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SUPERNOVAE

NEW CONSTRAINTS ON M , ?,AND w FROM AN INDEPENDENT SET OF 11HIGH-REDSHIFT

SUPERNOVAE OBSERVED WITH THE HUBBLE SPACE TELESCOPE 1R.A.Knop,2,3,4G.Aldering,4,5R.Amanullah,6P.Astier,7G.Blanc,5,7M.S.Burns,8A.Conley,5,9S.E.Deustua,5,10

M.Doi,11R.Ellis,12S.Fabbro,4,13G.Folatelli,6A.S.Fruchter,14G.Garavini,6S.Garmond,5,9K.Garton,8R.Gibbons,5G.Goldhaber,5,9A.Goobar,6D.E.Groom,4,5D.Hardin,7I.Hook,15D.A.Howell,5A.G.Kim,4,5B.C.Lee,5C.Lidman,16J.Mendez,17,18S.Nobili,6P.E.Nugent,4,5R.Pain,7N.Panagia,14C.R.Pennypacker,5

S.Perlmutter,5R.Quimby,5J.Raux,7N.Regnault,5,19P.Ruiz-Lapuente,18G.Sainton,7B.Schaefer,20

K.Schahmaneche,7E.Smith,2A.L.Spadafora,5V.Stanishev,6M.Sullivan,12,21N.A.Walton,22

L.Wang,5W.M.Wood-Vasey,5,9and N.Yasuda 23(The Supernova Cosmology Project)

Received 2003May 24;accepted 2003July 16

ABSTRACT

We report measurements of M , ?,and w from 11supernovae (SNe)at z ?0:360:86with high-quality light curves measured using WFPC2on the Hubble Space Telescope (HST ).This is an independent set of high-redshift SNe that con?rms previous SN evidence for an accelerating universe.The high-quality light curves available from photometry on WFPC2make it possible for these 11SNe alone to provide measure-ments of the cosmological parameters comparable in statistical weight to the previous https://www.wendangku.net/doc/9817570816.html,bined with earlier Supernova Cosmology Project data,the new SNe yield a measurement of the mass density

M ?0:25t0:07

à0:06estatistical T?0:04(identi?ed systematics),or equivalently,a cosmological constant of ??0:75t0:06à0:07estatistical T?0:04(identi?ed systematics),under the assumptions of a ?at universe and that the dark energy equation-of-state parameter has a constant value w ?à1.When the SN results are combined with independent ?at-universe measurements of M from cosmic microwave background and galaxy redshift

distortion data,they provide a measurement of w ?à1:05t0:15

à0:20estatistical T?0:09(identi?ed systematic),if w is assumed to be constant in time.In addition to high-precision light-curve measurements,the new data o?er 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 (B àV )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 (B àV )distribution.Our cosmological ?ts using full extinction corrections con?rm that dark energy is required with P e ?>0T>0:99,a result consistent with previous and current SN analyses that rely on the identi?cation of a low-extinction subset or prior assumptions concerning the intrinsic extinction distribution.

Subject headings:cosmological parameters —cosmology:observations —supernovae:general

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 scienti?c 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 ?nancial 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-0586and 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 Scienti?que de France,and the University of Hawaii.

2Department of Physics and Astronomy,Vanderbilt University,P.O.Box 1803,Station B,Nashville,TN 37240.

3Visiting 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.

4Visiting 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 https://www.wendangku.net/doc/9817570816.html,wrence Berkeley National Laboratory,1Cyclotron Road,Berkeley,CA 94720.6Department of Physics,Stockholm University,SCFAB,S-10691Stockholm,Sweden.7Laboratoire de Physique Nucle ′aire et de Haute Energies,CNRS-IN2P3,University of Paris VI and VII,Paris,France.8Colorado College,14East Cache La Poudre Street,Colorado Springs,CO 80903.

9Department of Physics,University of California at Berkeley,366LeConte Hall,Berkeley,CA 94720-7300.10American Astronomical Society,2000Florida Avenue,NW,Suite 400,Washington,DC 20009.

11Department of Astronomy,and Research Center for the Early Universe,School of Science,University of Tokyo,Bunkyo-ku,Tokyo 113-0033,Japan.12California Institute of Technology,East California Boulevard,Pasadena,CA 91125.13Centro,Multidisiplinar de Astrof?′sica,Instituto Superior Te ′cnico,P-1300Lisbon,Portugal.14Space Telescope Science Institute,3700San Martin Drive,Baltimore,MD 21218.

15Department of Physics,University of Oxford,Nuclear and Astrophysics Laboratory,Keble Road,Oxford OX13RH,UK.16European Southern Observatory,St.Alonso de Co ′rdova 3107,Vitacura,Casilla 19001,Santiago 19,Chile.

17Isaac Newton Group of Telescopes,Apartado de Correos 321,Santa Cruz de La Palma,E-38780Canary Islands,Spain.18Department of Astronomy,University of Barcelona,E-08028Barcelona,Spain.

19Now at Laboratoire Leprince-Ringuet,CNRS-IN2P3,Ecole Polytechnique,Palaiseau,France.20Department of Astronomy,University of Texas at Austin,RLM 15.308,Austin,TX 78712.21Department of Physics,University of Durham,South Road,Durham DH13LE,UK.

22Institute of Astronomy,University of Cambridge,Madingley Road,Cambridge CB30HA,UK.23National Astronomical Observatory of Japan,2-21-1,Ohsawa,Mitaka,Tokyo 181-8588,Japan.

The Astrophysical Journal ,598:102–137,2003November 20

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 review see Perlmutter& Schmidt2003).These results ruled out a?at,matter-dominated( M?1, ??0)universe.For a?at universe, motivated by in?ation theory,these studies 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 than99%con?dence.

The SN results combined with observations of the power spectrum of the cosmic microwave background(CMB;e.g., Ja?e et al.2001;Bennett et al.2003;Spergel et al.2003),the properties of massive clusters(e.g.,Turner2001;Allen, Schmidt,&Fabian2002;Bahcall et al.2003),and dynami-cal redshift-space distortions(Hawkins et al.2002)yield a consistent picture of a?at universe with M’0:3and ?’0:7(Bahcall et al.1999).Each of these measurements is sensitive to di?erent combinations of the parameters; hence,they complement each other.Moreover,because there are three di?erent 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 di?erent epochs of the universe’s history suggests a vindication of the standard model of the expanding universe.

In the redshift range around z?0:40:7,the SN results are most sensitive to a linear combination of M and ?close to Mà ?.In contrast,galaxy clustering and dynamics are sensitive primarily to M alone,while the CMB is most sensitive to Mt ?.Although combinations of other measurements lead to a separate con?rmation 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 dark energy.Therefore,it is of importance to improve the precision of the SN result,to con?rm the result with additional independent high-redshift SNe,and also to limit the possible e?ects 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 e?ect of host galaxy dust.For a given mass density,the e?ect 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 ??0.Dust extinction from within the host galaxy of the high-redshift SNe could have a similar e?ect;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 e?ect 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(‘‘?t 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;‘‘?t E’’of P99).

In Sullivan et al.(2003),we set stronger limits on the e?ects of host galaxy extinction by comparing the extinc-tion,cosmological parameters,and SN peak magnitude dis-persion for subsets of the SCP SNe observed in di?erent types of host galaxies,as identi?ed 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,Hoe?ich,&Wheeler1997). This subset of the P99sample—in hosts unlikely to be strongly a?ected by extinction—independently provided evidence at the5 level that ?>0in a?at universe and con?rmed that host galaxy dust extinction was unlikely to be a signi?cant systematic in the results of P99,as had been suggested previously(e.g.,Rowan-Robinson2002).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(BàV)measurements that allow us to directly measure the e?ect of host galaxy extinc-tion on each SN event without resorting to a prior on the color excess distribution.

The current paper presents11new SNe discovered and observed by the SCP at redshifts0:36

The HST provides two primary advantages for photom-etry of point sources such as SNe.First,the sky background is much lower,allowing 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-pli?es 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 11SNe in this paper than was possible for previous ground-based observations.These11SNe themselves provide a high-precision new set of high-redshift SNe to test the accel-erating universe results.Moreover,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?rst describe the point-spread function(PSF)?t photometry method used for extracting the light curves from the WFPC2images(x2.1).Next,in x2.2we describe the light-curve?tting procedure,including the methods used for calculating accurate K-corrections.So that all SNe may be treated consistently,in x2.3we apply the slightly

M, ?,AND w FROM HST-OBSERVED SN e I a103

updated K-correction procedure to all of the SNe used in P99.In x2.4the cosmological?t methodology we use is described.In x3we discuss the evidence for host galaxy extinction(only signi?cant for three of the11new SNe) from the RàI light-curve colors.In x4.1we 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 x4.2we perform a combined?t with our data and the high-redshift SNe of Riess et al.(1998). Finally,in x4.3we 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 x5.

2.OBSERVATIONS,DATA REDUCTION,

AND ANALYSIS

2.1.WFPC2Photometry

The SNe discussed in this paper are listed in Table1.They were discovered during three di?erent SN searches,follow-ing the techniques described in Perlmutter et al.(1995,1997) and P99.Two of the searches were conducted with the4m Blanco telescope at the Cerro Tololo Inter-American Observatory(CTIO),in1997November/December and 1998March/April.The?nal search was conducted at the Canada-France-Hawaii Telescope(CFHT)on Mauna Kea in Hawaii in2000April/May.In each case,two to three nights of reference images were followed3–4weeks later by two to three nights of search images.The two images of each search?eld 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 the1998March/April search.Out of the three searches,11of the resulting SN discoveries were followed with extensive HST photometry.These SNe are spaced approximately evenly in the redshift range0:3

Spectra were obtained with the red side of LRIS on the Keck10m telescope(Oke et al.1995),with FORS1on Antu (VLT-UT1;Appenzeller et al.1998)and with EFOSC224on the ESO3.6m telescope.These spectra were used to con?rm the identi?cation of the candidates as SNe Ia and to meas-ure the redshift of each candidate.Nine of the11SNe in the set have strong con?rmation as Type Ia through the pres-ence of Si ii 6150,Si ii 4190,or Fe ii features that match those of a Type Ia observed at a similar epoch.SN1998ay and SN1998be have spectra that are consistent with SN Ia spectra,although this identi?cation 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 e?ect of removing those two SNe from the set in x5.2.)

