The Astrophysical Journal Supplement Series, 185:32–84, 2009 November doi:10.1088/0067-0049/185/1/32
C
2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
FIRST-YEAR SLOAN DIGITAL SKY SURVEY-II SUPERNOVA RESULTS: HUBBLE DIAGRAM AND
COSMOLOGICAL PARAMETERS
Richard Kessler
1,2
, Andrew C. Becker
3
, David Cinabro
4
, Jake Vanderplas
3
, Joshua A. Frieman
1,2,5
, John Marriner
5
,
Tamara M. Davis
6,7
, Benjamin Dilday
8
, Jon Holtzman
9
, Saurabh W. Jha
8
, Hubert Lampeitl
10
, Masao Sako
11
,
Mathew Smith
10,12
, Chen Zheng
13
, Robert C. Nichol
10
, Bruce Bassett
12,14
, Ralf Bender
15
, Darren L. Depoy
16
,
Mamoru Doi
17,18
, Ed Elson
12
, Alexei V. Filippenko
19
, Ryan J. Foley
19,20
, Peter M. Garnavich
21
, Ulrich Hopp
15
,
Yutaka Ihara
17,22
, William Ketzeback
23
, W. Kollatschny
24
, Kohki Konishi
17
, Jennifer L. Marshall
16
,
Russet J. McMillan
23
, Gajus Miknaitis
25,5
, Tomoki Morokuma
26
, Edvard M
¨
ortsell
27
, Kaike Pan
23
, Jose Luis Prieto
28
,
Michael W. Richmond
29
, Adam G. Riess
30,31
, Roger Romani
13
, Donald P. Schneider
32
, Jesper Sollerman
7,33
,
Naohiro Takanashi
26
, Kouichi Tokita
17,22
, Kurt van der Heyden
34
, J. C. Wheeler
35
, Naoki Yasuda
36
,
and Donald York
1,37
1
Department of Astronomy and Astrophysics, The University of Chicago, 5640 South Ellis Ave., Chicago, IL 60637, USA; kessler@kicp.uchicago.edu
2
Kavli Institute for Cosmological Physics, The University of Chicago, 5640 South Ellis Ave., Chicago, IL 60637, USA
3
Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA
4
Department of Physics and Astronomy, Wayne State University, Detroit, MI 48202, USA
5
Center for Particle Astrophysics, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA
6
School of Mathematics and Physics, University of Queensland, QLD 4072, Australia
7
Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø, Denmark
8
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854, USA
9
Department of Astronomy, MSC 4500, New Mexico State University, P.O. Box 30001, Las Cruces, NM 88003, USA
10
Institute of Cosmology and Gravitation, Dennis Sciama Building, Burnaby Road, University of Portsmouth, Portsmouth PO1 3FX, UK
11
Department of Physics and Astronomy, University of Pennsylvania, 203 South 33rd Street, Philadelphia, PA 19104, USA
12
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
13
Kavli Institute for Particle Astrophysics & Cosmology, Stanford University, Stanford, CA 94305-4060, USA
14
South African Astronomical Observatory, P.O. Box 9, Observatory 7935, South Africa
15
Universit
¨
ats-Sternwarte, Ludwig-Maximilians Universit
¨
at M
¨
unchen, Germany
16
Department of Physics, Texas A&M University, College Station, TX 77843, USA
17
Institute of Astronomy, University of Tokyo, 2-21-1 Osawa, Mitaka-shi, Tokyo, 181-0015, Japan
18
Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8568, Japan
19
Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA
20
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
21
University of Notre Dame, 225 Nieuwland Science, Notre Dame, IN 46556-5670, USA
22
Department of Astronomy, Graduate School of Science, University of Tokyo, Bunkyo-Ku, Tokyo, 113-0033, Japan
23
Apache Point Observatory, P.O. Box 59, Sunspot, NM 88349, USA
24
Institut f
¨
ur Astrophysik, Universit
¨
at G
¨
ottingen, Friedrich-Hund Platz 1, D-37077 G
¨
ottingen, Germany
25
Center for Neighborhood Technology, 2125 W. North Ave., Chicago, IL 60647, USA
26
National Astronomical Observatory of Japan, Mitaka, 181-8588, Japan
27
Department of Physics, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden
28
Department of Astronomy, Ohio State University, 140 West 18th Ave., Columbus, OH 43210-1173, USA
29
Physics Department, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, NY 14623-5603, USA
30
