PASJ:Publ.Astron.Soc.Japan,1–??, (cid:13)c 2008.AstronomicalSocietyofJapan. Implications for Galaxy Evolution from the Cosmic Evolution of Supernova Rate Density Takeshi Oda 1, Tomonori Totani 1, Naoki Yasuda 2, Takahiro Sumi 3, Tomoki Morokuma 5, Mamoru Doi 4, George Kosugi 5 1Department of Astronomy, School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan [email protected] 2Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, 227-8582, Japan 3Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan 8 4Institute of Astronomy, School of Science, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo, 181-0015, Japan 0 5National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan 0 2 (Received ;accepted ) n Abstract a J We report a comprehensive statistical analysis of the observational data of the cosmic evolution of 5 supernova (SN) rate density, to derive constraintson cosmic star formationhistoryand the nature of type 1 Ia supernova (SN Ia) progenitor. We use all available information of magnitude, SN type, and redshift informationofbothtypeIaandcore-collapse(CC)SNeinGOODSandSDF,aswellasSNIaratedensities ] h reported in the literature. Furthermore, we also add 157 SN candidates in the past Subaru/Suprime-Cam p data that are newly reported here, to increase the statistics. We find that the current data set of SN rate - density evolution already gives a meaningful constraint on the evolution of the cosmic star formation rate o (SFR) at z <1, though strong constraints cannot be derived for the delay time distribution (DTD) of r t SNe Ia. We∼derive a constraint of α 3–4 [the evolutionary index of SFR density (1+z)α at z <1] s ∼ ∝ a with an evidence for a significant evolution of mean extinction of CC SNe [E(B V) 0.5 at z ∼0.5 [ compared with 0.2 at z =0], which does not change significantly within a reason−able∼range of va∼rious 1 DTD models. T∼his result is nicely consistent with the systematic trend of α estimates based on galactic v SFR indicators in different wavelengths (ultraviolet, Hα, and infrared), indicating that there is a strong 4 evolution in mean extinction of star forming regions in galaxies at relatively low redshift range of z<0.5. 9 These results are obtained by a method that is completely independent of galaxy surveys, and espe∼cially, 1 there is no detection limit about the host galaxy luminosity in our analysis, giving a strong constraint on 2 the star formation activity in high-z dwarf galaxies or intergalactic space. . 1 Key words: supernovae:general— galaxies:evolution— cosmology:observations 0 8 0 1. INTRODUCTION SN Ia progenitor (Madau et al. 1998; Yungelson & Livio : 1998,2000;Dahlen&Fransson1999;Gillilandetal. 1999; v i In recent years a number of searches for high redshift Gal-Yam & Maoz 2004;Strolger et al. 2004, 2005;Barris X supernovae(SNe)havebeenconducted. Althoughthepri- et al. 2004; Oda & Totani 2005, hereafter OT05; Strigari r mary purpose of most of these surveys is measurement of et al. 2005). a thecosmicexpansion,thesesurveysalsoallowedmeasure- However, it is not an easy task to actually extract use- ments of the cosmic supernova rate density and its evolu- ful constraints from the SN rate density evolution data. tion (Pain et al. 2002; Tonry et al. 2003; Madgwick et al. Previous studies (Maoz & Gal-Yam 2004; Strolger et al. 2003; Gal-Yam & Maoz 2004; Blanc et al. 2004; Maoz & 2004;F¨orster et al. 2006) mainly concentrated on the de- Gal-Yam2004;Dahlenetal.2004;Cappellaroetal.2005; termination of DTD, using the rate density evolution of BarrisandTonry 2006;Neill etal.2006;Poznanskiet al. SNe Ia. In such an analysis, sometimes CSFH models 2007;Sharonetal.2007;Mannuccietal.2007;Kuznetsova are assumed based on the observational estimates from et al. 2007). Studying these data should provide us with high-z galaxy surveys. However, as argued by F¨orster et importantinformationnotonlyforthecosmicstarforma- al. (2006), the constraint on DTD models sensitively de- tionhistory(CSFH)butalsothestillunknownprogenitor pends on the assumed CSFH, and hence it is difficult to of type Ia supernovae (SNe Ia). The progenitorof SNe Ia derive a robust constraint on DTD. isbelievedto be abinarysystemincluding awhite dwarf, Theprimarypurposeofthispaperistoperformacom- andtheSNIaratedensityevolutionisaconvolutionofthe prehensive likelihood analysis using all available SN rate cosmic star formation history and the delay time distri- density evolution data in the literature, to derive con- bution (DTD) fromstarformationto SN Ia events. DTD straintsonDTD and/orCSFH.After