THE ASTROPHYSICAL JOURNAL, 517 :565È586, 1999 June 1

1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

MEASUREMENTS OF ) AND " FROM 42 HIGH-REDSHIFT SUPERNOVAE

S. PERLMUTTER,1 G. ALDERING,G.GOLDHABER,1 R. A. KNOP,P.NUGENT,P.G.CASTRO,2 S. DEUSTUA,S.FABBRO,3

A. GOOBAR,4 D. E. GROOM,I.M.HOOK,5 A. G. KIM,1,6 M. Y. KIM,J.C.LEE,7 N. J. NUNES,2 R. PAIN,3

C. R. PENNYPACKER,8 AND R. QUIMBY

Institute for Nuclear and Particle Astrophysics, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720

C. LIDMAN

European Southern Observatory, La Silla, Chile

R. S. ELLIS,M.IRWIN, AND R. G. MCMAHON

Institute of Astronomy, Cambridge, England, UK

P. RUIZ-LAPUENTE

Department of Astronomy, University of Barcelona, Barcelona, Spain

N. WALTON

Isaac Newton Group, La Palma, Spain

B. SCHAEFER

Department of Astronomy, Yale University, New Haven, CT

B. J. BOYLE

Anglo-Australian Observatory, Sydney, Australia

A.VFILIPPENKO AND T. MATHESON

Department of Astronomy, University of California, Berkeley, CA

A. S. FRUCHTER AND N. PANAGIA9

Space Telescope Science Institute, Baltimore, MD

H. J. M. NEWBERG

Fermi National Laboratory, Batavia, IL

AND

W. J. COUCH

University of New South Wales, Sydney, Australia

(THE SUPERNOVA COSMOLOGY PROJECT)

Received 1998 September 8 ; accepted 1998 December 17

ABSTRACT

We report measurements of the mass density, and cosmological-constant energy density, of)

M

, )

"

,

the universe based on the analysis of 42 type Ia supernovae discovered by the Supernova Cosmology

Project. The magnitude-redshift data for these supernovae, at redshifts between 0.18 and 0.83, are Ðtted

jointly with a set of supernovae from the Supernova Survey, at redshifts below 0.1, to yieldCala

n/Tololo

values for the cosmological parameters. All supernova peak magnitudes are standardized using a SN Ia

light-curve width-luminosity relation. The measurement yields a joint probability distribution of the

cosmological parameters that is approximated by the relation in the region0.8)

M

[ 0.6)

"

B [0.2 ^ 0.1

of interest For a Ñat cosmology we Ðnd (1 p statistical)()

M

[ 1.5). ()

M

] )

"

\ 1) )

M

flat \ 0.28

~0.08

`0.09

~0.04

`0.05

(identiÐed systematics). The data are strongly inconsistent with a " \ 0 Ñat cosmology, the simplest

inÑationary universe model. An open, " \ 0 cosmology also does not Ðt the data well: the data indicate

that the cosmological constant is nonzero and positive, with a conÐdence of P("[0) \ 99%, including

the identiÐed systematic uncertainties. The best-Ðt age of the universe relative to the Hubble time is

Gyr for a Ñat cosmology. The size of our sample allows us to perform a variety oft

0

flat \ 14.9

~1.1

`1.4(0.63/h)

statistical tests to check for possible systematic errors and biases. We Ðnd no signiÐcant di†erences in

either the host reddening distribution or Malmquist bias between the low-redshift sampleCala

n/Tololo

and our high-redshift sample. Excluding those few supernovae that are outliers in color excess or Ðt

residual does not signiÐcantly change the results. The conclusions are also robust whether or not a

width-luminosity relation is used to standardize the supernova peak magnitudes. We discuss and con-

strain, where possible, hypothetical alternatives to a cosmological constant.