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
31
Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
32
Department of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA
33
The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden
34
Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa
35
Department of Astronomy, McDonald Observatory, University of Texas, Austin, TX 78712, USA
36
Institute for Cosmic Ray Research, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8582, Japan
37
Enrico Fermi Institute, University of Chicago, 5640 South Ellis Ave., Chicago, IL 60637, USA
Received 2009 April 13; accepted 2009 August 4; published 2009 October 14
ABSTRACT
We present measurements of the Hubble diagram for 103 Type Ia supernovae (SNe) with redshifts 0.04 <z<0.42,
discovered during the first season (Fall 2005) of the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey. These
data fill in the redshift “desert” between low- and high-redshift SN Ia surveys. Within the framework of the mlcs2k2
light-curve fitting method, we use the SDSS-II SN sample to infer the mean reddening parameter for host galaxies,
R
V
= 2.18 ± 0.14
stat
± 0.48
syst
, and find that the intrinsic distribution of host-galaxy extinction is well fitted
by an exponential function, P (A
V
) = exp(−A
V
/τ
V
), with τ
V
= 0.334 ± 0.088 mag. We combine the SDSS-II
measurements with new distance estimates for published SN data from the ESSENCE survey, the Supernova Legacy
Survey (SNLS), the Hubble Space Telescope (HST), and a compilation of Nearby SN Ia measurements. A new feature
in our analysis is the use of detailed Monte Carlo simulations of all surveys to account for selection biases, including
those from spectroscopic targeting. Combining the SN Hubble diagram with measurements of baryon acoustic
oscillations from the SDSS Luminous Red Galaxy sample and with cosmic microwave background temperature
anisotropy measurements from the Wilkinson Microwave Anisotropy Probe, we estimate the cosmological
parameters w and Ω
M
, assuming a spatially flat cosmological model (FwCDM) with constant dark energy equation
of state parameter, w. We also consider constraints upon Ω
M
and Ω
Λ
for a cosmological constant model (ΛCDM)
with w =−1 and non-zero spatial curvature. For the FwCDM model and the combined sample of 288 SNe Ia,
32
No. 1, 2009 FIRST-YEAR SLOAN DIGITAL SKY SURVEY-II SUPERNOVA RESULTS 33
we find w =−0.76 ± 0.07(stat)±0.11(syst), Ω
M
= 0.307 ±0.019(stat)±0.023(syst) using mlcs2k2 and
w =−0.96 ± 0.06(stat) ± 0.12(syst), Ω
M
= 0.265 ± 0.016(stat) ± 0.025(syst) using the salt-ii fitter. We
trace the discrepancy between these results to a difference in the rest-frame UV model combined with a different
luminosity correction from color variations; these differences mostly affect the distance estimates for the SNLS
and HST SNe. We present detailed discussions of systematic errors for both light-curve methods and find that
they both show data-model discrepancies in rest-frame U band. For the salt-ii approach, we also see strong
evidence for redshift-dependence of the color-luminosity parameter (β). Restricting the analysis to the 136 SNe Ia
in the Nearby+SDSS-II samples, we find much better agreement between the two analysis methods but with larger
uncertainties: w =−0.92 ±0.13(stat)
+0.10
−0.33
(syst) for mlcs2k2 and w =−0.92 ± 0.11(stat)
+0.07
−0.15
(syst) for salt-ii.
Key words: cosmological parameters – cosmology: observations – distance scale – methods: data analysis –
supernovae: general – surveys
Online-only material: color figures, machine-readable tables
1. INTRODUCTION
Ten years ago, measurements of the Hubble diagram of
Type Ia supernovae (SNe) provided the first direct evidence for
cosmic acceleration (Riess et al. 1998; Perlmutter et al. 1999).
