CMB give w ¼ 0:969þ0:059
(sys).While ourresultsare consistent witha cosmologicalconstant, we ob-
tainonly relatively weak constraintson a wthat varieswithredshift. Inparticular,thecurrentSNdata donot yet sig-
niﬁcantlyconstrainw atz > 1.WiththeadditionofournewnearbyHubble-ﬂowSNeIa,theseresultingcosmological
constraints are currently the tightest available.
Subject headinggs: cosmological parameters — cosmology: observations — supernovae: general
Online material: color ﬁgures, machine-readable tables
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titlegrplabelColor ﬁgures/labelentrytitlegrptitleﬁgref rid="fg2" place="NO"Figure 2/ﬁgref/title/
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entryentrytitlegrptitleﬁgref rid="fg8" place="NO"Figure 8/ﬁgref/title/titlegrp/
entryentrytitlegrptitleﬁgref rid="fg9" place="NO"Figure 9/ﬁgref/title/titlegrp/
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The evidence for dark energy hasevolved fromtheﬁrst hints,
forthe case ofa ﬂatuniverse (Perlmutteret al.1998; Garnavich
et al. 1998; Schmidt et al. 1998), through the more deﬁnite ev-
idence for the general case of unconstrained curvature (Riess
et al. 1998; Perlmutter et al. 1999), to the current work, which
aimsto explore the properties of dark energy (for a review, see
ment techniquesandseveral new Type Ia supernova (SN Ia)data
sets have helped begin the laborious process of narrowing in on
the parametersthat describe the cosmological model. The SN Ia
measurements remain a key ingredient in all current determina-
tions of cosmological parameters (see, e.g., the recent CMB re-
how the current world data set of SN Ia measurements is con-
structed and how it canbe used coherently,particularlysinceno
one SN Ia sample by itself provides an accurate cosmological
Untilrecently,the SNIa compilations (e.g., Riesset al. 1998;
et al. 2006; Wood-Vasey et al. 2007) primarily consisted of a
relatively uniform high-redshift (z 0:5)data set from a single
studyputtogetherwitha low-redshift(z 0:05)samplecollected
in a different study or studies.However, once there were several
independent data sets at high redshift, it became more important
and interesting to see the cosmological constraintsobtainable by
combining several groups’ work. Riess et al. (2004, 2007) pro-
vided a ﬁrst compilation analysis of this kind, drawing on data
et al. (1998), Knop et al. (2003), Tonry et al.(2003), and Barris
et al. (2004). Many of the subsequent cosmology studies have
usedthis compilation asthe representation ofthe SN Ia sample,
in particular the selection of supernovae that Riess et al. (2004,
that have been used are those of Wood-Vasey et al. (2007) and
Daviset al. (2007).
At present a number of updatesshould be made to the SN Ia
data sets, and a numberof analysis issues should be addressed,
including several that will recur with every future generation of
SN compilations. These include the following major goals:
1. It is important to add a new low-redshift SN Ia sample to
Especially valuable are the SNe in the smooth, nearby Hubble
ﬂow (z above 0.02). Since this part of the Hubble diagram is
large incremental improvement (Linder 2006). It isinteresting to
note that the largest contributionin thisredshift range still comes
from the landmark Calan/Tololo survey (Hamuy et al. 1996).
2. Theanalysisshouldreﬂect the heterogeneousnatureofthe
data set. In particular, it is important that a sample of poorer
quality will not degrade the impact of the higher quality data,
such as the Supernova Legacy Survey (SNLS) and ESSENCE
high-redshift data sets, which have recently been published.
3. The different supernova data setsshould be analyzed with
measurementsand peak-magnitude ﬁtsthat were obtained with
disparate light curve ﬁtting functions and analysis procedures,
particularly for handling the colorcorrection forboth extinction
and any intrinsic color-luminosity relation.
4. A reproducible, well-characterized approach to selecting
the good SNe Ia and rejecting the questionable and outlier SNe
should be used.Previouscompilationsrelied to alargeextenton
Gold compilation ofRiess etal.(2004,2007) excluded SNe that
5. To the extent possible, the analysis should not introduce
biases into the ﬁt, including some that have only recently been
propertiesof SNe Ia.
in this papera new SN compilation, a new nearby-Hubble-ﬂow
SN Ia data set,and new analysisprocedures. Several additional
smaller enhancements are also presented.