the GOODShigh-z dependsontheprogenitormodels,andhencetoconstrain supernovasurvey(Dahlenetal.2004;Strolgeretal.2004), DTD observationally is a useful approach to reveal the whose data was used in Strolgeret al. (2004)and F¨orster 2 Oda et al. [Vol. , et al. (2006), a number of observational estimates of SN Thefollowingaretheplanofthispaper. In 2and 3we § § rate density evolution have been published (mostly for describetheSSSdatasetandanalysisprocedureofselect- SNe Ia,but somedataalsoforCCSNe). Ourapproachis ingSNcandidates. Formulationsofthecomparisonofthe to derive constraints only by using SN rate data, without theoretical model and the observationaldata are given in using information of CSFH from galaxy surveys. We will 4. ConstraintsontheCSFHfromourcomprehensivepa- § perform a simultaneous fit to both the SN Ia and CC SN rametersurveyarederivedin 5. Conclusionsaregivenin § rate density evolution data, surveying parameters of the 6. Throughoutthis paper, the standardΛCDM universe § CSFH model with a variety of DTD models. We will find is assumed with the following values of the cosmological that, though a strong constraint on DTD models cannot parameters: Ω = 0.3, Ω = 0.7, h H / (70 km s−1 M Λ 70 0 be derived even from all the available data so far, we can Mpc−1) = 1. All magnitudes are given≡in the AB magni- setinterestingconstraintsonCSFHandevolutionofmean tude system. dust extinction of CC SNe, which can be compared with those inferred from galaxy surveys. 2. The SSS Data Althoughthereareanumberofobservationalestimates on CSFH at a variety of redshifts from galaxy surveys, The SSS data set consists of the following three fields, there is still a large uncertainty in the star formation namedA2152,MS1520.1,andthespringfield(SF),whose rate (SFR) density estimated from galaxy observations, positions on the sky are given in Table 1. All images because of extinction, initial mass function, or extrapo- aretakenwith the Subaru/Suprime-Cam(Miyazakietal. lation of luminosity functions to fainter magnitudes be- 2002)having an effective field-of-view (FOV) of 30′ 24′, × low the detection limits (see Hopkins 2004 and Hopkins with a time interval of about one month that is suitable & Beacom 2006, and reference therein). Therefore it is for a high-z supernova search. We describe details of the useful andimportantto derive constraintsonCSFH from observations at each field below. SNe independently of galaxy surveys. In contrast to SFR A2152 field – A single FOV of the Suprime-Cam cen- density estimates by galaxies, detectability of SNe does teredonthegalaxyclusterAbell2152wasobserved,where not depend on the host galaxy brightness, and even in- two galaxy clusters (A2152 at z =0.04 and A2152-B at tergalacticstarformationactivity canbe probedby host- z = 0.13) closely overlap on the line of sight (Blakeslee less SNe. Searches for z 1 SNe are typically performed et al. 2001). About one month after the first imaging of at wavelength around th∼e i′ and z′ band roughly corre- this field(2003May5),the fieldwasimagedagainduring sponding to the rest-frame visual bands, and hence the four consecutive nights (June 1–4). Images were taken effect ofextinctionby dustis expected to be smallerthan with V and I band filters and typical exposure time is c c the CSFHestimatesbasedonthe rest-frameUVemission a few hours for each filter per day, but we use only the of galaxies. It is not trivial that a unit mass of star for- I band images for our supernova search. About 40 % of c mation always produces the same number of SNe, but it supernova candidates found in I band data of this field c could evolve with redshift or physicalproperties of galax- were not detected on V band images, while there is no c ies. IfasignificantdifferencebetweenCSFHinferredfrom SN candidate that was detected only in V band. c galaxysurveysandthatfromSNsurveysisfound,itmight MS1520.1field –AsingleFOVoftheSuprime-Camwas indicate that the relation between star formation and su- observedaroundthegalaxyclusterMS1520.1+3002atz= pernovaproductionisnotassimpleasnormallyassumed. 