Subject headings: cosmology: observations È distance scale È supernovae: general

1 Center for Particle Astrophysics, University of California, Berkeley, California.

2 Instituto Superior Lisbon, Portugal.Te

cnico,

3 LPNHE, CNRS-IN2P3, and University of Paris VI and VII, Paris, France.

4 Department of Physics, University of Stockholm, Stockholm, Sweden.

5 European Southern Observatory, Munich, Germany.

6 PCC, CNRS-IN2P3, and de France, Paris, France.Colle

`

ge

7 Institute of Astronomy, Cambridge, England, UK.

8 Space Sciences Laboratory, University of California, Berkeley, California.

9 Space Sciences Department, European Space Agency.

565

566 PERLMUTTER ET AL. Vol. 517

1. INTRODUCTION

Since the earliest studies of supernovae, it has been sug-

gested that these luminous events might be used as standard

candles for cosmological measurements (Baade 1938). At

closer distances they could be used to measure the Hubble

constant if an absolute distance scale or magnitude scale

could be established, while at higher redshifts they could

determine the deceleration parameter (Tammann 1979;

Colgate 1979). The Hubble constant measurement became

a realistic possibility in the 1980s, when the more homoge-

neous subclass of type Ia supernovae (SNe Ia) was identiÐed

(see Branch 1998). Attempts to measure the deceleration

parameter, however, were stymied for lack of high-redshift

supernovae. Even after an impressive multiyear e†ort by

et al. (1989), it was only possible toNÔrgaard-Nielsen

follow one SN Ia, at z \ 0.31, discovered 18 days past its

peak brightness.

The Supernova Cosmology Project was started in 1988 to

address this problem. The primary goal of the project is the

determination of the cosmological parameters of the uni-

verse using the magnitude-redshift relation of type Ia super-

novae. In particular, Goobar & Perlmutter (1995) showed

the possibility of separating the relative contributions of the

mass density, and the cosmological constant, ",to)

M

,

changes in the expansion rate by studying supernovae at a

range of redshifts. The Project developed techniques,

including instrumentation, analysis, and observing stra-

tegies, that make it possible to systematically study high-

redshift supernovae (Perlmutter et al. 1995a). As of 1998

March, more than 75 type Ia supernovae at redshifts

z \ 0.18È0.86 have been discovered and studied by the

Supernova Cosmology Project (Perlmutter et al. 1995b,

1996, 1997a, 1997b, 1997c, 1997d, 1998a).

A Ðrst presentation of analysis techniques, identiÐcation

of possible sources of statistical and systematic errors, and

Ðrst results based on seven of these supernovae at redshifts

z D 0.4 were given in Perlmutter et al. (1997e; hereafter

referred to as P97). These Ðrst results yielded a conÐdence

region that was suggestive of a Ñat, " \ 0 universe but with

a large range of uncertainty. Perlmutter et al. (1998b) added

a z \ 0.83 SN Ia to this sample, with observations from the

Hubble Space Telescope (HST ) and Keck 10 m telescope,

providing the Ðrst demonstration of the method of separat-

ing and " contributions. This analysis o†ered prelimi-)

M

nary evidence for a lowÈmass-density universe with a

best-Ðt value of assuming " \ 0. Indepen-)

M

\ 0.2 ^ 0.4,

dent work by Garnavich et al. (1998a), based on three

supernovae at z D 0.5 and one at z \ 0.97, also suggested a

low mass density, with best-Ðt for " \ 0.)

M

\[0.1 ^ 0.5

Perlmutter et al. 1997f presented a preliminary analysis

of 33 additional high-redshift supernovae, which gave a

conÐdence region indicating an accelerating universe and

barely including a low-mass " \ 0 cosmology. Recent inde-

pendent work of Riess et al. (1998), based on 10 high-

redshift supernovae added to the Garnavich et al. (1998a)

set, reached the same conclusion. Here we report on the

complete analysis of 42 supernovae from the Supernova

Cosmology Project, including the reanalysis of our pre-

viously reported supernovae with improved calibration

data and improved photometric and spectroscopic SN Ia

templates.