With respect togoal 1,itisimportant tonote that bothnearby
and distant supernovae are needed to measure cosmological pa-
the dynamics of the universe—might appear dimmer or brighter
than expected for a reference cosmology. Nearby SN light curves
typically have better observational coverage andsignal-to-noise
ratio (S/N) than their high-redshift counterparts.However, they
are signiﬁcantly more difﬁcult to discover since vast amounts
of sky have to be searched to obtain a sizable number of super-
novae, due to the smallvolume ofthe low-redshift universe.We
consisted primarily of wide-ﬁeld magnitude-limited searches and
extensive photometric andspectroscopicfollow-upobservations
using a large number of ground-based telescopes. We provide
published data of nearby and distant supernovae to construct the
largest Hubble diagramto date (but presumablynotfor long). In
thiscombinationwe adjustthe weightofSNe belongingtoasam-
pletoreﬂectthedispersionwedetermine forthe sample.Withour
prescription, SN samples with signiﬁcant unaccounted-for sta-
tistical orsystematic uncertainties are effectively deweighted.
AllSN lightcurvesare ﬁttedconsistentlyintheobserverframe
systemusingthe spectral-template–based ﬁtmethodofGuyetal.
(2005)(alsoknown asSALT).Where possible,theoriginalband-
pass functionsare used (goal 3).
To addressgoal4,weadopt arobustanalysistechniquebased
on outlier rejection that we show is resilient against contamina-
tion. The analysis strategy wasdeveloped to limit the inﬂuence
most subjective component ofSN cosmology (primarilybecause
KOWALSKI ET AL.
nova spectroscopy),and we avoiddecisionsofwhetherto include
aspeciﬁc SN that are based on spectroscopic features that go
beyond that of the authors’ classiﬁcation.
Following Conley et al. (2006), the full analysis chain was
developed in a blind fashion—that is, hiding the best-ﬁtting
cosmological parameters until the analysis was ﬁnalized. This
helps resist the impulse to stop searching for systematic effects
oncethe‘‘right’’answerisobtained.We derive constraintsonthe
sources of bias introduced in the ﬁtting procedure (goal 5).
The paper is organized as follows. In x 2 we methodically
present thedata reductionand photometric calibration ofthe light
curves from the SCP Nearby 1999 Supernova Campaign: the
reader more interested in goals 2–5 and the subsequent cosmo-
logical analysis might want to only skim this section. In x 3 we
combine thenewsupernovaewitha largesetofnearbyand high-
redshift supernovae fromthe literature and ﬁt the full setoflight
curves in a consistent manner. We then proceed to determine
stringent constraintson the dynamics of the universe. Section 4
explains the methods employed for cosmological parameter es-
timation, which includesblinding the analysis and using robust
statistics. We evaluate the systematic errorsof themeasurements
inx 5andsummarizethe resultingconstraintson
other parameters in x 6.
2. A NEW SAMPLE OF NEARBY SUPERNOVAE
TheSNlightcurvedata presentedin thispaperwere obtained
aspart oftheSCP Nearby1999 Supernova Campaign(Aldering
2000). The search portion of this campaign was designed to
discover Type Ia supernovae in the smooth nearby Hubble ﬂow
and wasperformed incollaboration with a numberofwide-ﬁeld
2003), QUEST-I (Rengstorf et al. 2004), NEAT (Pravdo et al.
