Analytic Photometric Redshift Estimator for Type Ia Supernovae From the Large Synoptic Survey Telescope

4.1 MB·English

by  Yun Wang

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed13May2015 (MNLATEXstylefilev2.2)
Analytic Photometric Redshift Estimator for Type Ia Supernovae
From the Large Synoptic Survey Telescope
Yun Wang1,2⋆, E. Gjergo3, and S. Kuhlmann3
1InfraredProcessingandAnalysisCenter,CaliforniaInstituteofTechnology,770SouthWilsonAvenue,Pasadena,CA91125
2HomerL.DodgeDepartmentofPhysics&Astronomy,Univ.ofOklahoma,440WBrooksSt.,Norman,OK73019,U.S.A.
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3ArgonneNationalLaboratory,9700SouthCassAvenue,Lemont,IL60439,USA
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2
13May2015
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ABSTRACT
Accurate and precise photometric redshifts (photo-z’s) of Type Ia supernovae(SNe Ia) can
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enable the use of SNe Ia, measured only with photometry, to probe cosmology. This dra-
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matically increases the science return of supernova surveys planned for the Large Synop-

tic Survey Telescope (LSST). In this paper we describe a significantly improved version
]
O of the simple analytic photo-z estimator proposed by Wang (2007) and further developed
C by Wang, Narayan, and Wood-Vasey (2007). We apply it to 55,422 simulated SNe Ia gen-
erated using the SNANA package with the LSST filters. We find that the estimated er-
.
ph zro’srsthoantthhaevpehhoitgoh-z’psr,eσczispihoont/,(a1cc+urzapchyo,t)a,ncdanpubreityu.seUdsiansgfiSltNersIatocporloordsucaesawseellt oasf pShNotoIa-
- peak magnitude in the i band, we obtain a set of photo-z’s with 2 percent accuracy (with
o
r σ(zphot−zspec)/(1+zspec)=0.02),abiasinzphot(themeanofzphot−zspec)of−9×10−5,
t andanoutlierfraction(with|(z −z )/(1+z )|>0.1)of0.23percent,withthere-
s phot spec spec
a quirementthat σzphot/(1+zphot) < 0.01. Using the SN Ia colors only, we obtain a set of
[ photo-z’swithsimilarqualitybyrequiringthatσzphot/(1+zphot)<0.007;thisleadstoaset
2 ofphoto-z’swith2percentaccuracy,abiasinzphot of5.9×10−4,andanoutlierfractionof
v 0.32percent.
9
3 Keywords: cosmology:observations,distancescale
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6
0
.
1 1 INTRODUCTION thatcanbeusedtomeasurecosmicexpansionhistoryinthecom-
0 ingyearsanddecades.ThousandsofSNeIaareexpectedfromthe
5 TheuseofTypeIasupernovae(SNeIa)ascosmologicalstandard Dark EnergySurvey (DES) (Bernsteinetal. 2012), and hundreds
1 candles is a corner stone of modern cosmology, and led to the
ofthousands ofSNeIaareexpectedfromLargeSynopticSurvey
: observational discovery of cosmicacceleration (Riessetal.1998;
v Telescope(LSST)(Abelletal.2009).2
Perlmutteretal. 1999). The true nature of cosmic acceleration,
i The majority of the SNe Ia from LSST will only have pho-
X dubbed“darkenergy”forconvenience, remainsshroudedinmys-
tometry, and willnot have spectroscopic redshifts, due tothe ex-
r tery. We do not even know if it is an unknown form of energy pensiveresourcesrequired toobtainfollow-upspectroscopy. For-
a (hence appropriately named “dark energy”), or a consequence of
tunately,theredshiftsoftheSNeIacanbeestimatedusingmulti-
themodificationofEinstein’stheoryofgeneralrelativity(“modi-
bandphotometry(theseapproximateredshiftsarecalledphotomet-
fiedgravity”).1 Probingthetruenatureofcosmicaccelerationre-
ricredshifts,orphoto-z’s).However,theobservedphotometricSNe
quiresthemeasurement ofbothcosmicexpansionhistoryandthe
needtobeclassifiedfirstusingphotometry(see“SupernovaPho-
growthhistoryoflargescalestructure(Knox,Song,&Tyson2006;
tometric Classification Challenge” by Kessleretal. (2010b) for a
Guzzoetal.2008;Wang2008).TheuseofSNeIaremainsoneof
detaileddiscussion).Evenapplyinganoptimizedversionofthetop
themostimportantmethodsformeasuringcosmicexpansionhis-
performingmethodfromtheSupernovaPhotometricClassification
tory.
Challenge, the photometric-classification algorithm of Sakoetal.
