progenitor formation show very low likelihoods
and are rejected at the 95% condence level. Therefore,
SNe Ia cannot generally be prompt events, nor can they be
expected to closely follow the star formation rate history.
Tests conducted by Gal-Yam & Maoz (2004) similarly
conclude that the characteristic delay times of SNe Ia
should be large (> 1 2 Gyr) for SFR(z) models simi-
lar to those used in this paper. However, there are a few
important dierences in these analyses. In Dahlen et al.
(2004) we show from the data presented in this paper that
there is a peak in the SN Ia rate at z  1. The data
used in Gal-Yam & Maoz (2004) study, based on observa-
tions from the Supernova Cosmology Project (Pain et al.
2002), do not extend beyond this observed peak, and are
limited to z < 0:8. Moreover, the nature of the e-folding
(t d ;  ) used in Gal-Yam & Maoz (2004) is similar to the
e-fold model used in this paper, except that it accounts for
the relatively short main sequence lifetime of the progen-
itor WD. Therefore, a similar trend is expected in which
increasing  generally attens the expected SN redshift
distribution. Due to the limited number and range in the
observed SN Ia redshift distribution, the Gal-Yam & Maoz
(2004) analysis was only moderately sensitive to the slope
of the increase in the SN rate.
The data presented herein not only covers a much larger
range in redshift, but they also appear to be unbounded
by the volume surveyed at low redshift and the survey ef-
ciency at high redshift; the combination of which would
overestimate the observed number by a factor of  2 (as-
suming the SN rate remains constant with time). It is cer-
tainly apparent that the observed sample is bounded by
something more intrinsic to the SN Ia rate history, which
we interpret as the star formation history convolved with
the SN delay time distribution. The analysis presented in
this paper is unique because it probes delay time models
which allow for a larger variation in the breadth of the
redshift distributions without imposing generally unsup-
ported SFR histories.
Our e-folding model, comparable to those previously
tested in similar analyses, cannot adequately reproduce
the observed redshift distribution of SNe Ia from this sur-
vey for   2 Gyr. This would also be true for the de-
lay time distribution function inferred from the Kobayashi
et al. (1998) SD model. We nd that  must be & 2 Gyr
for the e foliding model at a 95% condence. We also
nd that the e folding model itself becomes untestable at
 > 5 7 Gyrs as predicted redshift distributions are virtu-
ally indistinguishable above this limit. Applying a redshift
cutto due to metallicity eects based on the Kobayashi
et al. (1998) SD model only weakly aected the predicted
distributions, and produced similar results. The e folding
model with large  was statistically acceptable by the data,
however upon visual comparison with the observed sam-
ple, there were apparent inconsistencies with number ob-
served at z  1:5, and the strength of the vertex of the
distribution. The e folding model for large  is similar to

The Hubble Higher-z Supernova Search Project 13
the DD models shown in Tutukov & Yungelson (1994) and
Ruiz-Lapuente & Canal (1998), and therefore, these DD
models cannot be signicantly rejected. However the rel-
atively low likelihoods from the Bayesian analysis present
here suggests that this mechanism for SN Ia production is
unlikely the dominant channel used by SN Ia progenitors.
We also note that the detection of H in the spectra of
SN 2002ic (Hamuy et al. 2003) cannot by itself be taken
as evidence against the DD scenario (see Livio & Riess
2003).
We tested two Gaussian delay time distribution models.
From the maximum likelihood tests, we nd that a nar-
row dispersion of 1/5 the mean delay time is signicantly
more favored than a wide dispersion (1/2 the mean de-
lay). This narrow Gaussian model also better reproduces
the observed redshift distribution of SNe Ia.
In Figure 15 we show our best-t models for the three de-
lay time distribution functions. Yungelson & Livio (2000)
explore in detail four evolutionary channels which possi-
bly produce SNe Ia: the ignition of C in the core of a
merged DD system, the ignition of central C induced by
ignition in an accreted shell (commonly called edge-lit det-
onation or ELD) from a He-rich RG companion, ELD in-
duced from a H-rich subgiant or MS companion, and the
central C ignition from normal accretion (no ELD) from a
subgiant or MS companion. Figure 2 of Yungelson & Livio
(2000) shows the expected delay time distributions for each
channel. We reproduce the predicted distributions for the
DD and MS models in Figure 15 of this paper for com-
parisons to our best-t models. As can be seen, there is
some similarity between the Yungelson & Livio (2000) sub-
giant companion models and our best-t Gaussian mod-
els, specically the narrow Gaussian model, which is also
largely inconsistent with what is expected from their DD
models. This similarity can also be seen in comparison
to general WD+MS models suggested by Hachisu, Kato,
& Nomoto (1996), Hachisu et al. (1999), Ruiz-Lapuente
& Canal (1998), and Han & Podsiadlowski (2003). Our
best-t model does appear similar to the MS+WD (with
ELD) models in the range of the distribution, but it is dif-
ferent in that the width is larger and the peak is a few Gyr
later than what is expected from these models. This may
suggest that these models are largely inconsistent with the
data. However, It should be noted that the testing done in
this paper does not exhaustively cover the possible range
in characteristic delay times or widths of the distribution,
and therefore some dissimilarity is expected.
It is also important to note that systematic uncertain-
ties have been largely ignored in this analysis. Uncertainty
in our models derive from the uncertainties in the derived
control times. These errors stem from uncertainties in

