NEW CONSTRAINTS ON
M
,
, AND w FROM AN INDEPENDENT SET OF 11 HIGH-REDSHIFT
SUPERNOVAE OBSERV ED WITH THE HUBBLE SPACE TELESCOPE
1
R. A. Knop,
2,3,4
G. Aldering,
4,5
R. Amanullah,
6
P. Astier,
7
G. Blanc,
5,7
M. S. Burns,
8
A. Conley,
5,9
S. E. Deustua,
5,10
M. Doi,
11
R. Ellis,
12
S. Fabbro,
4,13
G. Folatelli,
6
A. S. Fruchter,
14
G. Garavini,
6
S. Garmond,
5,9
K. Garton,
8
R. Gibbons,
5
G. Goldhaber,
5,9
A. Goobar,
6
D. E. Groom,
4,5
D. Hardin,
7
I. Hook,
15
D. A. Howell,
5
A. G. Kim,
4,5
B. C. Lee,
5
C. Lidman,
16
J. Mendez,
17,18
S. Nobili,
6
P. E. Nugent,
4,5
R. Pain,
7
N. Panagia,
14
C. R. Pennypacker,
5
S. Perlmutter,
5
R. Quimby,
5
J. Raux,
7
N. Regnault,
5,19
P. Ruiz-Lapuente,
18
G. Sainton,
7
B. Schaefer,
20
K. Schahmaneche,
7
E. Smith,
2
A. L. Spadafora,
5
V. Stanishev,
6
M. Sullivan,
12,21
N. A. Walton,
22
L. Wang,
5
W. M. Wood-Vasey,
5,9
and N. Yasuda
23
(The Supernova Cosmology Project)
Received 2003 May 24; accepted 2003 July 16
ABSTRACT
We report measurements of
M
,
, and w from 11 supernovae (SNe) at z ¼ 0:36 0:86 with high-quality
light curves measured using WFPC2 on the Hubble Space Telescope (HST). This is an independent set of
high-redshift SNe that confirms previous SN evidence for an accelerating universe. The high-quality light
curves available from photometry on WFPC2 make it possible for these 11 SNe alone to provide measure-
ments of the cosmological parameters comparable in statistical weight to the previous results. Combined with
earlier Supernova Cosmology Project data, the new SNe yield a measurement of the mass density
M
¼ 0:25
þ0:07
0:06
ðstatisticalÞ0:04 (identified systematics), or equivalently, a cosmological constant of
¼
0:75
þ0:06
0:07
ðstatisticalÞ0:04 (identified systematics), under the assumptions of a flat universe and that
the dark energy equation-of-state parameter has a constant value w ¼1. When the SN results are combined
with independent flat-universe measurements of
M
from cosmic microwave background and galaxy redshift
distortion data, they provide a measurement of w ¼1:05
þ0:15
0:20
ðstatisticalÞ0:09 (identified systematic), if
w is assumed to be constant in time. In addition to high-precision light-curve measurements, the new data
offer greatly improved color measurements of the high-redshift SNe and hence improved host galaxy extinc-
tion estimates. These extinction measurements show no anomalous negative E(BV ) at high redshift. The
precision of the measurements is such that it is possible to perform a host galaxy extinction correction directly
for individual SNe without any assumptions or priors on the parent E(BV ) distribution. Our cosmological
fits using full extinction corrections confirm that dark energy is required with Pð
> 0Þ > 0:99, a result
consistent with previous and current SN analyses that rely on the identification of a low-extinction subset or
prior assumptions concerning the intrinsic extinction distribution.
Subject headings: cosmological parameters — cosmology: observations — supernovae: general
1
Based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated
by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs
GO-7336, GO-7590, and GO-8346. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partner-
ship among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory
was made possible by the generous financial support of the W. M. Keck Foundation. Based in part on observations obtained at the WIYN Observatory, which
is a joint facility of the University of Wisconsin at Madison, Indiana University, Yale University, and the National Optical Astronomy Observatory. Based in
part on observations made with the European Southern Observatory telescopes (ESO programs 60.A-0586 and 265.A-5721). Based in part on observations
made with the Canada-France-Hawaii Telescope, operated by the National Research Council of Canada, le Centre National de la Recherche Scientifique de
France, and the University of Hawaii.