We can expect adramatic increase inthe number of SNeIa
(2011)resultinover25%oftheresultantphotometricSNIasam-
pleremaining non-Ia SNe(Campbelletal.2013).3 Wewill defer
⋆ E-mail:[email protected]
1 For recent reviews, see Ratra&Vogeley (2008); 2 http://www.lsst.org/lsst/science
Frieman,Turner,&Huterer (2008); Caldwell&Kamionkowski (2009); 3 Thephotometric-classificationmethodofCampbelletal.(2013)isbased
Uzan(2010);Wang(2010);Lietal.(2011);Weinbergetal.(2013). ontheSNclassificationtechniqueofSakoetal.(2011),butmadeadditional
(cid:13)c 0000RAS
2 Wang,Gjergo, &Kuhlmann
thedifficulttaskofphotometricclassificationofuturework,andfo- wherethedatavectorp={1,g ,r ,i ,z ,i2,i3,∆i }.Theco-
f f f f f f 15
cus on the relatively easier task of estimating redshifts of known efficientsc (i=1,2,...,8)arefoundbyusingatrainingsetofSNeIa
i
SNeIausingphotometryonly. with griz (or riz, for which c = 0) lightcurves and measured
2
SNeIawithsufficientlyaccurateandprecisephoto-z’scanbe spectroscopicredshifts.Thejackknifetechnique(Lupton1993)is
usedforprobingcosmology.Thiswoulddramaticallyincreasethe usedtoestimatethemeanandthecovariancematrixofc .
i
science return of supernova surveys planned for LSST. Accurate
photo-z’s can also enhance the ability of observers to accurately
target high redshift SNe Ia for spectroscopy, allowing flexibility 2.2 Photo-zEstimatorAppliedtoLSSTFilters
andoptimizationinsurveydesignforStageIIIandStageIVdark
For application to SNe Ia from LSST with photometry only, we
energyprojects(Albrechtetal.2006).
havesimplifiedandmodifiedtheanalyticphoto-zestimatorforeas-
Inthispaper,webuildonthepreviousworkbyWang(2007)
ierapplicationandbetterperformanceasfollows:
and Wang,Narayan,&Wood-Vasey (2007), and present a sim-
(1)Insteadofusingthefluxesinallfiltersexceptiattheepochof
ple analytic photo-z estimator. We apply this photo-z estimator
imaximumfluxtomakeaneffectiveK-correctiontotheiflux,we
to55,422simulatedSNeIageneratedusingtheSNANApackage
justusethepeakmagnitudesinallfiltersforeachSNtoconstruct
(Kessleretal.2009b)withtheLSSTfilters.Wepresentourmethod
anindicatorofthespectralshapeoftheSN.
inSec.2,describethesimulationofLSSTSNeIainSec.3,showour
(2)Weadd2ndordertermsinthecolorsforimprovedaccuracyand
resultsinSec.4,anddiscussourfindingsinSec.5.
precisionoftheestimator.
(3) We replace ∆i with ∆i = 2.5log(f12d/f ), to increase
15 12 i i
thesamplesize,wherewheref12d istheibandfluxat12daysaf-
2 THEMETHOD i
tertheifluxmaximumintheestimatedrest-frame,corresponding
The analytic photo-z estimator for SNe Ia proposed by Wang totheepochof∆t12d = 12(1+z0 )daysaftertheepochofi
phot
(2007) is empirical, model independent (no templates used), and fluxmaximum.
usesobservablesthatreflectthepropertiesofSNeIaascalibrated Notethatouruseof∆i wasfirstintroducedbyWang(2007)
15
standardcandles.ItwasdevelopedusingtheSNIadatareleasedby toreducethescatterintheestimatedSNIaphotometricredshifts;
theSupernovaLegacySurvey(Astieretal.2006). itisanalogoustotheuseof∆m15inSNIacalibration,buttheuse
This method requires a training set of SNe Ia with spectro- ofibandmagnitudeallowsustoincludealargersetofSNeIain
scopicredshifts.TheSNeIainthetrainingsetarethesameasthe ouranalysis(Wang2007).
data,butwithknownredshifts.Thetrainingsetisrandomlychosen Thekeytoobtainingasetofreliablephoto-z’sforSNeisto
fromthedatatospantherangesofthecolorsandmagnitudesofthe exclude theSNethat areinferredtohave unreliablephoto-z esti-
entiredataset.Thismimicswhatshouldbedoneinpracticewhen matesbasedonthephotometrydataalone.Wemakeafirstcutin
realdatabecomeavailable:chooseatrainingsetfromthedatato SNetobeusedasfollows:
carryoutspectroscopicredshiftmeasurements. (1)ExcludethefewSNethat havenoi-band photometry. Thisis
necessarysinceweusetheimagnitudeatmaximumlightinesti-
matingthephoto-z’s.
2.1 ThePrototypePhoto-zEstimator
(2) Exclude SNe that have measured flux uncertainties at
The prototype photo-z estimator we use here was developed in maximum light in any passband that exceeds 0.2 magni-
Wang (2007) and Wang, Narayan, and Wood-Vasey (2007). This tude. This is useful in reducing the number of outliers with
estimatorusesthefluxesingriz (or riz)attheepoch ofimaxi- |(zphot−zspec)/(1+zspec)|>0.1.
mumfluxtomakeaneffectiveK-correctiontotheiflux.Thefirst (3) Exclude SNethat do not have i-band lightcurve data that ex-
estimateofredshiftisgivenby tends to 12 days after maximum light in the estimated SN rest-
frame.Thisenablestherefinementofthephoto-zestimatedusing
z0 =c +c g +c r +c i +c z +c i2 +c i3 (1)
phot 1 2 f 3 f 4 f 5 f 6 f 7 f thefluxesatmaximumlightalone.