0.117 (Stocke et al. 1991). Observations were performed In addition to the available SN rate density data in on April 25 and May 20 in 2001 with the i′ band filter. the literature, we also utilize the photometric sample The exposure time is about one hour. of SN candidates found in the past observations using It should be noted that the expected number of super- Subaru/Sprime-Cam. This Subaru Supernova Survey novae in the galaxy clusters in the MS 1520.1 and A2152 (SSS)sampleincludes157supernovacandidates,61outof fields is too small to affect the conclusions of this paper which have clear offsets from the centers of host galaxies (Gal-Yam et al. 2002; Sharon et al. 2007), and hence the andhencetheyaremostlikelySNe. Thisdatasetiscom- existenceoftheseclustersisnottakenintoaccountinour plementary to GOODS, SNLS and the IfA deep survey theoretical modeling. (Strolger et al. 2004; Neill et al. 2006; Barris and Tonry Thespringfield –TherearefouradjacentSuprime-Cam 2006) in terms of the combination of the survey area and images of this field in i′ band, which we call SF 1-4. The depth; the covered area of SSS, 1.4 deg2, is wider than first images were taken on March 19, and the second and the GOODS, and the SSS depth, i′ 26.0,is deeper than third oneswereonApril 9and11,in 2002. Typicalexpo- ∼ the SNLS and the IfA deep survey. Though no SN type sure time of each field is about one hour, but the obser- or redshift information is available for the SSS sample, vational conditions of SF2 and SF3 are better than those we addthis data set to our likelihoodanalysis to increase of SF1 and SF4. This field and the MS1520.1 field were the statistics especially for CC SNe. Compared with SNe observed as a part of the Supernova Cosmology Project. Ia, there are not many data of the rate density for CC Thus, the observation was designed to find high redshift SNe. Combined analysis of the SSS counts including all SNe Ia for the cosmological purpose, and follow-up spec- SNeandotherdataforSNIaratedensityevolutionshould troscopicobservationsofsomesupernovacandidateswere givesomeconstraintsontheCCSNratedensityevolution performed. As a result, three SNe (2002fc, 2002fd and and hence CSFH. 2002fe) are clearly identified to be SNe Ia, and another No. ] Cosmic Supernova Rate Density Evolution 3 SN (2002ff) is a possible candidate of SN Ia. Their red- ent values of m are fitted to the simulations in different 0 shifts are 0.88, 0.278, 1.086, and 1.1, respectively. (See fields. The fitting results of m are given in Table 2. 0 IAUcirc. 7971formoredetails.) Alloftheseareincluded We estimate the accuracy of position recovery by mea- in our SN candidates, but the information obtained with suring the positional offsets of detected objects from the spectroscopic follow-up is not used, because the majority original positions. As shown in Fig. 2, the offsets well of the SNe in the SSS sample do not have spectroscopic obeys the two-dimensional Gaussian distribution. Their information, and adding these spectroscopic information standard deviations in one dimension derived by least hardly affects the conclusions of this paper. square fits are σ = 0.34 and 0.51 pixel for m = 25.0 var and 25.8,respectively, in the A2152 field (1 pixel = 0.′′2). 3. Selection of the SSS Supernova Candidates 3.2. Host Galaxies Herewedescribehowweselectedsupernovacandidates Many extragalactic variable objects should be associ- fromtheSSSdataindetail,andaschematicflow-chartof ated with host galaxies, and their nature and positional these processes is presented in Fig. 1. relation to variable objects are important information to select supernovae. First we simply define a tentative host 3.1. Variable Object Detection, Detection Efficiency and galaxy as the object in the reference image whose surface Position Accuracy brightness peak is the closest to a detected variable ob- First,wemadedifferentialimagesfromimagepairssep- ject. Sometimes the host galaxies are classified as point arated by about one month, using the image subtraction sources (the SExtractor stellarity parameter greater than method ISIS (Alard & Lupton 1998;Alard 2000). Source 0.8), and their positions are the same as those of variable detection was carried out using the SExtractor software pointsources. Insuchcasestheycouldbesimplythevari- (Bertin & Arnouts 1996). We detected candidate vari- ablesourcessuchasQSOsorvariablestars. Furthermore, able objects requiring that they have five or more con- wecannotexcludeapossiblecontributionfromunresolved nected pixels whose counts are more than 1σ level of the host galaxies. In these cases, we assign the next closest surfacebrightnessfluctuation,after0.