2
Department of Physics and Astronomy, Vanderbilt University, P.O. Box 1803, Station B, Nashville, TN 37240.
3
Visiting Astronomer, Kitt Peak National Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities
for Research in Astronomy (AURA), Inc., under cooperative agreement with the National Science Foundation.
4
Visiting Astronomer, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of
Universities for Research in Astronomy (AURA), Inc., under cooperative agreement with the National Science Foundation.
5
E. O. Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720.
6
Department of Physics, Stockholm University, SCFAB, S-106 91 Stockholm, Sweden.
7
Laboratoire de Physique Nucle
´
aire et de Haute Energies, CNRS-IN2P3, University of Paris VI and VII, Paris, France.
8
Colorado College, 14 East Cache La Poudre Street, Colorado Springs, CO 80903.
9
Department of Physics, University of California at Berkeley, 366 LeConte Hall, Berkeley, CA 94720-7300.
10
American Astronomical Society, 2000 Florida Avenue, NW, Suite 400, Washington, DC 20009.
11
Department of Astronomy, and Research Center for the Early Universe, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
12
California Institute of Technology, East California Boulevard, Pasadena, CA 91125.
13
Centro, Multidisiplinar de Astrofı
´
sica, Instituto Superior Te
´
cnico, P-1300 Lisbon, Portugal.
14
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218.
15
Department of Physics, University of Oxford, Nuclear and Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, UK.
16
European Southern Observatory, St. Alonso de Co
´
rdova 3107, Vitacura, Casilla 19001, Santiago 19, Chile.
17
Isaac Newton Group of Telescopes, Apartado de Correos 321, Santa Cruz de La Palma, E-38780 Canary Islands, Spain.
18
Department of Astronomy, University of Barcelona, E-08028 Barcelona, Spain.
19
Now at Laboratoire Leprince-Ringuet, CNRS-IN2P3, Ecole Polytechnique, Palaiseau, France.
20
Department of Astronomy, University of Texas at Austin, RLM 15.308, Austin, TX 78712.
21
Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK.
22
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK.
23
National Astronomical Observatory of Japan, 2-21-1, Ohsawa, Mitaka, Tokyo 181-8588, Japan.
The Astrophysical Journal, 598:102–137, 2003 November 20
# 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
102
1. INTRODUCTION
Five years ago, the Supernova Cosmology Project (SCP)
and the High-z Supernova Search Team both presented
studies of distant Type Ia supernovae (SNe Ia) in a series of
reports, which gave strong evidence for an acceleration of
the universe’s expansion, and hence for a nonzero cosmo-
logical constant, or dark energy density (Perlmutter et al.
1998, 1999, hereafter P99; Garnavich et al. 1998a; Schmidt
et al. 1998; Riess et al. 1998; for a revie w see Perlmutter &
Schmidt 2003). These results ruled out a flat, matter-
dominated (
M
¼ 1,
¼ 0) universe. For a flat universe,
motivated by inflation theory, these studi es yielded a value
for the cosmological constant of
’ 0:7. Even in the
absence of assumptions about the geometry of the universe,
the SN measurements indicate the existence of dark energy
with greater than 99% confidence.
The SN results combined with observations of the power
spectrum of the cosmic microwave background (CMB; e.g.,
Jaffe et al. 2001; Bennett et al. 2003; Spergel et al. 2003), the
properties of massive clusters (e.g., Turner 2001; Allen,
Schmidt, & Fabian 2002; Bahcall et al. 2003), and dynami-
cal redshift-space distortions (Hawkins et al. 2002) yield a
consistent picture of a flat universe with
M
’ 0:3 and
’ 0:7 (Bahcall et al. 1999). Each of these measurements
is sensitive to different combinat ions of the parameters;
hence, they complement each other. Moreover, because
there are three different measurements of two parameters,
the combination provides an important consistency check.