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 measurements in z is typically 0.001.In cases in which there were not su?cient host galaxy features(SN1998aw and SN1998ba),redshifts were measured from the SN itself;in these cases,z is measured with a(conservative)precision of0.01(Branch&van den Bergh1993).Even in the latter case,redshift measurements do not contribute signi?cantly to the uncertainties in the ?nal cosmological measurements since these are dominated by the photometric uncertainties.

Each of these SNe was imaged with two broadband?lters using the Planetary Camera(PC)CCD of the WFPC2on the HST,which has a scale of0>046pixelà1.Table1lists the dates of these observations.The F675W and F814W broad-band?lters 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?lters at the targeted redshifts. (Note that all of our WFPC2observing parameters except the exact target coordinates were?xed prior to the SN dis-coveries.)The e?ective 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?lters roughly correspond to redshifted B-and V-band?lters for the SNe at z<0:7and redshifted U-and B-band?lters for the SNe at z>0:7.

The HST images were reduced through the standard HST‘‘on-the-?y 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 reject cosmic rays using the ‘‘crrej’’procedure(a part of the STSDAS IRAF package). Photometric?uxes were extracted from the?nal images using a PSF-?tting procedure.Traditional PSF-?tting 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?ux is the same in all of the images,we used a PSF-?tting procedure that?ts a PSF simultaneously to every image of a given SN observed through a given photometric?lter.The model we?t was

f iex;yT?f0i PSFexàx0i;yày0iT

tbgexàx0i;yày0i;a jTtp i;e1Twhere f iex;yTis the measured?ux in pixel(x,y)of the i th image,(x0i,y0i)is the position of the SN on the i th image,f0i is the total?ux in the SN in the i th image,PSFeu;vTis a nor-malized PSF,bgeu;v;aTis a temporally constant back-ground parametrized by a j,and p i is a pedestal o?set for the i th image.There are4ntmà1parameters in this model, where n is the number of images(typically2,5,or6 previously summed images)and m is the number of param-eters a j that specify the background model(typically3or6). (Theà1is 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,x0i,y0i,p i,and a j.

Because of the scarcity of objects in our PC images, geometric transformations between the images at di?erent epochs using other objects on the four chips of WFPC2 together allowed an a priori determination of(x0i,y0i)good to$1pixel.Allowing those parameters to vary in the?t (e?ectively,using the point-source signature of the SN to determine the o?set of the image)provided position

24See https://www.wendangku.net/doc/9817570816.html,/lasilla/sciops/efosc.

104KNOP ET AL.

TABLE1

WFPC2Supernova Observations

SN Name z F675W Observations F814W Observations

1997ek..................0.8631998Jan05(400s,400s)1998Jan05(500s,700s)

1998Jan11(400s,400s)1998Jan11(500s,700s)

1998Feb02(1100s,1200s)

1998Feb14(1100s,1200s)

1998Feb27(1100s,1200s)

1998Nov09(1100s,1300s)

1998Nov16(1100s,1300s)

1997eq..................0.5381998Jan06(300s,300s)1998Jan06(300s,300s)

1998Jan21(400s,400s)1998Jan11(300s,300s)

1998Feb02(500s,700s)

1998Feb11(400s,400s)1998Feb11(500s,700s)

1998Feb19(400s,400s)1998Feb19(500s,700s)

1997ez...................0.7781998Jan05(400s,400s)1998Jan05(500s,700s)

1998Jan11(400s,400s)1998Jan11(500s,700s)

1998Feb02(1100s,1200s)

1998Feb14(1100s,1200s)

1998Feb27(100s,1200s,1100s,1200s) 1998as...................0.3551998Apr08(400s,400s)1998Apr08(500s,700s)

1998Apr20(400s,400s)1998Apr20(500s,700s)

1998May11(400s,400s)1998May11(500s,700s)

1998May15(400s,400s)1998May15(500s,700s)

1998May29(400s,400s)1998May29(500s,700s)

1998aw..................0.4401998Apr08(300s,300s)1998Apr08(300s,300s)

1998Apr18(300s,300s)1998Apr18(300s,300s)

1998Apr29(400s,400s)1998Apr29(500s,700s)

1998May14(400s,400s)1998May14(500s,700s)

1998May28(400s,400s)1998May28(500s,700s)

1998ax..................0.4971998Apr08(300s,300s)1998Apr08(300s,300s)

1998Apr18(300s,300s)1998Apr18(300s,300s)

1998Apr29(300s,300s)1998Apr29(500s,700s)

1998May14(300s,300s)1998May14(500s,700s)

1998May27(300s,300s)1998May27(500s,700s)

1998ay..................0.6381998Apr08(400s,400s)1998Apr08(500s,700s)

1998Apr20(400s,400s)1998Apr20(500s,700s)

1998May11(1100s,1200s)

1998May15(1100s,1200s)

1998Jun03(1100s,1200s)

1998ba..................0.4301998Apr08(300s,300s)1998Apr08(300s,300s)

1998Apr19(300s,300s)1998Apr19(300s,300s)

1998Apr29(400s,400s)1998Apr29(500s,700s)

1998May13(400s,400s)1998May13(500s,700s)

1998May28(400s,400s)1998May28(500s,700s)

1998be..................0.6441998Apr08(300s,300s)1998Apr08(300s,300s)

1998Apr19(300s,300s)1998Apr19(300s,300s)

1998Apr30(400s,400s)1998Apr30(500s,700s)

1998May15(400s,400s)1998May15(500s,700s)

1998May28(400s,400s)1998May28(500s,700s)

1998bi...................0.7401998Apr06(400s,400s)1998Apr06(500s,700s)

1998Apr18(400s,400s)1998Apr18(500s,700s)

1998Apr28(1100s,1200s)

1998May12(1100s,1200s)

1998Jun02(1100s,1200s)

2000fr...................0.5432000May08(2200s)

2000May15(600s,600s)2000May15(1100s,1100s)

2000May28(600s,600s)2000May28(600s,600s)

2000Jun10(500s,500s)2000Jun10(600s,600s)

2000Jun22(1100s,1300s)2000Jun22(1100s,1200s)

2000Jul08(1100s,1300s)2000Jul08(110s,1200s)

measurements a factor of$10better.25The model was?tted to13?13pixel patches extracted from all of the images of a time sequence of a single SN in a single?lter(except for SN 1998ay,which is close enough to the host galaxy that a7?7 pixel patch was used to avoid having to?t the core of the galaxy with the background model).In four out of the99 patches used in the?ts to the22light curves,a single bad pixel was masked from the?t.The series of f0i values,cor-rected as described in the rest of this section,provided the data used in the light-curve?ts described in x2.2.For one SN(SN1997ek at z?0:86),the F814W background was further constrained by an SN-free‘‘?nal reference’’image taken11months after the SN explosion.26

A single Tiny Tim PSF(Krist&Hook2003)was used as PSFeu;vTfor all images of a given?lter.The Tiny Tim PSF used was subsampled to10?10subpixels;in the?t proce-dure,it was shifted and integrated(properly summing frac-tional subpixels).After shifting and resampling to the PC pixel scale,it was convolved with an empirical3?3electron di?usion kernel with75%of the?ux in the central element (A.Fruchter2000,private communication).27The PSF was normalized in a0>5radius aperture,chosen to match the standard zero-point calibration(Holtzman et al.1995; Dolphin2000).Although the use of a single PSF for every image is an approximation(the PSF of WFPC2depends 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-?tting 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?uxes were not signi?cantly di?erent, showing di?erences in both directions generally within 1%–2%of the SN peak?ux 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 su?ers from an imperfect charge transfer e?ciency(CTE)e?ect,which can lead to a systematic underestimate of the?ux of point sources(Whitemore, Heyer,&Casertano1999;Dolphin2000,2003).28On the PC,these e?ects can be as large as$15%.The measured?ux values(f0i 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?uxes,although in all cases these uncer-tainties were smaller than the uncertainties in the raw measured?ux 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?ux whose fraction of the total?ux 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 a?ects 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?uxes were extracted from images using the same aperture photometry procedure of P99.A complete light curve in a given?lter(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(0.003for F814W or 0.006for 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?uxes.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 con?rmed over two or more nights.Ground-based zero-point uncertainties are generally d0.02–0.03;the R-band ground-based zero point for SN1998ay is only good to?0.05.We have compared our ground-based aperture photometry with our HST PSF-?tting photometry using the limited number of su?ciently bright stars present in the PC across the11SNe?elds.We ?nd the di?erence between the HST and ground-based photometry to be0:02?0:02in both the R and I bands, consistent with no o?set.The correlated uncertainties between di?erent 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?ts(see x2.4).

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?ts to the time series of photometric data for each SN.In addition to the11SNe described here,light-curve?ts were also per-formed to the SNe from P99,including18SNe 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 H96SNe(having data within6days of maxi-mum light and located at cz>4000km sà1,limiting distance modulus error due to peculiar velocities to less than0.15 mag).Because of new templates and K-corrections(see below),light-curve?ts to the SNe from H96and P99used in

25Note that this may introduce a bias toward higher?ux,as the?t will

seek out positive?uctuations on which to center the PSF.However,the

covariance between the peak?ux and position is typically less than$4%of

the product of the positional uncertainty and the?ux uncertainty,so the

e?ects of this bias will be very small in comparison to our photometric

errors.

26Although obtaining?nal references to subtract the galaxy background

is standard procedure for ground-based photometry of high-redshift SNe,

the higher resolution of WFPC2provides su?cient separation between the

SN and host galaxy that such images are not always necessary,particularly

in this redshift range.