M peak (from the coeôcients in the
M 15 (B) and stretch
relations), uncertainties in the "(
m) parameters, and the
pseudo-Shaw Eect between epochs. When combined in
quadrature, they result in systematic uncertainties which
do not signicantly eect the eôciency with redshift for
the survey. The systematic uncertainties on the control
times are shown in Figure 14. We, therefore, do not ac-
count for these errors in the Bayesian analysis.
This analysis has used all transients identied as SNe Ia
in Table 1, regardless of the condence in the identica-
tion. However, it is known that some SN Ib/c can have
light curves and colors which are similar to SNe Ia. There-
fore, some SNe Ia could have been misidentied as Bronze
SNe CC, and conversely some SNe Ib/c may pollute our
Bronze SN Ia category. However, there were no Bronze
SNe CC at z > 1, and only one Bronze SN Ia at z > 1. If
we considered all Bronze SNe CC as additional SNe Ia, the
overall number will increase at lower redshifts, but there
would be no additional SNe Ia at z > 1. Removing all
Bronze SNe Ia also does not greatly aect the high-z sam-
ple. Neither rejection would relax the requirement of a
substantially large mean delay time, thus the most signif-
icant conclusion of this study would remain intact. One
could, however, expect minor changes to the width of the
best-t delay time distributions.
The key implications of our results are that SNe Ia are
not prompt events, and generally require at least  2 Gyr
to explode from formation. It is also likely that SN Ia
progenitors prefer a specic channel to explosion, marked
by a mean delay time of perhaps as long as  4 Gyr, with
some scatter in the conditions of the channel. While the
implied delay appears to be surprisingly long, this chan-
nel is apparently in the range of single degenerate systems
which accrete from a main-sequence, or somewhat evolved,
non-degenerate companions. The channel would be simi-
lar to that which produces supersoft X-ray sources (Livio
1995, 2001; Hachisu & Kato 2003).
We thank Dan Maoz for his valuable comments
and suggestions which have greatly contributed to this
manuscript. Financial support for this work was provided
by NASA through programs GO-9352 and GO-9583 from
the Space Telescope Science Institute, which is operated
by AURA, Inc., under NASA contract NAS 5-26555. Some
of the data presented herein were obtained at the W. M.
Keck Observatory, which is operated as a scientic part-
nership among the California Institute of Technology, the
University of California, and NASA; the Observatory was
made possible by the generous nancial support of the W.
M. Keck Foundation. The work of D.S. was carried out
at the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with NASA.
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The Hubble Higher-z Supernova Search Project 15
Fig. 1.| HDFN eld observed by the GOODS project. North is up, and east is to the left. The tiles show the ACS pointings for the rst
(dark) and second (grey) epochs. Epochs 3 and 5 are rotated by 90 ô and 180 ô (respectively) relative to epoch 1. Epoch 4 is rotated by 90 ô
relative to epoch 2. The SNe discovered in this eld are marked and labeled.

16 L. -G. Strolger et al.
Fig. 2.| Same as in Figure 1, but for rst (dark) and second (grey) epochs the CDFS eld. Subsequent epochs are rotated by the same
amounts as indicated in Figure 1.