While the current observations of galaxy clusters and
dynamics, as well as of high-redshift SNe, primarily probe
the ‘‘ recent ’’ universe at redshifts of z < 1, the CMB meas-
urements probe the early universe at z 1100. That consis-
tent results are obtained by measurements of vastly different
epochs of the universe’s history suggests a vindication of the
standard model of the expanding universe.
In the redshift range around z ¼ 0:4
0:7, the SN results
are most sensitive to a linear combination of
M
and
close to
M
. In contrast, galaxy clustering and
dynamics are sensitive primarily to
M
alone, while the
CMB is most sensitive to
M
þ
. Although combinations
of other measurements lead to a separate confirmation of
the universe’s acceleration (e.g., Efstathiou et al. 2002),
taken alone it is the SNe that provide the best direct evi-
dence for da rk energy. Therefore, it is of importance to
improve the precision of the SN result, to confirm the result
with additional independent high-redshift SNe, and also to
limit the possible effects of systematic errors.
Perlmutter et al. (1997) P99, and Riess et al. (1998)
presented extensive accounts of, and bounds for, possible
systematic uncertainties in the SN measurements. One
obvious possible source of systematic uncertainty is the
effect of host galaxy dust. For a given mass density, the effect
of a cosmological constant on the magnitudes of high-
redshift SNe is to make their observed brightnesses dimmer
than would have been the case with
¼ 0. Dust extinction
from within the host galaxy of the high-redshift SNe could
have a similar effect; however, normal dust will also redden
the colors of the SNe. Therefore, a measurement of the color
of the high-redshift SNe, compared to the known colors of
low-redshift SNe Ia, has been used to provide an upper limit
on the effect of host galaxy dust extinction or a direct
measurement of that extinction that may then be corrected.
Uncertainties on extinction corrections based on these color
measurements usually dominate the statistical error of pho-
tometric measurements. Previous analyses either have
selected a low-extinction subset of both low- and high-
redshift SNe and not applied corrections directly (‘‘ fit C,’’
the primary analysis of P99) or have used an asymmetric
Bayesian prior on the intrinsic extinction distribution to
limit the propagated uncertainties from errors in color
measurements (Riess et al. 1998; ‘‘ fit E ’’ of P99).
In Sullivan et al. (2003), we set stronger limits on the
effects of host galaxy extinction by comparing the extinc-
tion, cosmological parameters, and SN peak magni tude dis-
persion for subset s of the SCP SNe observed in different
types of host galaxies, as identified from both HST imaging
and Keck spectroscopy of the hosts. We found that SNe in
early-type (E and S0) galaxies show a smaller dispersion in
peak magnitude at high redshift, as had previously been
seen at low redshift (e.g., Wang, Hoeflich, & Wheeler 1997).
This subset of the P99 sample—in hosts unlikely to be
strongly affected by extinction—independently provided
evidence at the 5 level that
> 0 in a flat universe and
confirmed that host galaxy dust extinction was unlikely to
be a significant systematic in the results of P99, as had been
suggested previously (e.g., Rowan-Robinson 2002). The
natural next step following the work of Sullivan et al.
(2003)—presented in the current paper—is to provide high-
quality individual unbiased E(BV ) measurements that
allow us to directly measure the effect of host galaxy extinc-
tion on each SN event without resorting to a prior on the
color excess distribution.
The current paper presents 11 new SNe discovered and
observed by the SCP at redshifts 0:36 < z < 0:86, a range
very similar to that of the 42 high-redshift SNe reported in
P99. The SNe of that paper, with one exception, were
observed entirely with ground-based telescopes; 11 of the 14
new SNe reported by Riess et al. (1998) were also observed
from the ground. The 11 SNe of this work have light curves
in both the R and I bands measured with the Wide Field
Planetary Camera 2 (WFPC2) on the Hubble Space
Telescope (HST) and represent the largest sample to date of
HST-measured SNe Ia at high redshift.