27See also https://www.wendangku.net/doc/9817570816.html,/software/tinytim/tinytim_faq.html.

28Available at https://www.wendangku.net/doc/9817570816.html,/hst/HST_overview/documents/

calworkshop/workshop2002/CW2002_Papers/CW02_dolphin.

29These CTE corrections used updated coe?cients posted on

Dolphin’s web page(https://www.wendangku.net/doc/9817570816.html,/sta?/dolphin/wfpc2_calib/)

in September,2002.

106KNOP ET AL.Vol.598

the analyses below were redone for consistency.The results

of these?ts are slightly di?erent from those quoted in P99for the same SNe as a result of the change in the light-curve tem-plate,the new K-corrections,and the di?erent?t procedure,

all discussed below.For example,because the measured E(BàV)value was considered in the K-corrections(x2.3), whereas it was not in P99,one should expect to see randomly

distributed di?erences in?t SN light-curve parameters as a result of scatter in the color measurements.

Light-curve?ts were performed using a 2minimization

procedure based on MINUIT(James&Roos1975).For both high-and low-redshift SNe,color corrections and K-corrections are applied(see x2.3)to the photometric data. These data were then?tted to light-curve templates.Fits

were performed to the combined R-and I-band data for each high-redshift SN.For low-redshift SNe,?ts were performed using only the B-and V-band data(which corre-

spond to deredshifted R and I bands for most of the high-redshift SNe).The light-curve model?t to the SN has four parameters to modify the light-curve templates:time of rest-

frame B-band maximum light,peak?ux in R,RàI color at the epoch of rest-frame maximum B-band light,and time-scale stretch s.Stretch is a parameter that linearly scales the

time axis,so that an SN with a high stretch has a relatively slow decay from maximum and an SN with a low stretch has a relatively fast decay from maximum(Perlmutter et al. 1997;Goldhaber et al.2001).For SNe in the redshift range

z?0:30:7,a B template was?tted to the R-band light curve and a V template was?tted to the I-band light curve. For SNe at z>0:7,a U template was?tted to the R-band

light curve and a B template to the I-band light curve.Two of the high-redshift SNe from P99fall at z$0:18(SN1997I and SN1997N);for these SNe,V and R templates were?t-

ted to the R-and I-band data.(The peak B-band magnitude was extracted by adding the intrinsic SN Ia BàV color to the?t V-band magnitude at the epoch of B maximum.)

The B template used in the light-curve?ts was that of

Goldhaber et al.(2001).For this paper,new V-and R-band templates were generated following a procedure similar to that of Goldhaber et al.(2001),by?tting a smooth param-

eterized curve through the low-redshift SN data of H96and R99.A new U-band template was generated with data from Hamuy et al.(1991),Lira et al.(1998),Richmond et al.

(1995),Suntze?et al.(1999),and Wells et al.(1994);com-parison of our U-band template shows good agreement with the new U-band photometry from Jha(2002)at the relevant

epochs.New templates were generated by?tting a smooth curve,f(t0),to the low-redshift light-curve data,where t0?t=e1tzT=s;t is the number of observer frame days rela-tive to the epoch of the B-band maximum of each SN,z is

the redshift of each SN,and s is the stretch of each SN as measured from the B-band light curves.Light-curve tem-plates had an initial parabola with a20day rise time

(Aldering,Knop,&Nugent2000),joined to a smooth spline section to describe the main part of the light curve,then joined to an exponential decay to describe the?nal tail at greater than$70days past maximum light.The?rst100 days of each of the three templates is listed in Table2. Because of a secondary‘‘hump’’or‘‘shoulder’’$20 days after maximum,the R-band light curve does not vary strictly according to the simple time-axis scaling parameter-ized by stretch that is so successful in describing the di?erent U-,B-,and V-band light curves.However,for the two z$0:18SNe to which we?t an R-band template,the peak R-and I-band magnitudes are well constrained,and the stretch is also well measured from the rest-frame V-band light curve.

Some of the high-redshift SNe from P99lack an SN-free host galaxy image.These SNe were?tted with an additional variable parameter:the zero level of the I-band light curve. The SNe treated in this manner include SN1997O,SN 1997Q,SN1997R,and SN1997am.

The late-time light-curve behavior may bias the result of a light-curve?t(Aldering et al.2000);it is therefore important that the low-and high-redshift SNe are treated in as consis-tent a manner as possible.Few or none of the high-redshift SNe have high-precision measurements more than$40–50 rest-frame days after maximum light,so as in Perlmutter et al.(1997)and P99these late-time points were eliminated from the low-redshift light-curve data before the template ?t procedure.Additionally,to allow for systematic o?set uncertainties on the host galaxy subtraction,an‘‘error ?oor’’of0.007times the maximum light-curve?ux was applied;any light-curve point with an uncertainty below the error?oor had its uncertainty replaced by that value (Goldhaber et al.2001).

The?nal results of the light-curve?ts,including the e?ect of color corrections and K-corrections,are listed in Table3 for the11SNe of this paper.Table4shows the results of new light-curve?ts to the high-redshift SNe of P99used in this paper(see x2.5),and Table5shows the results of light-curve?ts for the low-redshift SNe from H96and R99.30The Appendix tabulates all of the light-curve data for the11 HST SNe in this paper.The light curves for these SNe(and the F675W WFPC2image nearest maximum light)are shown in Figure1.Note that there are correlated errors between all of the ground-based points for each SN in these ?gures,as a single ground-based zero point was used to scale each of them together with the HST photometry.

2.3.Color and K-Corrections

In order to combine data from di?erent telescopes,color corrections were applied to remove the di?erences in the spectral responses of the?lters relative to the Bessell system (Bessell1990).For the ground-based telescopes,the?lters are close enough to the standard Bessell?lters that a single linear color term(measured at each observatory with stan-dard stars)su?ces to put the data onto the Bessell system, with most corrections being smaller than0.01mag.The WFPC2?lters are di?erent enough from the ground-based ?lters,however,that a linear term is not su?cient.More-over,the di?erences between an SN Ia and standard-star spectral energy distribution are signi?cant.In this case, color corrections were calculated by integrating template SN Ia spectra(described below)through the system response.

In order to perform light-curve template?tting,a cross ?lter K-correction must be applied to transform the data in the observed?lter into a rest-frame magnitude in the?lter used for the light-curve template(Kim,Goobar,& Perlmutter1996).The color correction to the nearest stan-dard Bessell?lter followed by a K-correction to a rest-frame ?lter is equivalent to a direct K-correction from the observed?lter to the standard rest-frame?lter.In practice, 30These three tables are available in electronic form from

https://www.wendangku.net/doc/9817570816.html,.

No.1,2003 M, ?,AND w FROM HST-OBSERVED SN e I a107

we perform the two steps separately so that all photometry may be combined to provide a light curve e?ectively observed through a standard(e.g.,R-band)?lter,which may then be?tted with a single series of K-corrections. The data tabulated in the Appendix have all been color-corrected to the standard Bessell?lters.

Color and K-corrections were performed following the procedure of Nugent,Kim,&Perlmutter(2002).In order to perform these corrections,a template SN Ia spectrum for each epoch of the light curve,as described in that paper,is necessary.The spectral template used in this present work began with the template of that paper.To it was applied a smooth multiplicative function at each day such that inte-gration of the spectrum through the standard?lters would produce the proper intrinsic colors for an SN Ia(including a mild dependence of those intrinsic colors on stretch).

The proper intrinsic colors for the SN spectral template were determined in the BVRI spectral range by smooth?ts

TABLE2

U,V,and R Light-Curve Templates Used

Day a U Flux b V Flux b R Flux b Day a U Flux b V Flux b R Flux b

à19........ 6.712Eà03 4.960Eà03 5.779Eà0331........... 4.790Eà02 2.627Eà01 3.437Eà01

à18........ 2.685Eà02 1.984Eà02 2.312Eà0232........... 4.524Eà02 2.481Eà01 3.238Eà01

à17........ 6.041Eà02 4.464Eà02 5.201Eà0233........... 4.300Eà02 2.345Eà01 3.054Eà01

à16........ 1.074Eà017.935Eà029.246Eà0234........... 4.112Eà02 2.218Eà01 2.887Eà01

à15........ 1.678Eà01 1.240Eà01 1.445Eà0135........... 3.956Eà02 2.099Eà01 2.733Eà01

à14........ 2.416Eà01 1.785Eà01 2.080Eà0136........... 3.827Eà02 1.990Eà01 2.592Eà01

à13........ 3.289Eà01 2.430Eà01 2.832Eà0137........... 3.722Eà02 1.891Eà01 2.463Eà01

à12........ 4.296Eà01 3.174Eà01 3.698Eà0138........... 3.636Eà02 1.802Eà01 2.345Eà01

à11........ 5.437Eà01 4.017Eà01 4.681Eà0139........... 3.565Eà02 1.721Eà01 2.237Eà01

à10........ 6.712Eà01 4.960Eà01 5.779Eà0140........... 3.506Eà02 1.649Eà01 2.137Eà01

à9..........7.486Eà01 5.889Eà01 6.500Eà0141........... 3.456Eà02 1.583Eà01 2.046Eà01

à8..........8.151Eà01 6.726Eà017.148Eà0142........... 3.410Eà02 1.524Eà01 1.962Eà01

à7..........8.711Eà017.469Eà017.725Eà0143........... 3.365Eà02 1.471Eà01 1.884Eà01

à6..........9.168Eà018.115Eà018.236Eà0144........... 3.318Eà02 1.423Eà01 1.813Eà01

à5..........9.524Eà018.660Eà018.681Eà0145........... 3.266Eà02 1.378Eà01 1.747Eà01

à4..........9.781Eà019.103Eà019.062Eà0146........... 3.205Eà02 1.337Eà01 1.687Eà01

à3..........9.940Eà019.449Eà019.382Eà0147........... 3.139Eà02 1.299Eà01 1.630Eà01

à2.......... 1.000E+009.706Eà019.639Eà0148........... 3.072Eà02 1.263Eà01 1.578Eà01

à1..........9.960Eà019.880Eà019.834Eà0149........... 3.005Eà02 1.229Eà01 1.529Eà01

0.............9.817Eà019.976Eà019.957Eà0150........... 2.945Eà02 1.195Eà01 1.483Eà01

1.............9.569Eà01 1.000E+00 1.000E+0051...........