1999),and Spacewatch(Nugent etal.1999b).In some casesthe
(EROS-II and NGSS), while in other casesthe primary data had
different scientiﬁc goals,such asdiscovery ofnear-Earth objects
(NEAT, Spacewatch), quasars, or microlenses (QUEST-I). The
wide-ﬁeld cameras operated in either point and track (NGSS,
NEAT, EROS-II) or driftscan (QUEST-I, Spacewatch) modes,
2month periodbeginning in1999 February,a totalofmore than
commonsystematicseffects,such asMalmquistbias,are thenex-
pected to more nearly cancel when comparing low-redshift with
by the search component of thiscampaign. Of these, 22 were of
Type Ia, and 14 (ofthese) were discovered nearmaximum light,
making themuseful for cosmological studies. In addition, early
alertsof potentialSNe byLOTOSS(Filippenko et al.2001)and
similar galaxy-targeted searches, and the WOOTS-I (Gal-Yam
et al. 2008) and MSACS(Germany et al. 2004)cluster-targeted
searches, provided a supplement to the primary sample as the
wide-area searches ramped up. Extensive spectroscopic screen-
ingandfollow-up wasobtained usingguest observertimeonthe
CTIO4 m,KPNO4m,APO3.5 m,Lick 3m,NOT,INT,MDM
2.4 m, ESO 3.6 m, and WHT4.2 m telescopes. The results of
1999b; Aldering et al. 1999; Strolger et al. 1999a, 1999b, 2002;
Garavini et al. 2004, 2005, 2007; Folatelli 2004). Photometric
follow-up observationswere obtainedwiththe LICK1 m,YALO
and MLO 1 m telescopes. These consist of UBVRI photometry
with a nominal cadence of3–7 days. The follow-up observations
were performed between February and 1999 June, and additional
reference imagestodeterminethecontributionof hostgalaxylight
contamination were obtained in spring 2000.
Fromthiscampaignwe presentBVRIlight curvesforthe eight
TypeIa SNethatfallintotheredshift range0:015PzP0:15and
forwhich we wereable toobtainenoughphotometric follow-up
data:SN1999aa (Armstrong &Schwartz1999;Qiaoetal.1999),
SN 1999ao (Reiss et al. 1999), SN 1999ar (Strolger et al.
1999b), SN 1999aw (Gal-Yam et al. 1999), and SN 1999bi,
SN 1999bm, SN 1999bn, and SN 1999bp (Kim et al. 1999a).
Further information on these SNe is summarized in Table 1.
Photometric data on SN 1999aw have already been published
by Strolger et al. (2002); here we present a self-consistent re-
analysisof that photometry.
2.1. Data Reduction and Photometric Calibration
Thedata werepreprocessed usingstandardalgorithmsforbias
and ﬂat ﬁeld correction. In addition, images that showed sig-
niﬁcantfringingwerecorrectedbysubtractingthe structured sky
residualsobtained from the median offringing-affected images.
Reﬂecting an original goal of this program—to obtain data for
the SN light curves.For measurement of moderately bright point
sourcesprojected ontocomplexhost galaxy backgroundsinﬁelds
sparsely covered by foreground stars, aperture photometry has
than PSF ﬁtting. We usedan aperture radiusequal tothe FWHM
ofa point source, asdetermined fromthe ﬁeldstarsinthe image.
The aperture correction, which isdeﬁned as the fraction of total
light that isoutside the FWHM radius, is determined by approx-
imatinganinﬁniteaperture bya 4 ;FWHM radiusaperture. The
average forall the stars in the ﬁeld.
Inall, photometric observationsemployed atotal of12 differ-
ent telescopes and 14different detector/ﬁltersystems.Thispre-
sented the opportunity to obtain a more accurate estimate of
might otherwise be masked by apparent internal consistency—
and thereby come closer to achieving calibration on a system
Summary of Supernova Coordinates and Redshifts
R.A. (J2000.0) Decl. (J2000.0) Redshift
08 27 42.03
06 27 26.37
11 01 36.37
09 20 16.00
11 01 15.76
12 45 00.84
11 57 00.40
11 39 46.42
determinedusingnarrowhost-galaxyfeaturesforall but one SN. In thecaseof
IMPROVED COSMOLOGICAL CONSTRAINTS
No. 2, 2008
consistentwiththat ofhigh-redshift SNeasrequiredforaccurate
to account for the speciﬁc characteristics of these many different
instruments,and their cross-calibration,made the calibration a
particularly challenging component of this analysis, which we
have addressed in a unique fashion.
Our photometric calibration procedure issubdivided into three
1. Determinationofzero points,colorterms,andatmospheric
extinction for photometric nights on telescopes at high-quality
sites, simultaneously employing observations of both Landolt
(1992) standard stars and SN ﬁeld tertiary standard stars.
