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THE ASTROPHYSICAL JOURNAL, 507 : 46 õ 63, 1998 November 1
( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE HIGH-Z SUPERNOVA SEARCH : MEASURING COSMIC DECELERATION AND GLOBAL CURVATURE OF THE UNIVERSE USING TYPE Ia SUPERNOVAE1 BRIAN P. SCHMIDT,2 NICHOLAS B. SUNTZEFF,3 M. M. PHILLIPS,3 ROBERT A. SCHOMMER,3 ALEJANDRO CLOCCHIATTI,3,4 ROBERT P. KIRSHNER,5 PETER GARNAVICH,5 PETER CHALLIS,5 B. LEIBUNDGUT,6 J. SPYROMILIO,6 ADAM G. RIESS,5,7 ALEXEI V. FILIPPENKO,7 MARIO HAMUY,8 R. CHRIS SMITH,4,9 CRAIG HOGAN,10 CHRISTOPHER STUBBS,10 ALAN DIERCKS,10 DAVID REISS,10 RON GILLILAND,11 JOHN TONRY,12 JOSE MAZA,13 A. DRESSLER,14 J. WALSH,6 AND R. CIARDULLO15
Received 1997 December 30 ; accepted 1998 June 10

ABSTRACT The High-Z Supernova Search is an international collaboration to discover and monitor Type Ia supernovae (SNe Ia) at z [ 0.2 with the aim of measuring cosmic deceleration and global curvature. Our collaboration has pursued a basic understanding of supernovae in the nearby universe, discovering and observing a large sample of objects and developing methods to measure accurate distances with SNe Ia. This paper describes the extension of this program to z º 0.2, outlining our search techniques and follow-up program. We have devised high-throughput ïlters that provide accurate two-color rest frame B and V light curves of SNe Ia, enabling us to produce precise, extinction-corrected luminosity distances in the range 0.25 \ z \ 0.55. Sources of systematic error from K-corrections, extinction, selection eects, and evolution are investigated, and their eects estimated. We present photometric and spectral observations of SN 1995K, our programîs ïrst supernova (SN), and use the data to obtain a precise measurement of the luminosity distance to the z \ 0.479 host galaxy. This object, when combined with a nearby sample of SNe, yields an estimate for the matter density of the universe of ) \[0.2`1.0 if ) \ 0. For M a spatially ÿat universe composed of normal matter and a cosmological constant, we ~0.8 ) " 0.4`0.5 , ïnd \ M ) \ 0.6`0.4 . We demonstrate that with a sample of D30 objects, we should be able to determine ~0.4 rela" ~0.5 tive luminosity distances over the range 0 \ z \ 0.5 with sufficient precision to measure ) with an M uncertainty of ^0.2. Subject headings : cosmology : observations õ galaxies : distances and redshifts õ supernovae : general õ supernovae : individual (SN 1995K)
1

. INTRODUCTION

Measuring the cosmological parameters that describe the global properties of the universe has been a fundamental quest in astronomy ever since Robertson (1936) and Walker (1936) formulated the metric for a homogeneous and iso1 This work is based in part on observations at the European Southern Observatory, La Silla, Chile. 2 Mount Stromlo and Siding Spring Observatories, Private Bag, Weston Creek P.O., ACT 2611, Australia. 3 Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile ; National Optical Astronomy Observatories, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the National Science Foundation. 4 Present Address : Departamento de Astronomia y Astroïsica, Pontiïcia Universidad Catolica de Chile, Casilla 104, Santiago 22, Chile. 5 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138. 6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany. 7 Department of Astronomy, University of California, Berkeley, Berkeley, CA 94720-3411. 8 Steward Observatory, University of Arizona, Tucson, AZ 85721. 9 Department of Astronomy, University of Michigan, 834 Dennison, Ann Arbor, MI 48109-1090. 10 Department of Astronomy, University of Washington, Seattle, WA 98195-1580. 11 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 12 Institute for Astronomy, University of Hawaii, Manoa, Honolulu, HI 96822. 13 Departamento dîAstronomia, Universidad de Chile, Casilla 36-D, Santiago, Chile. 14 Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101. 15 Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802.

tropic universe. By observing how a standard candle dims as a function of redshift, usually shown as a Hubble diagram, the eects of curvature and cosmic deceleration can be observed and quantiïed (Sandage 1961). Early luminosity distance investigations (Humason, Mayall, & Sandage 1956 ; Baum 1957 ; Minkowski 1960) used brightest cluster galaxies as standard candles and measured galaxy brightnesses in the range 0.01 \ z \ 0.5. Attempts to trace luminosity distances versus redshifts with these galaxies at z [ 0.1 changed emphasis when it was realized both from theory (Tinsley 1972) and observation (see, e.g., Oke, Hoessel, & Gunn 1996) that the eects of galaxy evolution are much larger than the dierences due to cosmology. Although many other methods for measuring the global curvature and cosmic deceleration exist (see, e.g., Peebles 1993), none has yet delivered a deïnitive result. For example, measuring the number of galaxies as a function of magnitude maps out the volume of space as a function of redshift, and can be used to gauge the global geometry. Attempts to use this method (Shanks et al. 1984) have been hampered by galaxy evolution and merging, although some of the uncertainty may be eliminated by moving to the infrared (Yoshi & Peterson 1995). Another test examines the angular size of a standard rod as a function of redshift. Kellerman (1993) resolved a large sample of compact radio sources out to z B 3 using very long baseline interferometry. Although the angular sizes increase at z [ 1 as expected for a nonempty universe, evolutionary eects are hard to quantify. Stepanas & Saha (1995) have also shown that the unknown intrinsic distribution of source sizes makes it difficult to obtain a statistically signiïcant measurement of 46


THE HIGH-Z SN SEARCH cosmological parameters. Guerra & Daly (1998) have also used extended radio galaxies as standard rods and show that the results are consistent with a low-density universe. Type Ia supernovae (SNe Ia) have long been considered promising tools for measuring extragalactic luminosity distances, but only recent searches, the resulting sets of light curves and spectra, and new methods of analysis (Phillips 1993, hereafter P93 ; Hamuy et al. 1995, 1996a, 1996b, 1996c, 1996d, hereafter H95, H96a, H96b, H96c, H96d ; Riess, Press, & Kirshner 1995, 1996a, hereafter RPK95, RPK96) have quantiïed the nature, power, and limitations of SNe Ia as distance indicators. SNe Ia oer high intrinsic luminosity (M B [19.4 mag ; Saha et al. 1997) and as indiB vidual stars, may not be subject to the same evolutionary eects that plague galaxies (although this must be demonstrated). Even before this breakthrough in understanding SNe Ia, two searches for distant SNe Ia were initiated (Nòrgaard-Nielsen et al. 1989 ; Perlmutter et al. 1995) to measure cosmological parameters. These searches demonstrate that it is possible to ïnd supernovae (SNe) at z [ 0.3 with large-format CCD detectors and gives hope that a signiïcant sample of SNe Ia can be gathered in just a few years. Perlmutter et al. (1997, 1998) have already presented observations of eight objects at z [ 0.35. A sample of D30 objects, if carefully measured and shrewdly analyzed, will provide a statistically interesting measurement of global cosmological parameters. Recently, much eort has been put into examining how to use the power spectrum of ÿuctuations in the cosmic microwave background (CMB) to measure cosmological parameters (see Hu 1996 for a review). Future satellite missions, such as the Microwave Anisotropy Probe and Planck missions, will measure temperature ÿuctuations across the sky on scales substantially less than 1¡, determining the power spectrum of ÿuctuations out to a multipole expansion of l [ 500. Model ïts to these observations promise to provide simultaneous measurement of 10 cosmological parameters. However, because the ïts are degenerate for certain combinations of interesting parameters such as ) M and ) , the CMB observations will need to be combined " with other observational data, such as those from highredshift supernovae (Zaldarriaga, Spergel, & Seljak 1997), to determine ) and ) individually. M " This paper reports on the High-Z SN Search, a coordinated program to discover, spectroscopically classify, and measure photometrically in at least two ïlters a distant set of SNe Ia. This enterprise aims to measure the deceleration parameter, q , with an uncertainty smaller than 0.1 and will place strong 0 limits on combinations of cosmological parameters such as ) [ ) . The CMB observations provide a M nearly orthogonal set " parameters, so we will be able to of separate the eects of any exotic forms of matter/energy in the universe from normal matter. We will be able to discern whether the universe is open, closed, or has nearly zero global curvature. Preliminary results from our program were reported by Schmidt et al. (1996), Schmidt (1997), and Leibundgut & Spyromilio (1997). In addition, we have conïrmed the predicted time dilation of redshifted objects using SN Ia light curves (Leibundgut et al. 1996) and spectra (Riess et al. 1997 ) and presented observations of three objects observed with the Hubble Space T elescope (HST ) (Garnavich et al. 1998). In ° 2 we describe how the expansion, deceleration, and curvature of the universe are related to luminosity dis-

47

tances, and in ° 3 we discuss measuring distances with SNe Ia at z \ 0.1. Our supernova search and observational follow-up program are outlined in ° 4. In ° 5 we present the techniques and limitations of using SNe Ia to measure accurate luminosity distances at z [ 0.2. Observations of the ïrst SN discovered by this program, SN 1995K at z \ 0.479, are presented in ° 6, with the techniques discussed in °° 3, 4, and 5 applied to this object. We summarize the High-Z SN Search to date in ° 7 and use the results for SN 1995K to estimate the precision with which we will be able to constrain cosmological parameters.
2.