In the intervening decade, dedicated SN surveys have brought
tremendous improvements in both the quantity and quality of
SN Ia data, and SNe Ia remain the method of choice for precise
relative distance determination over cosmological scales (e.g.,
Leibundgut 2001; Filippenko 2005). We now have in hand large,
homogeneously selected samples of SNe Ia with relatively dense
time-sampling in multiple passbands at redshifts z 0.3, most
recently from the ESSENCE project (Miknaitis et al. 2007;
Wood-Vasey et al. 2007) and the Supernova Legacy Survey
(SNLS; Astier et al. 2006), augmented by smaller samples
from the Hubble Space Telescope (HST) that extend to higher
redshift (Garnavich et al. 1998; Knop et al. 2003; Riess et al.
2004, 2007). These data have confirmed and sharpened the
evidence for accelerated expansion. Cosmic acceleration is most
commonly attributed to a new energy-density component known
as dark energy (for a review, see Frieman et al. 2008a). The
recent SN measurements, in combination with measurements
of the baryon acoustic oscillation (BAO) feature in galaxy
clustering and of the cosmic microwave background (CMB)
anisotropy, have provided increasingly precise constraints on
the density, Ω
DE
, and equation of state parameter, w, of dark
energy.
Despite these advances, a number of concerns remain about
the robustness of current SN cosmology constraints. The SN Ia
Hubble diagram is constructed from combining low- and high-
redshift SN samples that have been observed with a variety of
telescopes, instruments, and photometric passbands. Photomet-
ric offsets between these samples are highly degenerate with
changes in cosmological parameters, and these offsets could be
hidden in part because there is a gap or “redshift desert” between
the low-redshift (z 0.1) SNe, found with small-aperture,
wide-field telescopes, and the high-redshift (z 0.3) SNe
discovered by large-aperture telescopes with relatively narrow
fields. In addition, the low-redshift SN measurements that are
used both to anchor the Hubble diagram and to train SN distance
estimators were themselves compiled from combinations of
several surveys using different telescopes, instruments, and se-
lection criteria. Increasing the robustness of the cosmological re-
sults calls for larger SN samples with continuous redshift cover-
age of the Hubble diagram; it also necessitates high-quality data,
with homogeneously selected, densely sampled, multi-band SN
light curves and well-understood photometric calibration.
The Sloan Digital Sky Survey-II Supernova Survey (SDSS-II
SN Survey; Frieman et al. 2008b), one of the three components
of the SDSS-II project, was designed to address both the paucity
of SN Ia data at intermediate redshifts and the systematic
limitations of previous SN Ia samples, thereby leading to more
robust constraints upon the properties of the dark energy. Over
the course of three three-month seasons, the SDSS-II SN Survey
discovered and measured well-sampled, multi-band light curves
for roughly 500 spectroscopically confirmed SNe Ia in the
redshift range 0.01 z 0.45. This data set fills in the redshift
desert and for the first time includes both low- and high-redshift
SN measurements in a single survey. The survey takes advantage
of the extensive database of reference images, object catalogs,
and photometric calibration previously obtained by the SDSS
(for a description of the SDSS; see York et al. 2000).
In this paper, we present the Hubble diagram based on
spectroscopically confirmed SNe Ia from the first full season
(Fall 2005) of the SDSS-II SN Survey. To derive cosmological
results, we include information from BAO (Eisenstein et al.
2005) and CMB measurements (Komatsu et al. 2009), and we
also combine our data with our own analysis of public SN Ia
data sets at lower and higher redshifts. We fit the SN Ia light
curves with two models, mlcs2k2 (Jha et al. 2007) and salt-ii
(Guy et al. 2007). We use the publicly available salt-ii software
with minor modifications, but we have made a number of
improvements to the implementation of the mlcs2k2 method,
as described in Section 5.