2. Use of the tertiary standard stars to simultaneously deter-
minecolortermsforallotherinstruments, andzero pointsforall
3. Determination of SN magnitudes, including the SN host
In steps1 and 2 the robustness ofthe ﬁts wasensuredby heavily
deweighting signiﬁcant outliers, using an automated iterative
isthe instrumental magnitude measuredin bandx, m
are the apparentmagnitudesinbandsx and y,isthe air
arethe atmospheric ex-
in two bandsof standard stars cataloged by Landolt (1992) and
ourSN ﬁeld starsalloweddeterminationof m
well as m
for our tertiary standard stars. In total, 125
Landolt standards, spread across 16 photometric nights, were
used for calibration in B, V, R, and I, respectively. Accordingly,
the uncertainties on the night and telescope-dependent termsk
are typically very small. Their covariance with the other
dard stars generated as a by-product of this procedure are re-
ported in Appendix B.
dard stars were used to determine color terms for all remaining
instruments and zero points for all images. Since BVRIdo not re-
quire airmass–colorcrosstermsoverthe rangeofairmassescov-
would be gray, it waspossible to absorb the atmospheric extinc-
tion intothe zero pointofeach image.The catalog oftertiarystan-
for all instruments are summarized in Table 7 of Appendix A.
Inorderto determine the counts fromthe SN in a given aper-
ture, the counts expected from the underlying host galaxy must
be subtracted. In our approach, the image with the SN and the
reference images without SN light are ﬁrst convolved to have
matching point-spread functions.Stars in the imagesare usedto
approximate the PSF asa Gaussian, which for the purposes of
anotherisusually adequate.The instrumental magnitudesofob-
jects(including galaxies) in the ﬁeld are then used to determine
the ratio of counts between the images. For a given image, the
countsdue to theSNare obtained bysubtractingthecountsfrom
the reference image scaled by the ratio of countsaveraged over
all objects. Note that with this approach the images are never
due to resampling.
Several contributions to the uncertainty were evaluated and
zero points, and uncertainties in the scaling between reference
during sky subtraction andﬂat-ﬁelding are evaluatedusing ﬁeld
stars. The variance of ﬁeld star residuals is used to rescale all
by investigation of the variance of the residuals asa function of
scale variation in the ﬂat-ﬁeld. An appropriate error ﬂoor was
found to be typically 1%–2% of the signal counts.
2.2. Bandpass Determination
The bandpasses for all telescopes have to be established in
order to correctfor potential mismatchesto the Landolt/Bessell
system (Landolt 1992; Bessell 1990).
The bandpass isthe product of the quantum efﬁciency of the
CCD,the ﬁlter transmission curve,the atmospheric transmission,
and the reﬂectivity of the telescope mirrors. Figure 1 showsthe
bandpass curves for the various instruments used in this work.
The relevant data were obtained either fromthe instrument doc-
umentation or through private communication.
tometry(for arelated study,see Stritzingeretal. 2002).Forthis,
stellarspectra thatbestmatchthe published UBVRIcolorsofour
standard stars are selected from the catalog of Gunn & Stryker
(1983). The spectra that best match the published colors of the
standardstars are furtheradjusted usingcubic splinestoexactly
matchthe published colors.Forinstrumentswithoutstandardstar
observations,a second catalog is generated using our determina-
and ﬁeld stars at hand, we perform synthetic photometry for the
in central wavelength by k until they optimally reproduce the
when shifting the passband is dc
/dk 0:001, 0.0008, 0.0005,
for B, V, R, and I, respectively. An alternative pro-
cedure is to evaluate the color terms for a given bandpass in an
analogousway as forthe observed magnitudes(see eq.).We
then determine the wavelength shift to apply to the bandpasses
in order to reproduce the instrumental color terms. The two ap-
proaches agree on average to within 1 8 with an rms of about
20 8.TheresultsaresummarizedinTable 8ofAppendixA.The
associated systematic uncertainty on the photometric zero point
due to this shift depends on the color of the object and for B
V 1 will remain below 0.02 mag.