The Hubble Higher-z Supernova Search Project 17
Fig. 3.| Discovery images for SN 2002fv through SN 2002kl. Each SN has three panels: the discovery image (left), a template constructed
from images without the SN (middle), and the subtraction of the two (right). The SN is labeled in the subtraction image. Arrows indicate the
position of each SN in the discovery and subtraction images. North and east are marked. The image scale is shown in the lower right-most
image.

18 L. -G. Strolger et al.
Fig. 4.| Same as in Figure 3, but for SN 2002lg through SN 2003er.

The Hubble Higher-z Supernova Search Project 19
Fig. 5.| Same as Figure 3, but for SN 2003es through SN 2003lv.
­0.3
­0.2
­0.1
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2
Dz/(1+z
spec
)
Spectroscopic Redshift (z spec )
CDFS HDFN
Fig. 6.| The accuracy of the photometric redshifts as a function of actual spectroscopic redshift for the 26 SN host galaxies. Photometric
redshifts were precise to  0:05 RMS (rejecting two > 7 outliers).

20 L. -G. Strolger et al.
Fig. 7.| Flow chart showing how SN types and condence ranks were determined from the data.

The Hubble Higher-z Supernova Search Project 21
Fig. 8.| The star formation rate history models (M1 and M2), shown relative to measurements of the star formation rate at various
redshift intervals.

22 L. -G. Strolger et al.
23.5 24 24.5 25 25.5 26 26.5 27 27.5
26.6 17.7 11.5 7.5 4.8 3.0 1.9 1.2
F850LP­band Difference Magnitude (Dm)
Optimum Signal to Noise
96%
94%
92%
m c =25.94, S=0.38
"Shaw Effect"
0.0
0.2
0.4
0.6
0.8
1.0
1.2
23.5 24 24.5 25 25.5 26 26.5 27 27.5
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Efficiency
[e
(Dm)]
SN Ia redshift at peak (M B =­19.5)
m c =25.8, S=0.4
Fig. 9.| The eôciency of the survey in recovering false SNe in a pair of images (discovery and template) of a given dierence magnitude.
The histograms from both the real-time test (left), and from the Monte Carlo test (right) are shown. The Monte Carlo histogram is shown
with Poisson errors (dark circles). The solid line shows the t of the form (
m) / (1 + e
m ) 1 used to represent the eôciency. The dotted
line (and open circles) show the maximum response to the psudo-Shaw Eect on the eôciency for this survey. For convenience, we roughly
correlate the dierence magnitude limits to redshift limits for SNe Ia discovered near maximum light, and to the optimum signal-to-noise
limits for a point source in a residual frame.

The Hubble Higher-z Supernova Search Project 23
0
0.2
0.4
0.6
0.8
1
e(Dm)
(r
<
5
pixels)
mc=25.8, s=0.4
mc=25.94, s=0.38
0
0.2
0.4
0.6
0.8
1
24.0 25.0 26.0 27.0 28.0
e(Dm)
(r
>
5
pixels)
0
20
40
60
80
Number
(r
<
5
pixels)
Added
Found
24.0 25.0 26.0 27.0 28.0
0
20
40
60
80
Number
(r
>
5
pixels)
Difference Magnitude (Dm)
Fig. 10.| Monte Carlo test eôciencies for populations which are either nearly coincident with, or well separated from, the nuclei of their
host galaxies (r < 5 and r > 5 pixels, respectively). Neither distribution, specically the nearly coincident sample, show detectable deviation
from ts drawn from the real-time test (dotted line), or the Monte Carlo simulation of the entire sample (solid line).

24 L. -G. Strolger et al.
0
0.5
1 t=1
t=2
t=3
t=4
0
0.5
1
Number
t=1
t=2
t=3
t=4
0
1
2
0 1 2 3 4 5 6 7 8
Delay Time (Gyrs)
t=1
t=2
t=3
t=4
Fig. 11.| The delay time distribution models for the e-folding (top), wide Gaussian (middle), and narrow Gaussian (bottom) functions.
Each model is plotted with several values of  .