Two companion papers explore related analyses with the same
SN data sets. Lampeitl et al. (2009) combine the SDSS-II SN
data with different BAO constraints and with measurements of
redshift-space distortions and of the Integrated Sachs–Wolfe
effect to derive joint constraints on dark energy from low-
redshift (z<0.4) measurements only; they also explore the
consistency of the SN and BAO distance scales. Sollerman et al.
(2009) use SN, BAO, and CMB measurements to constrain
cosmological models with a time-varying dark energy equation
of state parameter as well as more exotic models for cosmic
acceleration. In all three papers, we use a consistent analysis
of the SN data. Differences in cosmological inferences are
attributable to differences in (1) the SN data included, (2) the
other cosmological data sets included, and (3) the cosmological
model space considered.
The outline of the paper is as follows. In Section 2, we briefly
describe the operation and data processing for the SDSS-II SN
Survey, which have been more extensively described in Sako
et al. (2008). In Section 3, we summarize the spectroscopic
analysis leading to final redshift and SN-type determinations
(Zheng et al. 2008) and the photometric analysis leading to final
SN flux measurements (Holtzman et al. 2008) for SDSS-II SNe.
In Section 4, we present the SN samples and selection criteria
applied to the light-curve data. We describe and compare the
34 KESSLER ET AL. Vol. 185
mlcs2k2 and salt-ii methods in Section 5. In Section 6,we
describe detailed Monte Carlo simulations for the SDSS-II SN
Survey and other SN data sets that we use to determine survey
efficiencies and their dependences on SN luminosity, extinction,
and redshift. Modeling of the survey efficiencies is needed to
correct for selection biases that affect SN distance estimates. In
Section 7, we use a larger spectroscopic+photometric SDSS-II
SN sample to determine host-galaxy dust properties that are used
in the mlcs2k2 fits. In particular, we present new measurements
of the mean dust parameter, R
V
, and of the extinction (A
V
)dis-
tribution. In Section 8, we describe the cosmological likelihood
analysis, which combines the SN Ia Hubble diagram with BAO
and CMB measurements. In Section 9, we present a detailed
study of systematic errors, showing how uncertainties in model
parameters and in calibrations impact the results. In Section 10,
we discuss the SN Hubble diagrams using the mlcs2k2 and
salt-ii fitters and derive constraints on cosmological param-
eters. We provide a detailed comparison of the mlcs2k2 and
salt-ii results in Section 11, and we conclude in Section 12.
Appendices provide details on the methods for warping the
SN Ia spectral template for K-corrections, modeling the filter
passbands for the Nearby SN Ia sample, determining the mag-
nitudes of the primary photometric standard stars, extracting
the distribution of host-galaxy dust extinction from the SDSS-II
sample, and estimating error contours that include systematic
uncertainties. They also include discussion of the scatter in the
SDSS-II Hubble diagram and of the translation of the salt-ii
model into the mlcs2k2 framework.
2. SDSS-II SUPERNOVA SURVEY
The scientific goals, operation, and basic data processing for
the SDSS-II SN Survey are described in Frieman et al. (2008b),
and details of the SN search algorithms and spectroscopic
observations are given in Sako et al. (2008). Here we provide
a brief summary of the Fall 2005 campaign, in order to set the
context for the data analysis.
The SDSS-II SN Survey primary instrument was the SDSS
CCD camera (Gunn et al. 1998) mounted on a dedicated 2.5 m
telescope (Gunn et al. 2006) at Apache Point Observatory
(APO), New Mexico. The camera obtains, nearly simultane-
ously, images in five broad optical bands: ugriz (Fukugita et al.
1996). The camera was used in the time-delay-and-integrate
(TDI, or drift scan) mode, which provides efficient sky cov-
erage. The SN Survey scanned at the normal (sidereal) SDSS
survey rate, which yielded 55 s integrated exposures in each
passband; the instrument covered the sky at a rate of approxi-
mately 20 deg
2
hr
−1
.
On most of the usable observing nights in the period 1
September through 2005 November 30, the SDSS-II SN Survey
scanned a region (designated stripe 82) centered on the celestial
equator in the Southern Galactic Hemisphere that is 2.