The HST pro vides two primary advantages for photom-
etry of point sources such as SNe. First, the sky background
is much lower, allowi ng a much higher signal-to-noise ratio
in a single exposure. Second, because the telescope is not
limited by atmospheric seeing, it has very high spatial
resolution. This helps the signal-to-noise ratio by greatly
reducing the area of background emission that contributes
to the noise of the source measurement and, moreover, sim-
plifies the task of separating the variable SN signal from
the host galaxy. With these advantages, the precision of the
light-curve and color measurements is much greater for the
11 SNe in this paper than was possible for previous ground-
based observations. These 11 SNe themselves provide a
high-precision new set of high-redshift SNe to test the accel-
erating universe results. M oreover, the higher precision
light-curve measurements in both R and I bands allow us to
make high-quality, unbiased, individual host galaxy
extinction corrections to each SN event.
We first describe the point-spread function (PSF) fit
photometry method used for extracting the light curves
from the WFPC2 images (x 2.1). Next, in x 2.2 we describe
the light-curve fitting procedure, including the methods
used for calculating accurate K-corrections. So that all SNe
may be treated consistently, in x 2.3 we apply the slightly
M
,
, AND w FROM HST-OBSERVED SNe Ia 103
updated K-corr ection procedure to all of the SNe used in
P99. In x 2.4 the cosmological fit methodol ogy we use is
described. In x 3 we discuss the evidence for hos t galaxy
extinction (only significant for three of the 11 new SNe)
from the RI light-curve colors. In x 4.1 we present the
measurements of the cosmological parameters
M
and
from the new data set alone, as well as combining this set
with the data of P99. In x 4.2 we perform a combined fit with
our data and the high-redshift SNe of Riess et al. (1998).
Finally, in x 4.3 we present measurements of w , the dark
energy equation-of-state parameter, from these data, and
from these data combined with recent CMB and galaxy
redshift distortion measurements. These discussions of our
primary results are followed by updated analyses of
systematic uncertainties for these measurements in x 5.
2. OBSERVATIONS, DATA REDUCTION,
AND ANALYSIS
2.1. WFPC2 Photometry
The SNe discussed in this paper are listed in Table 1. They
were discovered during three different SN searches, follow-
ing the techniques described in Perlmutter et al. (1995, 1997)
and P99. Two of the searches were conducted with the 4 m
Blanco telescope at the Cerro Tololo Inter-American
Observatory (CTIO), in 1997 November/December and
1998 March/April. The final search was conducted at the
Canada-France-Hawaii Telescope (CFHT ) on Mauna Kea
in Hawaii in 2000 April/May. In each case, two to three
nights of reference images were followed 3–4 weeks later by
two to three nights of search images. The two images of each
search field were seeing-matched and subtracted, and they
were searched for residuals indicating an SN candidate.
Weather conditions limited the depth and hence the redshift
range of the 1998 March/April search. Out of the three
searches, 11 of the resulting SN discoveries were followed
with extensive HST photometry. These SNe are spaced
approximately evenly in the redshift range 0:3 < z < 0:9.
Nine out of the 11 SNe were discovered very close to
maximum light; two were discovered several days before
maximum light.
Spectra were obtained with the red side of LRIS on the
Keck 10 m telescope (Oke et al. 1995), with FORS1 on Antu
(VLT-UT1; Appenzeller et al. 1998) and with EFOSC2
24
on
the ESO 3.6 m telescope. These spectra were used to confirm
the identification of the candidates as SNe Ia and to meas-
ure the redshift of each candidate. Nine of the 11 SNe in the
set have strong confirmation as Type Ia through the pres-
ence of Si ii 6150, Si ii 4190, or Fe ii featu res that match
those of a Type Ia observed at a similar epoch. SN 1998ay
and SN 1998be have spectra that are consistent with SN Ia
spectra, although this identification is less secure for those
two. However, we note that the colors (measured at multiple
epochs with the HST light curves) are inconsistent with
other non-Ia types. (We explore the systematic effect of
removing those two SNe from the set in x 5.2.)