EXPANSION, DECELERATION, AND CURVATURE

The precise large-scale isotropy of the microwave background conïrms a picture in which the universe is accurately described on large scales by the maximally symmetric, Robertson-Walker line element (see, e.g., Weinberg 1972). For events with time separation dt, radial coordinate separation dr, and angular separation dh, the line element ds is given by ds2\ dt2[ a2(t)

A

dr2 ] r2 dh2 . 1 [ kr2

B

(1)

The global spatial geometry has the character of a hypersphere of radius k~1@2a(t), where a(t) is the cosmic scale factor that deïnes the physical scale of the hypersphere at each time. In these units the spatial curvature parameter k can be 1, 0, or [1, corresponding to a closed, ÿat, or open universe, respectively. The complete spacetime metric, which depends on a(t), is determined by the Friedmann equation, H2 4

AB

5 a 2 8nGo k \ [, a 3 a2

(2)

where o is the total density of all forms of matter/energy. Friedmann-Robertson-Walker (FRW) cosmologies are based on equations (1) and (2) and provide a complete description of an isotropic and homogeneous universe. We adopt a conventional model in which the matter content of the universe is composed of a sum of components each having a fraction ) of the current critical density i o 4 3H2/8nG and various equations of state with density crit (volume)~(1`ai) (e.g., a \ 0 for normal matter [) ], 0 oP M a i\[1 for a cosmological constant [) ], a \] 1 for radi" 3 [) ]). ation [) ], and a \[ 1 for noncommuting strings 3 It is rad convenient to adopt a parameter i S4 0 kc2/[a(t )2H2] representing the scalar curvature in units 0 0 with the density parameters ; the current commensurate physical radius of hypersphere curvature is k~1@2a(t ) \ 0 i~1@2cH~1 and the deïnition of critical density gives i \ 0 ) [ 0 We can then write the Friedmann equation in 0 ; 1. i i of these model parameters : terms (3) H2\ H2 ; ) (1 ] z)3`3ai [ i (1 ] z)2 . i 0 0 i It is conventional to deïne a "" deceleration parameter,îî q 4 [a (t )a(t )/a5 2(t ), characterizing the low-redshift 0 00 0 behavior, which can be expressed as q \ 1 ; ) (3]3a ) [ ; ) \ 1 ; ) (1 ] 3a ) . (4) 02 i i i2 i i i i i Distance measurements based on SN Ia light curves are described as luminosity distances, D , and are deïned by L

C

D


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the ratio of the intrinsic luminosity L to the observed ÿux F as L 1@2 . D\ L 4nF

AB

(5)

In FRW cosmologies D is derived by computing the area L of the sphere over which the ÿux is distributed from a source at a radial coordinate ïxed by the redshift. Including the eects of time dilation and redshift, the luminosity distance is D H \ (1 ] z) o i o~1@2S L0 0 z ~1@2 dz@ ; ) (1 ] z@)3`3ai [ i (1 ] z@)2 , ] o i o1@2 0 i 0 0 i (6)

G

PC

DH

where SMxN 4 sin (x), x, or sinh (x) for k \ 1, 0, [1, respectively (Coles & Lucchin 1995). Mattig (1958) showed that, when normal matter is the only contributor to ), 1 D H \ [q z ] (q [ 1)(J1 ] 2q z [ 1)] . L 0 q2 0 0 0 0 Alternatively, equation (6) can be expanded in z to give D H \ z ] z2 L0 (7)

A

1[q 0 ] O(z3) , 2

B

(8)
FIG. 1.õDierences in the (D , z) relation for various cosmological L models expressed as the dierence in distance modulus from an empty universe, ) \ 0.

which is valid for all models. The linear term of the expansion is the Hubble law and has been studied for many years. Its linear form has been veriïed to high precision in the nearby universe using SNe Ia with the same techniques we employ for this project (H96b ; RPK96 ; Tammann & Leibundgut 1990), using brightest cluster galaxies (Lauer & Postman 1992), and again using SNe Ia at larger redshifts (Kim et al. 1997). The current debate on the value of H 0 centers on obtaining an absolute calibration for these distance indicators in nearby galaxies through accurate absolute distances. The measurements of curvature and deceleration require only a relative distance indicator to obtain the shape of the (D , z) relation and are not aected by current uncertainties Ln H due to local calibration. i 0 Equation (8) shows that departures in the luminosity distance from a pure Hubble law, to lowest order in z, are proportional to q õthey depend only on deceleration and 0 not on curvature. With a distance modulus, m [ M \ 5 log (D /10 pc), measured to precision *m mag for an 10 L object at redshift z, equation (8) shows [using *m \ 5* log (H D )] that we measure q to a precision *q B 10 L 0 0 0.9*m/z ;0thus a single well-observed SN Ia at z \ 0.5 with p \ 0.15 mag (H96b ; RPK96) should yield a precision of about *q \ 0.27, almost a 2 p discrimination between an empty (q 0\ 0) and a ÿat (q \ 0.5) universe. However, we 0 caution 0 reader that already at z \ 0.5, O(z3) terms the cannot be neglected, especially in cosmologies with signiïcant cosmological constants. To illustrate the precise eects of cosmology on luminosity distance, we plot the dierences in distance modulus, m [ M, from an ) \ 0 universe as a function of redshift tot for a set of universes composed of dierent amounts and types of matter/energy (Fig. 1). Although ïrst-order deviations constrain only the linear combination of parameters corresponding to deceleration, data on objects over a range

of redshifts up to z B 1 can separate out the eects of the various forms of mass/energy in the (D , z) relation and L place limits on global curvature. In particular, it is possible to separate ÿat cosmological models with nonzero ) from " open universes containing only normal matter (Goobar & Perlmutter 1995).
3.

USING TYPE Ia SUPERNOVAE TO MEASURE LUMINOSITY DISTANCES

SNe Ia have been used as extragalactic distance indicators since Kowal (1968) published a Hubble diagram (p \ 0.6 mag) for SNe I. We now recognize that the old SN I spectroscopic class conÿated two distinct types of objects : SN Ib/c, which are probably massive stars that undergo core collapse after losing their hydrogen atmospheres, and SNe Ia, which are most likely thermonuclear explosions of white dwarfs (see Filippenko 1997 for a review). Modern versions of the SN I (now SN Ia) Hubble diagram shows scatter of about 0.3 õ 0.5 mag about the inverse-square line (Tammann & Leibundgut 1990 ; van den Bergh & Pazder 1992 ; Branch & Miller 1993 ; Sandage & Tammann 1993), which is remarkable given the heterogeneous sources and oftentimes poor observations upon which these diagrams are based. The advent of precise observations of nearby SNe Ia made with CCD detectors produced evidence for genuine dierences in the luminosities, light curve shapes, and spectra among the Type Ia family. SN 1984A (Branch 1987 ; Barbon, Rosino, & Iijima 1989), SN 1986G (Phillips et al. 1987), SN 1991bg (Filippenko et al. 1992b ; Leibundgut et


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THE HIGH-Z SN SEARCH

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al. 1993), and SN 1991T (Filippenko et al. 1992a ; Phillips et al. 1992) provided proof that SNe Ia were not all identical objects whose observed dierences could be attributed to measurement errors, but that real dierences among these explosions are undoubtedly present. The problem of understanding SNe Ia well enough to use them as cosmological probes despite their intrinsic variation was solved by assembling a sufficiently large, uniform, and well-observed data set. In 1990 a group of astronomers at Cerro Tololo Inter-American University (CTIO) and the University of Chile at Cerro Calan initiated a systematic photographic search for SNe Ia using the Curtis Schmidt telescope at CTIO (Hamuy et al. 1993b). Their program, which discovered 30 SNe Ia in 2.5 years, also acquired highquality spectral and photometric follow-up for these supernovae. The resulting data set (H96d) allows the precise determination of the properties of SNe Ia as distance indicators. At maximum light, SNe Ia have an intrinsic range of [2 mag in B and [1 mag in V . Although this is an interesting result for supernova physics, it does not bode well for using SNe Ia as high-precision distance indicators without additional information. Although their brightness at maximum light has a moderately large scatter, SNe Ia do exhibit a correlation (pB 0.15 mag) between the rate at which their luminosity declines and absolute magnitude. P93 demonstrated this relationship by plotting the absolute magnitude of 10 nearby SNe Ia that had dense photoelectric or CCD coverage versus the parameter *m (B), the amount by which 15 each SN decreased in brightness in the B-band over the 15 days following maximum light. The sample showed a correlation, which when taken into account, dramatically improved the predictive power of SNe Ia. The Calan/Tololo survey yielded an independent conïrmation of the P93 absolute magnitudeõdecline rate relationship from the sample of 30 SNe Ia by using a s2 ïtting technique to the B, V , and I light curves (H95 ; H96a). When corrected for their rate of decline, H96d demonstrated that the scatter in the Hubble diagram could be lowered to p D 0.15 mag in V for a sample of nearly 30 SNe Ia. Another technique, the multicolor light curve shape (MLCS) method, has been developed by RPK95 and RPK96. By "" training îî on a nearby set of objects (P93îs sample plus a few additions), they achieve p\ 0.2 mag on a sample of 20 objects (H95, augmented by 10 additional well-observed SNe Ia) in the Hubble ÿow. This result is encouraging because the Hubble diagram derived by RPK96 is independent of the objects on which their method was "" trained îî and therefore provides an upper limit for the true dispersion of this distancemeasuring technique. Other methods to correct for intrinsic luminosity dierences or limits on the input sample by various criteria have also been proposed to increase the precision of SNe Ia as distance indicators (Tammann & Sandage 1995 ; Fisher et al. 1995 ; van den Bergh 1995 ; Branch et al. 1996 ; Perlmutter et al. 1997). The analyses described above assume that all SNe Ia can accurately be described by a one-parameter family of light curves. We know this is not true because the scatter about the Hubble line in either H96d and RPK96 is larger than the observational errors would indicate (H96d ; RPK96). The inferred scatter beyond the observational uncertainties is small, (pB 0.12 mag), and the residuals (including observational uncertainties) are distributed about the mean consistent with a Gaussian distribution. To this date, no other

observable has been shown to successfully account for the remaining small intrinsic scatter about the one-parameter family of light curves. Unless supernovae are much dierent at high redshifts, the imperfection of SNe Ia as distance indicators will have a negligible impact on using SNe Ia as cosmological probes.
4