2.893Eà02 1.161Eà01 1.440Eà01

2.............9.213Eà019.958Eà019.952Eà0152........... 2.853Eà02 1.128Eà01 1.398Eà01

3.............8.742Eà019.856Eà019.803Eà0153........... 2.830Eà02 1.096Eà01 1.359Eà01

4.............8.172Eà019.702Eà019.545Eà0154........... 2.827Eà02 1.064Eà01 1.320Eà01

5.............7.575Eà019.502Eà019.196Eà0155........... 2.849Eà02 1.033Eà01 1.282Eà01

6............. 6.974Eà019.263Eà018.778Eà0156........... 2.793Eà02 1.003Eà01 1.244Eà01

7............. 6.375Eà018.991Eà018.313Eà0157........... 2.738Eà029.743Eà02 1.207Eà01

8............. 5.783Eà018.691Eà017.821Eà0158........... 2.684Eà029.467Eà02 1.170Eà01

9............. 5.205Eà018.369Eà017.324Eà0159........... 2.630Eà029.207Eà02 1.133Eà01

10........... 4.646Eà018.031Eà01 6.842Eà0160........... 2.578Eà028.964Eà02 1.097Eà01

11........... 4.113Eà017.683Eà01 6.396Eà0161........... 2.527Eà028.741Eà02 1.061Eà01

12........... 3.610Eà017.330Eà01 6.007Eà0162........... 2.477Eà028.538Eà02 1.026Eà01

13........... 3.145Eà01 6.977Eà01 5.691Eà0163........... 2.428Eà028.359Eà029.910Eà02

14........... 2.725Eà01 6.629Eà01 5.444Eà0164........... 2.380Eà028.207Eà029.568Eà02

15........... 2.356Eà01 6.293Eà01 5.254Eà0165........... 2.333Eà028.083Eà029.232Eà02

16........... 2.044Eà01 5.972Eà01 5.113Eà0166........... 2.287Eà027.927Eà028.902Eà02

17........... 1.783Eà01 5.667Eà01 5.011Eà0167........... 2.242Eà027.774Eà028.579Eà02

18........... 1.567Eà01 5.376Eà01 4.938Eà0168........... 2.197Eà027.624Eà028.264Eà02

19........... 1.388Eà01 5.099Eà01 4.887Eà0169........... 2.154Eà027.476Eà027.958Eà02

20........... 1.239Eà01 4.835Eà01 4.848Eà0170........... 2.111Eà027.332Eà027.660Eà02

21........... 1.115Eà01 4.583Eà01 4.814Eà0171........... 2.070Eà027.191Eà027.373Eà02

22........... 1.008Eà01 4.342Eà01 4.776Eà0172........... 2.029Eà027.052Eà027.096Eà02

23...........9.144Eà02 4.113Eà01 4.725Eà0173........... 1.989Eà02 6.916Eà02 6.832Eà02

24...........8.314Eà02 3.894Eà01 4.653Eà0174........... 1.949Eà02 6.782Eà02 6.581Eà02

25...........7.583Eà02 3.685Eà01 4.552Eà0175........... 1.911Eà02 6.651Eà02 6.344Eà02

26........... 6.941Eà02 3.486Eà01 4.414Eà0176........... 1.873Eà02 6.523Eà02 6.199Eà02

27........... 6.380Eà02 3.296Eà01 4.247Eà0177........... 1.836Eà02 6.397Eà02 6.057Eà02

28........... 5.891Eà02 3.115Eà01 4.058Eà0178........... 1.799Eà02 6.274Eà02 5.918Eà02

29........... 5.467Eà02 2.943Eà01 3.855Eà0179........... 1.764Eà02 6.153Eà02 5.783Eà02

30........... 5.102Eà02 2.781Eà01 3.645Eà0180........... 1.729Eà02 6.034Eà02 5.650Eà02

a Day is relative to the epoch of the maximum of the B-band light curve.The B-band template may be found in Goldhaber

et al.2001.

b Relative?uxes.

108KNOP ET AL.

T A B L E 3S u p e r n o v a L i g h t -C u r v e F i t s :H S T S u p e r n o v a e f r o m T h i s P a p e r

S N z

m X a m B b m e f f B

c m e f f B

+E x t i n c t i o n C o r r e c t i o n d

S t r e t c h R àI e E (B àV )G a l a c t i c f

E (B àV )h o s t g

E x c l u d e d f r o m S u b s e t s h

1997e k ......................0.86323.3224.51?0.0324.59?0.1924.95?0.441.056?0.0580.838?0.0540.042à0.091?0.0751997e q ......................0.53822.6323.21?0.0223.15?0.1823.02?0.170.960?0.0270.202?0.0300.0440.035?0.0341997e z .......................0.77823.1724.29?0.0324.41?0.1824.00?0.421.078?0.0300.701?0.0480.0260.095?0.0681998a s .......................0.35522.1822.72?0.0322.66?0.1722.02?0.150.956?0.0120.226?0.0270.0370.158?0.0302,31998a w ......................0.44022.5623.22?0.0223.26?0.17...1.026?0.0190.300?0.0240.0260.259?0.0261–31998a x ......................0.49722.6323.25?0.0523.47?0.1722.96?0.201.150?0.0320.212?0.0410.0350.113?0.0442,31998a y ......................0.63823.2623.86?0.0823.92?0.1923.85?0.331.040?0.0410.339?0.0670.0350.015?0.0843

1998b a ......................0.43022.3422.97?0.0522.90?0.1822.75?0.180.954?0.0200.094?0.0360.0240.040?0.0381998b e ......................0.64423.3323.91?0.0423.64?0.1823.26?0.270.816?0.0280.436?0.0510.0290.106?0.0653

1998b i .......................0.74022.8623.92?0.0223.85?0.1723.75?0.370.950?0.0270.552?0.0370.0260.026?0.0502000f r .......................0.54322.4423.07?0.0223.16?0.1723.27?0.141.064?0.0110.135?0.0220.030à0.031?0.025

M a g n i t u d e i n t h e o b s e r v e d ?l t e r a t t h e p e a k o f t h e r e s t -f r a m e B -b a n d l i g h t c u r v e ;X ?R f o r z <0:7,X ?I f o r z >0:7.b

T h i s v a l u e h a s b e e n K -c o r r e c t e d a n d c o r r e c t e d f o r G a l a c t i c e x t i n c t i o n :m B m X àK B X àA X ,w h e r e K B X i s t h e c r o s s ?l t e r K -c o r r e c t i o n a n d A X i s t h e G a l a c t i c e x t i n c t i o n c o r r e c t i o n .T h e s e w e r e t h e v a l u e s u s e d i n t h e c o s m o l o g i c a l ?t s .T h e q u o t e d e r r o r b a r i s t h e u n c e r t a i n t y o n t h e p e a k m a g n i t u d e f r o m t h e l i g h t -c u r v e ?t .c T h i s v a l u e i n c l u d e s t h e s t r e t c h c o r r e c t i o n :m e f f B

m B t es à1T; i s t h e b e s t -?t v a l u e o f t h e s t r e t c h -l u m i n o s i t y s l o p e f r o m t h e ?t t o t h e p r i m a r y l o w -e x t i n c t i o n s u b s e t (?t 3i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r n o n –e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.N o t e t h a t t h e s e v a l u e s a r e o n l y p r o v i d e d f o r c o n v e n i e n c e ;t h e y w e r e n o t u s e d d i r e c t l y i n a n y c o s m o l o g i c a l ?t s ,s i n c e i s a l s o a ?t p a r a m e t e r .d S i m i l a r t o t h e p r e v i o u s c o l u m n ,o n l y w i t h t h e h o s t g a l a x y e x t i n c t i o n c o r r e c t i o n a p p l i e d .T h e s t r e t c h -l u m i n o s i t y s l o p e u s e d f o r t h i s v a l u e i s t h a t f r o m t h e ?t t o t h e p r i m a r y s u b s e t (?t 6i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.E l l i p s e s i n d i c a t e a n S N t h a t d i d n o t a p p e a r i n t h e p r i m a r y s u b s e t (s e e x 2.5).e T h i s i s t h e o b s e r v e d R àI c o l o r a t t h e e p o c h o f t h e r e s t -f r a m e B -b a n d l i g h t -c u r v e p e a k .f S c h l e g e l e t a l .1998;t h i s e x t i n c t i o n i s a l r e a d y i n c l u d e d i n t h e q u o t e d v a l u e s o f m B

.g M e a s u r e m e n t u n c e r t a i n t y o n l y ;n o i n t r i n s i c c o l o r d i s p e r s i o n i n c l u d e d .h T h e s e S N e a r e e x c l u d e d f r o m t h e i n d i c a t e d s u b s e t s ;s e e x 2.5.