whereg = 2.5log(f ),r =2.5log(f ),i = 2.5log(f ),and Wethenapplythephoto-zestimatorasfollows:
f g f r f i
z = 2.5log(f ),andf ,f ,f ,f arefluxesincounts,normal- (1) Divide the SNe according to the passbands in which the SN
f z g r i z
izedtosomefiducialzeropoint,ingrizattheepochofimaximum magnitudesatmaximumlightareavailable.
flux. (2) For each set of SNe with photometry in the same passbands,
Next, thephoto-z estimator calibrateseach SNIainitsesti- constructtheinitialphoto-zestimategivenby
matedrest-frameusing
n−1
∆i15 =2.5log(fi15d/fi), (2) zp0hot = c1+ cj+1(mp,j−mp,j+1)
wheref15d istheibandfluxat15daysaftertheifluxmaximum Xj=1
intheesitimatedrest-frame,correspondingtotheepochof∆t15d = n−1
+ c (m −m )2
15(1+z0 )daysaftertheepochofifluxmaximum. n+j p,j p,j+1
phot
Thefinalestimateforthephotometricredshiftisgivenby Xj=1
+c i +c i 2+c i 3 (4)
8 2n p 2n+1 p 2n+2 p
zphot = cipi, (3) wheremp,jisthemagnitudeatmaximumlightinthej-thpassband,
Xi=1 ipisthemagnitudeatmaximumlightintheiband,nisthenumber
of filters or passbands with available photometry, and {c }, j =
j
cutsaidedbyhost-galaxyredshiftswith0.05 < z < 0.55.Thisenabled 1,2,...,2n+2,arethecoefficientstobeestimatedfromusingthe
themtoachievetheSNIaclassificationefficiencyof70.8%,withonly3.9% trainingsetofSNewithspectroscopicredshifts.
contaminationfromcore-collapseSNe. (3)Next,calibrateeachSNIainitsestimatedrest-frameusing
(cid:13)c 0000RAS,MNRAS000,000–000
PhotometricRedshiftEstimatorfor SNeIa fromLSST 3
∆i =i −i (5) 3 SIMULATIONOFDATA
12 12d p
where i is the i band magnitude at 12 days after the i maxi- ThenumberandlocationoftheLSSTdeepdrillingfieldsarestill
12d
mumlightintheestimatedrest-frame,correspondingtotheepoch tobedetermined; for ageneral discussion, seetheLSSTScience
of ∆t12d = 12(1+z0 ) days after the epoch of i maximuml Book.4 Assuming a plausible scenario of 10 fields covering 90
phot
light. square degrees, we obtained a set of 55,422 simulated SNe with
photometricdataincludingmagnitudeuncertainties,generatedus-
Thefinalestimateforthephotometricredshiftisgivenby
ingtheSNANApackage(Kessleretal.2009b)withtheLSSTfil-
2n+3 ters.Wehaveassumed10yearsofobservationsontheLSSTdeep-
zphot = cjpj, (6) drillingfields.WehaveusedmeasuredratesofSNIa(Dildayetal.
Xj=1 2008)asinputtothesimulations,andimposedtherequirementthat
threeLSSTfiltershaveaSNRgreaterthan5(whichgivestwocolor
where the data vector p = {1,(mp,1 − mp,2),(mp,2 − measurementsessentialforphoto-zestimates).
mp,3),...,(mp,n−1 − mp,n),(mp,1 − mp,2)2,(mp,2 − Wehaveapplied0.005magofsmearingtothebandpass ze-
mp,3)2,...,(mp,n−1 − mp,n)2,ip,i2p,i3f,∆i12}. The coeffi- ropoints; this simulates the variations due to the atmosphere. We
cientscj (j = 1,2,...,2n+3) arefound byusing atrainingset donotincludeLSSTPhotonSimulatoreffectsorsystematicband-
ofSNeIawithlightcurvesinnpassbands andmeasuredspectro- passzeropoint shiftsatpresent.5 Theseeffectsareexpectedtobe
scopicredshifts.Weusethesamemodifiedjackknifetechniqueas
smallerthanthevariationsduetotheatmosphere.
inWang, Narayan, and Wood-Vasey (2007) toestimatethe mean
Toexcludeincompleteorverynoisydata,wemakeafewba-
andthecovariancematrixofcj (seeSec.4). siccutsfordataquality.Only55,414ofthe55,422simulatedSNe
The improvements that we have made to the photo-z havepeakimags,andonly49,993haveibandlightcurves.Requir-
estimator in this work reduces the estimated errors on the ingthattheilightcurvedataincludeinfooftheipeakandextend
photo-z’s, σzphot/(1 + zphot), from 2.5% to 2%, compared to to12daysintheestimatedSNrestframe,andthatallthepeakmag-
Wang,Narayan,&Wood-Vasey (2007). More importantly, it re- nitudeshaveerrorslessthan0.2magnitudes,wearriveatasample
ducesthebiasinzphot (themeanofzphot−zspec),from−1.5× of29,702simulatedSNe.Thedataqualitycutsthatwehavemade
10−3to−9×10−5(areductionfactorof16.67). herearelessstrictthatthosemadebycurrentsurveys;nevertheless
wefindthemtobesufficientbecauseofthehigherqualityphotom-
etry expected from the LSST. We will use this sample of 29,702
SNe Ia that have passed our data quality cut in the remainder of
thispaper.