◦
5wideand
runs between right ascensions of 20
hr
and 4
hr
, covering a total
area of 300 deg
2
. Due to gaps between the CCD columns, on a
given night slightly more than half of the declination range of the
stripe was imaged; on succeeding nights, the survey alternated
between the northern (N) and southern (S) declination strips
of stripe 82 (see Stoughton et al. 2002 for a description of
the SDSS observing geometry). Accounting for CCD gaps, bad
weather, nearly full Moon, and other observing programs, a
given region was imaged on average every four to five nights
under a variety of conditions. This relatively high cadence
enabled us to obtain well-sampled light curves, typically starting
well before peak light.
At the end of each night of imaging, the SN data were
processed using a dedicated 20-CPU computing cluster at
APO. Images were processed through the PHOTO photometric
reduction pipeline to produce corrected u, g, r, i, z frames
(Lupton et al. 2001; Ivezi
´
cetal.2004), each with an astrometric
solution (Pier et al. 2003), point-spread-function (PSF) map, and
zero point. A co-added template image, consisting of typically
eight stacked images taken in previous years, was matched to
the new image and subtracted from it. Subtracted gri images
were searched for pixel clusters with an excess flux (roughly
3σ ) above the noise in the subtracted image, and a position and
total PSF flux were assigned for each significant detection. We
positionally matched detections in multiple passbands: objects
are detections in at least two of the three gri passbands with a
displacement of less than 0.
8 between detections in each filter.
This displacement cut was chosen to ensure high efficiency
for objects with low signal to noise. The g and r exposures
of a given object were taken five minutes apart, enabling
many fast asteroids to be removed by the 0.
8 requirement.
Finally, a catalog of 10
5
previously detected variables (mainly
stars and active galactic nuclei (AGNs)) and 4 million stars
(r<21.5) was used to reject detections within 1
of any object
in the catalog; nearly 40,000 such detections were automatically
vetoed during the Fall 2005 survey.
During the season, 20
× 20
cutouts of the resulting
∼140,000 object images were visually scanned by humans,
38
typically within 24 hr of when the data were obtained. The hu-
man scanning was done to eliminate objects that were clearly
not SNe, such as unsubtracted diffraction spikes, other subtrac-
tion artifacts, and obvious asteroids. To monitor the software
pipelines and human scanning efficiency, “fake” SNe were in-
serted on top of galaxies in the images during processing. Ap-
proximately 11,400 of the objects were tagged by a scanner as a
possible SN candidate. Nearly 60% of the candidates appeared
only once during the survey; most of these are likely slow-
moving solar system objects. After a night of observations, each
candidate light curve (in g, r, i) was updated and compared with
a set of SN light-curve templates that include SNe Ia as a func-
tion of redshift, intrinsic luminosity, and extinction, as well as
non-Ia SN types. Light curves that matched best to an SN Ia
template (at any reasonable redshift, luminosity, and extinction)
were preferentially scheduled for spectroscopic follow-up ob-
servations. Candidates with r-band magnitude r 20.5were
given highest priority for follow-up, regardless of photometric
SN type; for SNe Ia, this magnitude cut corresponds roughly to
redshifts z<0.15. For fainter SN Ia candidates, spectroscopic
priority was given to candidates with the best chance of acquir-
ing a useful spectrum. In order of importance, the prioritization
criteria were: (1) SN is well-separated ( 1
) from the core of
its host galaxy, (2) reasonable SN/galaxy brightness contrast
based on visual inspection, and (3) SN host galaxy is relatively
red (early-type). In most cases, a detection in at least two epochs
was required before a spectrum was obtained.
Spectra of SN candidates and, where possible, their host
galaxies were obtained in 2005 September–December with
a number of telescopes (Frieman et al. 2008b; Zheng et al.
