Type Ia supernova diversity: Standardizing the candles Tamara M. Davis∗, J. Berian James†, Brian P. Schmidt∗∗ and Alex G. Kim‡ ∗DarkCosmologyCentre,NielsBohrInstitute,U.Copenhagen.JulianeMariesVej30,DK-2100 7 CopenhagenØ,Denmark 0 †InstituteforAstronomy,RoyalObservatory,BlackfordHill,Edinburgh,EH93HJUnitedKingdom 0 ∗∗ResearchSchoolofAstronomyandAstrophysics,AustralianNationalUniversity,CotterRd, 2 WestonACT2612Australia n ‡PhysicsDivision,LawrenceBerkeleyNationalLaboratory,1CyclotronRoadBerkeley,CA94720 a USA J 1 3 Abstract. FutureuseoftypeIasupernovaeforcosmologyaimsnotonlytodeterminetheequation of state of darkenergy,butalso to constrainpossible variationsin its value.To achievethisgoal, 1 supernovaeneedtobecomebettercalibratedstandardcandles—notonlytoimprovetheprecision v of the measurement, but more importantly to gain better control over systematic uncertainties in 4 ordertoensuretheaccuracyoftheresult. 0 HerewereportonaprojecttoquantifythediversityintypeIasupernovae,andtolookfortrends 9 and/orsub-typesthatcanbe used to improvetheircalibrationas standardcandles. We implement 1 a version of principalcomponentanalysis on type Ia supernovaspectra. Althoughthe quantity of 0 dataisnotsufficienttodrawanyfirmconclusionswe showthatthismethodholdspromisefor,at 7 theveryleast,effectivelyseparatingpeculiarsupernovae.Whetheritcanbefurtherusedtoimprove 0 / thecalibrationofnormaltypeIa’sremainsaprojectforfuturestudy. h p Keywords: supernovae:general - PACS: 97.60.Bw o r t s INTRODUCTION a : v i Type Ia supernovae (SNe Ia) have proven to be excellent tools for measuring the ex- X pansion history of the universe. Nevertheless they are not perfect standard candles and r a futuresupernovaexperiments(suchasSNAP[1]), whichaimtoconstrainthetimevari- ation of the equation of state of dark energy, will be greatly enhanced if the diversityin typeIa supernovaeis betterunderstood.Thispointhardlyneeds elaboration,and Irefer the reader to [2] for a more thorough discussion of the motivation for studying SN Ia diversity. In these proceedings we present preliminaryresults of an investigationinto using the statistical tool Principal Component Analysis (PCA) to quantify the diversity in SN Ia spectra.PCA,frequentlyusedinimagecompression,isamethodbywhichcomplicated informationcan besimplifiedby expressingitin termsofan orthogonalbasisset thatis derived from the data. In the case of supernova spectra it can be thought of as deriving a set of eigenspectra, or “principal component spectra” (PCS), with a different set of coefficients for each supernova. This technique is used in [3, 4] as applied to quasar spectra, and in what follows we have adapted code originally used in [3]. An excellent description of PCA as applied to spectra can be found in [4], and we follow their FIGURE 1. The average spectrum and the first five principal component spectra calculated for our spectralsample.Eachofthespectraintheoriginalsamplecanbereconstructedfromdifferentweightings of these components. PC1 is primarily responsible for the overall shape (colour) of the spectrum. PC2 and PC3 can be related to velocityterms that respectivelyred- and blue-shiftthe lines in the spectrum. Thesefirstthreecomponentsdealwiththedominantspectralfeatures(representing72%ofthevariance, seeTable1).Higherordercomponentsbecomeincreasinglynoisy. terminology here. An alternative attempt to use PCA on the spectra of supernovae can befound in[5]. Such an analysissees utilityina numberofways. Firstly,it allowsoneto reconstruct anysupernovaspectrumgivenonlyasmallnumberofcoefficients,ratherthanthevalue of the spectrum at each wavelength (presuming you know the eigenspectra, of course). In addition, once you know the distributionof each coefficient you can randomly select a set of coefficients based on these distributions and reconstruct a ‘typical’ supernova spectrum. This procedure could be useful for simulations in which many realistic su- pernovaspectraare required, and forfilling outthedistributionofspectrawhen onlyan incompletesampleexists(as isthesituationwefind