2.3 Photo-zEstimatorUsingColorsOnly
We now describe our Type Ia SN light curve simulations
SinceourultimategoalistouseSNeIawithphotometrytoprobe in greater technical detail. We employ the SNANA package
cosmology,itisdesirabletohaveaphoto-zestimatorthatdoesnot (Kessleretal.2009b)tosimulatethelightcurvesusingtheSALT2
usetheibandfluxinformation,toreducethelikelihoodofpossible Type Ia SN model. 6 The SNANA package was first used by
doublecountingofdistanceinformation.NotethatSNIacolorsare the LSST collaboration to forecast SN observations (Abelletal.
alsousedinfittingforcosmology,onemayarguethatincludingthe 2009), and has been used extensively by the SDSS collabora-
ibandfluxinformationisnomoredouble-countingthanincluding tion(Kessleretal.2009a),toforecastobservationsfortheDarkEn-
SNIacolors. However, theiband fluxof aSNIaisclosely cor- ergySurvey(Bernsteinetal.2012),andformanyothersystematic
relatedwithitsdistancefromus,sinceweareusingthebrightness studiesforsupernovacosmology.ThespecificSALT2modelused
ofSNeIaasdistanceindicators.SNcolorisalsousedinthedis- is the extended version of the Guy 2010 model (Guyetal. 2007,
tanceestimation,butonlyforthecorrectiontothedistance,soitis 2010).TheSALT2modelrest-framefluxF(p,λ)asafunctionof
amuchsmallereffectcomparedtotheSNbrightness.Finally,the phasepandwavelengthλ,isgiveninequation8.Thetwospectral
estimationofphotometricredshiftsaremadepossiblebytheuseof timeseries,M0andM1,andthecolorlawCLarepartofthespe-
colors,thustheyareessentialingredientsinanyphotometricred- cificSALT2inputmodel.Theparametersx0,x1,c,arerandomly
shiftestimator.Therefore,havinganestimatorforSNIaphotomet- drawnfromdistributionsthathavebeenfitpreviouslytoTypeIaSN
ricredshiftsthatusescolorsonly(theminimalingredients)enables dataincludingtheeffectsofdust extinction.Giventheseparame-
a more robust approach to probing cosmology using photometric terstherest-framefluxasafunctionofphaseisavailableforuse.
SNeIa. The redshift is likewise randomly drawn from a previously mea-
Wearriveataphoto-zestimatorusingcolorsonlysimplyby sured distribution, and the observer-frame flux is integrated with
omittingthelast4termsinEq.(6).Thusthesimplifiedphoto-zes- theLSSTfiltertransmissions.
timatorthatusescolorsonlyisgivenby F(p,λ)=x [M (p,λ)+x M (p,λ)]e−cCL(λ). (8)
0 0 1 1
n−1
OursampleofsimulatedLSSTSNeIaisrepresentativeofdata
zc = c + c (m −m )
phot 1 j+1 p,j p,j+1 expectedfromtheLSST,basedonourcurrentknowledgeofSNe
Xj=1
n−1
+ cn+j(mp,j−mp,j+1)2 (7) 4 http://www.lsst.org/lsst/scibook
Xj=1 5 TheLSSTPhotonSimulator(seehttp://lsstdesc.org/WorkingGroups/PhoSim)
includes a very detailed simulation of the LSST hardware, and takes a
wherem isthemagnitudeatmaximumlightinthej-thpassband,
p,j starorgalaxylocationandbrightnessandpropagatesthelightthroughthe
nisthenumberoffiltersorpassbandswithavailablephotometry, opticsandcamera.
and{cj},j =1,2,...,2n−1,arethecoefficientstobeestimated 6 TheSALT2modelweareusingisthemostrecentlyupdatedmodelavail-
fromusingthetrainingsetofSNewithspectroscopicredshifts. able,withthelatestdata.
(cid:13)c 0000RAS,MNRAS000,000–000
4 Wang,Gjergo, &Kuhlmann
Ia. The SNANA simulations of SNe Ia have been heavily tested fitting,andareusedasavalidationsetfortheanalyticphoto-zesti-
onSDSSphotometricdatauptoz < 0.7(see,e.g.,Hlozeketal. mator.
(2012);Campbelletal.(2013)),andonSNLSdatauptoz <1.0. Table1showsthatweneed 1000SNIaspectraforthetrain-
Thisissimilartotheredshiftrangeweareusing. ingsetsforthe29,702 simulatedSNeIathat satisfyour minimal
dataqualitycuts(seeSec.3).WhentherealLSSTphotometricSN
Iadataareavailable,wecanchoosethetrainingsetineachcolor
groupdescribedinTable1inarandomfashion,whileensuringthat
4 RESULTS
theSNeIachosenforthetrainingsetspanstherequiredcolorand
4.1 Photo-z’susingSNIacolorsandibandpeakflux magnituderange.Thenspectroscopicredshiftscanbeobtainedfor
theSNeIainthetrainingsets.