2008): the Hobby-Eberly 9.2 m at McDonald Observatory,
the Astrophysical Research Consortium 3.5-meter at APO, the
Subaru 8.2-meter on Mauna Kea, the Hiltner 2.4 m at MDM
Observatory, the 4.2 m William Herschel Telescope on La
38
During the 2006 season we implemented more aggressive software cuts that
reduced the number of objects scanned by over an order of magnitude.
No. 1, 2009 FIRST-YEAR SLOAN DIGITAL SKY SURVEY-II SUPERNOVA RESULTS 35
Palma, and the Keck 10 m on Mauna Kea. Approximately 90%
of the SN Ia candidates that were spectroscopically observed
were confirmed as SNe Ia.
As noted below (Section 3.1), 146 spectroscopically observed
candidates from 2005 were classified as definitive or possible
SNe Ia based on analysis of their spectra. For these candidates,
there are a total of more than 2000 photometric epochs, where
each epoch corresponds to a measurement (not necessarily a
detection) in the ugriz passbands within a time window of −15
days to +60 days relative to peak brightness in the SN rest-
frame. About half of the epochs were recorded in “photometric”
conditions, defined as no moon, PSF less than 1.
7, and no clouds
as indicated by the SDSS cloud camera, which monitors the sky
at 10 μm (Hogg et al. 2001). Another 30% of the measurements
were recorded in non-photometric (but moonless) conditions.
The remaining 20% of the measurements were taken with the
moon above the horizon.
3. SDSS SN SPECTROSCOPIC AND PHOTOMETRIC
REDUCTION
For each SN candidate found during the survey, the on-
mountain software pipeline described in Section 2 delivered pre-
liminary photometric measurements. Similarly, spectroscopic
observations were reduced in near-real time so that estimates of
SN type and redshift could be made. Although these initial mea-
surements were sufficient for discovering and confirming SNe,
for the final analysis and sample selection we require more ac-
curate photometry (Holtzman et al. 2008) and a more uniform
spectroscopic analysis (Zheng et al. 2008). This section briefly
describes these techniques.
3.1. Supernova Typing and Redshift Determination
After the finish of the Fall 2005 season, all of the SN
spectra were processed with IRAF (Tody 1993). Classification
of the reduced SN spectra was aided by the IRAF package
rvsao.xcsao (Tonry & Davis 1979), which cross-correlates
the spectra with libraries of SN spectral templates and searches
for significant peaks. Details of this analysis are described in
Zheng et al. (2008). About half of the SN spectra had an
excellent template match, while the other half required more
human judgment for the SN typing. Based on this analysis,
130 candidates were classified as confirmed SNe Ia and 16
candidates were classified as probable SNe Ia.
For 29 of these 146 candidates, we have used the SDSS
host-galaxy spectroscopic redshift as reported in the SDSS
DR4 database; typical redshift uncertainties are 1–2 ×10
−4
.
For SN 2005hj, a host-galaxy spectroscopic redshift and its
uncertainty were obtained by Quimby et al. (2007). For 82
of the candidates that do not have a host spectroscopic red-
shift in the DR4 database, we use the redshift from host-galaxy
spectral features obtained with our own spectroscopic obser-
vations. The redshift precision in those cases is estimated to
be 0.0005, the rms difference between our host-galaxy red-
shifts and those measured by the SDSS spectroscopic survey
(DR4) for a sample in which both redshifts are available. For
the remaining 34 candidates, our redshift estimate is based on
spectroscopic features of the SNe, with an estimated uncer-
tainty of 0.005, the rms spread between the SN redshifts and
host-galaxy redshifts. In summary, 77% of the spectroscopically
confirmed and probable SNe Ia have spectroscopic redshifts de-
termined from host-galaxy features, while the rest have redshifts
based on SN spectral features. The redshifts are determined in
the heliocentric frame and then transformed to the CMB frame
as described in Section 8.