2. BASIC DATA AND PROCEDURES

The new supernovae in this sample of 42 were all dis-

covered while still brightening, using the Cerro Tololo

Inter-American Observatory (CTIO) 4 m telescope with the

20482 pixel prime-focus CCD camera or the 4 ] 20482 pixel

Big Throughput Camera.10 The supernovae were followed

with photometry over the peak of their light curves and

approximately 2È3 months further (D40È60 days rest

frame) using the CTIO 4 m, Wisconsin-Indiana-Yale-

NOAO (WIYN) 3.6 m, ESO 3.6 m, Isaac Newton Telescope

(INT) 2.5 m, and the William Herschel Telescope (WHT) 4.2

m telescopes. (SN 1997ap and other 1998 supernovae have

also been followed with HST photometry.) The supernova

redshifts and spectral identiÐcations were obtained using

the Keck I and II 10 m telescopes with the Low-Resolution

Imaging Spectrograph (Oke et al. 1995) and the ESO 3.6 m

telescope. The photometry coverage was most complete in

Kron-Cousins R-band, with Kron-Cousins I-band photo-

metry coverage ranging from two or three points near peak

to relatively complete coverage paralleling the R-band

observations.

Almost all of the new supernovae were observed spectro-

scopically. The conÐdence of the type Ia classiÐcations

based on these spectra taken together with the observed

light curves, ranged from ““ deÐnite ÏÏ (when Si II features

were visible) to ““ likely ÏÏ (when the features were consistent

with type Ia and inconsistent with most other types). The

lower conÐdence identiÐcations were primarily due to host-

galaxy contamination of the spectra. Fewer than 10% of the

original sample of supernova candidates from which these

SNe Ia were selected were conÐrmed to be nonÈtype Ia, i.e.,

being active galactic nuclei or belonging to another SN

subclass; almost all of these nonÈSNe Ia could also have

been identiÐed by their light curves and/or position far from

the SN Ia Hubble line. Whenever possible, the redshifts

were measured from the narrow host-galaxy lines rather

than the broader supernova lines. The light curves and

several spectra are shown in Perlmutter et al. (1997e, 1997f,

1998b); complete catalogs and detailed discussions of the

photometry and spectroscopy for these supernovae will be

presented in forthcoming papers.

The photometric reduction and the analyses of the light

curves followed the procedures described in P97. The super-

novae were observed with the Kron-Cousins Ðlter that best

matched the rest-frame B and V Ðlters at the supernovaÏs

redshift, and any remaining mismatch of wavelength cover-

age was corrected by calculating the expected photometric

di†erenceÈthe ““ cross-Ðlter K-correction ÏÏÈusing template

SN Ia spectra as in Kim, Goobar, & Perlmutter (1996). We

have now recalculated these K-corrections (see Nugent et

al. 1998) using improved template spectra, based on an

extensive database of low-redshift SN Ia spectra recently

made available from the survey (Phillips et al.Cala

n/Tololo

1999). Where available, IUE and HST spectra (Cappellaro,

Turatto, & Fernley 1995; Kirshner et al. 1993) were also

added to the SN Ia spectra, including those published pre-

viously (1972E, 1981B, 1986G, 1990N, 1991T, 1992A, and

1994D: in Kirshner & Oke 1975; Branch et al. 1993; Phil-

lips et al. 1987; Je†ery et al. 1992; Meikle et al. 1996; Patat

et al. 1996). In Nugent et al. (1998) we show that the K-

corrections can be calculated accurately for a given day on

the supernova light curve and for a given supernova light-

10 Big Throughput Camera information is provided by G. Bernstein &

J. A. Tyson, 1998, at http://www.astro.lsa.umich.edu/btc/user.html.

No. 2, 1999 ) AND " FROM 42 HIGH-REDSHIFT SUPERNOVAE 567

curve width from the color of the supernova on that day.

(Such a calculation of K-correction based on supernova

color will also automatically account for any modiÐcation

of the K-correction due to reddening of the supernova; see

Nugent et al. 1998. In the case of insigniÐcant reddening the

SN Ia template color curves can be used.) We Ðnd that these

calculations are robust to mis-estimations of the light-curve

width or day on the light curve, giving results correct to

within 0.01 mag for light-curveÈwidth errors of ^25% or

light-curve phase errors of ^5 days even at redshifts where

Ðlter matching is the worst. Given small additional uncer-

tainties in the colors of supernovae, we take an overall sys-

tematic uncertainty of 0.02 mag for the K-correction.