We use a slightly modified version of the jackknife technique Even1000SNIaspectrawillrequiresubstantialobservational
(Lupton1993)toestimatethemeanandthecovariancematrixof resources. The sizes of the training sets can be reduced to meet
cj.FromthetrainingsetcontainingN SNeIa,weextractN sub- theconstraintsof theavailableresources, whichmaydegrade the
sampleseachcontainingN−1SNeIabyomittingoneSNIa.The accuracyandprecisionofthephotometricredshifts.However,the
coefficientsc(s) (j = 1,2,...,2n+3)forthes-thsubsampleare performance of the photometric redshifts can be recovered when
j
foundbyamaximumlikelihoodanalysismatchingthepredictions thetrainingsetsareexpandedlaterviaSNIahostgalaxyredshift
ofEq.(6)withthespectroscopicredshifts. measurements. Two strategies can be used to reduce the number
Themeanofthecoefficientscj(j =1,2,...,2n+3)aregiven ofSNIaspectraneededforthetrainingsets:(1)RemovetheSNe
by Iabelongingtothecolorgroupscontainingverysmallfractionsof
theoverallsample(G16,G22,G61,andperhapsG21inTable1).
N
hc i= 1 c(s). (9) Notethattheseminoritycolorgroupsrequireamuchlargerfraction
j N j ofspectroscopicredshifts,andhavelesswellestimatedphoto-z’s.
s=1
X Dropping these will save resources (100 less spectroscopic red-
Notethatthisisrelatedtotheusual“bias-correctedjackknifeesti-
shifts) with minimal impact on the cosmological constraints. (2)
mate”forc ,cJ,asfollows:
i i Reduce the sizes of the training sets of the other color groups as
cJ ≡cN +(N −1) cN −hc i , (10) needed.
j j j j
Inapplying thephoto-z estimator tosimulateddata,wefind
where cN are estim(cid:0)ated from (cid:1)the entire training set (with N thatforeachgroupofSNewithagivensetofavailablephotomet-
j
SNe Ia). Wang,Narayan,&Wood-Vasey (2007) found that for ricpassbands,applyingasinglefittingformulaetoitstrainingset
smalltrainingsets(withN <20)thatincludeSNeIaatz∼0,cJ mayleadtosubstructureintheestimatedz .Therefore,wehave
j phot
givebiasedestimatesofc bygivingtoomuchweighttotheSNIa dividedeachgroupintosubgroupsasshowninTable1,andderived
j
with the smallest redshift. For training sets not including nearby thephoto-zestimatorforeachsubgroupusingitsowntrainingset.
SNeIa, hc iand cJ areapproximately equal. Wehavechosen to Table1tabulatestheresultant precision andaccuracy of our
j j
usehc ifromEq.(9)asthemeanestimatesforc toavoidbiased photo-zestimatorforeachcolorgroup.Wemeasureprecisionwith
j j
z forSNeIaatzclosetozero(Wang,Narayan,&Wood-Vasey σ(z − z )/(1 + z , and the accuracy by the mean of
phot phot spec spec
2007). z − z , as well as the fraction of outliers (also listed are
phot spec
Thecovariancematrixofc (j = 1,2,...,2n+3)aregiven thenumberofoutliersthatareflaggedashavinglargeuncertainties
j
by inz ).
phot
Fig.1shows(z −z )/(1+z )versusz forthean-
N phot spec spec spec
Cov(c ,c )= N−1 c(s)−hc i c(s)−hc i (11) alyticphoto-zestimatorappliedtosimulatedSNefromtheLSST,
i j N i i j j with cut σ /(1+ z ) < 0.1. The cut is made for better
Xs=1(cid:16) (cid:17) (cid:16) (cid:17) presentatioznp;hoontly12SNpehootutof1040ofthetrainingset,and109
Usingzphot = cjpj,wefindthat∆zphot = pj∆cj,since outof28662ofthetestsethaveσzphot/(1+zphot) > 0.1. Dif-
the uncertainty in zphot is dominated by the uncertainty in cj. ferent colors indicate SNe with different photometric passbands,
ThereforeestimaPtederrorinzphotis P as described in Table 1. For SNe represented by the same color,
differentpointtypesrepresentsubdivisionsbasedonbrightnessto
2n+32n+3 1/2
improve precision. The histogram of the number of SNe versus
dz = [p ]Cov(c ,c )[p ] , (12)
phot i i j j (z −z )/(1+z ) corresponding to Fig.1 is shown in
( ) phot spec spec
Xi=1 Xj=1 Fig.2.
where p and p (i,j = 1,2,...2n + 3) are the i-th and j- Fig.3andFig.4arethesameasFig.1andFig.2,butforimpos-
i j
th components of the data vector where the data vector p = ingthecutσzphot/(1+zphot)<0.01.Thereare45outliers(with
{1,(mp,1−mp,2),(mp,2−mp,3),...,(mp,n−1−mp,n),(mp,1− |(zphot−zspec)/(1+zspec)|> 0.1)inthebottompanelinFig.3
mp,2)2,(mp,2−mp,3)2,...,(mp,n−1−mp,n)2,ip,i2p,i3f,∆i12}. (the majority are from the rizY color groups G11 through G15),
ThesimulatedSNearedividedintogroupsaccordingtotheir representing0.23%ofall19,640SNeIafromthetestsamplethat
photometricproperties,seeTable1.Eachtrainingsetforagroup passedthiscut.