ourselvesin). Secondly, and possibly most importantly, this technique could be used to identify subsetsoftheSN Iapopulationwithsimilarcharacteristics.In whatfollowswedemon- stratethisconcept on asmallset ofpreviouslypublishedtypeIasupernovaspectranear maximumlight. DETAILS The spectral sample we used consists of 19 spectra of 10 supernovae. These are a subset of published normal type Ia supernova spectra that were taken within two days of maximumlight [6, 7, 8, 9, 10, 11]. More detail about the sample and the preparation can be found in [2]. In summary, we performed extinction correction and warped the spectra to give the correct broadband magnitudes under synthetic photometry. We then logarithmicallybinnedthespectra,andcombinedthespectraintooneaveragespectrum foreach object. Since more than one spectrum was often available for each supernova we were able to use the variation in the spectra for an individual supernova to estimate the amount of non-intrinsic diversity in the sample (for example the variations due to instrumen- tal/observational effects and the range of times about peak magnitude). We confirmed that this intra-object dispersion was much smaller than the inter-object dispersion and considerthe difference to be the size of the intrinsicdiversityin SN Ia spectra. We also confirmedthatthespacingofthelogarithmicbinswasnotsignificantforthefinalresult. WethentookthesespectraandperformedPCA.Thefirstfiveoftheresultingprincipal componentspectraareshowninFig.1.InFig.2wedemonstratehowtwoverydifferent supernovae, SN 1992A and SN 1991T, can both be reconstructed by using different weightingsoftheseprincipalcomponents. Now that we have the components we can measure how much of the variation in the spectral sample can be accounted for by each component. Table 1 shows the amount of variation absorbed by each component. In this case the first four components absorb 80%ofthevariationinthespectralsample,andeightcomponentsaccountforessentially all (98%) of the variation. In fact this is probably over-correcting the spectra, as not all variation in the input spectra is intrinsic to the supernovae. The last few components in thisanalysiswillbefittinginstrumentaland observationalnoise. Theindividualsupernovaspectrainoursamplecanbecomparedbyconsideringtheir coefficients(orweights)ineachoftheprincipalcomponentspectra.Spectrathataresim- ilar should have similar arrays of coefficients (similar weightings of each component). TABLE 1. Residual variance fraction. Amountofvariationin thespectralsample thatcanbeaccountedforbyeachprincipal component. Component Variance Cumulative fraction variance 1 0.40 0.40 2 0.17 0.57 3 0.15 0.72 4 0.07 0.80 5 0.07 0.87 6 0.05 0.92 7 0.04 0.96 8 0.02 0.98 FIGURE 2. Examples of reconstructing spectra from principal components. The lowest spectrum in eachplotistheaveragespectrum(thinline)over-plottedwiththespectrumofthesupernova–SN1992A ontheleft,SN1991Tontheright.Eachsuccessivespectrumabovethatistheaveragespectrum(offsetby anarbitraryamount)plustheinclusionofoneadditionalweightedprincipalcomponent.TheSNspectrum is again shown over-plotted as the thick line after 3 principal components have been added and then againafter7.Youcansee thatmuchofthe variationinthespectrumhasbeenaccountedforin thefirst three components and by the time the 7th principal component has been included (top spectrum) the reconstructedspectrumisvirtuallyindistinguishablefromtheoriginal.Thisshowshowtwoverydifferent spectracanbereconstructedfromthesameprincipalcomponents,weighteddifferently. In Fig. 3 we plot the weight of the first component against the weight of the second (left) and third (right) for each of the supernovaein our sample. The weights havebeen normalized so they represent standard deviations from the mean. It is clear that in this diagram that SN 1991bgis peculiar in the first component,being more than 2.5 s from the average, while SN 1991T is somewhat peculiar in the second component. The third componentpicksout thedifferences between SN 1994S and SN 1999ee. This is a promising result, because the two SNe that are known to be peculiar, i.e. the under-luminous SN 1991bg and the over-luminous SN 1991T are picked out as the most peculiar objects in the first two principal components. It is significant that they are peculiar in two different components, showing that this test can not only pick out peculiar supernovae, but also distinguish between the spectra of the over-luminous and under-luminous supernovae. It will be interesting to see whether this remains a robust test with a larger spectral sample, when more than one examplefrom each class is used intheanalysis. 