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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