′′7FWHMGaussian object in the reference frame as the tentative host galax- smoothingonthesubtractedimages. Thevariabilitymag- ies. Therefore,positionsofthevariableobjectsarealways nitude (m )correspondingtothe fluxonthe subtracted different from the centers of their tentative host galaxies var image was measured by the SExtractor’sautomatic aper- by definition. ture magnitude. From these candidates, objects having Basedontheestimatesofthepositionaccuracyforvari- high signal-to-noise (S/N) were selected. The criteria are ableobjects,wecallanobject“on-center”whend < 1.5, p S/N=7-10,whichdependonobservationalconditionsof where d is the distance from the center of host galaxies p the fields. Finally we checked the images of these objects to variable objects measuredin units of pixel. The center on the subtracted and original frames by eye in order to ofhostgalaxiesissimplydefinedbythesurfacebrightness eliminate spurious objects. peak. About 97 % and 85 % of the bright (m =25.0) var The detection efficiency ε(m ) and the position accu- andfaint(m =25.8)pointsourcesarefoundwithin1.5 var var racyofvariableobjectsonthe subtractedimagesareesti- pixels (= 0”.3) from the original position, respectively, mated by simulations using artificial point sources placed according to the simulation using artificial sources in the randomlyononeofthe pre-subtractionimages,underthe A2152 field. exactly same object selection criteria as described above. We define the distance between a variable object and Ideally, this test should be performed on various back- itshostgalaxycenterthatisnormalizedbythesizeofthe ground conditions (e.g., in the blank field or on a host host galaxy, as d d /r , where r is the effective n p p,gal p,gal ≡ galaxy),sincethedetectionefficiencycouldbechangedby size ofthe hostgalaxy,defined as the radius of the ellipse the location of variable sources. However, we ignore this fromthehostcentertothedirectionofthevariableobject. effectinthispaper,becausethetypicalsurfacebrightness The ellipse is obtained by the fitting to the host galaxy, of supernova host galaxies at z >0.5 is fainter than the ascalculatedinthe SExtractor,anditssizeis determined sky level, and hence the noise o∼f image is dominated by so that the squares of the major and minor axes are the the sky background. In fact, we confirmed that there is same as the second order moments along the axes, i.e., no marked difference in the fluctuation of photon counts F x2 ofthe subtractedimage betweenthe blank field and loca- a2 i∈S i i,j , (2) j ≡ F tions of galaxies having typical magnitudes of supernova P i∈S i hosts. This result is in agreement with previous stud- where thePsubscript i denotes for each pixel, Fi the flux ies (e.g., Strolger et al. 2004; Poznanski et al. 2007). counts in a pixel in I - (A2152 field) or i′-band (other c Following Strolger et al. (2004), detection efficiency esti- fields), x is the distance from the host center to the i- i,j mated for various magnitudes of flux variability is fitted th pixel projected onto the major or minor axis (denoted by the following function: by the subscript j), and the summation is over the whole 1 region of the host galaxy. ε(mvar)= 1+exp[(m m )/S ]. (1) Now we examine the dn distribution of the tentative var 0 fit − host galaxies, which is shown in Fig. 3. The distribu- WeuseasinglevalueofSfit=0.43forallfields,butdiffer- tion clearly shows a strongercorrelationbetween variable 4 Oda et al. [Vol. , Table 1. BasicInformationoftheSSSObservations Field name R.A. Decl. Area Observing dates Typical exposure time Band filter [deg2] (hour) A2152 16h05m22s +16◦26′55′′ 0.21 2003 May 5, June 1-4 3 I , V C C MS1520.1 15h22m13s +29◦51′59′′ 0.23 2001 April 25, May 20 1 i′ SF 1 14h00m56s +05◦40′48′′ 0.24 2002 March 19, April 9, 11 1 i′ SF 2 13h58m36s +05◦22′30′′ 0.23 2002 March 19, April 9, 11 1 i′ SF 3 14h03m46s +05◦11′04′′ 0.23 2002 March 19, April 9, 11 1 i′ SF 4 14h13m18s +05◦40′43′′ 0.24 2002 March 19, April 9, 11 1 i′ Fig. 1. Aflow-chartshowingthedetection andselectionproceduresofthesupernovacandidates inSSS. No. ] Cosmic Supernova Rate Density Evolution 5 Fig. 2. HistogramsofthedistancebetweenoriginalandrecoveredpositionsofartificialpointsourcesintheA2152field. Leftand rightpanelsshowthecasesoftwodifferentmagnitudesoftheartificialsources(mvar=25.0and25.8),respectively. Errorbarsshow a1σ statisticalerror. Solidlinesarefitsbytwo-dimensionalGaussiandistribution[∝rexp(−r2/2σ2)]withσ=0.34and0.51pixel, respectively. objects and host galaxies than that expected for objects that are randomly distributed on the sky, indicating that the majority of variable objects are physically associated with galaxies. The radial distribution of supernovae in their host galaxies is still uncertain (e.g., Bartunov et al. 1992; Howell et al. 2000), and here we test the galaxy surfacebrightnessprofilesoftenusedintheliterature,i.e., the exponential and the de Vaucouleurs profile. Here, we