of SNeconsists of thefirst100 SNeinthat group, assuming that Table 2 shows that we can arrive at photo-z’s with higher
thesimulateddata arerandomly ordered. Forgroups thatcontain accuracy, precision, and purity by using the estimated errors on
verysmallnumbersofSNe,weusethefirst20SNeineachgroup z to exclude SNe with large σ /(1 + z ). If we ex-
phot zphot phot
asthetrainingset,orincreasethenumberofSNeusedinthetrain- clude SNe with σ /(1+z ) > 0.01, we arrive at a pre-
zphot phot
ingsetuntilnonegativez results.Thisledustoatrainingset cisionofσ(z −z )/(1+z )=0.02,abiasinz (the
phot phot spec spec phot
containingatotalof1040SNeusedforfittingtheanalyticphoto-z meanofz −z )of−9×10−5,andanoutlierfraction(with
phot spec
estimator, anda“test set”of 28,662 SNethat arenot used inthe |(z −z )/(1+z )| > 0.1) of0.23percent (seeFig.3).
phot spec spec
(cid:13)c 0000RAS,MNRAS000,000–000
PhotometricRedshiftEstimatorfor SNeIa fromLSST 5
Figure2.Thedistributionof(zphot−zspec)/(1+zspec)fromFig.1.
Figure1.Theperformanceoftheanalyticphoto-zestimatorappliedtosim-
ulatedSNefromtheLSST,asindicatedby(zphot−zspec)/(1+zspec)
versuszspec,withcutσzphot/(1+zphot) < 0.1forcleaner presenta- therearenooutliersinthetrainingset.Thereare58outliers(with
tion(thenumbersofoutliersaregiveninTable1)..Differentcolorsindicate |(z −z )/(1+z )| > 0.1) in the second panel from
phot spec spec
SNewithdifferentphotometricpassbands,asdescribedinTable1.ForSNe thetopinFig.7(themajorityarefromtherizYcolorgroupsG11
representedbythesamecolor,differentpointtypesrepresentsubdivisions throughG15—similartoFig.3),representing0.32%ofall18,370
basedonbrightnesstoimproveprecision.
SNeIafromthetestsamplethatpassedthiscut.Wedonotexpect
suchasmallfractionofoutlierstohavenoticeable impact onthe
cosmologicalfit;wewillinvestigatethisinfuturework.
Note that for the threshold of σ /(1+z ) < 0.01, there
zphot phot
arenooutliersinthetrainingset.Wecanrequirethatthereareno
outliers in the training set in order to arrive at this threshold for
σ /(1+z ).
zphot phot
5 SUMMARYANDDISCUSSION
Wehave shown that a simple analytic photo-z estimator for SNe
4.2 Photo-z’susingSNIacolorsonly
IacanbebuiltfortheLSST,givensuitablychosentrainingsetsof
AswediscussedinSec.2.3,havinganalternativephotometricred- SNe Ia with spectroscopic redshifts that are representative of the
shift estimator that uses SN Ia colors only is helps increase the general properties of SNe Ia from the LSST. While our method
robustness of cosmological constraints obtained using photomet- is based on that proposed by Wang (2007), and advanced by
ricSNeIa.Table1tabulatestheresultantprecisionandaccuracyof Wang,Narayan,&Wood-Vasey (2007), it represents a significant
ourphoto-zestimatorusingSNIacolorsonly,foreachcolorgroup. improvement over previous work (which require the use of both
Thecolorsonlyresultsaretabulatedimmediatelybelowtheresults colorsandimagnitudesofSNeIa)inenablingtheuseofSNIacol-
forcolorsplusibandpeakflux(seetheprevioussubsection),and orsonly.Thiseliminatesthepossiblecomplicationsthatcanarise
indicated by “Y” under the column for “colors only”. Using SN fromusingSNIabrightnessinestimatingphoto-z’s,sincethepeak
colorsonlyleadstoslightlyworseprecision,butsimilaraccuracy brightnessofaSNIaiscloselycorrelatedwithitsdistancefromus.
fortheresultantphoto-z’s. OursampleofsimulatedLSSTSNeIaisrepresentativeofdata
Fig.5andFig.7areresultscorresponding toFig.1andFig.3, expectedfromtheLSST,basedonourcurrentknowledgeofSNe
but for z obtained using Eq.(7), which uses SN Ia colors Ia.Themultiple-bandphotometryfromtheLSSTenablesustodi-
phot
only. Using the SN Ia colors only, we obtain a set of photo- vide the SNeIainto different sets (see Sec.2.2and Table 1). For
z’s with similar quality to using SN Ia color and i band peak each set, a photo-z estimator is constructed using only quadratic
flux by requiring that σ /(1 + z ) < 0.007; this leads functionsofcolors(seeEq.[7]),withtheconstantcoefficientsgiven
zphot phot
to a set of photo-z’s with 2 percent accuracy, a bias in z of byfittingtoatrainingsetthatcontainsamaximumof100SNeIa
phot
5.9×10−4,andanoutlierfractionof0.32%.Thethresholdlevel with spectroscopic redshifts (see Table 1). Note that the division
of σ /(1+z ) < 0.007 isset naturallyby requiringthat ofSNeIaintocolorgroupsisempirical,dependentontheproper-
zphot phot
(cid:13)c 0000RAS,MNRAS000,000–000
6 Wang,Gjergo, &Kuhlmann
Figure4.Thedistributionof(zphot−zspec)/(1+zspec)fromFig.3.