The Hubble Higher-z Supernova Search Project 25
0.00
0.01
0.02
0.03
M1
Exponential
no cutoff
w/ cutoff
M2
Exponential
no cutoff
w/ cutoff
0.00
0.05
0.10
0.15
Bayesian
Probability Wide Gaussian Wide Gaussian
0.00
0.05
0.10
0.15
0 1 2 3 4 5 6 7 8
t
Narrow Gaussian
0 1 2 3 4 5 6 7 8
t
Narrow Gaussian
Fig. 12.| The probability distributions for the e-folding (top panels; shown with and without metallicity cuto), wide Gaussian (middle
panels), and narrow Gaussian (bottom panels) models shown as a function of  for the M1 (left panels) and M2 (right panels) SFR histories.
Note that none of the e-folding models shows a clear maximum likelihood value of  , and that the overall probability values are low for the
e-folding and wide Gaussian models. Only in the narrow Gaussian models are there maximum likelihood values and overall high probabilities.

26 L. -G. Strolger et al.
0.00
0.20
0.40
0.60
0.80
M1
Exponential
no cutoff
w/ cutoff
M2
Exponential
no cutoff
w/ cutoff
0.00
0.20
0.40
0.60
0.80
Success
Fraction Wide Gaussian Wide Gaussian
0.00
0.20
0.40
0.60
0.80
0 1 2 3 4 5 6 7 8
t
Narrow Gaussian
0 1 2 3 4 5 6 7 8
t
Narrow Gaussian
Fig. 13.| The fraction of Monte Carlo runs which produce likelihood values equal to or less than the likelihood of the data for each
model. Models which could not often produce redshift distributions similar to the observed distribution had a low success fractions (less than
50 60%) and were therefore rejected as improbable models for the data. The selected range in success fraction was consistent with the 95%
condence interval in likelihood for each model.

The Hubble Higher-z Supernova Search Project 27
0.0
2.0
4.0
6.0
8.0
e­fold
t=10.0
0.0
2.0
4.0
6.0
8.0
Number
t=4.0
0.0
2.0
4.0
6.0
8.0 t=2.0
0.0
2.0
4.0
6.0
8.0
0.0 0.5 1.0 1.5 2.0
t=0.2
G(t,0.5t)
t=10.0
t=4.0
t=2.0
0.0 0.5 1.0 1.5 2.0
Redshift
t=0.2
G(t,0.2t)
t=10.0
t=4.0
BEST FIT
t=2.0
0.0 0.5 1.0 1.5 2.0
t=0.2
Fig. 14.| The predicted number distributions of SNe Ia for each model for selected values of  . The solid line is for the M1 SFR(z) and
the dash-dotted line is for the M2 model. The dotted line shows the control time (or survey eôciency, scaled) with redshift. The systematic
eects on the control time are shown in the top left panel (black points).These predicted distributions are compared to the observed number
distribution of SNe Ia from this survey. Most models cannot adequately reproduce the observed redshift distribution. Only for the narrow
Gaussian model in the range of   4 Gyr does the predicted distribution appear similar to the observed distribution.

28 L. -G. Strolger et al.
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
Relative
SN
Frequency
t d (Gyr)
E (10)
G (4.0, 2.0)
G (4.0, 0.8)
DD­Ch
SG­ELD
SG­Ch
­4
­3
­2
­1
0
7 7.5 8 8.5 9 9.5 10
Relative
SN
Frequency
(10
y
)
log (t d /yr)
E (10)
G (4.0, 2.0)
G (4.0, 0.8)
DD­Ch SG­ELD
SG­Ch
Fig. 15.| SN distributions, in linear and log space, for the maximum likelihood values of  of each delay time function (solid lines). Shown
are the e-folding (t d ) for  = 10 [E(10)], the wide Gaussian for  = 4:0 [G(4.0, 2.0)], and the narrow Gaussian for  = 4:0 [G(4.0, 0.8)]. The
dashed lines represent predicted distributions of SN Ia delay times from various models (Yungelson & Livio 2000, reproduced from Figure
2). Shown are the predictions from double degenerate mergers (DD-Ch), edge-lit detonations from subgiant donors (SG-ELD), and normal
accretion/detonations from subgiant donors (SG-Ch). There is some similarity to our best-t models.