T A B L E 4S u p e r n o v a L i g h t -C u r v e F i t s :N e w F i t s t o P 99S N e

S N z m X a m B b m e f f B

c m e f f B

+E x t i n c t i o n C o r r e c t i o n d

S t r e t c h R àI e E (B àV )G a l a c t i c f

E (B àV )h o s t g

E x c l u d e d f r o m S u b s e t s h

1995a r .......................0.46522.8023.48?0.0823.35?0.2221.54?0.970.909?0.1040.509?0.2220.0220.448?0.2421995a s .......................0.49823.0323.69?0.0723.74?0.2323.52?0.871.035?0.0900.155?0.1970.0210.051?0.2123

1995a w ......................0.40021.7822.28?0.0322.57?0.1823.17?0.451.194?0.037à0.127?0.1030.040à0.160?0.1071995a x ......................0.61522.5623.21?0.0623.38?0.2223.98?1.021.112?0.0730.152?0.2040.033à0.153?0.2491995a y ......................0.48022.6423.07?0.0422.90?0.1922.74?0.700.880?0.0640.209?0.1580.1140.047?0.1701995a z .......................0.45022.4622.70?0.0722.66?0.2023.04?0.580.973?0.0640.087?0.1350.181à0.089?0.1441995b a ......................0.38822.0722.64?0.0622.60?0.1822.74?0.450.971?0.0470.006?0.1050.018à0.033?0.1101996c f .......................0.57022.7123.31?0.0323.30?0.1823.53?0.450.996?0.0450.162?0.0910.040à0.054?0.10731996c g .......................0.49022.4623.09?0.0323.11?0.1822.26?0.451.011?0.0400.300?0.0990.0350.205?0.1073

1996c i .......................0.49522.1922.83?0.0222.78?0.1822.92?0.320.964?0.0400.083?0.0700.028à0.033?0.0751996c l .......................0.82823.3724.53?0.1724.49?0.4625.92?0.970.974?0.2390.549?0.1840.035à0.344?0.2511996c m .....................0.45022.6723.26?0.0723.11?0.1822.63?0.770.899?0.0610.214?0.1740.0490.124?0.18531996c n ......................0.43022.5823.25?0.0323.09?0.19...0.890?0.0660.379?0.0900.0250.332?0.0971–3

1997F ........................0.58022.9323.51?0.0623.57?0.2023.30?0.951.041?0.0660.275?0.1970.0400.063?0.2321997H .......................0.52622.7023.26?0.0423.09?0.1922.51?0.800.882?0.0430.303?0.1740.0510.150?0.1941997I .........................0.17220.1820.34?0.0120.29?0.1720.19?0.280.967?0.0090.065?0.0470.0510.026?0.0641997N .......................0.18020.3920.38?0.0220.48?0.1721.28?0.521.067?0.015à0.141?0.0930.031à0.200?0.1231997O .......................0.37422.9923.53?0.0623.60?0.18...1.048?0.0540.087?0.1520.0290.049?0.1621–3

1997P ........................0.47222.5323.16?0.0422.99?0.1823.24?0.910.888?0.0390.058?0.2070.033à0.052?0.2191997Q .......................0.43022.0122.61?0.0222.52?0.1722.55?0.620.935?0.0240.061?0.1400.030à0.002?0.1481997R .......................0.65723.2923.89?0.0523.80?0.1923.68?0.900.940?0.0590.393?0.1750.0300.032?0.2221997a c .......................0.32021.4221.87?0.0221.96?0.1721.95?0.331.061?0.0150.063?0.0650.0270.001?0.0721997a f .......................0.57922.9423.60?0.0723.38?0.1824.31?1.090.850?0.0450.045?0.2260.028à0.215?0.2651997a i .......................0.45022.3422.94?0.0522.63?0.2222.58?0.590.788?0.0840.143?0.1330.0450.026?0.1421997a j .......................0.58122.5823.24?0.0723.16?0.1824.05?0.790.947?0.0450.045?0.1640.033à0.213?0.1931997a m .....................0.41622.0122.58?0.0822.63?0.1822.65?0.461.032?0.0600.037?0.1130.036à0.008?0.1191997a p ......................0.83023.1624.35?0.0724.38?0.1823.74?0.501.023?0.0450.903?0.0820.0260.155?0.118

X ?R f o r z <0:7,X ?I f o r z >0:7.b

m B t es à1T; i s t h e b e s t -?t v a l u e o f t h e s t r e t c h -l u m i n o s i t y s l o p e f r o m t h e ?t t o t h e p r i m a r y l o w -e x t i n c t i o n s u b s e t (?t 3i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r n o n -e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.N o t e t h a t t h e s e v a l u e s a r e o n l y p r o v i d e d f o r c o n v e n i e n c e ;t h e y w e r e n o t u s e d d i r e c t l y i n a n y c o s m o l o g i c a l ?t s ,s i n c e i s a l s o a ?t p a r a m e t e r .d S i m i l a r t o t h e p r e v i o u s c o l u m n ,o n l y w i t h t h e h o s t g a l a x y e x t i n c t i o n c o r r e c t i o n a p p l i e d .T h e s t r e t c h -l u m i n o s i t y s l o p e u s e d f o r t h i s v a l u e i s t h a t f r o m t h e ?t t o t h e p r i m a r y s u b s e t (?t 6i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.E l l i p s e s i n d i c a t e a n S N t h a t d i d n o t a p p e a r i n t h e p r i m a r y s u b s e t (s e e x 2.5).e T h i s i s t h e o b s e r v e d R àI c o l o r a t t h e e p o c h o f t h e r e s t -f r a m e B -b a n d l i g h t -c u r v e p e a k .f S c h l e g e l e t a l .1998;t h i s e x t i n c t i o n i s a l r e a d y i n c l u d e d i n t h e q u o t e d v a l u e s o f m B

110

T A B L E 5S u p e r n o v a L i g h t -C u r v e F i t s :L o w -z S N e f r o m H 96a n d R 99

S N a z

m m e a s B b m B c m e f f B

d m

f f B

+E x t i n c t i o n C o r r e c t i o n e

S t r e t c h R àI f E (B àV )G a l a c t i c g

E (B àV )h o s t h

E x c l u d e d f r o m S u b s e t s i

1990O ......................0.03016.5816.18?0.0316.33?0.2016.30?0.171.106?0.0260.043?0.0250.0980.001?0.0261990a f ......................0.05017.9217.76?0.0117.39?0.1817.42?0.130.749?0.0100.077?0.0110.0350.011?0.0111992P .......................0.02616.1216.05?0.0216.14?0.1916.16?0.161.061?0.027à0.045?0.0180.020à0.008?0.0191992a e ......................0.07518.5918.42?0.0418.35?0.1818.35?0.150.957?0.0180.098?0.0280.0360.003?0.0311992a g .....................0.02616.6716.26?0.0216.34?0.2015.55?0.161.053?0.0150.220?0.0200.0970.189?0.0212,3

1992a l ......................0.01414.6114.48?0.0114.42?0.2314.53?0.200.959?0.011à0.054?0.0120.034à0.025?0.0131992a q .....................0.10119.3819.30?0.0219.12?0.1719.24?0.150.878?0.0170.142?0.0230.012à0.019?0.0261992b c .....................0.02015.1815.10?0.0115.18?0.2015.36?0.161.053?0.006à0.087?0.0090.022à0.046?0.0091992b g .....................0.03617.4116.66?0.0416.66?0.2016.68?0.161.003?0.0140.128?0.0250.181à0.006?0.0261992b h .....................0.04517.7117.60?0.0217.64?0.1817.22?0.141.027?0.0160.101?0.0180.0220.100?0.0191992b l ......................0.04317.3717.31?0.0317.03?0.1817.10?0.140.812?0.0120.017?0.0230.012à0.002?0.0241992b o .....................0.01815.8915.78?0.0115.42?0.2115.31?0.170.756?0.0050.048?0.0120.0270.043?0.0121992b p .....................0.07918.5918.29?0.0118.16?0.1818.41?0.130.906?0.0140.088?0.0150.068à0.056?0.0171992b r ......................0.08819.5219.37?0.0818.93?0.20...0.700?0.0210.186?0.0470.0270.030?0.0521–3

1992b s ......................0.06318.2618.20?0.0418.26?0.1818.37?0.141.038?0.0160.011?0.0220.013à0.031?0.0241993B .......................0.07118.7418.37?0.0418.40?0.1818.10?0.151.021?0.0190.181?0.0270.0800.071?0.0291993O ......................0.05217.8717.64?0.0117.53?0.1817.61?0.130.926?0.0070.042?0.0120.053à0.014?0.0121993a g .....................0.05018.3217.83?0.0217.73?0.1817.26?0.150.936?0.0150.217?0.0200.1110.120?0.0212,3

1994M .....................0.02416.3416.24?0.0316.07?0.2015.84?0.160.882?0.0150.043?0.0220.0230.063?0.0221994S .......................0.01614.8514.78?0.0214.83?0.2214.86?0.191.033?0.026à0.061?0.0190.018à0.010?0.0191995a c ......................0.04917.2317.05?0.0117.17?0.1817.17?0.131.083?0.0120.026?0.0110.042à0.005?0.0111995b d .....................0.01617.3415.32?0.0115.37?0.30...1.039?0.0080.735?0.0080.4900.348?0.0091–3

1996C ......................0.03016.6216.57?0.0416.74?0.1916.50?0.161.120?0.0200.012?0.0260.0140.051?0.0271996a b .....................0.12519.7219.57?0.0419.47?0.1919.82?0.160.934?0.0320.174?0.0250.032à0.082?0.0291996b l ......................0.03517.0816.66?0.0116.71?0.1916.55?0.141.031?0.0150.093?0.0120.0990.036?0.0121996b o .....................0.01616.1815.85?0.0115.65?0.22...0.862?0.0060.406?0.0080.0770.383?0.008

1–3

S N e t h r o u g h 1993a g a r e f r o m H 96;l a t e r o n e s a r e f r o m R 99.b

T h i s i s t h e m e a s u r e d p e a k m a g n i t u d e o f t h e B -b a n d l i g h t c u r v e .c T h i s i n c l u d e s t h e G a l a c t i c e x t i n c t i o n c o r r e c t i o n a n d a K -c o r r e c t i o n :M àB m m e a s B

àK B àA B ,w h e r e K B i s t h e K -c o r r e c t i o n a n d A B i s t h e G a l a c t i c e x t i n c t i o n c o r r e c t i o n .T h e q u o t e d e r r o r b a r i s t h e u n c e r t a i n t y o n t h e p e a k m a g n i t u d e f r o m t h e l i g h t -c u r v e ?t .d T h i s v a l u e i n c l u d e s t h e s t r e t c h c o r r e c t i o n :m e f f B m m e a s B