3. LIGHT CURVES
3.1. Light Cur
es from the SCP Nearby 1999
Figure 2 shows the BVRI light curves from the SCP Nearby
uncorrected photometric data, and ﬁlled symbols represent data
correctedfornonstandardbandpasses, theso-called S-corrections
(Suntzeff 2000). The S-corrections represent the magnitude shift
needed to bring the data obtained with different bandpasses to
acommonstandard system(inourcasetheBessell system).The
S-corrections are obtained from a synthetic photometry calcu-
lation using the ‘‘instrument-dependent’’ bandpass functions
KOWALSKI ET AL.
described above anda spectrophotometric lightcurve model.The
spectrophotometric SN light curve model was adjusted using
spline functionsto match the colorsofthe light curve modelsof
ourSNe. The lightcurve modelsare shown inFigure 2 to guide
the eye only.They are obtainedintwo differentwaysdepending
with z< 0:1, we have used the ﬁt method explained in Wang
et al. (2006), which has six parameters per band. This method
allowseffective ﬁtting ofR- and I-band data, which exhibits a
second ‘‘bump’’ of variable strength appearing approximately
30 daysafterthemaximum.However,since thisﬁtmethod has
sixfree parametersperﬁtted band, one can use it only for light
curveswithdense temporal sampling withhighsignal-to-noise
ratio. For the more distant SNe 1999ar, 1999bi, 1999bm, and
1999bn we use a more constrained light curve ﬁtting method
based on template matching. A library of template light curves
served redshift. The best-matching light curve is chosen as a
model for the supernova. The light curve models along with the
not be used in the remainder of the paper; we continue with the
concept of using instrumental magnitudesalongwithinstrument-
dependent passbands when ﬁtting the light curve parameters.
The light curve parameters such as peak magnitude, stretch,
and color at maximum are obtained using the spectral template
methodofGuyetal.(2005),whichisdescribed in moredetailin
speciﬁc bandpassfunctionsformodeling theobserver-frame light
curves. The B-band (left)and V-band (right)observer-frame light
curves are shown in Figure 3, along with the light curves pre-
dicted by the spectral template for the corresponding bandpass.
In the bottom part of the plots we show the residuals from the
sonably well, with
/dof 1. Systematic deviations, such as
observed in the late-time behavior of the B-band light curve of
SN1999aw,are likelyto be attributable to the limitations of the
two-parameter spectral template model in capturing the full di-
versity of Type Ia supernovae light curves.
Figure 4 (right and middle) shows the ﬁtted BV color at
hasonelow-stretchsupernova(SN 1999bm)butisotherwise dom-
were found in these searchesbut are notpresented here because of
theirfaintness—inonecase combined withproximitytothecuspy
core ofan elliptical host—prevented an analysisusing the tech-
supernovae is not very signiﬁcant (a K-S test resulted in a 20%
been published. Jha et al. (2006), Krisciunas et al. (2000), and
Altavilla etal.(2004)presentedindependent dataonSN1999aa.
When comparing the ﬁt results for SN 1999aa we ﬁnd agree-
ment to within 1% in maximum B-band luminosity,color, and
stretch. Spectroscopic and photometric data on SN 1999aw
werepreviously reportedbyStrolgeret al.(2002).While theraw
data of Strolger et al. (2002) are largely the same as that pre-
sented here, the reduction pipelines used are independent. A
main difference isthe treatment of nonstandard bandpasses. We
passes during the ﬁt of the light curve, while in Strolger et al.
Fig. 1.—BandpassesforthevariousinstrumentsusedintheSpring1999NearbySupernovaCampaign.Forcomparison,the ﬁlledregionsrepresentthe passband
transmissionfunctionsof the Bessell (1990) system.
IMPROVED COSMOLOGICAL CONSTRAINTS
No. 2, 2008
to the data. When ﬁtting for peak B-band magnitude, color, and
stretch,weobtaindifferencesofB ¼ 0:04; (BV) ¼ 0:02,
and s ¼ 0:005.
Figure 4 (left) shows the redshift distribution relative to the
sample of othernearby supernovae (see x 3.2 for a deﬁnition of
thatsample).Ascanbe seen,the distributionextendsto redshifts
z0:15, an underpopulated region in the Hubble diagram.
3.2. Literature Superno
Here we discuss the set of previously published nearby and
are of sufﬁciently good quality to allow theiruse in the following
cosmological analysis. Forall supernovae in the sample,we re-
quire that data from at least two bands with rest-frame central
and that there are in total at least ﬁve data points available.