. SEARCH AND FOLLOW-UP PROGRAM

Many techniques have been successfully used to discover supernovae, including visual observations of nearby galaxies (Evans 1994), photographic surveys (Zwicky 1968 ; Mueller 1989 ; McNaught 1990 ; Hamuy et al. 1993b ; Pollas 1992), and CCD surveys (Perlmutter et al. 1992, 1995 ; Treers et al. 1993 ; Martin, Williams, & Woodings 1997 ; Reiss et al. 1998). Although it is possible to discover objects up to z B 1 (Schmidt et al. 1997b) by using large format CCDs coupled with wide ïelds on telescopes with the best image quality, it is efficient to measure cosmological parameters by observing objects in the range 0.35 \ z \ 0.55. When systematic eects are small, the leverage gained with high-redshift objects is oset by the difficulty in obtaining accurate measurements. It is challenging to obtain accurate rest frame B and V photometry of objects observed at 0.55 \ z \ 0.9 because they are outside the optimum K-correction window (Fig. 2), and these SNe are currently less powerful tools for measuring cosmological parameters than their lower redshift siblings. The HST ] WFPC2/ NICMOS could acquire accurate rest frame B and V measurements for SNe Ia at z B 1. These objects hold the

FIG. 2.õUncertainty in transforming to rest frame (upper panel) B and (lower panel) V as a function of redshift for V , R , and I , HST 850LP C (WFPC) and 110M (NICMOS), and the B35, V 35, B45, C and V 45 ïlters described in the Appendix.


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-0.5

0

0.5

FIG. 3.õResidual of SN Ia distances from RPK96 plotted as a function of galaxy type. The oset between the early-type and late-type galaxies is 0.006 ^ 0.07 mag.

promise of establishing powerful constraints on cosmology within this more distant observational window. From the ground, however, the band 0.35 \ z \ 0.55 gives the best combination of measurements and systematics to investigate cosmology. 4.1. Observing Strategy To maximize the number of SNe Ia discovered in our target redshift range, 0.35 \ z \ 0.55, we observe a large area and aim to achieve a limiting magnitude of m B 23 R mag, which is D1 mag fainter than the expected brightness of a z \ 0.5 SN Ia at maximum light (Fig. 3). Finding objects is not the only consideration ; the objects must be found near or before maximum light, and we need to follow discoveries with spectra and multicolor photometry. To ensure that our objects are discovered young, we use the technique described by Hamuy et al. (1993b) and Perlmutter et al. (1995), imaging ïelds near the end of a dark run, and then reimaging the ïelds at the beginning of the next dark run. These two runs, separated by approximately 21 days (close to the rise time of a time-dilated SN Ia at z \ 0.5), provide objects that are at or before maximum light.16 Observations are generally made near the celestial equator so that we can use telescopes in both hemispheres for follow-up spectroscopy and photometry. At least two observations are made at each search position
16 To target objects in the other advantageous K-correction window, z B 1, observations to m \ 24 mag, separated by 30 days, will efficiently deliver young SNe Ia. I

to detect motion of asteroids, eliminate cosmic rays, and remove chip defects. As an outgrowth of this project, Riess et al. (1997) developed a method to measure the age of an SN Ia relative to maximum light from its spectrum alone. This technique is especially valuable because it provides another way to identify young objects, ideally while still observing at the telescope. Since we need to schedule large blocks of telescope time months in advance to follow the supernovae, it is essential to have candidates after each supernova discovery run, and not be derailed by weather. During the summer months of December through March, the Chilean Atacama desert has nearly 100% clear weather. We have concentrated our search eorts at the CTIO 4 m telescope, the instrument that currently provides the widest ïeld of view of any large telescope in Chile. On the CTIO 4 m telescope we image approximately 3 deg2 night~1 with a single 20482 detector, taking two consecutive 150 s B45 exposures of each ïeld. In good conditions (1A seeing), a combined frame has a limiting magnitude of m B 23 and provides a sufficiently long time baseline to R remove Kuiper belt objects, which have a typical parallax motion of 3A hr~1. Since 1997 January, the "" Big Throughput Camera îî (BTC) has been available at the CTIO 4 m telescope. This mosaic of four chips quadruples the imaging area but has a somewhat longer readout time. We have recently used the BTC to obtain two consecutive 300 s R exposures at every pointing, enabling us to cover 7 deg2 night~1 to a depth of m \ 23.5 mag. R 4.2. Search Software Our supernova search is automated, with ïnal cuts on potential candidates being made by eye. The automated processing program is written in PERL, and calls IRAF tasks, DoPHOT (Schechter, Mateo, & Saha 1993), and various programs written in C. In brief, the program aligns the second-epoch image with the ïrst, initially ïnding the bright stars using DoPHOT and then matching stars in the two frames using a triangle-matching algorithm similar to that described by Groth (1986). The images are then registered using the IRAF tasks GEOMAP and GEOTRAN. After registration, we match the point-spread functions (PSF) of the two epochs applying the method of Phillips & Davis (1995), which computes a convolution kernel in Fourier space and ïts the high frequencies with a Gaussian proïle. The DoPHOT analytic PSF measurements show which image needs to be degraded and indicates if the PSF matching cannot be made in a single convolution. This is the case when the images are elongated with respect to each other such that neither image has a FWHM that is smaller than the other at all position angles. In these cases, we convolve one of the images with an appropriate Gaussian kernel and then apply the Phillips & Davis method. After PSF matching, the images are scaled to the same intensity and sky brightness values by plotting the intensity of each pixel in one image against the intensity of the corresponding pixel in the other in a subraster centered on a star. We ït for an oset (dierence in sky brightness) and a scale (dierential atmospheric transparency) and then subtract the intensity-scaled images. This procedure is carried out on both second-epoch images, and these dierenced images are averaged, rejecting any high pixels that are discordant by more than 3 p.


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The resulting image is searched using a point-source detection algorithm. Our algorithm samples the combined dierence image at many locations over the image, estimating the average noise within a PSF, and then scans the image for objects above this threshold by a certain number of p (p[ 4 being a typical choice). A list of candidates, eliminating those near known bright stars, is sorted by magnitude. This entire process takes about 6 minutes to run on a 170 MHz Sun UltraSparc for a pair of 20482 images. For inspection of candidates, the examiner is presented with subrasters of the candidateîs region from the ïrst epoch, both second epochs, and the subtracted image. These images can be viewed simultaneously as a mosaic, or stacked and blinked. The number of candidates to examine depends on the detection threshold and the quality of the match between the two epochs. Typically, 5 õ50 objects are examined on each pair of search images, but most are easily eliminated by inspection. Our approach is to minimize false alarms from a night of observing. We usually have 5 õ20 possible SN candidates per night that are detected by our software ïlter and that are not discarded by visual inspection. When there is doubt about the reality of a candidate, we make a repeat observation of the ïeld. At this point, the candidate list is sent to collaborators for spectroscopic observations that can show whether or not the object is a supernova, give some information on its type and age, and provide the redshift. Roughly 75% of these candidates are conïrmed as SNe Ia, the remainder consisting of other supernova types, active galactic nuclei, and occasional mystery objects. These mystery objects typically have no visible host galaxy and fade by more than 2 mag within 24 hr (and in one case, at least 2 mag in 3 hr). It is conceivable that these are ÿare stars in the halo of the Milky Way or the unbeamed optical counterparts to gamma-ray bursts (Rhoads 1997). There is no bias in our selection against SNe in which there is no visible galaxy since the whole CCD ïeld is searched. 4.3. Data Reduction Procedures We extract the high-redshift photometry in the same way we have measured the z \ 0.1 sample (H96d ; RPK96). We ïrst calibrate a local photometric sequence of stars that appears in the CCD ïeld of each supernova. These stars are calibrated by observing standard stars on photometric nights, deriving color and atmospheric extinction transformations, and then applying these to the local sequence. The local photometric sequence, which typically spans a substantial range of color and brightness, is then combined, correcting for any color term of the system used in the observation, with relative photometry between the supernova and sequence stars to produce a standard magnitude for the supernova. In general, the color terms of our dierent systems are small, since most of the supernova observations are taken with identical ïlters, as described in the Appendix. To produce precise relative photometry for our highredshift supernovae, we follow the same procedure employed in the Calan/Tololo survey for galaxy subtraction (Hamuy et al. 1994). A template image, in which the supernova is absent, is required for every object/ïlter combination. Ideally, these images would have better seeing than any of the other observations, so that the observations are not degraded in the PSF matching process and should have more than twice the signal-to-noise ratio (S/N) to