havetakenintoaccounttheeffectofseeingforthesurface brightness profile, by relating the effective radius of the originalprofiles to the seeing-convolvedsecond order mo- ments. It should be noted that the simple exponential or de Vaucouleurs law may not be sufficient to describe all galaxies; there may be contribution from irregular galax- ies, and cosmological surface brightness dimming effect mayaltersignificantlytheapparentprofile(e.g.,Totani& Yoshii 2000). However these effects are difficult to model quantitatively, and they are ignored here for the simplic- ity. We find that the observeddistribution is different from what expected when all variable objects obey the ex- ponential or the de Vaucouleurs profile. However, the Fig. 3. Cumulative(top)anddifferential(bottom)distribu- distribution is well described by the combination of the tions of the normalizeddistance dn between the positions of two components: a galaxy profile (exponential or de variableobjects and the centers of host galaxies. Model dis- Vaucouleurs) and a random distribution. We find the tributions derived from the exponential and de Vaucouleurs lawsareshownwiththicksolidanddashedlines,respectively. best-fit relative proportion by the Kolmogorov-Smirnov The distribution expected for objects located randomly on test as 94 (88)% for the exponential (de Vaucouleurs) thereferenceimagesisshownwiththedotted line. Thethin profile and the rest for a random distribution. The de solid/dashed lines are the combined distribution of the ex- Vaucouleurs profile gives an especially good fit to the ob- ponential/de Vaucouleurs law and the random distribution. serveddistribution. However,itdoesnotnecessarilymean The relative proportions between the different components areindicatedinthefigure. thatthedeVaucouleursprofileisbetterthantheexponen- tial for SN distribution, since there may be a significant contribution from AGNs. From this figure, we find that almost all objects with d >5 are likely to be unrelated n to the tentativelyassignedhostobjects,andhencewe de- fine objects with d >5 as those without detectable host n galaxies. 6 Oda et al. [Vol. , Table 2. Depthofsurveysandnumberofdetected SNcandidates. Number of SN candidates Field m [mag] All On-center Off-center No host 0 A2152 25.8 33 12 17 4 MS1520.1 26.1 13 5 7 1 SF 1 25.3 20 11 5 4 SF 2 26.0 30 15 12 3 SF 3 26.0 41 20 15 6 SF 4 25.6 20 10 5 5 Total 157 73 61 23 3.3. The Supernova Candidates ing to the exponential profile). In fact, as mentioned in the previous subsection, we expect about 40AGNs in the 3.3.1. Off-center Supernova Candidates SSSfromthestatisticsoftheSXDSvariableobjectsearch Nowwehavearobustsampleofsupernovae,i.e.,the61 (Morokumaetal. 2007),i.e.,aboutahalfoftheon-center variable objects associated with host galaxies and their candidates. locations are off-center on the host galaxies (d >1.5 pix p TheeffectofAGNcontaminationinthe on-centersam- and d 5). Because of these properties, the majority of n≤ plewillbeexaminedwhenwewillcomparethetheoretical them should be supernovae rather than AGNs. A possi- model of supernova rate evolution to the observed data. ble contaminationis chancesuperpositionsofbackground 3.3.3. No-host Supernova Candidates AGNs infrontofunrelatedforegroundgalaxies(Gal-Yam The variable objects without host galaxies should also etal. 2007). Wecanmakearoughestimateofsuchevents be examined since supernovae may be included in them. as follows. From the statistics of a similar variable ob- Firstwenoticethatthereareobjectsthatareclearlymuch ject search by Morokuma et al. (2007) using the Subaru brighter than expected for supernovae. In the off-center XMM-Newton Deep Survey (SXDS) data set, about 40 supernovasample,thereisnoobjectbrighterthanm = AGNs are expected in the SSS data. The surface area var 22.5 in the variability magnitude. However, 10 objects covered by galaxies with a similar magnitude to that of inthe no-hostsample arebrighterthanthis magnitude in host galaxies in the SSS is about 5% of the total survey spiteoftheno-detectionofahost. Theseobjectsaremost area, and hence we expect a few random superpositions. likelyvariablequasarsorvariablestarsinourGalaxy,and This number is much smaller than the off-center super- hence they are rejected from the supernova candidates. nova candidates, and hence this effect can be neglected. Then, the remaining 23 objects are defined as the no- 3.3.2. On-center Supernova Candidates host supernovacandidates without detectable host galax- When variable objects are on the center of their host ies, and there is no marked difference between the vari- galaxies, we cannot discriminate between the two possi- ability magnitude distributions of this sample and the bilities of supernovae or AGNs. However, some of these off-center supernovae. Thus, although we cannot exclude objectsshowveryfaintvariabilityfluxcomparedwiththe significantcontaminationfromquasarsandGalactic vari- totalmagnitudeofthehostgalaxies,andtheseobjectsare able stars, most of these are possibly supernovae with most likely to be low-luminosity AGNs (LLAGNs) with hostgalaxiesthatarefainterthanthedetectionthreshold verylowaccretionrateasreportedinTotanietal.