Where possible, the redshift, z, of each candidate was
measured by matching narrow features in the host galaxy of
the SNe; the precision of these measur ements in z is typically
0.001. In cases in which there were not sufficient host galaxy
features (SN 1998aw and SN 1998ba), redshifts were
measured from the SN itself; in these cases, z is measured
with a (conservative) precision of 0.01 (Branch & van den
Bergh 1993). Even in the latter case, redshift measurements
do not contribute significantly to the uncertainties in the
final cosmol ogical measurements since these are dominated
by the photometric uncertainties.
Each of these SNe was imaged with two broadband filters
using the Planetary Camera (PC) CCD of the WFPC2 on
the HST, which has a scale of 0>046 pixel
1
. Table 1 lists the
dates of these observations. The F675W and F814W broad-
band filters were chosen to have maximum sensitivity to
these faint objects, while being as close a match as practical
to the rest-frame B and V filters at the targeted redshifts.
(Note that all of our WFPC2 observing parame ters except
the exact target coordinates were fixed prior to the SN dis-
coveries.) The effective system transmission curves provided
by the Space Telescope Science Institute indicate that, when
used with WFPC2, F675W is most similar to ground-based
R band while F814W is most similar to ground-based I
band. These filters roughly correspond to redshifted B-and
V-band filters for the SNe at z < 0:7 and redshifted U- and
B- band filters for the SNe at z > 0:7.
The HST images were reduced through the standard
HST ‘‘ on-the-fly reprocessing ’’ data reduction pipeline
provided by the Space Telescope Science Institute. Images
were then background subtracted, and images taken in the
same orbit were combined to rejec t cosmic rays using the
‘‘ crrej ’’ procedure (a part of the STSDAS IRAF package).
Photometric fluxes were extracted from the final images
using a PSF-fitting procedure. Traditional PSF-fitting
procedures assume a single isolated point source above a
constant background. In this case, the point source was
superimposed on the image of the host galaxy. In all cases,
the SN image was separated from the core of the host gal-
axy; however, in most cases the separation was not enough
that an annular measurement of the background would be
accurate. Because the host galaxy flux is the same in all of
the images, we used a PSF-fitting procedu re that fits a PSF
simultaneously to every image of a given SN observed
through a given photometric filter. The model we fit was
f
i
ðx; yÞ¼ f
0i
PSFðx x
0i
; y y
0i
Þ
þ bgðx x
0i
; y y
0i
; a
j
Þþp
i
; ð1Þ
where f
i
ðx; yÞ is the measured flux in pixel (x, y) of the ith
image, (x
0i
, y
0i
) is the position of the SN on the ith image, f
0i
is the total flux in the SN in the ith image, PSFðu; vÞ is a nor-
malized PSF, bgðu; v; aÞ is a temporally constant back-
ground parametrized by a
j
, and p
i
is a pedestal offset for the
ith image. There are 4n þ m 1 parameters in this model,
where n is the number of images (typically 2, 5, or 6
previously summed images) and m is the number of param-
eters a
j
that specify the background model (typically 3 or 6).
(The 1 is due to the fact that a zeroth-order term in the
background is degenerate with one of the p
i
terms.)
Parameters varied include f
i
, x
0i
, y
0i
, p
i
, and a
j
.
Because of the scarcity of objects in our PC images,
geometric transformations between the images at different
epochs using other objects on the four chips of WFPC2
together allowed an a priori determination of (x
0i
, y
0i
) good
to 1 pixel. Allowing those parameters to vary in the fit
(effectively, using the point-source signature of the SN to
determine the offset of the image) provided position
24
See http://www.ls.eso.org/lasilla/sciops/efosc.