minimize the addition of shot noise in the subtractions. In most cases, images of our SN discovery regions that are appropriate for use as templates are not in hand before the time of explosion, so we must return to these ïelds after about a year to obtain templates. One of our most difficult tasks is to obtain good seeing images with long integration times to serve as acceptable templates. The analysis of our data set will be continuously improved as we build up improved templates for the supernovae we follow. We have developed a pipeline closely related to our search software for extracting photometry from our CCD frames. After normal processing in which the frames are bias subtracted and ÿat ïelded, this pipeline uses the search software to align an image to the template, match the two imagesî PSFs, scale the intensity of the observation to the template, and then subtract the template from the observation in a region around the galaxy. The software then runs DoPHOT on the galaxy-subtracted frame, using a ïxed position of the supernova17 and a sequence of comparison stars, to extract the magnitude of the supernova. After measuring the SNîs brightness, the script builds a PSF from the comparison stars using DAOPHOT (Stetson 1987) and adds this PSF to user-speciïed galaxies in the image so that they have the same brightness as the SN measurement. After subtracting the template from the areas containing the added PSFs, DoPHOT is once again run to extract the magnitudes of these artiïcial SNe. These synthetic objects provide an eective method to estimate the relative photometric errors and can give a strong indication if something has gone wrong in the reduction process. Our spectra are reduced in a typical manner, except that we generally extract only a small region along the slit at the position of the supernova to minimize host galaxy contamination. We also bin the spectra as necessary in the dispersion direction, after ïnal reduction, to increase the S/N per pixel, to aid in classifying the objects.
5

. MEASURING ACCURATE RELATIVE DISTANCES BETWEEN NEARBY AND HIGH-z SNe Ia

The distances derived to SNe Ia are well characterized and tested in the nearby universe, but accurately comparing these objects to their more distant counterparts requires great care. Selection eects can introduce systematic errors as a function of redshift, as can uncertain K-corrections or an evolution of the SN Ia progenitor population as a function of look-back time. These eects, if they are large, will limit our ability to measure the (D , z) relation accurately L and have the potential to sap the potency of high-redshift SNe Ia for measuring cosmological parameters. 5.1. Extinction Most attempts at using SNe Ia as distance indicators have not corrected for extinction in the supernova host galaxy. The majority of the SNe Ia discovered at z \ 0.1, which comprise the current sample of well-observed SNe Ia, have been detected using photography at Schmidt telescopes, and it is possible that many SNe Ia embedded in dusty spiral arms or galaxy nuclei were missed by these searches. Distant SNe Ia are discovered with CCD observations by subtracting a digital template from the data and
17 In low S/N situations, allowing the centroid of the PSF to be a free parameter would cause a systematic overestimate of the objectîs ÿux.


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are more aected by galaxy surface brightness than by galaxy morphology. Additional complications arise because magnitude-limited selection might prevent extinguished objects from being discovered with equal efficiency in both nearby and distant samples or because the smaller angular size of distant objects makes it more difficult to detect SNe deep inside spiralsõthose likely to be extinguished. In short, it would not be surprising to have systematic dierences between the average extinctions of objects discovered in the nearby and distant supernova searches. Rather than attempt to untangle this hopelessly knotted set of selection eects, we believe it is more straightforward to correct for extinction of individual objects that are in the samples based on their colors. Except for a small group of very rapidly fading supernovae, H95 show that, at maximum light, SNe Ia have a relatively small range in their (B[V ) color, which can be used to estimate their extinction. Even so, it is worthwhile to correct for extinction according to the prescription of P93/H95 or RPK95. Using the framework set out earlier in this section, but for two ïlters, a relative reddening estimate of any SN Ia can be extracted from its observations by simultaneously ïtting B and V (or any set of two or more photometric bands) and deriving the E(B[V ) oset. This procedure does not require the training set to be free of reddening, as the calculated color excess will be relative to the average extinction of the training set. In practice, using an iterative process, it is possible to deïne an essentially reddening-free set of synthetic light curves, weeding out the reddened objects on the basis of their color evolution. RPK96 have demonstrated that using B, V , R, and I light curves within their framework, dispersions of less than 0.15 mag are attainable. Furthermore, they show that their best estimate of the reddening law from a few heavily reddened objects in their sample of SNe Ia is indistinguishable from the mean Galactic reddening law (Riess, Press, & Kirshner 1996b). A recent study by Phillips et al. (1998) based on previous work by Lira (1996) on the intrinsic color evolution of SNe Ia has also developed a consistent method to deredden Type Ia light curves. Correcting SNe Ia for extinction does not necessarily decrease their dispersion as distance indicators (extinction corrections only decrease the scatter when the error in the derived extinction is less than the dispersion caused by extinction to a sample of objects) but is essential to remove the systematic bias that absorption might introduce. It is possible that the average properties of dust might evolve as a function of look-back time ; e.g., the LMC and SMC have extinction laws that dier signiïcantly from that of the Milky Way (Bouchet et al. 1985). Such an eect could signiïcantly bias the comparison of nearby and distant objects if the average extinction to either the nearby or distant sample is large. Although the nearby sample of objects has few reddened objects (RPK96), and indications are that the high-z sample has low extinction as well (Riess et al. 1998), this possible bias warrants further investigation. For example, observations of reddened objects in rest frame BV R I at large redshifts could be used to investigate the CC extinction law at these look-back times and limit uncertainties introduced by this eect. 5.2. K-Corrections When comparing objects at signiïcant redshifts with nearby counterparts, it is necessary to account for the wave-

length shift of light. The eect of redshift on luminosity distances, dubbed the K-correction, was tabulated for galaxies in modern photometric bands by Oke & Sandage (1968). They deïned the K-correction K such that an i objectîs magnitude m in ïlter i as a function of redshift z is i m (z) \ m (z \ 0) ] K (z) . (9) i i i An object with spectrum F(j) (in units of power per unit area per unit wavelength) observed in a ïlter with sensitivity function S (j) has i / S (j)F(j) dj i m (z \ 0) \[2.5 log ]Z , (10) i i / S (j) dj i where Z is the zero point of the ïlter.18 Oke & Sandage i demonstrated that / F(j)S (j) dj i , (11) K \ 2.5 log (1 ] z) i / F[j/(1 ] z)]S (j) dj i where K accounts for the (1 ] z) shift of the photons in i wavelength and the (1 ] z) increase in the unit dj that they occupy. In the case of SNe Ia, K-corrections have an added complication caused by the changing spectral energy distribution of a supernova as it evolves. SNe Ia change rapidly when they are near maximum, which translates to rapidly changing (and hence uncertain) K-corrections (Hamuy et al. 1993a). This evolution is particularly pronounced blueward of 4000 A because of line blanketing, and therefore using K-corrections in the traditional manner on the observed B and V light curves of SNe Ia at z \ 0.5 is an extremely risky proposition. Following the precepts of Gunn (1978), Perlmutter et al. (1995) demonstrated that by observing distant SNe Ia with the R broadband ïlter, C K-correction uncertainties could be substantially reduced, because at z \ 0.5 the R ïlter approximates the rest frame C B ïlter. Kim, Goobar, & Perlmutter (1996) show that this modiïed K-correction is / F(j)S (j) dj i ]Z [Z , K \ 2.5 log (1 ] z) j i ij / F[j/(1 ] z)]S (j) dj j (12) where K (z) is the correction for going from ïlter i to ïlter j. ij Note that if ïlter i is exactly the redshifted counterpart of ïlter j, then at this redshift K is not zero but has a constant ij value corresponding to the (1 ] z) stretching of the wavelength region dj photons occupy combined with the dierence in the zero points of the ïlters. Rather than constrain ourselves to existing broadband ïlter sets, we decided to deïne our own set of redshifted ïlters, created as broadband interference ïlters. We currently have deïned four ïlters : pairs of B and V ïlters redshifted to z \ 0.35 and z \ 0.45 (henceforth referred to as the B35, V 35, B45, and V 45 ïlters). Although adopting this new photometric system adds the complication of deïning standards for these ïlters, we believe the ability to translate SNe Ia observed in the range 0.25 \ z \ 0.55 to standard B and V ïlters with small systematic and statistical uncertainties makes it worthwhile. An overview of our system is given in the Appendix.
18 Traditionally Z has been set such that, when equation (10) is applied i to the spectrum of Vega, it yields m \ 0.03 mag. However, many photoi metric systems have Z that vary slightly from this deïnition. i