The improved K-corrections have been recalculated for

all the supernovae used in this paper, including those pre-

viously analyzed and published. Several of the low-redshift

supernovae from the survey have relativelyCala

n/Tololo

large changes (as much as 0.1 mag) at times in their K-

corrected light curves. (These and other low-redshift super-

novae with new K-corrections are used by several

independent groups in constructing SN Ia light-curve tem-

plates, so the templates must be updated accordingly.) The

K-corrections for several of the high-redshift supernovae

analyzed in P97 have also changed by small amounts at the

light-curve peak mag] and somewhat[*K(t \ 0) [ 0.02

larger amounts by 20 days past peak [*K(t \ 20) [ 0.1

mag]; this primarily a†ects the measurement of the rest-

frame light-curve width. These K-correction changes

balance out among the P97 supernovae, so the Ðnal results

for these supernovae do not change signiÐcantly. (As we

discuss below, however, the much larger current data set

does a†ect the interpretation of these results.)

As in P97, the peak magnitudes have been corrected for

the light-curve width-luminosity relation of SNe Ia:

m

B

corr \ m

B

] *

corr

(s) , (1)

where the correction term is a simple monotonic func-*

corr

tion of the ““ stretch factor,ÏÏ s, that stretches or contracts the

time axis of a template SN Ia light curve to best Ðt the

observed light curve for each supernova (see P97; Perlmut-

ter et al. 1995a; Kim et al. 1999; Goldhaber et al. 1999; and

see Phillips 1993; Riess, Press, & Kirshner 1995, 1996

[hereafter RPK96]). A similar relation corrects the V -band

light curve, with the same stretch factor in both bands. For

the supernovae discussed in this paper, the template must

be time-dilated by a factor 1 ] z before Ðtting to the

observed light curves to account for the cosmological

lengthening of the supernova timescale (Goldhaber et al.

1995; Leibundgut et al. 1996a; Riess et al. 1997a). P97 cal-

culated by translating from s to (both describ-*

corr

(s) *m

15

ing the timescale of the supernova event) and then using the

relation between and luminosity as determined by*m

15

Hamuy et al. (1995). The light curves of the Cala

n/Tololo

supernovae have since been published, and we have directly

Ðtted each light curve with the stretched template method

to determine its stretch factor s. In this paper, for the light-

curve width-luminosity relation, we therefore directly use

the functional form

*

corr

(s) \ a(s [ 1) (2)

and determine a simultaneously with our determination of

the cosmological parameters. With this functional form, the

supernova peak apparent magnitudes are thus all

““ corrected ÏÏ as they would appear if the supernovae had the

light-curve width of the template, s \ 1.

We use analysis procedures that are designed to be as

similar as possible for the low- and high-redshift data sets.

Occasionally, this requires not using all of the data avail-

able at low redshift, when the corresponding data are not

accessible at high redshift. For example, the low-redshift

supernova light curves can often be followed with photo-

metry for many months with high signal-to-noise ratios,

whereas the high-redshift supernova observations are gen-

erally only practical for approximately 60 rest-frame days

past maximum light. This period is also the phase of the

low-redshift SN Ia light curves that is Ðtted best by the

stretched-template method and that best predicts the lumi-

nosity of the supernova at maximum. We therefore Ðtted

only this period for the light curves of the low-redshift

supernovae. Similarly, at high redshift the rest-frame

B-band photometry is usually much more densely sampled

in time than the rest-frame V -band data, so we use the

stretch factor that best Ðts the rest-frame B-band data for

both low- and high-redshift supernovae, even though at

low-redshift the V -band photometry is equally well

sampled.