104 KNOP ET AL.
TABLE 1
WFPC2 Supernova Observations
SN Name z F675W Observations F814W Observations
1997ek .................. 0.863 1998 Jan 05 (400 s, 400 s) 1998 Jan 05 (500 s, 700 s)
1998 Jan 11 (400 s, 400 s) 1998 Jan 11 (500 s, 700 s)
1998 Feb 02 (1100 s, 1200 s)
1998 Feb 14 (1100 s, 1200 s)
1998 Feb 27 (1100 s, 1200 s)
1998 Nov 09 (1100 s, 1300 s)
1998 Nov 16 (1100 s, 1300 s)
1997eq .................. 0.538 1998 Jan 06 (300 s, 300 s) 1998 Jan 06 (300 s, 300 s)
1998 Jan 21 (400 s, 400 s) 1998 Jan 11 (300 s, 300 s)
1998 Feb 02 (500 s, 700 s)
1998 Feb 11 (400 s, 400 s) 1998 Feb 11 (500 s, 700 s)
1998 Feb 19 (400 s, 400 s) 1998 Feb 19 (500 s, 700 s)
1997ez................... 0.778 1998 Jan 05 (400 s, 400 s) 1998 Jan 05 (500 s, 700 s)
1998 Jan 11 (400 s, 400 s) 1998 Jan 11 (500 s, 700 s)
1998 Feb 02 (1100 s, 1200 s)
1998 Feb 14 (1100 s, 1200 s)
1998 Feb 27 (100 s, 1200 s, 1100 s, 1200 s)
1998as................... 0.355 1998 Apr 08 (400 s, 400 s) 1998 Apr 08 (500 s, 700 s)
1998 Apr 20 (400 s, 400 s) 1998 Apr 20 (500 s, 700 s)
1998 May 11 (400 s, 400 s) 1998 May 11 (500 s, 700 s)
1998 May 15 (400 s, 400 s) 1998 May 15 (500 s, 700 s)
1998 May 29 (400 s, 400 s) 1998 May 29 (500 s, 700 s)
1998aw.................. 0.440 1998 Apr 08 (300 s, 300 s) 1998 Apr 08 (300 s, 300 s)
1998 Apr 18 (300 s, 300 s) 1998 Apr 18 (300 s, 300 s)
1998 Apr 29 (400 s, 400 s) 1998 Apr 29 (500 s, 700 s)
1998 May 14 (400 s, 400 s) 1998 May 14 (500 s, 700 s)
1998 May 28 (400 s, 400 s) 1998 May 28 (500 s, 700 s)
1998ax .................. 0.497 1998 Apr 08 (300 s, 300 s) 1998 Apr 08 (300 s, 300 s)
1998 Apr 18 (300 s, 300 s) 1998 Apr 18 (300 s, 300 s)
1998 Apr 29 (300 s, 300 s) 1998 Apr 29 (500 s, 700 s)
1998 May 14 (300 s, 300 s) 1998 May 14 (500 s, 700 s)
1998 May 27 (300 s, 300 s) 1998 May 27 (500 s, 700 s)
1998ay .................. 0.638 1998 Apr 08 (400 s, 400 s) 1998 Apr 08 (500 s, 700 s)
1998 Apr 20 (400 s, 400 s) 1998 Apr 20 (500 s, 700 s)
1998 May 11 (1100 s, 1200 s)
1998 May 15 (1100 s, 1200 s)
1998 Jun 03 (1100 s, 1200 s)
1998ba .................. 0.430 1998 Apr 08 (300 s, 300 s) 1998 Apr 08 (300 s, 300 s)
1998 Apr 19 (300 s, 300 s) 1998 Apr 19 (300 s, 300 s)
1998 Apr 29 (400 s, 400 s) 1998 Apr 29 (500 s, 700 s)
1998 May 13 (400 s, 400 s) 1998 May 13 (500 s, 700 s)
1998 May 28 (400 s, 400 s) 1998 May 28 (500 s, 700 s)
1998be .................. 0.644 1998 Apr 08 (300 s, 300 s) 1998 Apr 08 (300 s, 300 s)
1998 Apr 19 (300 s, 300 s) 1998 Apr 19 (300 s, 300 s)
1998 Apr 30 (400 s, 400 s) 1998 Apr 30 (500 s, 700 s)
1998 May 15 (400 s, 400 s) 1998 May 15 (500 s, 700 s)
1998 May 28 (400 s, 400 s) 1998 May 28 (500 s, 700 s)
1998bi ................... 0.740 1998 Apr 06 (400 s, 400 s) 1998 Apr 06 (500 s, 700 s)
1998 Apr 18 (400 s, 400 s) 1998 Apr 18 (500 s, 700 s)
1998 Apr 28 (1100 s, 1200 s)
1998 May 12 (1100 s, 1200 s)
1998 Jun 02 (1100 s, 1200 s)
2000fr ................... 0.543 2000 May 08 (2200 s)