G

H

G

H


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53

An important advantage in designing new ïlters is that modern transmission coatings have peak transmissions in excess of 85%, whereas traditional R and I ïlters are C C typically around 60%. In addition, our ïlters have a sharp cut-o on the long wavelength side, which results in signiïcantly lower backgrounds from night sky lines than their Kron-Cousins counterparts. In Figure 2 we have plotted the uncertainty in the K-corrections in translating to rest frame B and V from both our specialized ïlters (Appendix), the R and I ïlters (Bessell 1990), and selected HST ïlters. C C These corrections have been calculated using the series of SN Ia spectra in Hamuy et al. (1993a), augmented with additional spectra of SN 1994D by Filippenko (1997). The resulting K-corrections are ït as a function of SN age for each redshift with a low-order polynomial, and the residual scatter of this ït is used to gauge the uncertainty of the K-corrections. The estimated uncertainties are insensitive to the exact order of the polynomial used and provide an estimate of the random component of K-correction uncertainties due to errors in our SN Ia spectrophotometry and intrinsic dierences in supernovae. For proper redshift-ïlter matches, the resulting K-corrections in transforming to rest frame B and V are accurate to better than 3% for SNe Ia observed between 14 days before maximum and 50 days past maximum over the range of 0.25 \ z \ 0.55 (and, using HST , between 0.90 \ z \ 1.1). For objects that are extinguished, it is necessary to modify the spectra used for determining the K-corrections iteratively with reddening curves, using ïts to their light curves to estimate the amount of extinction. In addition, if the SN diers signiïcantly from those used to construct the K-corrections, a substantial error can result, especially when the object is at a redshift where the ïlter is not a close match to its rest frame counterpart. In these cases, the ïrst order dierence between the spectra is usually color, and the spectra used for determining the K-corrections can be adjusted with a power law to match the color evolution of the object. The systematic uncertainty in translating between ïlter systems limits the accuracy with which we are able to measure luminosity distances at high redshift. Note that K-correction zero point errors are magniïed through extinction corrections : since A \ 3.1E(B[V ), a 0.02 mag uncertainty of V (B[V ) translates to a 0.06 mag uncertainty in distance modulus. It is a very difficult task to ensure systematic errors in (B[V ) \ 0.02 mag in either the nearby or distant sample, and we believe that this uncertainty will be our largest source of systematic error. 5.3. Evolution An attractive feature of using SNe Ia as distance indicators at signiïcant redshifts is the possibility of minimizing the evolutionary eects that plague distance indicators based on the properties of galaxies. Initial models proposed that SNe Ia arise from the explosions of carbon-oxygen white dwarfs as they reach the Chandrasekhar mass (Hoyle & Fowler 1960 ; Arnett 1969 ; Colgate & McKee 1969). This mechanism for SN Ia explosions leads to a burning front that propagates outward from the white dwarfîs center, burning nearly the entire star to nuclear statistical equilibrium. A broader range of models for the presupernova star and for the behavior of the burning wave is needed to account for the intermediate-mass elements that are seen in the spectra of SNe Ia (Wheeler & Harkness 1990) and to reproduce the observed range of SN Ia luminosities. Suc-

cessful models have been produced by several groups employing a variety of mechanisms (Nomoto, Thielemann, & Yokoi 1984 ; Livne 1990 ; Khokhlov, Muller, & Hoÿich 1993 ; Woosley & Weaver 1994 ; Hoÿich, Khokhlov, & Wheeler 1995). Although the details of the explosion mechanism remain an active area for research, many plausible (but similar) models match the spectral features of SNe Ia and can produce the relation between light curve shape and luminosity detected by P93. The local sample of SNe Ia shows that the light curve shapes and luminosities are weakly correlated with the type of galaxy in which they occur (H96a). Spirals show a wide range of light curve shapes while ellipticals show a narrow range. If left untreated, the relation between stellar population and the luminosities of SNe Ia could poison the inference of cosmological parameters by introducing a subtle drift in SN Ia properties with look-back time (von Hippel, Bothun, & Schommer 1997). We know that the rate of SNe Ia per unit B luminosity is almost twice as high in spirals as in ellipticals at the present epoch (Cappellaro et al. 1997). If we assume that this increased rate of SN Ia production is related to the higher rate of star formation in spirals, then the SNe Ia in spirals come from progenitors that are likely to be younger than the progenitors of SNe Ia in ellipticals. Incidentally, this is the conclusion reached by Oemler & Tinsley (1979) nearly two decades ago. However, our local sample calibrates the eect. Figure 4 shows that the calibration of RPK96, which does not use any information about galaxy type as an input, results in distances to early-type (eight objects) and late-type galaxies (19 objects) that are consistent to 0.006 ^ 0.07 mag (SNe Ia with elliptical hosts give slightly closer distances). To obtain limits on the possible osets between SNe Ia with early-type and late-type progenitors, we perform a Monte Carlo simulation with the following assumptions. Late-type galaxies have SNe Ia with young and old progenitors at a ratio of 1 : 1 (a conservative limit from their ratesõspirals have twice the rate of supernovae as ellipticals, so 1 of the pro2 genitors are old and 1 are young), and ellipticals contain 2 only old progenitors. Simulated data sets demonstrate that with the above assumptions, and the observed osets between distances to ellipticals and spirals, the allowed range in the distance osets between objects with young

FIG. 4.õMagnitude at maximum of a typical SN Ia as a function of redshift for as observed in R and I for ) \ ) \ 0. C C M


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and old progenitors is 0.02 ^ 0.15 mag. If the ratio of young to old progenitors in spirals were to be 2 : 1, then the limits become 0.01 ^ 0.11 mag. This unsophisticated analysis, while not providing hard limits on evolution, demonstrates there is no obvious dependence on SN Ia distances with respect to the age of the stellar population in which they reside. Since, at z \ 0.5, we still expect to see SNe Ia originating from a mixture of young and old progenitors, the average evolution should be smaller than the maximum possible dierences quoted above. A larger sample of objects and a better understanding of the local rates as a function of progenitor type, as will be provided by the Mount Stromlo Abell Cluster Supernova Search (Reiss et al. 1998), will increase the power of this type of test. Theory provides another avenue by which to explore the possible eects of evolution. Hoÿich, Wheeler, & Thiele mann (1997) have calculated the dierences in light curve shape, luminosity, and spectral characteristics of SNe Ia as a function of the initial composition and metallicity of their white dwarf progenitors. Their calculations show that although changes in rest frame U can be considerable, the eects in the B- and V -bands are only D0.05 mag, even when considerable changes are made to the metallicity and C-to-O ratio of the white dwarf progenitors. Changes to the light curve shapes of the objects may also occur, and in total their calculations suggest that distances could drift by as much as 0.3 mag in B and 0.15 mag in V . At what redshift such dierences could appear is unclear, but these types of changes would be accompanied by signiïcant spectral differences and should not go undetected. We assume that the relation between light curve shape and luminosity that holds for a wide range of stellar populations at low redshift also covers the range of stellar populations we encounter in our high-redshift sample. The range of ages for SN Ia progenitors in the nearby sample is likely to be larger than the look-back time to the galaxies in our high-redshift sample, so we expect that our local calibration will work well at eliminating any pernicious drift in the supernova distances between the local and distant samples. Although we expect this approach to be valid for joining our nearby and distant samples, until we know more about the stellar ancestors of SNe Ia, we need to be vigilant for changes in the properties of the SNe at signiïcant lookback times. These might be detected as changes in the spectra or colors of SNe Ia with redshift. 5.4. Selection Biases Like every sample selected by a ÿux limit, our SN Ia sample will be aected by the shift of the mean to intrinsically brighter objects near our redshift limit because of the dispersion of their intrinsic luminosities ; this is often referred to as Malmquist bias (see, e.g., Gonzalez & Faber 1997). Generally speaking, the bias is proportional to p2 of the distance indicator. Since we suer only the bias left after the correction for light curve shape, the average bias is much smaller than for uncorrected SN Ia peak brightnesses. This is fortunate, because it is not a straightforward task to correct for luminosity biases in the limited sample of objects produced by a particular SN search. In addition to classic Malmquist bias, the SNe Ia we discover at high redshift are subject to a number of selection eects. These could aect the average properties of our sample as a function of redshift and could possibly bias our measurement of the (D , z) relation. The supernovae disL

covered by the High-Z SN Search are limited by their detectability between two epochs (typically 25 days apart in the observerîs frame), and only those objects that increase in ÿux by an amount greater than our detection threshold are discovered. Therefore, our ability to discover a supernova depends not only on its brightness at maximum light but also on its age, the light curve shape of the object, and the redshift due to time dilation of the light curves. We have performed Monte Carlo simulations in which we randomly explode SNe Ia assuming their rate is constant with look-back time, identifying which objects would be discovered in a search by our supernova program. These simulations show that with SN Ia distances of precision p \ 0.15 mag, our average measurement of ) will be M biased high by D0.05 for 0 \) \ 1 ( ) \ 0). Though it M " may seem surprising, selection biases are signiïcantly less than other sources of error, such as the uncertainty in (B[V ), because the scatter in luminosity, after correction for light curve shape, is so small. Nevertheless, selection eects are a source of systemic error that should be removed. Corrections could be computed through Monte Carlo simulations for equation (6) provided that the selection function (completeness vs. magnitude) for ïnding objects were known. Unfortunately, the selection function for discovering SNe Ia is not sharply deïned ; it depends critically on the PSF of both the prediscovery and discovery images, and our procedure ultimately rests on a human decision of whether an object is real. Since false detections waste scarce observing time, observers are reluctant to follow the light curve of an object unless the probability that the object is real is very high. Perlmutter et al. (1997) performed simulations to determine the magnitude limit for each of their discovery frames, adding stars to galaxies and then measuring their ability to recover them in software. Our experience with similar simulations is that our software selects fainter objects than human reviewers will accept as being real. By comparing Monte Carlo simulations of the expected redshift distribution of objects to the actual sample, it should be possible to estimate corrections to these detection thresholds. Rather than apply corrections to individual objects, it would be better to employ a maximum likelihood approach in which one ïnds the most likely cosmological model, given the SN redshifts, estimated detection thresholds, SN distances and light curves, and detection simulations. This is an involved, computationally expensive procedure, which is probably not yet warranted given the small size of the corrections and the limited set of data. 5.5. W eak Gravitational L ensing It has been pointed out by Kantowski, Vaughan, & Branch (1995) that large-scale structure could magnify (or demagnify) a SNîs light through weak gravitational lensing as it travels to an observer. Wambsganss et al. (1997) have computed the eect for ) -dominated and ) -dominated " M ÿat universes and ïnd that weak lensing could produce a modest increase in the dispersion of a distance indicator (approximately 5% at z \ 1). It also leads to a small systematic shift in observed SN brightnesses to fainter magnitudesõapproximately 1% at z \ 1. The average line of sight to a SN is more likely to pass through voids than clusters and ïlaments, leading to an average demagniïcation. Holz & Wald (1997) have calculated a "" worst case îî