The Hubble Higher-z Supernova Search Project 29
Table 1
HHZSS+GOODS Supernovae
SN Nickname U. T. R. A. (2000) Decl. (2000) SN Type Condence Redshift Source N (arcsec) E (arcsec)
2002fv Apollo a 2002 Sep 19.6 03:32:22.73 -27:51:09.4 CC bronze












2002fw Aphrodite 2002 Sep 19.9 03:32:37.52 -27:46:46.6 Ia gold 1.30 spectrum 0.21 -0.51
2002fx Athena 2002 Sep 20.8 03:32:06.80 -27:44:34.4 Ia silver 1.40 spectrum -0.04 -0.09
2002fy Hades 2002 Sep 20.9 03:32:18.12 -27:41:55.6 Ia silver 0.88 phot-z 0.00 0.00
2002fz Artemis 2002 Sep 21.6 03:32:48.54 -27:54:17.6 CC silver 0.84 spectrum -1.66 1.30
2002ga Atlas 2002 Sep 22.5 03:32:32.62 -27:53:16.7 Ia bronze 0.99 spectrum -0.08 0.21
2002hp Thoth 2002 Nov 01.5 03:32:24.79 -27:46:17.8 Ia gold 1.30 spectrum 0.02 -0.01
2002hq Re 2002 Nov 01.5 03:32:29.94 -27:43:47.2 CC bronze 0.67 spectrum -0.18 -0.91
2002hr Isis 2002 Nov 01.6 03:32:22.57 -27:41:52.2 Ia gold 0.53 spectrum 0.05 0.03
2002hs Bast b 2002 Nov 02.2 03:32:18.59 -27:48.33.7 CC bronze 0.39 spectrum 2.50 -0.27
2002ht Osiris 2002 Nov 02.5 03:32:09.32 -27:41:29.3 Ia bronze 0.90 phot-z 0.48 0.34
2002kb Denethor 2002 Dec 20.1 03:32:42.42 -27:50:25.4 CC gold 0.58 spectrum -0.20 -0.01
2002kc Bilbo 2002 Dec 21.5 03:32:34.72 -27:39:58.3 Ia gold 0.21 spectrum -0.85 -0.28
2002kd Frodo 2002 Dec 21.6 03:32:22.34 -27:44.26.9 Ia gold 0.74 spectrum -0.98 -3.13
2002ke Smeagol 2002 Dec 21.9 03:31:58.77 -27:45:00.7 CC bronze 0.58 spectrum -0.26 1.15
2002kh Balder 2003 Jan 04.3 12:36:16.78 +62:14:37.7 Ia bronze 0.71 phot-z 0.30 -1.20
2002ki Nanna 2003 Jan 04.6 12:37:28.37 +62:20:39.1 Ia gold 1.14 spectrum 0.00 -0.10
2002kl Agugux 2003 Feb 22.0 12:37:49.30 +62:14:06.1 CC silver 0.41 spectrum -0.45 0.15
2002lg Prometheus 2002 Jul 04.2 03:32:35.77 -27:47:58.8 Ia gold 0.66 spectrum -0.10 0.13
2003aj Inanna 2003 Feb 03.2 03:32:44.33 -27:55:06.4 Ia bronze 1.31 spectrum -0.08 -0.03
2003ak Gilgamesh 2003 Feb 03.2 03:32:46.90 -27:54:49.4 Ia gold 1.55 spectrum -0.39 0.28
2003al Enki 2003 Feb 05.7 03:32:05.39 -27:44:29.2 Ia silver 0.91 phot-z 0.07 -0.03
2003az Torngasak 2003 Feb 20.9 12:37:19.67 +62:18:37.5 Ia gold 1.27 spectrum -0.08 -0.06
2003ba Sedna 2003 Feb 21.0 12:36:15.88 +62:12:37.7 CC bronze 0.29 spectrum 0.09 -0.18
2003bb Raven 2003 Feb 21.6 12:36:24.47 +62:08:35.3 CC silver 0.95 spectrum -1.31 0.40
2003bc Michabo 2003 Feb 21.8 12:36:38.06 +62:09:53.3 CC silver 0.51 spectrum -0.55 -1.10
2003bd Anguta a 2003 Feb 22.0 12:37:25.06 +62:13:17.5 Ia gold 0.67 spectrum