2000 May 15 (600 s, 600 s) 2000 May 15 (1100 s, 1100 s)
2000 May 28 (600 s, 600 s) 2000 May 28 (600 s, 600 s)
2000 Jun 10 (500 s, 500 s) 2000 Jun 10 (600 s, 600 s)
2000 Jun 22 (1100 s, 1300 s) 2000 Jun 22 (1100 s, 1200 s)
2000 Jul 08 (1100 s, 1300 s) 2000 Jul 08 (110 s, 1200 s)
measurements a factor of 10 better.
25
The model was fitted
to 13 13 pixel patches extracted from all of the images of a
time sequence of a single SN in a single filter (except for SN
1998ay, which is close enough to the host galaxy that a 7 7
pixel patch was used to avoid having to fit the core of the
galaxy with the background model) . In four out of the 99
patches used in the fits to the 22 light curves, a single bad
pixel was masked from the fit. The series of f
0i
values, cor-
rected as described in the rest of this section, provided the
data used in the light-curve fits described in x 2.2. For one
SN (SN 1997ek at z ¼ 0:86), the F814W background was
further constrained by an SN-free ‘‘ final reference ’’ image
taken 11 months after the SN explosion.
26
A single Tiny Tim PSF (Krist & Hook 2003) was used as
PSFðu; vÞ for all images of a given filter. The Tiny Tim PSF
used was subsampled to 10 10 subpixels; in the fit proce-
dure, it was shifted an d integrated (properly summing frac-
tional subpixels). After shifting and resampling to the PC
pixel scale, it was convolved with an empirical 3 3 electron
diffusion kernel with 75% of the flux in the central element
(A. Fruchter 2000, private communication).
27
The PSF was
normalized in a 0>5 radius aperture, chosen to match the
standard zero-point calibration (Holtzman et al. 1995;
Dolphin 2000). Although the use of a single PSF for every
image is an approximation (the PSF of WFPC2 depends on
the epoch of the observation and the position on the CCD),
this approximation should be valid, especially given that for
all of the observations the SN was positioned close to the
center of the PC. To verify that this approximation is valid,
we reran the PSF-fitting procedure with individually gener-
ated PSFs for most SNe; we also explored using an SN spec-
trum instead of a standard-star spectrum in generating the
PSF. The measured fluxes were not significantly different,
showing differences in both directions generally within
1%–2% of the SN peak flux value, much less than our
photometric uncertainties on individual data points.
Although one of the great advantages of the HST is its
low background, CCD photometry of faint objects over a
low background suffers from an imperfect charge transfer
efficiency (CTE) effect, which can lead to a systematic
underestimate of the flux of point sources (Whitemore,
Heyer, & Casertano 1999; Dolphin 2000, 2003).
28
On the
PC, these effects can be as large as 15%. The measured flux
values ( f
0i
above) were corrected for the CTE of WFPC2
following the standard procedure of Dolphin (2000).