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THE HIGH-Z SN SEARCH
TABLE 1 SUMMARY OF ERROR CONTRIBUTIONS TO HIGH SUPERNOVA DISTANCES Systematic Uncertainties (1 p) Photometric system zero point a ...... Selection eects ........................ Evolution ............................... Evolution of extinction law .......... Gravitational lensing .................. Magnitude 0.05 0.02 \0.17 0.02 0.02 Statistical Uncertainties (1 p) Individual zero points ....... Shot noise ..................... K-corrections ................. Extinction ..................... p of SN Ia ..................... Magnitude 0.02 0.15 0.03 0.10 0.15

55

a Includes propagated eect on extinction, 3.1 p E(B[V ).

scenario for the eect of gravitational lensing, a case in which the universeîs mass is made up of randomly distributed objects with mass greater than 0.01 M . At z \ 0.5 for _ ) \ 1, an average standard candle is made 0.15 mag M fainter by the lensing. The eect is more pronounced at z B 1 and is diminished as ) approaches 0, as suggested M by the SN observations presented here, by Garnavich et al. (1998), and by Perlmutter et al. (1998). Given the size of other systematic errors, uncertainties due to gravitational lensing are not likely to be of major concern up to z B 1. It is unlikely that we might ïnd an event that has undergone signiïcant lensing so that it can be readily separated from the intrinsic dispersion of SN Ia brightnesses, although Kolatt & Bartelmann (1998) suggest how to maximize these

events by searching through galaxy clusters. 5.6. Summary of Uncertainties The data presented by Garnavich et al. (1998) and Riess et al. (1998) indicate that we can measure the distances to high-z supernovae with a statistical uncertainty of p \ 0.2 mag (10%) per object. With only 10 objects, a comparison of z B 0 and z B 0.5 can be made to a precision of better than 5%õleaving systematic uncertainties as a major contributor to the total error budget. A summary of the contributions to high-redshift supernova distance uncertainties is given in Table 1. This table shows that our program to measure cosmology will most likely be limited by the possibility of the evolution of SN Ia explosions with look-back

FIG. 5.õTemplate image of SN 1995K taken 1995 March 7, the discovery image of SN 1995K taken 1995 March 30, and the resulting subtracted image obtained as described in ° 4.2.


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time. Future work to address this possible problem will be as important as obtaining large numbers of objects at high redshift.
6

. OBSERVATIONS AND ANALYSIS OF SN 1995K

6.1. Photometry and Spectroscopy In 1995 February and March, our team imaged approximately 2.5 deg2 with the CTIO 4 m telescope ] 20482 CCD. Our ïrst attempts at searching for supernovae in these data were hampered by distortions caused by curvature in the CCD and general inexperience. However, in an image taken on March 30 (UT dates are used throughout this paper), a new object was discovered in a galaxy at position (J2000.0) a \ 10h50m47s , d \[09¡15@07A4 (Fig. .0 . 5). This object was reported to the IAU and designated SN 1995K (Schmidt et al. 1995). We obtained spectra of SN 1995K using the European Southern Observatory (ESO) NTT]EMMI on 1995 April 3. CCD images containing the SN spectra were bias subtracted, and the spectrum of the object extracted as a single pixel row, to minimize the contribution of the host galaxy. The spectra were then wavelength calibrated with comparison lamp spectra interspersed with the SN observations, and the resulting individual spectra were combined. The extracted host galaxy spectrum was scaled and subtracted. The host galaxyîs redshift, measured from its Ha emission, is z \ 0.479. The spectrum was binned to increase the S/N per resolution element, and the resulting spectrum is plotted in Figure 6. Also plotted is the spectrum of SN 1994D (Filippenko 1997) near maximum light, binned to the same resolution as SN 1995K. The spectrum of SN 1995K appears to be typical of SNe Ia, exhibiting the characteristic Si II absorption at a rest wavelength of 6150 A and is incom patible with peculiar SNe Ia such as SN 1991T (Filippenko et al. 1992a ; Phillips et al. 1992 ; Ruiz-Lapuente et al. 1992 ; Ford et al. 1993) and SN 1991bg (Filippenko et al. 1992b ; Leibundgut et al. 1993 ; Turatto et al. 1996). Using the spectral aging technique of Riess et al. (1997), we estimate the age of the SN on this date, 1995 April 3, to be 1 ^ 2 days past maximum light, independent of and in agreement with its light curve. An additional spectrum of SN 1995Kîs host galaxy was obtained on 1995 April 25 with the CTIO 4 m telescope (Fig. 6). Comparison of the galaxy spectrum with the catalog of Kennicutt (1992) shows this galaxy to be consistent with a star-forming galaxy of type Sb/c. CCD images of SN 1995K were obtained at several telescopes in B45 and V 45 ïlters, and in some cases R and I . C C The sequence of stars shown in Figure 7 was calibrated on three photometric nights by observing the spectrophotometric standards listed in the Appendix and standards of Landolt (1992a) for R and I measurements, C C measuring the color and extinction transformation coefficients, and applying these to observations of the SN 1995K ïeld. The resulting magnitudes were averaged from multiple nights and are given in Table 2, with uncertainties calculated from the dispersion of the observations. Relative photometry between the supernova and the stellar sequence was carried out as prescribed in ° 4.3, using a template for galaxy subtraction obtained with the CTIO 4 m ] 20482 CCD on 1996 March 15. SN 1995Kîs light curve was brought to the standard system by osetting from the standard star sequence and applying color corrections derived for each instrumental setup [these corrections ranged from

FIG. 6.õSpectrum of SN 1995K obtained with the ESO NTT on 1995 April 3 (UT), compared to that of SN Ia 1994D (Filippenko 1997) near maximum light. The spectra have been binned to the same resolution, and the good match indicates SN 1995K is an SN Ia caught near peak brightness. Also shown is the spectrum of SN 1995Kîs host galaxy as obtained on 1995 April 25 with the CTIO 4 m telescope.

[0.01 to 0.04 mag per mag of (B [ V )]. The resulting 45 45 light curve is listed in Table 3. 6.2. T he L uminosity Distance to SN 1995K The K-corrections to translate B45 and V 45 observations of SNe Ia at a redshift of z \ 0.479 to rest frame B and V ,
TABLE 2 A PHOTOMETRIC SEQUENCE NEAR SN 1995K Star 1 2 3 4 5 6 7 8 9 1 1 1 1 ....... ....... ....... ....... ....... ....... ....... ....... ....... 0 ...... 1 ...... 2 ...... 3 ...... B45 21.72(3) 20.06(1) 17.05(1) 20.51(2) 17.28(2) 17.18(2) 20.72(3) 19.75(2) 18.16(2) 20.64(4) 18.57(2) 19.83(2) 19.63(2) V 45 20.91(4) 19.60(1) 16.40(1) 18.88(4) 16.51(3) 16.83(3) 20.31(3) 19.40(3) 17.72(3) 19.11(3) 17.60(2) 19.46(3) 17.99(3) R 21.66(3) 20.03(2) 17.01(2) 20.40(3) 17.22(3) 17.15(3) 20.69(4) 19.73(3) 18.13(3) 20.53(4) 18.50(2) 19.81(3) 19.52(3) I 20.85(4) 19.57(3) 16.36(2) 18.77(4) 16.45(4) 16.80(4) 20.28(5) 19.37(3) 17.69(3) 19.01(3) 17.54(3) 19.44(3) 17.88(3)

NOTE.õUncertainties in units of 0.01 mag are listed in parentheses.