Further,we requirethat there isatleast one observation exist-
ing between15 daysbefore and6 daysafterthedate ofmaximal
(see x 3.3). The 6 day cut is scaled by stretch for consistency. In
addition, we observed that for a smaller number of poorer light
curves, the uncertainties resulting from the ﬁts are unphysically
small compared to what is expected from the photometric data.
Inthesecases,werandomlyperturb eachdatapointbya tenth(or
if necessary bya ﬁfth) of itsphotometric error and reﬁt the light
curves. The remaining 16 SNe, where convergence cannot be
obtained even after perturbation of the data, are excluded from
further analysis (note that these SNe are generally poorly mea-
sured and wouldhave lowweightinany cosmologicalanalysis).
Forthe nearbySNsample,we useonlysupernovaewithCMB-
centric redshifts z > 0:015, in order to reduce the impact of un-
certainty due to host galaxy peculiarvelocities. We checked that
cutoff (tested for a range z ¼ 0:01
The number of SNe passing these cuts are summarized in
Table 2. Eachindividual supernova islistedin Table 11,andthe
last column indicates any cutsthat the supernova failed.
The list contains 17 supernovae from Hamuy et al. (1996),
11fromRiessetal.(1999),16from Jha etal.(2006),and6 from
Krisciunaset al.(2004a, 2004b, 2001). Our light curve data for
SN 1999aa are merged with that ofJha et al. (2006). To thislist
of nearby supernovae fromtheliterature we addthe newnearby
supernovaepresentedhere. ForSN1999aw,weuseonlythe light
curvedata presented inthispaper.Hence,thesample contains58
Fig. 2.—SNelightcurvesofthe SCPNearby1999campaign. TheﬁlledsymbolsrepresenttheS-correcteddata, andtheemptysymbolstherawphotometricdata.
the electronic edition of the Journal foracolorversion of thisﬁgure.]
KOWALSKI ET AL.
Fig. 3.—Band Vlight curvesand residuals. The multiple curvesrepresent the model predictionsfor the differentbandpassesand are obtainedbyintegratingthe
product of passbandandtheredshifted spectral template. [See the electronic editionof theJournal foracolorversion of thisﬁgure.]
The sample of high-redshift supernovae iscomparably hetero-
geneous. We use all of the 11 SNe from Knop et al. (2003) that
havelightcurvesobtained with HST.Ofthe 42supernovae from
Perlmutter et al. (1999), 30 satisfy the selection cuts described
above (ascanbeseeninthephotometrydataof Table12).Of the
16 SNe used by the High-Z Team (HZT; Riess et al. 1998;
Garnavich et al. 1998; Schmidt et al. 1998), two are already in-
cludedin the Perlmutteret al.(1999)sample,andofthe remain-
ing 14, 12 pass our cuts.
Included also are 22 SNe from Barris et al. (2004) and the
8SNe from Tonry et al. (2003) that are typed to be secure or
likelySNe Ia. We do not use SN 1999fv and SN1999 fh, asthe
Fig. 4.—Left: Redshift distribution; middle:stretch distribution; right: BVj
IMPROVED COSMOLOGICAL CONSTRAINTS
number of available data points does not exceed the number of
light curve ﬁt parameters.
Weaddthe 73 SNe Ia fromtheﬁrstyearofSNLS(Astieretal.
2006), of which one doesnot pass the ﬁrst phase cut (03D3cc).
Note that in Astieret al.(2006) 2of the 73 supernovae were ex-
cluded fromtheircosmological parameterﬁtsbecause theywere
signiﬁcant outliers (see discussion in x 4.3). Riess et al. (2004,
2007) have published 37 supernovae that were discovered and
followed using HST.Of these, 29 passed ourlight curve quality
compilation. Finally, we use the 84 SNe from the ESSENCE
75 pass our cuts.