3 3 94S 2 2 81B 1 92A 89B 1 969X4D 949D88a9qB 2 0 98aq 3 0 96X81B91T s s 91bg 94S 99ee 91bg 92A -1 -1 99ee 91T -2 -2 -3 -3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 s s 1 1 FIGURE3. Plotsoftheweights(coefficients)oftheprincipalcomponentspectraforeachsupernovain oursample.Weightshavebeennormalizedtorepresentstandarddeviations.Intheleftpanelweseethat SN1991bgisa2.5s outlierinthefirstcomponent,whileSN1991Tisthefurthestoutlierinthesecond component.The third componentpicks up the difference between SN 1994S and SN 1999ee, which is primarilyadifferenceinlinevelocity. FUTURE WORK Thereismuchyettobedoneonthisanalysis.Firstandforemostitneedstobeappliedon a much larger sample ofspectra. These are becomingavailable as more groups proceed withlow-redshiftsearches and publishtheirresults.1 The componentsof thespectra need to be related to otherfeatures of thesupernovae, such as peak magnitude, D m or stretch, ejecta velocities, line ratios and equivalent 15 widths. Only when we have understood the relationship between these features and the differenttypesofspectrawillwehaveausefultoolforstampingoutsystematicerrorin ourcosmology. Currently we have only looked at spectra near the time of peak brightness. This can be extended to other epochs, and most powerfully to a combined multi-epoch analysis. Once this is done we need to turn it into a tool that takes spectra that are not part of the originalsampleandtestswhere theyfit inthearray ofdiversity. Finally we may be able to run PCA on grids of model supernova spectra and thus relatethecomponentstophysicalfeaturessuchaspressure,temperatureandmetallicity. This could give us a much more complete understanding of the causes of diversity in, andtherangeofprogenitorsof, typeIasupernovae. 1 For example the CfA Supernova Archive has recently become pub- licly available and will be a great resource for this kind of study, see http://www.cfa.harvard.edu/cfa/oir/Research/supernova/SNarchive.html. ACKNOWLEDGMENTS We thank Paul Francis for the initial version of the PCA code used in this paper. TMD appreciates the support of the Villum Kann Rasmussen Fonden. The Dark Cosmology Centreisfunded by theDanishNationalResearch Foundation. REFERENCES 1. SNAPCollaboration(2005),astro-ph/0507459. 2. J.B.James,T.M.Davis,B.P.Schmidt,andA.G.Kim,MNRAS370,933–940(2006). 3. P.J.Francis,P.C.Hewett,C.B.Foltz,andF.H.Chaffee,ApJ398,476–490(1992). 4. N.Suzuki,ApJS163,110–121(2006). 5. M.E.Salvo,Ph.D.thesis,AustralianNationalUniversity(2006). 6. D.Branch,C.H.Lacy,M.L.McCall,P.G.Sutherland,A.Uomoto,J.C.Wheeler,andB.J.Wills, ApJ270,123–125(1983). 7. R. P. Kirshner, D. J. Jeffery, B. Leibundgut, P. M. Challis, G. Sonneborn, M. M. Phillips, N. B. Suntzeff,R.C.Smith,P.F.Winkler,C.Winge,M.Hamuy,D.A.Hunter,K.C.Roth,J.C.Blades, D. Branch, R. A. Chevalier, C. Fransson, N. Panagia, R. V. Wagoner, J. C. Wheeler, and R. P. Harkness,ApJ415,589–615(1993). 8. F. Patat, S. Benetti, E. Cappellaro, I. J. Danziger, M. della Valle, P. A. Mazzali, and M. Turatto, MNRAS278,111–124(1996). 9. M.E.Salvo,E.Cappellaro,P.A.Mazzali,S.Benetti,I.J.Danziger,F.Patat,andM.Turatto,MNRAS 321,254–268(2001). 10. M.Hamuy,J.Maza,P.A.Pinto,M.M.Phillips,N.B.Suntzeff,R.D.Blum,K.A.G.Olsen,D.J. Pinfield,V.D.Ivanov,T.Augusteijn,S.Brillant,M.Chadid,J.-G.Cuby,V.Doublier,O.R.Hainaut, E.LeFloc’h,C.Lidman,M.G.Petr-Gotzens,E.Pompei,andL.Vanzi,AJ124,417–429(2002). 11. D. Branch,P. Garnavich,T. Matheson,E. Baron, R. C. Thomas,K. Hatano,P. Challis, S. Jha, and R.P.Kirshner,AJ126,1489–1498(2003).