Each supernova peak magnitude was also corrected for

Galactic extinction, using the extinction law of Cardelli,A

R

,

Clayton, & Mathis (1989), Ðrst using the color excess,

at the supernovaÏs Galactic coordinates pro-E(B[V )

SFÔD

,

vided by Schlegel, Finkbeiner, & Davis (1998) and thenÈ

for comparisonÈusing the value provided byE(B[V )

BÔH

D. Burstein & C. Heiles (1998, private communication; see

also Burstein & Heiles 1982). Galactic extinction, wasA

R

,

calculated from E(B[V ) using a value of the total-to-selec-

tive extinction ratio, speciÐc to eachR

R

4 A

R

/E(B[V ),

supernova. These were calculated using the appropriate

redshifted supernova spectrum as it would appear through

an R-band Ðlter. These values of range from 2.56 atR

R

z \ 0 to 4.88 at z \ 0.83. The observed supernova colors

were similarly corrected for Galactic extinction. Any extinc-

tion in the supernovaÏs host galaxy or between galaxies was

not corrected for at this stage but will be analyzed separa-

tely in ° 4.

All the same corrections for width-luminosity relation,

K-corrections, and extinction (but using wereR

B

\ 4.14)

applied to the photometry of 18 low-redshift SNe Ia

(z ¹ 0.1) from the supernova survey (HamuyCala

n/Tololo

et al. 1996) that were discovered earlier than 5 days after

peak. The light curves of these 18 supernovae have all been

reÐtted since P97, using the more recently available photo-

metry (Hamuy et al. 1996) and our K-corrections.

Figures 1 and 2a show the Hubble diagram of e†ective

rest-frame B magnitude corrected for the width-luminosity

relation,

m

B

eff \ m

R

] *

corr

[ K

BR

[ A

R

, (3)

as a function of redshift for the 42 Supernova Cosmology

Project high-redshift supernovae, along with the 18

low-redshift supernovae. (Here is theCala

n/Tololo K

BR

cross-Ðlter K-correction from observed R band to rest-

frame B band.) Tables 1 and 2 give the corresponding IAU

names, redshifts, magnitudes, corrected magnitudes, and

their respective uncertainties. As in P97, the inner error bars

in Figures 1 and 2 represent the photometric uncertainty,

while the outer error bars add in quadrature 0.17 mag of

intrinsic dispersion of SN Ia magnitudes that remain after

568 PERLMUTTER ET AL. Vol. 517

FIG. 1.ÈHubble diagram for 42 high-redshift type Ia supernovae from the Supernova Cosmology Project and 18 low-redshift type Ia supernovae from the

Supernova Survey after correcting both sets for the SN Ia light-curve width-luminosity relation. The inner error bars show the uncertainty dueCala

n/Tololo

to measurement errors, while the outer error bars show the total uncertainty when the intrinsic luminosity dispersion, 0.17 mag, of light-curveÈwidth-

corrected type Ia supernovae is added in quadrature. The unÐlled circles indicate supernovae not included in Ðt C. The horizontal error bars represent the

assigned peculiar velocity uncertainty of 300 km s~1. The solid curves are the theoretical for a range of cosmological models with zero cosmologicalm

B

eff(z)

constant: on top, (1, 0) in middle, and (2, 0) on bottom. The dashed curves are for a range of Ñat cosmological models: on()

M

, )

"

) \ (0, 0) ()

M

, )

"

) \ (0, 1)

top, (0.5, 0.5) second from top, (1, 0) third from top, and (1.5, [0.5) on bottom.

applying the width-luminosity correction. For these plots,

the slope of the width-brightness relation was taken to be

a \ 0.6, the best-Ðt value of Ðt C discussed below. (Since

both the low- and high-redshift supernova light-curve

widths are clustered rather closely around s \ 1, as shown

in Fig. 4, the exact choice of a does not change the Hubble

diagram signiÐcantly.) The theoretical curves for a universe

with no cosmological constant are shown as solid lines for a

range of mass density, 1, 2. The dashed lines)

M

\ 0,

represent alternative Ñat cosmologies, for which the total

mass energy density (where)

M

] )

"

\ 1 )

"

4 "/3H

0

2).

The range of models shown are for (0.5,()

M

, )

"

) \ (0, 1),

0.5), (1, 0), which is covered by the matching solid line, and

(1.5, [0.5).