2003be Qiqirn 2003 Feb 22.1 12:36:25.97 +62:06:55.6 Ia gold 0.64 spectrum 0.00 -0.12
2003dx Phidippides 2003 Apr 04.5 12:36:31.70 +62:08:48.7 CC bronze 0.46 phot-z 0.10 0.15
2003dy Borg 2003 Jan 02.8 12:37:09.14 +62:11:01.2 Ia gold 1.37 spectrum -0.35 0.25
2003dz Ashe 2003 Apr 04.8 12:36:39.91 +62:07:52.7 CC bronze 0.48 phot-z 0.00 -0.25
2003ea Connors 2003 Apr 05.7 12:37:12.04 +62:12:38.3 CC bronze 0.89 phot-z 0.15 0.00
2003eb McEnroe 2003 Apr 05.7 12:37:15.18 +62:13:34.6 Ia gold 0.92 spectrum -0.75 0.50
2003en Odin 2003 Jan 03.2 12:36:33.12 +62:13:48.1 Ia bronze 0.54 phot-z 0.10 0.07
2003eq Elvis 2003 May 24.7 12:37:48.34 +62:13:35.3 Ia gold 0.85 spectrum 0.10 -0.42
2003er Janice 2003 May 25.4 12:36:32.27 +62:07:35.2 CC silver 0.63 phot-z 0.70 -0.70
2003es Ramone 2003 May 25.5 12:36:55.39 +62:13:11.9 Ia gold 0.97 spectrum 0.30 -0.49
2003et Jimi 2003 May 25.7 12:35:55.87 +62:13:32.8 CC silver 0.83 phot-z 0.14 -0.50
2003eu Lennon 2003 May 25.7 12:36:05.90 +62:11:01.6 Ia silver 0.76 phot-z 0.30 -0.70
2003ew Jagger 2003 May 21.8 12:36:27.78 +62:11:25.1 CC bronze 0.66 phot-z -0.10 -0.21
2003N Loki 2003 Apr 04.7 12:37:09.14 +62:11:01.2 CC bronze 0.43 spectrum 0.20 0.00
2003lv Vilas 2003 Apr 04.7 12:37:28.89 +62:11:28.7 Ia silver 0.86 spectrum 0.00 0.00
Note. | Osets are given from the center of the host galaxy to supernova.
a No host galaxies were detected for SNe 2002fv and 2003bd to within the magnitude limits of the survey.
b SN 2002hs has at least two neighboring galaxies, the closest of which had a phot-z = 1.1, and the other had a spectroscopically measured z = 0:39.
Light-curve ts to the photometry showed that it was less consistent with any SN type at z  1:1 and more consistent with a SN Ib/c at z = 0:39.

30 L. -G. Strolger et al.
Table 2
HST Photometry
SN Filter JD + 2,452,000 Magnitude
2002fv F850LP 536.74 25.07 (0.06)
580.32 25.72 (0.11)
628.29 26.27 (0.18)
F775W 536.74 25.34 (0.06)
F606W 536.83 26.54 (0.06)
2002fy F850LP 490.30 23.77 (0.02)
538.20 25.23 (0.07)
579.72 26.40 (0.20)
F775W 490.32 24.37 (0.03)
538.19 26.06 (0.12)
F606W 490.30 26.15 (0.04)
538.18 28.16 (0.25)
2002fz F850LP 538.96 24.94 (0.06)
578.71 26.30 (0.19)
F775W 538.92 25.20 (0.05)
578.45 26.73 (0.21)
2002ga F850LP 488.72 25.90 (0.13)
539.65 24.50 (0.04)
578.95 26.18 (0.17)
628.70 26.79 (0.29)
F775W 488.70 27.50 (0.41)
539.65 25.26 (0.06)
628.70 28.90 (1.25)
F606W 488.64 27.87 (0.20)
539.65 26.42 (0.05)
628.70 29.0 (0.53)
2002hq F850LP 580.90 25.34 (0.08)
F775W 579.50 26.43 (0.11)
2002hs F850LP 580.52 25.27 (0.07)
F775W 580.37 26.05 (0.12)
F606W 580.32 26.77 (0.07)
2002ht F850LP 581.00 25.64 (0.10)
630.17 26.13 (0.16)
F775W 580.95 26.33 (0.15)
2002kb F850LP 488.72 24.62 (0.04)
539.79 25.10 (0.06)
578.95 25.60 (0.10)
F775W 488.70 24.83 (0.04)
539.78 25.17 (0.05)
578.80 25.84 (0.09)
F606W 488.65 25.02 (0.02)
539.71 27.01 (0.06)
2002ke F850LP 630.11 25.52 (0.09)
F775W 630.03 26.00 (0.11)
F606W 630.02 27.60 (0.15)
2002kh F850LP 642.27 24.62 (0.04)
F775W 642.27 25.64 (0.11)
F606W 642.22 28.4 (0.8)
2002kl F850LP 600.04 24.95 (0.08)
642.66 25.42 (0.09)
F775W 600.04 25.39 (0.06)
642.66 26.32 (0.14)
F606W 599.99 26.37 (0.05)