(2005), (i′ = 25.0) or truly intergalactic supernovae. To exam- because supernovae are generally as bright as the bright- ine the former possibility, we estimate η(z), which is the est class of galaxies. In fact, we found no off-center SN fractionofsupernovaeinhostgalaxiesthataredetectable candidates associated with galaxies brighter than i′=20. by SSS. We assume that the supernova rate in a galaxy Thereforeweremoved15variableobjectsthatarelocated is proportional to the rest-frame V-band luminosity of a at the center of very bright galaxies (i′<20). host galaxy. This is an assumption that should not be The remaining 73 on-center variable objects are then accuratelycorrect;CC SNe are expected to trace galactic called as “on-center supernova candidates”, though we light in shorter wavelength such as rest-frame UV, and cannot exclude a contamination of AGNs in this sample. SNe Ia with a long delay time would trace longer wave- However, if we assume that supernovae trace the light of length light that is related to the stellar mass. However, thehostgalaxies,wecanestimatetheexpectednumberof our data set is limited about available band filters, and on-centersupernovaefromthenumberofoff-centersuper- we make this assumption for the present data set. novae,byextrapolationofasurfacebrightnessprofile. We Then we can estimate η(z) by the V-band luminos- findthat32and129on-centersupernovaeareexpectedfor ity function of galaxies at a given z and the SSS de- the exponential and de Vaucouleurs profiles, respectively. tection limit for galaxies. We assume the following val- Therealityislikelybetweenthetwo,andifweassumethe ues and redshift evolution of the Schechter parameters S´ersic profile, we find that the expected number becomes of the luminosity function: α = 1.15 log(1+z) and the same as the observed number with the S´ersic’s index − − M = 20.5 5.0 log(1+z), from the observations by of nser ∼ 3. These results indicate that at least about Ilb∗ert −et al. −(2005). The K-correction between the ob- half of the on-center objects are supernovae (correspond- No. ] Cosmic Supernova Rate Density Evolution 7 served band (i′ or I) and the rest-frame V are calculated icantly affect our conclusions even if this effect is com- assumingtheSbcgalaxytemplate. Thecalculatedcorrec- pletely ignored. tion factors in this way is η= 0.90, 0.79 and 0.72 for z= 0.5,0.8,and1.0,respectively. ThetypicalredshiftsofSNe 4. Theoretical Model of SN Rate Evolution that should be detectable in SSS is 0.5 and 1.0 for CC ∼ 4.1. Cosmic Star Formation History SNe and SNe Ia, respectively,and we detected 134super- nova candidateswith detectable hostgalaxies. Therefore, For the parametrizationof CSFH, we use the following most or perhaps all of the 23 no-host candidates can be functional form (Gal-Yam & Maoz 2004): explained by those associatedwith galaxiesunder the de- 5α 5β −0.2 tection limit. In other words, there is no evidence for a 1+zbreak 1+zbreak Φ(z) + . (3) significant population of intergalactic supernova popula- ∝"(cid:18) 1+z (cid:19) (cid:18) 1+z (cid:19) # tion. Here, α and β are indices of the CSFH at low and high 3.4. Summary of SN Candidate Selections redshift,respectively. TheCCSNrateevolutionissimply As a result of the above selection procedures, we find assumedtobeproportionaltotheCSFH,becauseoftheir 157supernovacandidatesintotal,including73on-center, shortlife. TheSNIaratedensityrIa(z)iscalculatedfrom 61 off-center, and 23 no-host candidates. Images of rep- the CSFH convolved with the DTD, fD(tIa), where the resentativeobjects of these classificationare givenin Fig. delay time tIa is elapsed fromstar formationto the SN Ia 4, as well as the images of those classified as non-SNe ob- events. In this paper, the parameterα is treatedasa free jects. A summaryofthe resultsfor eachfieldis presented parameter that we constrain, while other two parameters in Table 2. The distribution of the variability magnitude