àK B àA B t es à1T; i s t h e b e s t -?t v a l u e o f t h e s t r e t c h -l u m i n o s i t y s l o p e f r o m t h e ?t t o t h e p r i m a r y l o w -e x t i n c t i o n s u b s e t (?t 3i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r n o n –e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.N o t e t h a t t h e s e v a l u e s a r e o n l y p r o v i d e d f o r c o n v e n i e n c e ;t h e y w e r e n o t u s e d d i r e c t l y i n a n y c o s m o l o g i c a l ?t s ,s i n c e t h e i s a l s o a ?t p a r a m e t e r .e S i m i l a r t o t h e p r e v i o u s c o l u m n ,o n l y w i t h t h e h o s t g a l a x y e x t i n c t i o n c o r r e c t i o n a p p l i e d .T h e s t r e t c h -l u m i n o s i t y s l o p e u s e d f o r t h i s v a l u e i s t h a t f r o m t h e ?t t o t h e p r i m a r y s u b s e t (?t 6i n x 4).T h e q u o t e d e r r o r b a r i n c l u d e s a l l u n c e r t a i n t i e s f o r e x t i n c t i o n -c o r r e c t e d ?t s d e s c r i b e d i n x 2.4.E l l i p s e s i n d i c a t e a n S N t h a t d i d n o t a p p e a r i n t h e p r i m a r y s u b s e t (s e e x 2.5).f T h i s v a l u e h a s b e e n K -c o r r e c t e d a n d c o r r e c t e d f o r G a l a c t i c e x t i n c t i o n .g T h i s i s t h e m e a s u r e d B àV c o l o r a t t h e e p o c h o f r e s t -f r a m e B -b a n d l i g h t -c u r v e m a x i m u m .h S c h l e g e l e t a l .1998;t h i s e x t i n c t i o n i s a l r e a d y i n c l u d e d i n t h e q u o t e d v a l u e s o f m B

i n t h e f o u r t h c o l u m n .i T h e s e S N e a r e e x c l u d e d f r o m t h e i n d i c a t e d s u b s e t s ;s e e x 2.5.

111

to the low-redshift SN data of H96and R99.For each color (B àV ,V àR ,and R àI ),every data point from those papers was K -corrected and corrected for Galactic extinction.These data were plotted together,and then a smooth curve was ?tted to the plot of color versus date relative to maxi-mum.This curve is given by two parameters,each of which is a function of time and is described by a spline under ten-sion:an ‘‘intercept ’’b (t )and a ‘‘slope ’’m (t ).At any given date the intrinsic color is

color t 0eT?b t 0eTtm t 0eT1=s 3à1àá

;e2Twhere t 0?t =s e1tz T? ,z is the redshift of the SN,and s is

the timescale stretch of the SN from a simultaneous ?t to the B and V light curves (matching the procedure used for most of the high-redshift SNe).This arbitrary functional form was chosen to match the stretch versus color distribution.

As the goal was to determine intrinsic colors without making any assumptions about reddening,no host galaxy extinction corrections were applied to the literature data at this stage of the analysis.Instead,host galaxy extinction was handled by performing a robust blue-side ridgeline ?t to the SN color curves,so as to extract the unreddened intrinsic color.Individual color points that were outliers were prevented from having too much weight in the ?t with a small added dispersion on each point.The blue ridgeline was selected by allowing any point more than 1 to the

red

Fig.1.—Light curves and images from the PC CCD on WFPC2for the HST SNe reported in this paper.The left-hand column shows the R -band light curves (including F675W HST data),and the middle column shows I -band light curves (including F814W HST data).Open circles represent ground-based data points,and ?lled circles represent WFPC2data points.Note that there are correlated errors between all of the ground-based points for each SN in these ?gures,as a single ground-based zero point was used to scale each of them together with the HST photometry.The right-hand column shows 600?600images,summed from all HST images of the SN in the indicated ?lter.

112KNOP ET AL.Vol.598

side of the ?t model only to contribute to the 2as if it were 1 away.Additionally,those SNe that were most reddened were omitted.The resulting ?t procedure provided B àV ,V àR ,and R àI as a function of epoch and stretch;those colors were used to correct the template spectrum as described above.

Some of our data extend into the rest-frame U -band range of the spectrum.This is obvious for SNe at z >0:7where a U -band template is ?tted to the R -band data.How-ever,even for SNe at z e 0:55,the deredshifted R -band ?lter begins to overlap the U -band range of the rest-frame spec-trum.Thus,it is also important to know the intrinsic U àB color so as to generate a proper spectral template.We used data from the literature,as given in Table 6.Here there is an insu?cient number of SN light curves to reasonably use the sort of ridgeline analysis used above to eliminate the e?ects of host galaxy extinction in determining the intrinsic BVRI colors.Instead,for U àB ,we perform extinction corrections using the E (B àV )values from Phillips et al.(1999).Based on Table 6,we adopt a U àB color of à0.4at the epoch

Fig.1.—Continued

No.1,2003

M , ?,AND w FROM HST -OBSERVED SN e I a

113

rest-B maximum.This value is also consistent with the data shown in Jha(2002)for SNe with timescale stretch of s$1, although the data are not determinative.In contrast to the other colors,UàB was not considered to be a function of stretch.Even though Jha(2002)does show UàB depending on light-curve stretch,the SNe in this work that would be most a?ected[those at z>0:7where E(BàV)is estimated from the rest-frame UàB color]cover a small range in stretch;current low-redshift UàB data do not show a signi?cant slope within that range.See x5.4for the e?ect of systematic error in the assumed intrinsic UàB colors.

Any intrinsic uncertainty in BàV is already subsumed within the assumed intrinsic dispersion of extinction-corrected peak magnitudes(see x2.4);however,we might expect a larger dispersion in intrinsic UàB due to,e.g.,metal-licity e?ects(Hoe?ich,Wheeler,&Thielemann1998;Lentz et al.2000).The low-redshift U-band photometry may also have unmodeled scatter,e.g.,related to the lack of extensive UV SN spectrophotometry for K-corrections.The e?ect on extinction-corrected magnitudes will be further increased by the greater e?ect of dust extinction on the bluer U-band light. The scatter of our extinction-corrected magnitudes about the best-?t cosmology suggests an intrinsic uncertainty in UàB of0.04mag.This is also consistent with the UàB data of Jha (2002)over the range of timescale stretch of our z>0:7SNe Ia,after two extreme color outliers from Jha(2002)are removed;there is no evidence of such extreme color objects in our data set.Note that this intrinsic UàB dispersion is in addition to the intrinsic magnitude dispersion assumed after extinction correction.

The template spectrum that has been constructed may be used to perform color and K-corrections on both the low-and high-redshift SNe to be used for cosmology.However, it must be further modi?ed to account for the reddening e?ects of dust extinction in the SN host galaxy and extinc-tion of the redshifted spectrum due to Galactic dust.To cal-culate the reddening e?ects of both Galactic and host galaxy extinction,we used the interstellar extinction law of O’Donnell(1994)with the standard value of the parameter R V?3:1.Color excess[E(BàV)]values due to Galactic extinction were obtained from Schlegel,Finkbeiner,& Davis(1998).

The E(BàV)values quoted in Tables3,4,and5are the values necessary to reproduce the observed RàI color at the epoch of the maximum of the rest-frame B light curve.This reproduction was performed by modifying the spectral tem-plate exactly as described above,given the intrinsic color of the SN from the?t stretch,the Galactic extinction,and the host galaxy E(BàV)parameter.The modi?ed spectrum was integrated through the Bessell R-and I-band?lters,and E(BàV)was varied until the RàI value matched the peak color from the light-curve?t.

For each SN,this?nally modi?ed spectral template was integrated through the Bessell and WFPC2?lter transmis-sion functions to provide color and K-corrections.The exact spectral template needed for a given data point on a given SN is dependent on parameters of the?t:the stretch,the time of each point relative to the epoch of rest-B maximum, and the host galaxy E(BàV)(measured as described above). Thus,color and K-corrections were performed iteratively with light-curve?tting in order to generate the?nal correc-tions used in the?ts described in x2.2.An initial date of maximum,stretch,and host galaxy extinction was assumed in order to generate K-corrections for the?rst iteration of the?t.The parameters resulting from that?t were used to generate new color and K-corrections,and the whole procedure was repeated until the results of the?t converged. Generally,the?t converged within two to three iterations.

2.4.Cosmological Fit Methodology Cosmological?ts to the luminosity distance modulus equation from the Friedmann-Robertson-Walker metric followed the procedure of P99.The set of SN redshifts(z) and K-corrected peak B magnitudes(m B)were?tted to the equation

m B?Mt5log D Lez; M; ?Tà esà1T;e3Twhere s is the stretch value for the SN,D L H0d L is the ‘‘Hubble constant–free’’luminosity distance(Perlmutter et al.1997),and M M Bà5log H0t25is the‘‘Hubble constant–free’’B-band peak absolute magnitude of an s?1SN Ia with true absolute peak magnitude M B.With this procedure,neither H0nor M B need be known independ-ently.The peak magnitude of an SN Ia is mildly dependent on the light-curve decay timescale,such that SNe with a slow decay(high stretch)tend to be overluminous,while SNe with a fast decay(low stretch)tend to be under-luminous(Phillips1993); is a slope that parameterizes this relationship.