3.3. Light Cur
The spectral-template–based ﬁt method of Guy et al. (2005),
also known as SALT, is used to ﬁt consistently both new and
literature light curve data. This method is based on a spectral
template (Nugent et al. 2002) that has been adapted in an iter-
ativeprocedure toreproduce a trainingset of nearbySNe UBVR
light curve data. The training set consists of mostly z < 0:015
SNe and hence does not overlap with the sample we use for
determinationofcosmological parameters.Toobtain an expected
magnitudefora supernova ata certainphase,themodelspectrum
is ﬁrst redshifted to the corresponding redshift followed by an
Thespectral-template–basedﬁt methodhastheadvantagethat it
with arbitrary (but known) bandpass transmission functions. In
view of the large numberof ﬁlters and instruments used for the
found in the literature, this is particularly important here. In ad-
such as the propagation of photometric errors—are handled
forthe time ofmaximum,theﬂux normalization as wellas rest-
frame color at maximum deﬁned as c ¼ BVj
and timescale stretch s. It is worth noting that by construction,
the stretch in SALT has a related meaning to the conventional
time-axisstretch(Perlmutteretal.1997;Goldhaber et al. 2001).
However,asaparameterof the light curve modelitalsoabsorbs
The same is true for the colorc.
Recently, direct comparisons between alternative ﬁtters,such
asSALT, itsupdate (Guy et al. 2007),and MLCS2k2 (Jha et al.
2007) show good consistency between the ﬁt results, e.g., the
amount of reddening (Conley et al. 2007). Our own tests have
shown that forwell-observed supernovae, the method produces
to the more traditional method of using light-curve templates
(Perlmutter et al. 1997).However, we noticed that ﬁtsof poorly
observed light curves in some cases do not converge properly.
Part ofthe explanation isthatinthecase of the spectraltemplate
basedﬁt method,the databeforet < 15daysarenotusedasan
an apparent false minimum, and we then found it necessary to
restart it repeatedly to obtain convergence. Note that the small
differencesbetweenthe lightcurveﬁtparametersof Table11and
the values shown in Table 10 of Wood-Vasey et al. (2007) are
primarilycaseswhere the Wood-Vaseyetal.(2007)SALTﬁt did
not converge (some of which are noted in Wood-Vasey et al.
2007)anda fewcaseswherewefounditnecessary to remove an
extreme outlier photometry point from the light curve.
Thelight curvesfrom Barrisetal.(2004)and the I-band light
curvesof4 supernovae ofP99 (SNe1997O,1997Q,1997R,and
1997am; see also Knop et al. 2003) need a different analysis
procedure, since in these cases the light of the host galaxy was
notfully subtracted duringtheimagereduction.Wehence allow
for a constant contribution of light from the host galaxy in the
light curve ﬁts. The supernovae were ﬁtted with additional pa-
fourSNe fromthe P99setand thezerolevelofallthebandsinthe
case of the Tonry et al. (2003)data. The additional uncertainties
due to these unknown zero levels have been propagated into the
resulting light curve ﬁt parameters.
The ﬁtted light curve parameters of all SNe can be found in
4. HUBBLE DIAGRAM CONSTRUCTION
AND COSMOLOGICAL PARAMETER FITTING
The full set of light curves as described in x 3.2 have been
ﬁtted,yielding B-bandmaximummagnitude mmax
color c ¼ BVj
þ0:057. In this section, these are input
to the determination of the distance modulus. The analysis
method is chosen to minimize bias in the estimated parameters
(seex 4.2).An outlierrejectionbasedontruncationisperformed
that is further described in x 4.3,before constraintson the cosmo-
logical parameters are computed.
4.1. Blind Analysis
egy. The basic aim of pursuing a blind analysis is to remove
potential bias introduced by the analyst. In particular, there is a
documented tendency (see, e.g.,Yaoet al. 2006) foran analysis
to bechecked forerrors in the procedure (even astrivialasbugs
in the code)up until the expected resultsare foundbutnot much
beyond.The idea of a blind analysisis to hide the experimental
outcome until the analysis strategy is ﬁnalized and debugged.
However,one doesnotwant to blind oneselfentirelytothedata,
as the analysisstrategy will be partially determinedby the prop-
ﬁt assuming a CDM cosmology, with the resulting ﬁt for
stored without being reported. The ﬂux of each supernova data
point is then rescaled according to the ratio of luminosity dis-
tancesobtainedfromthe ﬁtted parametersand arbitrarily chosen
dummy parameters(in this case
procedure preserves the stretch and color distribution and, as
Number of Supernovae after Consecutive
Application of Cuts
First phase <6 days...........................
5 data points...................................
KOWALSKI ET AL.
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