arefixedatβ=0andzbreak=1.5inourbaselinemodel,in of these supernova candidates is shown in Fig. 5, as well order to reduce the number of free parameters. Although as the estimated detection efficiency. The behavior of the SNe Ia have a time delayfrom starformation, mostDTD faint end of the distribution is in reasonable agreement modelshavethepeakofthedistributionatrelativelysmall with the detection efficiency estimate. No considerable tIa and supernova rate data used in our analysis are at field-to-field variation is found. z<1. Therefore the dependence of our results on β and z∼ is not large (see 5.2). break 3.5. The Sample Used for the Statistical Analysis § 4.2. Delay Time Distribution In the following likelihood analysis including the SSS data, we will present two cases of (i) using all of the on- To test a variety of DTD of SNe Ia, we use the theo- and off-center SSS samples and (ii) using only the off- retical models constructed by Greggio (2005) for a wide center SSS sample. In the former case, all on-center and varietyoftheprogenitormodels(singleordoubledegener- off-center SN candidates are assumed to be the real su- ate, and others). We use four representative models; two pernovae. In the latter case, the effect of the removal of of them are based on the single degenerate scenario with centralregionsofhostgalaxiesiscorrectedassumingthat two different distributions of the secondarystellar masses the supernova distribution obeys the exponential profile adopted in Greggio (2005) or Greggio & Renzini (1983), ascalculatedin 3.3.2. Forthiscorrectionwesimplymul- which are labeled as “SD-G05” and “SD-GR83”, respec- tiplied a factor o§f 0.65 to the theoreticalpredictionof the tively. The other two models are based on the double cosmicSNratedensity,sincethe meanfractionoflightin degenerate scenario with two different treatments of the central regions of all host galaxies in the SSS is 0.35. As commonenvelopephase,whicharelabeledas“close-DD” describedin 3.3.2,the exponentialprofilecorrespondsto and “wide-DD”, respectively. assuming tha§t about half of on-center candidates are the In addition to these models based on the stellar evo- real supernovae. Since the exponential profile is the least lution theory and SN Ia progenitor scenarios, we also concentrated one among the various profiles assumed in test more phenomenological DTD models based on sim- theliterature,therealityshouldbebetweentheabovetwo ple functional forms as frequently used in SN rate stud- cases and hence we can check the systematic uncertainty ies (Madau et al. 1998; Strolger et al. 2004). One is the about the AGN contamination by this treatment. Gaussian distribution, We do not include the no-host supernova candidates in 1 (t τ )2 Ia Ia tthame ifnoalltoiwoninbgyavnaarliyasbisle, sqiunacseawrseocraGnnaolatcetixcclvuadreiabthleesctoanrs- fD(tIa,τIa)= √2π(0.2τIa)exp(cid:20)− 2(0.−2τIa)2 (cid:21), (4) in this sample. We have already shown in 3.3.3 that the and the other is an exponential distribution, § number of no-host candidates is similar to that expected exp( t /τ ) Ia Ia by SNe with host galaxies under the detection limit, and fD(tIa,τIa)= − . (5) τ hence there is no evidence for a significant population of Ia truly intergalactic supernovae. Therefore, we only make All of the above DTD models are shown in Fig. 6. acorrectionforSNe that areclassifiedasno-hostbecause Recentobservationsaboutthedependenceofsupernova their hostgalaxiesarefainter thanthe detectionlimit, by rate onthe hostgalaxyproperties(e.g., galaxytype, stel- using the quantity η(z) calculated in 3.3.3. This correc- larmass,starformation,radioactivity)provideevidences tion factor is not far from unity, and§it does not signif- forasignificantpopulationofSNeIawhoserateisdirectly 8 Oda et al. [Vol. , Fig. 4. Imagesofthesupernovacandidatesaswellasrejectedobjects(seetext). Ineachpanel,theleftimageisthereference(first epoch),thecentralimageisthesecondepochimage,andtherightimageisthesubtractedimage. Thepositionsofvariabilitiesare indicatedasthecrossingpointsoftwowhitebars. Thescaleofthisimageisshownintheupperrightpanel. No. ] Cosmic Supernova Rate Density Evolution 9 Fig. 5. Variability magnitude (i′ or Ic) distributions of the supernova candidates detected in the six different SSS fields. The distributionsoftheoff-centerSNsample(solidline),theoff-centerpluson-centersamples(dottedline),andallthesamplesincluding theno-hostsampleareshown. Solidcurvesinthesmallbottom panelsshowthedetectionefficiencyineachfield. proportional to the star formation activity (Dallaporta prompt population is not important in this work. 1973; Oemler & Tinsley 1979; Della Valle et al. 1994, 4.3. Comparison with the Data 2005;Mannuccietal. 