Figure3.ThesameasFig.1,butwithcutσzphot/(1+zphot)<0.01for
improvedaccuracy,precision,andoutlierreduction.
tiesofthetrainingset,assumedtoberepresentativeoftheoverall
sample.
InadditiontohowthephotometricSNeIashouldbegrouped,
andtheperformanceofourphoto-zestimatorforeachcolorgroup,
Table1containsotherhelpfulinformationaswell.Asexpected,the
performanceofthephoto-zestimatorimproveswiththeincreasing
numberoffiltersinwhichphotometricdataareavailable;notethat
knowingthefiltersinwhichtheSNeIaarevisibleprovidesacrude
estimateoftheredshiftrangeoftheSNeIa.Notsurprisingly, the
performanceofthephoto-zestimatorgenerallydegradeswiththe
increasingredshiftoftheSNeIa.
WhileTable1listsalltheSNeIathatpassedourdataquality
cut(seeSec.3),Table2showsushowtoderiveahighpuritysample
ofphoto-z’sbymakingcutsontheSNeIabasedontheestimated
errorsofthephoto-z’s.Thisisveryusefulsincewearesystematics
limited,ratherthanstatisticslimited,inusingphotometricSNeIa
forcosmology.
The performance of our simple analytic SN Ia photo-z es-
timator is quite impressive when applied to simulated LSST SN
Ia photometric data (see Table 2). We find that the estimated er-
rors on the photo-z’s, σ /(1+z ), can be used as filters
zphot phot
to produce a set of photo-z’s that have high precision, accuracy,
and purity. Using SN Ia colors as well as SN Ia peak magnitude
intheiband,weobtainasetofphoto-z’swith2percentaccuracy Figure5.Thesameas Fig.1,butforzphot obtained usingSNIacolors
(withσ(z −z )/(1+z ) = 0.02),abiasinz (the only.
phot spec spec phot
meanofz −z )of−9×10−5,andanoutlierfraction(with
phot spec
|(z −z )/(1+z )|> 0.1)of0.23percent,withthere-
phot spec spec
(cid:13)c 0000RAS,MNRAS000,000–000
PhotometricRedshiftEstimatorfor SNeIa fromLSST 7
Figure6.Thedistributionof(zphot−zspec)/(1+zspec)fromFig.5.
quirementthatσ /(1+z )<0.01.UsingtheSNIacolors
zphot phot
only,weobtainasetofphoto-z’swithsimilarqualitybyrequiring Figure7.ThesameasFig.5,butwithcutσzphot/(1+zphot) < 0.007
thatσzphot/(1+zphot) < 0.007; thisleadstoasetofphoto-z’s forimprovedaccuracy,precision,andoutlierreduction.
with2percentaccuracy,abiasinz of5.9×10−4,andanoutlier
phot
fractionof0.32percent.
can be obtained using LSST SNe Ia with photometry only, with
Infuturework,wewillinvestigatewhethertheprecisionand
photo-z’sestimatedusingthemethodpresentedinthispaper.
accuracyachievedbyourphoto-zestimatorisadequateforcosmol-
ogy,WewillfirstneedtosimulattemorerealisticsamplesofLSST
SNe,whichincludenon-Ia’s.Wewillneedtoexpandandadvance
ourphoto-zestimatorforweedingoutnon-IaSNe.Thereismuch ACKNOWLEDGMENTS
worktodobeforeourphoto-zestimatorcanbeappliedtothereal
Wearegrateful toMichelWood-VaseyandAlexKimforhelpful
LSSTdata.
discussions,andKirkGilmoreforaninternalreviewofourpaper
Inprinciple,ourmethodforestimatingphoto-z’sshouldbeap- on behalf of the LSST Dark Energy Science Collaboration. YW
plicabletoothersurveys,butitsperformancedependsonthepreci-
wassupportedinpartbyNASAgrant12-EUCLID12-0004.