The redshift distribution for the 130 confirmed SNe Ia from
the 2005 season is shown below in Figure 2(e). The relative
deficit of confirmed SNe at redshifts between 0.15 and 0.25 is
due to the finite spectroscopic resources that were available for
the Fall 2005 campaign and to the relative priorities given to
low- and high-redshift candidates for the different telescopes
(Sako et al. 2008). Subsequently, host-galaxy redshifts have
been obtained for most of the “missing” SN Ia candidates with
SN Ia like light curves in this redshift range. These photometri-
cally identified (but spectroscopically unconfirmed) candidates
with host-galaxy redshifts are used in the determination of host-
galaxy dust properties (Section 7), but we do not include them
in the Hubble diagram for this analysis. Compared to the Fall
2005 season, spectroscopic observations during the 2006 and
2007 seasons were more complete around redshifts z ∼ 0.2.
3.2. Supernova Photometry
To achieve precise and reliable SN photometry, we developed
a new technique called “Scene Model Photometry” (SMP) that
optimizes the determination of SN and host–galaxy fluxes. This
method and the Fall 2005 SN photometry results are described
in detail in Holtzman et al. (2008).
The basic approach of SMP is to simultaneously model the
ensemble of survey images covering an SN location as a time-
varying point source (the SN) and sky background plus time-
independent galaxy background and nearby calibration stars,
all convolved with a time-varying PSF. The calibration stars
are taken from the SDSS catalog for stripe 82 produced by
Ivezi
´
cetal.(2007). The fitted parameters are SN position,
SN flux for each epoch and passband, and the host host-
galaxy intensity distribution in each passband. The galaxy
model for each passband is a 20 × 20 grid (with a grid scale
set by the CCD pixel scale, 0.
4 × 0.
4) in sky coordinates,
and each of the 400 × 5 = 2000 galaxy intensities is an
independent fit parameter. As there is no pixel re-sampling or
image convolution, the procedure yields correct statistical error
estimates. Holtzman et al. (2008) describes the rigorous tests that
were carried out to validate the accuracy of SMP photometry
and of the error estimates.
Although we have obtained additional imaging on other
telescopes for a subsample of the confirmed SNe Ia, only
photometry from the SDSS 2.5 m telescope is used in this
analysis. Figure 1 shows four representative SDSS-II SN Ia
light curves processed through SMP and provides an indication
of the typical sampling cadence and signal to noise as a function
of redshift.
The fluxes and magnitudes returned by SMP are in the native
SDSS system (Ivezi
´
cetal.2007). The SDSS photometric
system is nominally on the AB system, but the native flux
in each filter differs from that of a true AB system by a
small amount. AB magnitudes are obtained by adding the
AB offsets in Table 1 to the native magnitudes. The offsets
are determined by comparing photometric measurements of
the HST standard solar analogs P3330E, P177D, and P041C
with synthetic magnitudes based on the published HST spectra
(Bohlin 2007) and SDSS filter bandpasses. Since the standard
stars are too bright to be measured directly with the SDSS 2.5 m
telescope, the measurements are taken with the 0.5 m SDSS
Photometric Telescope (the PT) and transformed to the native
system of the SDSS telescope. The technique of transferring
the PT magnitudes to the native SDSS system is identical to
36 KESSLER ET AL. Vol. 185
0
1000
2000
0
1000
2000
SN 2005ff z=0.09
g
r
i
T
obs
- 53634.7
Fl
u
x
0
1000
2000
-20-100 102030405060
0
200
400
600
0
200
400
600
800
SN 2005fb z=0.18
g
r
i
T
obs
- 53632.8
Flux
0
200
400
600
-20-10 0 102030405060
0
100
200
0
100
200
300
SN 2005fr z=0.29
g
r
i
T
obs
- 53633.4
Fl
ux
0
100
200
-20-10 0 102030405060
0
25
50
75
0
50
100
150
SN 2005gq z=0.39
g
r
i
T
obs
- 53646
Flux
0
100
200
-20-10 0 102030405060
Figure 1. Light curves for four SDSS-II SNe Ia at different redshifts: SN 2005ff at z = 0.09, SN 2005fb at z = 0.18, SN 2005fr at z = 0.29, and SN 2005gq at
z = 0.39. The passbands are SDSS g (top), r (middle), and i (bottom). Points are the SMP flux measurements (flux = 10
(11−0.4m)
,wherem is the SN magnitude) with
±1σ photometric errors indicated. Solid curves show the best-fit mlcs2k2 model fits (see Section 5.1), and dashed curves give the ±1σ error bands on the model fits.