29
Uncertainties on the CTE corrections were propagated into
the corrected SN fluxes, although in all cases these uncer-
tainties were smaller than the uncertainties in the raw
measured flux values. Because the host galaxy is a smooth
background underneath the point source, it was considered
as a contribution to the background in the CTE correction.
For an image that was a combination of several separate
exposures within the same orbit or orbits, the CTE calcula-
tion was performed assuming that each SN image had a
measured SN flux whose fraction of the total flux was equal
to the fraction of that individual image’s exposure time to
the summed image’s total exposure time. This assumption is
correct most of the time, with the exception of the few
instances where earthshine affects part of an orbit.
In addition to the HST data, there exists ground-based
photometry for each of these SNe. This includes the images
from the search itself, as well as a limited amount of follow-
up. The details of which SNe were observed with which tele-
scopes are given with the light curves in the Appendix.
Ground-based photometric fluxes were extracted from
images using the same aperture photometry procedure of
P99. A complete light curve in a given filter (R or I ) com-
bined the HST data with the ground-based data (using the
color correction procedure described in x 2.3), using
measured zero points for the ground-based data and the
Vega zero points of Dolphin (2000) for the HST data. The
uncertainties on those zero points (0.003 for F814W or
0.006 for F675W) were added as correlated errors between
all HST data points when combining with the ground-based
light curve. Similarly, the measured uncertainty in the
ground-based zero point was added as a correlated error to
all ground-based fluxes. Ground -based photometric
calibrations were based on observations of Landolt (1992)
standard stars observed on the same photometric night as
an SN observation; each calibration is confirmed over two
or more nights. Ground-based zero-point uncertainties are
generally d0.02–0.03; the R-band ground-based zero point
for SN 1998ay is only good to 0.05. We have compared
our ground-based aperture photometry with our HST PSF-
fitting photometry using the limited number of sufficiently
bright stars present in the PC across the 11 SNe fields. We
find the difference between the HST and ground-based
photometry to be 0:02 0:02 in both the R and I bands,
consistent with no offset. The correlated uncertainties
between different SNe arising from ground-based zero
points based on the same calibration data, as well as
between the HST SNe (which all share the same zero
point), were included in the covariance matrix used in all
cosmological fits (see x 2.4).
2.2. Light-Curve Fits
It is the magnitude of the SN at its light-curve peak that
serves as a ‘‘ calibrated candle ’’ in estimating the cosmologi-
cal parameters from the luminosity-distance relationship. To
estimate this peak magnitude, we performed template fits to
the time series of photometric data for each SN. In addition
to the 11 SNe described here, light-curve fits were also per-
formed to the SNe from P99, including 18 SNe from Hamuy
et al. (1996b, hereafter H96) and eight from Riess et al.
(1999b, hereafter R99) that match the same selection criteria
used for the H96 SNe (having data within 6 days of maxi-
mum light and located at cz > 4000 km s
1
, limiting distance
modulus error due to peculiar velocities to less than 0.15
mag). Because of new templates and K-corrections (see
below), light-curve fits to the SNe from H96 and P99 used in
25
Note that this may introduce a bias toward higher flux, as the fit will
seek out positive fluctuations on which to center the PSF. However, the
covariance between the peak flux and position is typically less than 4% of
the product of the positional uncertainty and the flux uncertainty, so the
effects of this bias will be very small in comparison to our photometric
errors.
26
Although obtaining final references to subtract the galaxy background
is standard procedure for ground-based photometry of high-redshift SNe,
the higher resolution of WFPC2 provides sufficient separation between the
SN and host galaxy that such images are not always necessary, particularly
in this redshift range.
27
See also http://www.stsci.edu/software/tinytim/tinytim_faq.html.
28
Available at http://www.stsci.edu/hst/HST_overview/documents/
calworkshop/workshop2002/CW2002_Papers/CW02_dolphin.
29
These CTE corrections used updated coefficients posted on
Dolphin’s web page (http://www.noao.edu/staff/dolphin/wfpc2_calib/)
in September, 2002.
106 KNOP ET AL. Vol. 598