sionofthephotometryofthesurveys.However,itcanstillbeused
asaquickwayofestimatingphoto-z’sthatismodel-independent,
and complementary to the template-based methods. The applica-
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(cid:13)c 0000RAS,MNRAS000,000–000
PhotometricRedshiftEstimatorfor SNeIa fromLSST 9
set bands subdivision symbolinFig.1 Ns Ntest colors σ 1∆+zz hzphot−zi outliers flagged
&Fig.5 only training,test training,test training,test intest
(cid:2) (cid:3)
G11 rizY i>24.8 redfilledcircles 100 2904 N .0255, .0299 −2.6E-7, −.0074 0,22 15
Y .0264, .0261 −1.6E-7, −.0032 0,8 0
G12 rizY i=[24.5,24.8) redemptycircles 100 3060 N .0308, .0280 −8.1E-8, −.0039 1,11 0
Y .0313, .0280 −6.0E-7, −.0051 1,14 0
G13 rizY i=[24,24.5),r>25.2 redfilledtriangles 100 4184 N .0274, .0290 2.5E-7, −.0017 0,25 0
Y .0280, .0289 −1.0E-7, −8.7E-4 1,26 0
G14 rizY i=[24,24.5),r<25.2 redemptytriangles 100 1505 N .0301, .0369 1.1E-7, 3.5E-5 1,23 4
Y .0306, .0362 −6.5E-8, 6.1E-4 1,22 2
G15 rizY i=[23,24) redfilledsquares 100 4900 N .0279, .0346 1.1E-7, −8.5E-4 0,75 0
Y .0292, .0352 −3.2E-7, .0021 0,92 0
G16 rizY i<23 redemptysquares 40 53 N .0408, .0526 −7.1E-8, −.033 1,4 2
Y .0494, .0612 −2.6E-8, −.039 2,5 3
G21 izY i>24.5 bluefilledcircles 20 174 N .0202, .0472 −1.0E-7, −.0097 0,6 0
Y .0251, .0393 1.4E-8, .0032 0,3 0
G22 izY i<24.5 blueemptycircles 20 18 N .055, .108 −1.3E-8, −.068 1,7 2
Y .0627, .0798 4.3E-8, −.0508 2,5 0
G31 grizY i>23.5 greenfilledcircles 100 2508 N .0163, .0196 −1.5E-7, .0023 0,3 2
Y .0165, .0192 −3.0E-8, .0035 0,1 0
G32 grizY i=[23.1,23.5) greenemptycircles 100 3242 N .0122, .0155 2.1E-7, −.0027 0,2 0
Y .0125, .0157 1.6E-7, −.0016 0,3 0
G33 grizY i<23.1 greenemptytriangles 100 3888 N .0137, .0179 2.0E-7, −.0069 0,4 0
Y .0151, .0183 −3.8E-8, −.0025 0,6 0
G4 griz cyanfilledcircles 50 480 N .0055, .0229 2.7E-8, .0018 0,8 6
Y .0059, .0421 −5.7E-8, .0088 0,11 9
G5 ugriz magentafilledcircles 50 1361 N .0048, .0094 −1.9E-8, −5.2E-4 0,1 1
Y .0063, .0123 7.2E-8, 9.6E-4 0,1 0
G61 ugri r>21 blackemptytriangles 20 75 N .0049, .048 −1.1E-7, .0091 0,4 4
Y .0097, .0507 −2.1E-8, −.010 0,4 1
G62 ugri r<21 blackemptysquares 40 310 N .0082, .026 −2.1E-7, .0019 0,1 1
Y .0168, .0319 8.5E-9, .0039 0,6 1
Table1.DivisionofSNeintosetsaccordingtoavailablephotometricpass-
bands,andintosubsetsineachsetforimprovedprecision.The“outliers”
columnindicatesthenumberofSNeinthetrainingsetandtestsetthathave
(zphot−zspec)/(1+zspec) >0.1.The“flaggedintest”columnindi-
(cid:12)catesthenumberofoutliersinth(cid:12)etestsetthathaveσzphot/(1+zphot)>
(cid:12)0.1. (cid:12)
(cid:13)c 0000RAS,MNRAS000,000–000
10 Wang,Gjergo,& Kuhlmann
set 1σ+zzmmpphhoott < colorsonly Ntot Ncut σ 1∆+zz hzphot−zi flaggedoutlier outliers
training 100 N 1040 0 .02(cid:2)41 (cid:3) −9.6E-8 0 4
Y 1040 0 .0259 −1.8E-6 0 7
test 100 N 28662 0 .0270 −.0027 0 196(0.68%)
Y 28662 0 .0271 −6.9×10−4 0 207(0.72%)
training 0.1 N 1028 12 .0236 −3.1E-5 0 4
Y 1028 12 .0253 −4.2E-5 1 6
test 0.1 N 28553 109 .0261 −.0024 37 159(0.56%)
Y 28613 49 .0265 −7.9×10−4 15 192(0.67%)
training 0.05 N 1011 29 .0229 −.00022 1 3
Y 1017 23 .0242 −5.1E-4 3 4
test 0.05 N 28327 335 .0257 −.0021 53 143(0.50%)
Y 28499 163 .0262 −6.8×10−4 31 176(0.62%)
training 0.02 N 918 122 .0204 −.00073 3 1
Y 949 91 .0221 −3.0E-4 5 2
test 0.02 N 26606 2056 .0242 −.0010 95 101(0.38%)
Y 27480 1182 .0250 −3.0×10−4 74 133(0.48%)
training 0.01 N 705 335 .0173 −.00020 4 0
0.007 Y 636 404 .0175 −4.3E-4 7 0
test 0.01 N 19640 9022 .0212 −9.0E-5 151 45(0.23%)
0.007 Y 18370 10292 .0213 5.9×10−4 149 58(0.32%)
Table2.Obtainingsetsofphoto-z’s withhigheraccuracy, precision, and
puritybyusingtheestimated errors onzphot toexclude SNewithlarge
σzphot/(1+zphot).
(cid:13)c 0000RAS,MNRAS000,000–000