There are four parameters in the?t:the mass density M and cosmological constant ?,as well as the two nuisance parameters,M and .The four-dimensional( M, ?,M, )space is divided into a grid,and at each grid point a 2 value is calculated by?tting the luminosity distance equa-tion to the peak B-band magnitudes and redshifts of the SNe.The range of parameter space explored included M??0;3T, ???à1;3T(for?ts where host galaxy extinction corrections are not directly applied)or M??0;4T, ???à1;4T(for?ts with host galaxy extinc-tion corrections).The two nuisance parameters are?tted in the ranges ??à1;4Tand M??à3:9;3:2T.No further constraints are placed on the parameters.(These ranges for the four?t parameters contain greater than99.99%of the probability.)At each point on the four-dimensional grid,a 2is calculated,and a probability is determined from P/eà 2=2.The probability of the whole four-dimensional grid is normalized and then integrated over the two dimensions corresponding to the‘‘nuisance’’parameters. For each?t,all peak m B values were corrected for Galactic extinction using E(BàV)values from Schlegel

TABLE6

UàB SN I a Colors at Epoch of B-Band Maximum

SN Raw UàB a Corrected UàB b References

1980N...............à0.21à0.291

1989B................0.08à0.332

1990N...............à0.35à0.453

1994D...............à0.50à0.524

1998bu..............à0.23à0.515

a This is the measured UàB value from the cited paper.

b This UàB value is K-corrected and corrected for host galaxy and

Galactic extinction.

References.—(1)Hamuy et al.1991.(2)Wells et al.1994.(3)Lira

et al.1998.(4)Wu,Yan,&Zou1995.(5)Suntze?et al.1999.

114KNOP ET AL.Vol.598

et al.(1998),using the extinction law of O’Donnell(1994) integrated through the observed?lter.31For our primary ?ts,the total e?ective statistical uncertainty on each value of m B included the following contributions:

1.The uncertainty on m B from the light-curve?ts.

2.The uncertainty on s,multiplied by .

3.The covariance between m B and s.

4.A contribution from the uncertainty in the redshift due to peculiar velocity(assumed to have a dispersion of 300km sà1along the line of sight).

5.10%of the Galactic extinction correction.

6.0.17mag of intrinsic dispersion(H96).

Fits where host galaxy extinction corrections are explicitly applied use the?rst?ve items above plus the following:

1.The uncertainty on E(BàV)multiplied by R B.

2.The covariance between E(BàV)and m B.

3.0.11mag of intrinsic dispersion(Phillips et al.1999).

4.An additional0.04mag of intrinsic UàB dispersion for z>0:7.

Host galaxy extinction corrections used a value R B A B=EeBàVT?4:1,which results from passing an SN Ia spectrum through the standard O’Donnell(1994)extinction law.Except where explicitly noted below,the E(BàV) uncertainties are not reduced by any prior assumptions on the intrinsic color excess distribution.Although there is almost certainly some intrinsic dispersion either in R B or in the true BàV color of an SN Ia(Nobili et al.2003),we do not explicitly include such a term.The e?ect of such a dis-persion is included,in principle,in the0.11mag of intrinsic magnitude dispersion that Phillips et al.(1999)found after applying extinction corrections.

As discussed in x2.3,the intrinsic UàB dispersion is likely to be greater than the intrinsic BàV dispersion.For those SNe most a?ected by this(i.e.,those at z>0:7),we included an additional uncertainty corresponding to0.04mag of intrinsic UàB dispersion,converted into a magnitude error using the O’Donnell extinction law.

This set of statistical uncertainties is slightly di?erent from that used in P99.For these?ts,the test value of was used to propagate the stretch errors into the corrected B-band magnitude errors;in contrast,P99used a single value of for purposes of error propagation.

2.5.Supernova Subsets

In P99,separate analyses were performed and compared for the SN sample before and after removing SNe with less secure identi?cation as Type Ia.The results were shown to be consistent,providing a cross-check of the cosmological conclusions.For the analyses of this paper,adding and comparing11very well measured SNe Ia,we only consider from P99the more securely spectrally identi?ed SNe Ia with reasonable color measurements(i.e., RàI<0:25);those SNe are listed in Table4.Following P99,we omit one SN that is an outlier in the stretch distribution,with s<0:7(SN 1992br),and one SN that is a greater than6 outlier from the best-?t cosmology(SN1997O).We also omit those SNe that are most seriously reddened,with EeBàVT>0:25and greater than3 above zero;host galaxy extinction correc-tions have been found in studies of low-redshift SNe to overcorrect these reddest objects(Phillips et al.1999).This cut removes two SNe at low redshift(SN1995bd and SN 1996bo),one from P99(SN1996cn),and one of the11HST SNe from this paper(SN1998aw).The resulting‘‘full pri-mary subset’’of SNe Ia is identi?ed as subset1in the tables. For the analyses of a‘‘low-extinction primary subset,’’subset2,we further cull out four SNe with host galaxy EeBàVT>0:1and greater than2 above zero,including two of the HST SNe from this paper(SN1992ag,SN 1993ag,SN1998as,and SN1998ax).The low-extinction primary subset includes eight of the11new HST SNe presented in this paper.

Subset3,the‘‘low-extinction strict Ia subset,’’makes an even more stringent cut on spectral con?rmation,including only those SNe whose con?rmations as Type Ia SNe are unquestionable.This subset is used in x5.2to estimate any possible systematic bias resulting from type contamination. An additional six SNe,including two of the HST SNe from this paper,are omitted from subset3beyond those omitted from subset2;these are SN1995as,SN1996cf,SN1996cg, SN1996cm,SN1998ay,and SN1998be.

3.COLORS AND EXTINCTION

In this section we discuss the limits on host galaxy extinc-tion we can set based on the measured colors of our SNe. For the primary?t of our P99analysis,extinction was esti-mated by comparing the mean host galaxy E(BàV)values from the low-and high-redshift samples.Although the uncertainties on individual E(BàV)values for high-redshift SNe were large,the uncertainty on the mean of the distribu-tion was only0.02mag.P99showed that there was no signi?cant di?erence in the mean host galaxy reddening between the low-and high-redshift samples of SNe of the primary analysis(?t C).This tightly constrained the system-atic uncertainty on the cosmological results due to di?erences in extinction.The models of Hatano,Branch,& Deaton(1998)suggest that most SNe Ia should be found with little or no host galaxy extinction.By making a cut to include only those objects that have small E(BàV)values (and then verifying the consistency of low-and high-redshift mean reddening),we are creating a subsample likely to have quite low extinction.The strength of this method is that it does not depend on the exact shape of the intrinsic extinc-tion distribution but only requires that most SNe show low extinction.Figure2(discussed below)demonstrates that most SNe indeed have low extinction,as expected from the Hatano et al.(1998)models.Monte Carlo simulations of our data using the Hatano et al.(1998)extinction distribu-tion function and our low-extinction E(BàV)cuts con?rm the robustness of this approach and further demonstrate that similarly low extinction subsamples are obtained for both low-and high-redshift data sets despite the larger color uncertainties for some of the P99SNe.

Riess et al.(1998)used the work of Hatano et al.(1998) di?erently,by applying a one-sided Bayesian prior to their measured E(BàV)values and uncertainties.A prior formed from the Hatano et al.(1998)extinction distribution func-tion would have zero probability for negative values of E(BàV),a peak at EeBàVT$0with roughly50%of the probability,and an exponential tail to higher extinctions. As discussed in P99(see the‘‘?t E’’discussion,where P99

31This supersedes P99,where an incorrect dependence on z of the

e?ective R R for Galactic extinction was applied.The corrected procedure

decreases the?at-universe value of M by0.03.

No.1,2003 M, ?,AND w FROM HST-OBSERVED SN e I a115

apply the same method),when uncertainties on high-and low-redshift SN colors di?er,use of an asymmetric prior may introduce bias into the cosmological results,depending on the details of the prior.While a prior with a tight enough peak at low-extinction values introduces little bias (espe-cially when low-and high-redshift SNe have comparable uncertainties),it does reduce the apparent E (B àV )error bars on all but the most reddened SNe.As we will show in Figure 9(x 4.1)the use of this prior almost completely elimi-nates the contribution of color uncertainties to the size of the cosmological con?dence regions,meaning that an extinction correction using a sharp enough prior is much more akin to simply selecting a low-extinction subset than to performing an assumption-free extinction correction using the E (B àV )measurement uncertainties.

The high-precision measurements of the R àI color a?orded by the WFPC2light curves for the new SNe in this work allow a direct estimation of the host galaxy E (B àV )color excess without any need to resort to any prior assump-tions concerning the intrinsic extinction distribution.

Figure 2shows histograms of the host galaxy E (B àV )values from di?erent samples of the SNe used in this paper.For the bottom two panels,a line is overplotted that treats the H96low-extinction subset’s E (B àV )values as a parent distribution and shows the expected distribution for the other samples given their measurement uncertainties.The low-extinction subset of each sample (gray histogram )has a color excess distribution that is consistent with that of the low-extinction subset of H96.Table 7lists the variance-weighted mean E (B àV )values for the low-redshift SNe and for each sample of high-redshift SNe.Although varying amounts of extinction are detectable in the mean colors of each full sample,the SNe in the low-extinction primary sub-set (x 2.5)of each sample are consistent with E eB àV T?0.This subset is consistent with the models of Hatano et al.(1998),discussed above,in which most SNe Ia are observed in regions of very low extinction.We will consider cosmo-logical ?ts to both this low-extinction subset and the pri-mary subset with host galaxy reddening corrections applied.Figure 3shows E (B àV )versus redshift for the 11SNe of this paper.Three of the lowest redshift SNe are likely to be signi?cantly reddened:SN 1998as at z ?0:36,SN 1998aw at z ?0:44,and SN 1998ax at z ?0:50.This higher inci-dence of extincted SNe at the low-redshift end of our sample is consistent with expectations for a ?ux-limited survey,where extincted SNe will be preferentially detected at lower redshifts.Indeed,the distribution of E (B àV )values versus redshift shown in Figure 3is consistent with the results of a Monte Carlo simulation similar to that of Hatano et al.(1998),but including the e?ects of the survey ?ux

limit.