FIG. 7.õField around SN 1995K as observed by the CTIO 4 m telescope, with the position of the SN and photometric sequence stars marked

TABLE 3 PHOTOMETRIC DATA FOR SN 1995K JD 2449774.6 2449783.6 2449801.7 2449806.6 2449810.6 2449812.6 2449812.6 2449814.7 2449815.6 2449815.7 2449816.6 2449817.5 2449830.6 2449831.5 2449836.5 2449866.4 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... Date 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 Feb 26 Mar 07 Mar 25 Mar 30 Apr 03 Apr 05 Apr 05 Apr 07 Apr 08 Apr 08 Apr 09 Apr 10 Apr 23 Apr 24 Apr 29 May 29 B45 [24.5 24.09(38) 22.26(15) 22.19(06) ... ... 22.23(09) 22.44(14) 22.39(12) ... 22.62(12) 22.79(12) 23.62(30) ... 23.96(33) [24.30 V 45 ... ... ... ... 22.02(30) ... 22.18(10) 22.25(15) 22.48(22) ... 22.48(12) ... 22.95(30) ... 22.92(29) [23.50 R ... ... ... ... 22.37(12) 22.28(15) ... ... ... 22.64(14) ... ... ... 23.70(25)a ... ... I ... ... ... ... ... ... ... ... ... 22.36(14) ... ... ... 22.95(30)b ... ... Telescope CTIO 4m CTIO 4m CTIO 4m CTIO 4m ESO NTT ESO 3.6m LCO 2.4m LCO 2.4m LCO 2.4m KPNO 4m LCO 2.4m LCO 2.4m ESO NTT ESO NTT ESO 1.5m ESO NTT Observer Hamuy et al. Hamuy et al. Hamuy et al. Hamuy et al. Leibundgut & Spyromilio Walsh Dressler Dressler Dressler Ciardullo Dressler Dressler Leibundgut Leibundgut Leibundgut Spyromilio

NOTE.õUncertainties in units of 0.01 mag are listed in parentheses. a Gunn-r. b Gunn-i.


58
TABLE 4

SCHMIDT ET AL.
THE LIGHT CURVE OF SN 1995K CORRECTED TO THE REST FRAME JD Age (days) ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... [20.8 [14.7 [2.4 0.9 3.6 4.9 4.9 6.4 7.0 7.0 7.6 8.2 17.1 17.7 21.1 41.3 B [25.23 24.82(38) 23.01(15) 22.94(06) 23.11(12) 23.02(15) 22.96(09) 23.18(14) 23.13(12) 23.36(14) 23.35(12) 23.53(12) 24.34(28) 24.43(25) 24.69(33) [ 25.02 V ... ... ... ... 22.87(30) ... 23.02(10) 23.09(15) 23.32(22) 23.22(14) 23.32(12) ... 23.78(27) 23.72(30) 23.74(29) [ 24.31 K K

Vol. 507

2449774.6 2449783.6 2449801.7 2449806.6 2449810.6 2449812.6 2449812.6 2449814.7 2449815.6 2449815.7 2449816.6 2449817.5 2449830.6 2449831.5 2449836.5 2449866.4

B [0.73 [0.73 [0.75 [0.75 [0.74 [0.74 [0.73 [0.74 [0.74 [0.72 [0.73 [0.74 [0.72 [0.73 [0.73 [0.72

V ... ... ... ... [0.85 ... [0.84 [0.84 [0.84 [0.86 [0.84 ... [0.83 [0.77 [0.82 [0.81

NOTE.õUncertainties in units of 0.01 mag are listed in parentheses.

respectively, are plotted in Figure 8. The K-corrections are nearly constant because of the close match of these redshifted ïlters to their rest frame counterparts. Table 4 lists each corrected photometric measurement, the time-dilated age of the SN with respect to maximum ït from the light curve (iteratively determined by applying K-corrections, ïtting the light curve, and reïtting the K-corrections, until
FIG. 9.õ(L ower panel) Rest frame B and (upper panel) V light curves of SN 1995K. The data are K-corrected and time-dilated, and the RPK96 (solid lines) and H95 (dotted lines) ïts are superposed.

FIG. 8.õMeasured K-corrections for individual spectra plotted as a function of supernova age for transforming (upper panel) V 45 to V and (lower panel) B45 to B for SNe Ia at z \ 0.479. A ïfth-order polynomial is ït to the data.

convergence occurs), and the resulting rest frame magnitudes for SN 1995K. The light curve of SN 1995K has already successfully been used to provide strong evidence for the predicted eects of time dilation (Leibundgut et al. 1996) in SN light curves (Leibundgut 1990). The light curve of SN 1995K is plotted in Figure 9 and is of sufficient quality to provide an accurate luminosity distance to its z \ 0.479 host. Using the techniques described in H95 we derive *m (B) \ 1.15 ^ 0.1 mag for SN 1995K, 15 and rest frame brightnesses at maximum light of m \ 22.93 B ^ 0.08 mag and m \ 23.04 ^ 0.13 mag. This decline rate V and color at maximum are typical for the unreddened SNe Ia we observe in the nearby universe. The derived distance modulus, applying the *m (B) versus M relations of H96a 15 V (their Table 3), is (m [ M) \ 42.31 ^ 0.13 mag, and the V Hubble diagram that includes SN 1995K and the H96b distance measurements to 29 objects is shown in Figure 10. Applying MLCS (RPK96) to SN 1995K indicates that this SN is slightly overluminous relative to the average (* \ 0.07), is unreddened, and has a distance modulus of 42.40 ^ 0.25 mag on the RPK96 scale. This object and the distance measurements of RPK96 are plotted in Figure 11. Distances derived to the nearby and distant supernovae must be done in exactly the same manner, so the results of these two ways of using the light curve shape are not plotted on the same diagram. However, one can compare the resulting (D , z) relation, and the bottom halves of Figures L 10 and 11 demonstrate that a consistent result is obtained. With a single object, it is difficult to make serious conclusions about cosmological parameters, regardless of the distance precision it oers, because there is no way to judge


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59

FIG. 10.õUpper panel : Hubble diagram containing SN 1995K using the distances and techniques of H96b, and these distances plotted as a residual in distance modulus (m [ M), with respect to an empty () \ 0) universe.

FIG. 11.õUpper panel : Hubble Diagram containing SN 1995K using the distances and techniques of RPK96, and these distances plotted as a residual in distance modulus (m [ M), with respect to an empty () \ 0) universe.

systematic errors in an empirical way. However, taken at face value, if ) \ 0, SN 1995K yields an estimate of ) \ " M [0.2`1.0 for the matter density of the universe, where we ~0.8 the range to include both the H96 and RPK96 have taken distance uncertainties, extinction uncertainties, and uncertainties due the sources of systematic error described in ° 5. For a spatially ÿat universe composed of normal matter and a cosmological constant, we ïnd ) \ 0.4`0.5 , ) \ M ~0.4 " 0.6`0.4 . An ) \ ) \ 1 universe is excluded with greater ~0.5 conïdence from this single distance estimate. M than 80% Perlmutter et al. (1997) present luminosity distances to seven high-redshift supernovae. Direct comparison with our work is difficult because not all of their objects were positively identiïed as SNe Ia (two of their objects have decline rates more extreme than any other known SN Ia and do not have conïrming spectra), and their single-color results cannot be corrected for extinction in the host galaxy. However, taken on equal terms, SN 1995K suggests that ) may be lower than the central value of ) \ 0.88`0.69 M M ~0.60 they ïnd. Recent HST observations by the two groups (Garnavich et al. 1998 ; Perlmutter et al. 1998) seem to conïrm this view, yielding values of ) \[0.1 ^ 0.5 and M ) \ 0.2 ^ 0.4, respectively. More data will elevate this M discussion.
7

. THE FUTURE

SN 1995K is the ïrst of more than 30 conïrmed SNe Ia discovered by the High-Z SN Search (Schmidt et al. 1995, 1997a, 1997b ; Kirshner et al. 1995 ; Suntze et al. 1996 ; Garnavich et al. 1996a, 1996b, 1997). The observations pre-

sented here indicate that these objects, and those of Perlmutter et al. (1997), should provide an accurate method of tracing out luminosity distances to high redshifts. Figure 12 shows the level of precision likely to be achieved by a sample of N SNe Ia with observations of comparable precision to those of SN 1995K ; a measurement of ) to ^0.2 should be achieved from objects at z \ 0.5 M given our expected systematic uncertainties. The High-Z SN Search has been allocated sufficient orbits to follow about eight SNe Ia with the HST in two photometric bands. We have already obtained observations of three SNe Ia, one of which lies at z \ 0.97 (Garnavich et al. 1998). As demonstrated in Figure 2, this object lies in a window in which it would be possible to obtain accurate rest frame B and V observations of SNe Ia with HST . A sample of 10 such z \ 1 objects, coupled with the z \ 0.5 sample, would provide enough information to separate the individual eects of ) and ) " (Goobar & Perlmutter 1995). Figure 13 shows theM p joint 1 conïdence region for ) and ) that is obtainable with a M sample of 30 SNe Ia observed at " \ 0.5 augmented with 10 z SNe Ia observed at z \ 1 with HST . As can be seen from the ïgure, although ) and ) are not individually meaM " sured accurately, the combination ) [ ) is tightly con" strained. If we limit ourselves to ÿatM cosmological models, ) ] ) \ 1, the uncertainty in ) and ) would become M " M " small, with uncertainties in each quantity of approximately 0.1. Although measurements of the CMB anisotropy on small scales still have several years to reach maturity, the high-z SNe Ia and CMB observations are complementary. The error ellipses of these two measurements in the () , ) ) M"


60

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Vol. 507

FIG. 12.õUncertainty in ) \ ) as a function of the sample size for M objects with observations similar to SN 1995K observed at z \ 0.5. Four cases of systematic error are considered (p \ 0.0, 0.05 [expected], 0.10 sys mag, and 0.20 mag) and are plotted as separate lines in the ïgure.