3. FITS TO )

M

AND )

"

The combined low- and high-redshift supernova data sets

of Figure 1 are Ðtted to the Friedman-Robertson-Walker

(FRW) magnitude-redshift relation, expressed as in P97:

m

B

eff 4 m

R

] a(s [ 1) [ K

BR

[ A

R

\ M

B

] 5 log D

L

(z; )

M

, )

"

) , (4)

where is the ““ Hubble-constantÈfree ÏÏ lumi-D

L

4 H

0

d

L

nosity distance and log is theM

B

4 M

B

[ 5 H

0

] 25

““ Hubble-constantÈfree ÏÏ B-band absolute magnitude at

maximum of a SN Ia with width s \ 1. (These quantities

are, respectively, calculated from theory or Ðtted from

apparent magnitudes and redshifts, both without any need

for The cosmological-parameter results are thus alsoH

0

.

completely independent of The details of the ÐttingH

0

.)

procedure as presented in P97 were followed, except that

both the low- and high-redshift supernovae were Ðtted

simultaneously, so that and a, the slope of the width-M

B

luminosity relation, could also be Ðtted in addition to the

cosmological parameters and For most of the)

M

)

"

.

analyses in this paper, and a are statistical ““ nuisance ÏÏM

B

parameters; we calculate two-dimensional conÐdence

regions and single-parameter uncertainties for the cosmo-

logical parameters by integrating over these parameters, i.e.,

da.P()

M

, )

"

) \ // P()

M

, )

"

, M

B

, a)dM

B

As in P97, the small correlations between the photo-

metric uncertainties of the high-redshift supernovae, due to

shared calibration data, have been accounted for by Ðtting

with a correlation matrix of uncertainties.11 The low-

redshift supernova photometry is more likely to be uncor-

related in its calibration, since these supernovae were not

discovered in batches. However, we take a 0.01 mag system-

atic uncertainty in the comparison of the low-redshift

B-band photometry and the high-redshift R-band photo-

metry. The stretch-factor uncertainty is propagated with a

Ðxed width-luminosity slope (taken from the low-redshift

11 The data are available at http://www-supernova.lbl.gov.

No. 2, 1999 ) AND " FROM 42 HIGH-REDSHIFT SUPERNOVAE 569

FIG. 2.È(a) Hubble diagram for 42 high-redshift type Ia supernovae from the Supernova Cosmology Project and 18 low-redshift type Ia supernovae from

the Supernova Survey, plotted on a linear redshift scale to display details at high redshift. The symbols and curves are as in Fig. 1.Cala

n/Tololo

(b) Magnitude residuals from the best-Ðt Ñat cosmology for the Ðt C supernova subset, 0.72). The dashed curves are for a range of Ñat()

M

, )

"

) \ (0.28,

cosmological models: on top, (0.5, 0.5) third from bottom, (0.75, 0.25) second from bottom, and (1, 0) is the solid curve on bottom. The()

M

, )

"

) \ (0, 1)

middle solid curve is for Note that this plot is practically identical to the magnitude residual plot for the best-Ðt unconstrained cosmology()

M

, )

"

) \ (0, 0).

of Ðt C, with (c) Uncertainty-normalized residuals from the best-Ðt Ñat cosmology for the Ðt C supernova subset,()

M

, )

"

) \ (0.73, 1.32). ()

M

, )

"

) \

(0.28, 0.72).

supernovae; cf. P97) and checked for consistency after the

Ðt.

We have compared the results of Bayesian and classical,

““ frequentist,ÏÏ Ðtting procedures. For the Bayesian Ðts, we

have assumed a ““ prior ÏÏ probability distribution that has

zero probability for but otherwise has uniform)

M

\ 0

probability in the four parameters a, and For)

M

, )

"

, M

B

.

the frequentist Ðts, we have followed the classical statistical

procedures described by Feldman & Cousins (1998) to

guarantee frequentist coverage of our conÐdence regions in

the physically allowed part of parameter space. Note that

throughout the previous cosmology literature, completely