The Modified Julian Date (MJD) under each set of light curves is the fitted time of peak brightness for the rest-frame B band.
(A color version of this figure is available in the online journal.)
Tab le 1
AB Offsets and Central Wavelength Uncertainties for the SDSS Filters
AB Offset (mag) and Uncertainty (Å) on
SDSS Filter Its Uncertainty
a
Central Wavelength
u −0.037 ±0.014 8
g +0.024 ±0.009 7
r +0.005 ±0.009 16
i +0.018 ±0.009 25
z +0.016 ±0.010 38
Note.
a
Errors account for uncertainties in the central wavelengths of the SDSS
filters.
that used to obtain the SDSS photometric calibration (Tucker
et al. 2006). The uncertainty in the AB offsets is estimated to be
0.003, 0.004, 0.004, 0.007, 0.010 mag (for u, g, r, i, z) based on
the internal consistency of the three standard solar analogs. The
uncertainties given in Table 1 are larger, since they also account
for the ∼10 Å uncertainties in the central wavelengths (given in
the same table) of the SDSS filters.
4. SUPERNOVA SAMPLE SELECTION
In this section, we describe the light-curve selection criteria
used to define the SN Ia samples. To minimize systematic
errors associated with analysis methods and assumptions, we
perform a nearly uniform analysis on data from SDSS-II,
the published data from ESSENCE (Wood-Vasey et al. 2007;
hereafter WV07), SNLS (Astier et al. 2006), HST (Riess et al.
2007), and a Nearby SN Ia sample collected over a decade from
several surveys and a number of telescopes (Jha et al. 2007;
hereafter JRK07). Although these data samples are analyzed
in a homogeneous fashion, we present more details about the
SDSS-II analysis since these data are presented here for the first
time and, more importantly, because we use the SDSS-II sample
in Section 7 to make inferences about the SN Ia population that
we apply to all the data samples.
Light curves with good time sampling and good signal to
noise are needed to yield reliable distance estimates. We there-
fore apply stringent selection cuts to all five photometric data
samples used in this analysis. The cuts are also chosen to define
samples whose selection functions can be reliably modeled with
the Monte Carlo simulations described in Section 6. In future
analyses the cuts will be further refined based on studies with
simulated samples.
We first present the selection cuts we have applied and then
briefly discuss the rationale for each of them. Defining T
rest
as the rest-frame time, such that T
rest
= 0 corresponds to peak
brightness in rest-frame B band according to mlcs2k2, we select
for inclusion in the cosmology analysis SN Ia light curves that
satisfy the following criteria.
1. For SDSS-II, ESSENCE, SNLS, and HST, at least one
measurement is required before peak brightness (T
rest
< 0
days); for the Nearby sample, at least one measurement
is required with T
rest
< +5 days. The requirement on the
Nearby sample is relaxed, because nearly half the sample
would be rejected by the more stringent cut of T
rest
<
0 days.
2. At least one measurement with T
rest
> +10 days.
3. At least five measurements with −15 <T
rest
< +60 days.
4. At least one measurement with signal-to-noise ratio (S/N)
above 5 for: each of SDSS g, r, and i; both SNLS r and
i (no requirement on g, z); HST F814W_WFPC2 and at
least one other HST passband. For the ESSENCE sample,
we adopt the cuts from WV07: at least one measurement at
T
rest
< +4 days that has S/N > 5, at least one measurement
at T
rest
> +9 days that has S/N > 5, and at least eight
total measurements with S/N > 5. Since the Nearby SN Ia
sample includes only events with high S/N, no S/N
requirement is needed for that sample.
5.
P
fit
> 0.001, where P
fit
is the mlcs2k2 light-curve fit
probability based on the χ
2
per degree of freedom (see
Section 5.1).