The Hubble Higher-z Supernova Search Project 31
Table 2|Continued
SN Filter JD + 2,452,000 Magnitude
642.57 27.81 (0.18)
2002lg F850LP 464.83 24.31 (0.04)
489.17 25.89 (0.13)
F775W 489.19 26.80 (0.22)
2003aj F850LP 666.3 25.60 (0.10)
673.31 25.40 (0.10)
688.3 26.50 (0.23)
F775W 673.30 26.60 (0.19)
2003al F850LP 676.02 24.59 (0.04)
F775W 676.10 25.56 (0.08)
F606W 675.89 28.95 (0.51)
2003ba F850LP 691.24 23.63 (0.02)
F775W 691.24 24.04 (0.02)
F606W 691.16 25.03 (0.02)
2003bb F850LP 692.11 25.59 (0.10)
F775W 692.10 25.34 (0.06)
732.84 26.17 (0.13)
F606W 692.45 26.30 (0.05)
2003bc F850LP 692.35 24.08 (0.03)
733.84 24.66 (0.04)
780.75 25.72 (0.11)
F775W 692.12 24.10 (0.02)
733.74 25.32 (0.06)
781.06 25.96 (0.11)
F606W 691.1 25.00 (0.02)
733.84 27.33 (0.12)
781.06 28.40 (0.31)
2003dx F850LP 732.85 25.27 (0.07)
F775W 732.84 25.76 (0.11)
F606W 732.81 28.37 (0.31)
2003dz F850LP 733.86 25.14 (0.07)
F775W 733.86 25.39 (0.06)
F606W 733.86 26.14 (0.04)
2003ea F850LP 783.72 25.40 (0.09)
F775W 783.66 26.00 (0.11)
F606W 783.65 27.50 (0.14)
2003en F850LP 642.31 25.60 (0.10)
F775W 642.30 26.10 (0.20)
F606W 642.28 27.30 (0.12)
2003er F850LP 784.51 23.22 (0.02)
F775W 784.44 23.11 (0.01)
F606W 784.61 23.21 (0.01)
2003et F850LP 784.94 25.38 (0.08)
F775W 784.83 25.54 (0.07)
F606W 784.92 25.90 (0.04)
2003eu F850LP 784.94 24.40 (0.04)
F775W 784.93 25.04 (0.05)
F606W 784.92 26.79 (0.08)
2003ew F850LP 646.86 24.21 (0.03)
690.57 24.36 (0.04)
F775W 646.85 24.83 (0.04)
690.49 25.05 (0.05)
F606W 646.85 26.92 (0.08)

32 L. -G. Strolger et al.
Table 2|Continued
SN Filter JD + 2,452,000 Magnitude
690.49 27.51 (0.14)
2003N F850LP 642.21 26.21 (0.18)
F775W 642.19 26.43 (0.16)
F606W 642.23 27.11 (0.10)
Note. | Magnitudes are in the Vega-based system.
Photometric errors are in parentheses.
Table 3
Likelihood Statistics
Statistic SFR Model e-folding e-folding w/ MCO G(; 0:5) G(; 0:2)
Max. Likelihood  M1 9:8 9:8 4.0 4.0
M2 9:8 8:2 3.2 3.2
95% Interval  M1 > 2:6 > 2:8 > 2:8 3:6 4:6
M2 > 2:2 > 2:0 > 2:0 2:4 3:8
Note. | 95% interval for narrow Gaussian models are determined symmetrically about
maximum likelihood value. All others are given for  > 95% condence interval. Values are
given in Gyrs.