FIG. 13.õPredicted error contours (68.3% and 95.4% joint conïdence) in measuring ) and ) simultaneously for a sample of 30 z \ 0.5 SNe Ia M " augmented with 10 z \ 1 SNe Ia observed with HST . The underlying cosmology in the simulation is ) \ 0.4, ) \ 0. Also shown, as dotted M " lines, are the predicted uncertainty contours (68.3% and 95.4% conïdence) from future CMB anisotropy measurements to be made by the Planck Surveyor mission (Zaldarriaga et al. 1997).

plane will be nearly perpendicular to each other (Fig. 13). When combined, they could provide a deïnitive measurement of the global parameters of our universe. We wish to thank Ed Carter at NOAO for tracing the redshifted ïlter set. A. V. F. acknowledges support from NSF grant AST 94-17213. R. P. K. acknowledges support from NSF grants AST 95-28899 and AST 96 17058 and thanks the Institute for Theoretical Physics, University of California, Santa Barbara, for their generous hospitality. A. G. R. acknowledges support from the Miller Institute for Basic Research in Science, University of California, Berkeley. SN research at UW is supported by the NSF and NASA. C. W. S. acknowledges the generous support of the

Seaver Institute and the Packard Foundation. M. H. acknowledges support provided for this work by the NSF through grant number GF-1002-97 from the Association of Universities for Research in Astronomy, Inc., under NSF Cooperative Agreement No. AST 89-47990, and from Fundacion Andes under project C-12984 ; M. H. also acknowl edges support by Catedra Presidencial de Ciencias 1996-1997. Partial support for A. C. was provided by the NSF through grant GF-1001-95 from AURA, Inc., under NSF cooperative agreement AST 89-47990, and from Fundacion Antorchas Argentina under project A-13313. This research used IRAF, an astronomical reduction package distributed by the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the NSF.

APPENDIX THE HIGH-Z STANDARD SYSTEM We have created a new set of broadband ïlters that represent the Johnson B and V ïlters redshifted to z \ 0.35 and z \ 0.45. We call these B35, V 35, B45, and V 45, respectively. Traces of each ïlter have been supplied by the manufacturer, Omega Optical, and these traces have been veriïed at KPNO using a spectrophotometer. The sensitivity functions S , S , S , and S of our broadband ïlters have been derived by combining these ïlter traces with a quantum efficiency B35 V35a curve of B45 V45CCD and a normalized function that increases linearly with j (Table 5). This latter function is included because thinned SITE CCDs are photon detectors and standard sensitivity functions (see, e.g., Bessell 1990) assume that a star with spectrum F in j ïlter i has magnitude m given by i / S (j)F (j) dj i j (A1) m \[2.5 log ]Z . i i / S (j) dj i For the purposes of the High-Z SN Search, the exact deïnition of our zero points Z is not important. As long as we use a i consistent method in our calculations with equations (12) and (10), our derived K-corrections are sensitive only to the dierence in zero points between our redshifted ïlters and the Johnson ïlters, e.g., Z [ Z . Rather than establishing our B B45 standard systemîs zero point using Vega, we use the Hamuy et al. (1994) spectrophotometric standards. These stars have accurate broadband photometry in the standard systems of Cousins (1980) and Landolt (1992b), the systems with which our nearby supernova observations have been calibrated. This consistency is important because our programîs goal is to make as accurate a dierential measurement as possible of SN brightnesses as function of redshift. We deïne Z of our broadband ïlters such that A-type stars with (V [I) \ 0 mag have B35 \ V 35 \ B45 \ V 45 4 V . i Hamuy et al. (1994) have observed a set of A-type stars (referred to as secondary standards) that have V [I B 0. Since the C Hamuy stars do not have exactly V [I \ 0, we must apply small corrections to m of the stars to obtain magnitudes in our C V


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TABLE 5 SENSITIVITY FUNCTIONS OF THE HIGH-Z FILTER SET Wavelength (A) 5100.0 5200.0 5300.0 5400.0 5500.0 5600.0 5700.0 5800.0 5900.0 6000.0 6100.0 6200.0 6300.0 6400.0 6500.0 6600.0 6700.0 6800.0 6900.0 7000.0 7100.0 7200.0 7300.0 7400.0 7500.0 7600.0 7700.0 7800.0 7900.0 8000.0 8100.0 8200.0 8300.0 8400.0 8500.0 8600.0 8700.0 8800.0 8900.0 9000.0 9100.0 9200.0 9300.0 9400.0 9500.0 .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... S (B35) j 0.002 0.246 0.708 0.923 0.996 1.000 0.987 0.953 0.904 0.938 0.964 0.884 0.878 0.924 0.864 0.702 0.440 0.237 0.121 0.064 0.041 0.027 0.017 0.013 0.009 0.007 0.004 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 S (B45) j 0.000 0.000 0.000 0.000 0.000 0.127 0.628 0.933 0.930 0.962 0.987 0.909 0.944 1.000 0.934 0.917 0.927 0.887 0.857 0.795 0.573 0.330 0.180 0.095 0.055 0.036 0.023 0.017 0.013 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 S (V 35) j 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.128 0.606 0.868 0.950 0.965 1.000 0.962 0.892 0.861 0.837 0.817 0.832 0.849 0.814 0.578 0.323 0.168 0.088 0.048 0.029 0.018 0.012 0.009 0.006 0.005 0.003 0.002 0.001 0.000 0.000 S (V 45) j 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.080 0.329 0.649 0.860 0.978 1.000 0.952 0.908 0.882 0.855 0.849 0.829 0.719 0.500 0.312 0.171 0.097 0.054 0.034 0.021 0.014 0.009 0.006 0.003 0.001

61

ïlter system. We use equation (A1) to derive the magnitudes of the tertiary stars of Hamuy et al. (1994), which have [0.3 \ (V [I ) \ 0.8, in our bandpasses, and then obtain the linear transformation between our system and the Johnson/ Kron-CousinsCsystems of the form m \ a (V [I ) ] m . (A2) i ij C j The transformations used to convert the Johnson/Kron-Cousins system to our new system are listed in Table 6, and the ïts are shown in Figure 14. We use these values to transform the secondary standards of Hamuy to the high-redshift SN system, and these stars and their derived magnitudes are listed as the ïrst 10 stars in Table 7. Because of the near-zero color of the
TABLE 6 THE HIGH-Z FILTER SYSTEM TRANSFORMATIONS AND ZERO POINTS Transformation [I ) ] V ....... [IC) ] R ...... [IC ) ] I C ...... [IC) ] IC ...... C C a Zero point required for equation units of ergs cm~2 s~1 A~1. B35 B45 V 35 V 45 \[0.246(V \]0.027(V \]0.198(V \]0.034(V Zero Pointa ZP ZP ZP ZP \[21.339 \[21.582 \[22.045 \[22.292

(10) if F is in j


FIG. 14.õ(B35 [ V ), (B45 [ R ), (V 35 [ I ), and (V 45 [ I ) plotted as a function of (V [I ). The best ïtting linear transformation is superposed as given C C C C in Table 7.

TABLE 7 PRIMARY STANDARDS FOR THE HIGH-Z STANDARD SYSTEM Star Namea HR 718 ....... HR 1544 ...... HR 3454 ...... HR 4468 ...... HR 4963 ...... HR 5501 ...... HR 7596 ...... HR 7950 ...... HR 8634 ...... HR 9087 ...... L377 .......... L1020 ......... EG 21 ........ L1788 ......... L2415 ......... H600 .......... L3218 ......... L3864 ......... L4364 ......... F56............ L4816 ......... CD 32 ........ L6248 ......... EG 274 ....... L7379 ......... L7987 ......... L9239 ......... F110 .......... L9491 ......... B35 4.285 4.352 4.346 4.711 4.373 5.699 5.583 3.765 3.428 5.147 11.077 11.335 11.431 12.991 12.074 10.380 11.818 12.009 11.435 11.072 13.787 10.365 11.638 11.093 10.048 12.278 11.876 11.893 14.093 B45 4.299 4.344 4.378 4.721 4.369 5.696 5.548 3.761 3.439 5.163 10.947 11.180 11.468 12.854 11.955 10.326 11.776 11.870 11.362 11.085 13.791 10.290 11.493 11.140 9.892 12.311 11.711 11.957 14.067 V 35 4.329 4.340 4.448 4.749 4.373 5.699 5.499 3.764 3.474 5.207 10.750 10.938 11.513 12.636 11.761 10.245 11.698 11.649 11.266 11.126 13.770 10.185 11.261 11.215 9.656 12.350 11.452 12.081 14.043 V 45 4.340 4.333 4.480 4.760 4.370 5.699 5.473 3.764 3.489 5.228 10.656 10.820 11.536 12.527 11.662 10.200 11.662 11.539 11.221 11.141 13.758 10.135 11.147 11.258 9.543 12.372 11.326 12.138 14.037

a As listed in Hamuy et al. 1992.


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63

Hamuy secondary stars, the corrections, even for the B35 and V 35 ïlters, which have large transformation coefficients, are very small (\0.02 mag). We compute the Z for our ïlters by comparing the magnitudes for the Hamuy secondary stars i obtained from equation (A2) with the magnitudes obtained from equation (A1) and adjusting Z for each ïlter so that the i average oset between the two sets of magnitudes is zero. The resulting Z are given in Table 6. Table 7 lists the B35, V 35, i B45, and V 45 magnitudes of the Hamuy tertiary stars using these Z with equation (A1). The Hamuy secondary and tertiary i stars form the primary standards for the high-redshift SN photometric system. In a future paper, we will present observations of these standard stars and use them to calibrate selected Landolt (1992a) ïelds.
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