Fig.2.—Histograms of E (B àV )for the four samples of SNe used in this paper.The ?lled gray histogram represents just the low-extinction subset (subset 2).The open boxes on top of that represent SNe that are in the primary subset (subset 1)but excluded from the low-extinction subset.Finally,the dotted histogram represents those SNe that are in the full sample but omitted from the primary subset.The solid lines drawn over the bottom two panels are a simulation of the distribution expected if the low-extinction subset of the H96sample represented the true distribution of SN colors,given the error bars of the low-extinction subset of each high-redshift sample.

TABLE 7

Mean E (B àV )Values

Sample Complete Set Low-Extinction Primary Subset SNe a

Low z ................0.095?0.003à0.001?0.003P99....................0.018?0.024à0.004?0.025HST ..................

0.090?0.012

0.012?0.015

SNe omitted from our low-extinction primary subset,subset 2(x 2.5),have been omitted from these means.This excludes outliers,as well as SNe with both E eB àV T>0:1and E eB àV T>2 above zero.

116KNOP ET AL.Vol.598

Several authors (including Leibundgut 2001and Falco et al.1999)have suggested that there is evidence from the E (B àV )values in Riess et al.(1998)that high-redshift SNe are bluer statistically than their low-redshift counterparts.Our data show no such e?ect (nor did our P99SNe).

The mean host galaxy color excess calculated for the high-est redshift SNe is critically dependent on the assumed intrinsic U àB color (see x 2.3).An o?set in this assumed U àB will a?ect the high-redshift SNe much more than the low-redshift SNe (whose measurements are primarily of the rest frame B -and V -band light curves).The K -corrected,

rest-frame B -band magnitudes are also dependent on the assumed SN colors that went into deriving the K -corrections.If the assumed U àB color is too red,it will a?ect the cross ?lter K -correction applied to R -band data at z e 0:5,thereby changing derived rest-frame colors.In x 5we consider the e?ect of changing the reference U àB color.

4.COSMOLOGICAL RESULTS

4.1. M and ?

Figures 4–6show Hubble diagrams of e?ective B -band peak magnitudes and redshifts for the new SNe of this paper;these magnitudes have been K -and stretch-corrected and have been corrected for Galactic extinction.Figure 4shows all of the data in the low-extinction subset of SNe.For the sake of clarity,Figure 5shows the same subset,but for this ?gure SNe with redshifts within 0.01of each other have been combined in a variance-weighted average.The bottom panel of Figure 5shows the residuals from an empty universe ( M ?0, ??0),illustrating the strength with which dark energy has been detected.In both Figures 4and 5,the solid line represents the ?at-universe cosmology resulting from our ?ts to the low-extinction subset.Figure 6shows just the 11HST SNe from this paper.In the top panel of this ?gure,the stretch-and K -corrected e?ective m B values and uncertainties are plotted.In the bottom panel,e?ective m B values have also been corrected for host galaxy extinction based on measured E (B àV )values.The solid line in this ?gure represents the best-?t ?at-universe cosmology to the full primary subset with extinction corrections

applied.

Fig. 3.—Plot of E (B àV )as a function of redshift for the 11HST -observed SNe of this paper,showing that the blue edge of the distribution shows no signi?cant evolution with redshift.(The larger dispersion at lower redshifts is expected for a ?ux-limited sample.)Error bars include only measurement errors and no assumed intrinsic color dispersion.Filled circles are those SNe in the low-extinction subset (subset

2).

Filled circles represent The solid line is No.1,2003

M , ?,AND w FROM HST -OBSERVED SN e I a

117

high-redshift sample is treated separately.Note that?t2 provides comparable and consistent measurements of M and ?to?t1.Additionally,the sizes of the con?dence regions from the eight HST SNe in?t2are similar to those in?t1,which includes25high-redshift SNe from P99.

Fits4–6in Table8show the results for the primary subset when host galaxy extinction corrections have been applied. Figure9compares these results to those of the primary low-extinction?t.The primary?ts of Figure8are reproduced in the top row of Figure9.The second row has host galaxy E(BàV)error bars from being fully propagated into the cosmological con?dence regions and hence apparently tightens the constraints.However,for a peaked prior,this is very similar to assuming no extinction and not performing an extinction correction(but without testing the assump-tion),while for a wider prior there is a danger of introducing bias.Second,the current set of SNe provide much smaller con?dence regions on the ?versus M plane than do the SNe Ia from previous high-redshift samples when unbiased extinction corrections are applied.Whereas Figure8shows

118KNOP ET AL.Vol.598

that the current set of SNe give comparable measurements of M and ?when the low-extinction subsample is used with no host galaxy extinction corrections,Figure9shows that the much higher precision color measurements from the WFPC2data allow us directly to set much better limits on the e?ects of host galaxy extinction on the cosmological results.Finally,the cosmology that results from the extinc-tion-corrected?ts is consistent with the?ts to our low-extinction primary subset.Contrary to the assertion of Rowan-Robinson(2002),even when host galaxy extinction is directly and fully accounted for,dark energy is required with Pe ?>0T>0:99.

https://www.wendangku.net/doc/9817570816.html,bined High-Redshift Supernova Measurements Figure10shows measurements of M and ?that com-bine the high-redshift SN data of Riess et al.(1998)together with the SCP data presented in this paper and in P99.The contours show con?dence intervals from the54SNe of the low-extinction primary subset2(used in?t3of Table8), plus the nine well-observed con?rmed SNe Ia from Riess et al.(1998)(using the light-curve parameters resulting from their template-?tting analysis);following the criteria of sub-set2,SN1997ck from that paper has been omitted,as that

TABLE8 Cosmological Fits

Fit Number High-Redshift SNe

Included in Fit a N SNe

Minimum

M for

Flat b

?for

Flat b Pe ?>0TM Fits to the Low-Extinction Primary Subset

1..........................SNe from P9946520:25t0:08

à0:070:75t0:07

à0:07

0.9995à3.49?0.05 1.58?0.31

2..........................New HST SNe from this paper29300:25t0:09

à0:080:75t0:08

à0:09

0.9947à3.47?0.05 1.06?0.37

3..........................All SCP SNe54600:25t0:07

à0:060:75t0:06

à0:07

0.9997à3.48?0.05 1.47?0.29

Fits to Full Primary Subset,with Extinction Correction

4..........................SNe from P9948560:21t0:18

à0:150:79t0:15

à0:18

0.9967à3.55?0.05 1.30?0.30

5..........................New HST SNe from this paper33390:27t0:12

à0:100:73t0:10

à0:12

0.9953à3.54?0.05 1.29?0.28

6..........................All SCP SNe58650:28t0:11

à0:100:72t0:10

à0:11

0.9974à3.53?0.05 1.18?0.30

a All?ts include the low-redshift SNe from H96and R99.See x2.5for the de?nitions of the SN subsets.

b This is the intersection of the?t probability distribution with the line Mt ??1.

Fig.7.—Plot of68%,90%,95%,and99%con?dence regions for M and ?from this paper’s primary analysis,the?t to the low-extinction primary subset(?t

3).(

redshift SNe from the primary subset are included in all?ts.The new, independent sample of high-redshift SNe provide measurements of M and ?consistent with those from the P99sample.

No.1,2003 M, ?,AND w FROM HST-OBSERVED SN e I a119

SN was not con?rmed spectrally.We also omit from Riess et al.(1998)the SNe they measured using the ‘‘snapshot ’’method (as a result of the very sparsely sampled light curve)and two SCP SNe that Riess et al.(1998)used from the P99data set that are redundant with our sample.This ?t has a minimum 2of 65with 63SNe.Under the assumption of a ?at universe,it yields a measurement of the mass density of

M ?0:26t0:07

à0:06,or equivalently a cosmological constant of ??0:74t0:06à0:07.Recent ground-based data on eight new high-redshift SNe from Tonry et al.(2003)(not included in this ?t)are consistent with these results.Note that in this ?t,the nine SNe from Riess et al.(1998)were not treated in exactly the same manner as the others.The details of the template ?tting will naturally have been di?erent,which can introduce small di?erences (see x 5.1).More importantly,the K -corrections applied by Riess et al.(1998)to derive dis-tance moduli were almost certainly di?erent from those used in this paper.

4.3.Dark Energy Equation of State

The ?ts of the previous section used a traditional con-strained cosmology where M is the energy density of nonrelativistic matter (i.e.,pressure p ?0),and ?is the energy density in a cosmological constant (i.e.,pressure p ?à ,where is the energy density).In Einstein’s ?eld equations,the gravitational e?ect enters in terms of t3p .If w p = is the equation-of-state parameter,then for matter w ?0,while for vacuum energy (i.e.,a cosmological constant)w ?à1.In fact,it is possible to achieve an accelerating universe so long as there is a component with w d à1.(If there were no contribution from M ,only w <à1

3dark energy would be necessary for acceleration;however,for plausible mass densities M e 0:2,the dark energy must have a more negative value of w .)The Hubble diagram for high-redshift SNe provides a measurement of w (P99,Garnavich et

al.

Fig.9.—Plot of 68.3%,95.4%,and 99.7%con?dence regions for M and ?using di?erent data subsets and methods for treating host galaxy extinction corrections.The top row represents our ?ts to the low-extinction primary subset,where signi?cantly reddened SNe have been omitted and host galaxy extinction corrections are not applied.The second row shows ?ts where extinction corrections have been applied using a one-sided extinction prior.These ?ts are sensitive to the choice of prior and can either yield results equivalent to analyses assuming low extinction (but without testing the assumption)or yield biased results (see text).Note that the published contours from Riess et al.(1998,their Fig.6;solid contours )presented results from ?ts that included nine well-observed SNe (that are comparable to the primary subsets used in the other panels),but also four SNe with very sparsely sampled light curves,one SN at z ?0:97without a spectral con?rmation,as well as two SNe from the P99set.The third row shows ?ts with unbiased extinction corrections applied to our primary subset.The HST SNe presented in this paper show a marked improvement in the precision of the color measurements and hence in the precision of the M and ?measurements when a full extinction correction is applied.With full and unbiased extinction corrections,dark energy is still required with P e ?>0T?0:99.

120KNOP ET AL.Vol.598