2005;Scannapieco&Bildsten2005; Sullivanetal. 2006;Aubourgetal. 2007). Especially,the Theobserveddatasetwithwhichwecompareourtheo- correlation with radio galaxies may indicate a bimordal reticalmodelincludes (i)variabilitymagnitudes,redshift, DTD by twodistinct populations (Mannucciet al. 2005). and SN type information of the GOODS supernova sur- To test this possibility, we assume a bimodal delay time vey (Strolger et al. 2004) and a supernova survey in the distributionwhichcontainsthepromptandtardypopula- SubaruDeepField(SDF-SNS,Poznanskietal. 2007),(ii) tions. For the tardy populations we use the DTD models variabilitymagnitudedistributionofSSS,and(iii)various describedabove,andthecombinedDTDwiththeprompt SN rate density data at z =0 as well as high-z as tabu- population becomes lated in Table 3. The majority of the rate density data are for SNe Ia. f (t )=ǫ δ(t )+(1 ǫ )f (t ). (6) D Ia CSFH Ia − CSFH delay Ia While the shapes of CSFH or DTD have been modeled Here, the tardy part of fdelay(tIa) is normalized to the as above, we treat the overall normalizations of the SN unity when it is integrated over tIa. We set ǫCSFH=0.4, rate density evolution as free parameters, separately for which has been inferred from observations (e.g., Sullivan IaandCCSNe. (See 4.5formoredetailsofthelikelihood et al. 2006). As we will find later, constraints derived by method.) Therefore §our analysis is free from the uncer- ouranalysisaremainlyforCSFH,andtheDTDmodeling tainties in converting star formation rate into supernova doesnotsignificantlyaffectourmainconclusions. Infact, rate, such as the initial mass function, mass ranges of SN we find that our conclusions arenot significantly changed progenitors, or white dwarf explosion efficiency. if ǫ < 0.7, and hence the possible existence of the CSFH ∼ 10 Oda et al. [Vol. , 4.4. Dust Extinction The effect of dust extinction must be taken into ac- count. For comparison with the GOODS, SDF-SNS, and SSS data, we must calculate light curves of various SN types to calculate the expected detection number as a function of variability magnitude. Therefore we first in- troducetheextinction-correctedlightcurvesofvariousSN types, and then they are reddened and absorbed by the twoparametersofthemeancolorexcess,E(B V) and CC − E(B V) for CC and Ia SNe, respectively. We apply a Ia − typical Galactic extinction curve of Cardelli et al. (1989) as the extinction law of both CC SNe and SNe Ia. Some observationsindicatethattheextinctionlawoflow-z SNe Ia might be different from the Galactic law (Altavilla et al. 2004; Reindl et al. 2005; Wang 2005; Elias-Rosa et al. 2006), but it is still highly uncertain. We confirmed thatourresultsarehardlychangedevenwhenthe extinc- tion curve of the Small Magellanic Cloud (Gordon et al. Fig. 6. The delay time distribution function for the type 2003) is used. It should be noted that the Calzetti law Ia supernova used in this paper. Thick lines show the delay (Calzetti et al. 2000), which is often used in studies of time distribution derived in Greggio (2005), and thin lines high-z galaxies, is an empirical law for the effective at- showtheGaussianantexponential models. tenuation (rather than extinction) of flux from a whole galaxy,andis notappropriatefor the extinctionofflux of a source in a galaxy. According to the observations of SNe Ia for the cosmo- logical purpose, the degree of reddening for high redshift SNe Ia seemsto be similartothose oflocalSNe Ia(Knop et al. 2003). Thus, we assume E(B V) =0.05, which Ia − is a typical for local SNe Ia (Altavilla et al. 2004; Reindl et al. 2005), for SNe Ia in all redshifts. This value of Table 3. SNratedensitydata E(B V) issimilartothoseusedinotherSNratestud- Ia − z SN rate density Reference ies. Therefore, we use the reported values of SN Ia rate [10−4Mpc−3 yr−1] densities showninTable 3inourlikelihoodanalysis. One Data for SNe Ia may expect that the prompt SN Ia population may suffer 0.01 0.28 0.05∗ Cappellaro et al. (1999) heavier extinction because generally star forming regions 0.1 0.24 ± 0.12∗ Madgwick et al. (2003) are dusty. However,the inferredtime scale of the prompt 0.13 0.16 ± 0.07∗ Blanc et al. (2004) SNIaeventselapsedfromstarformationis 108yr,which 0.25 0.17± 0.17 Barris & Tonry (2006) is much larger than the lifetime of massiv∼e stars leading 0.30 0.34 ±0.15 Botticella et al. (2007) to CC SNe. 0.35 0.53±0.24 Barris & Tonry (2006) Incontrast,CCSNecouldsufferfromheavierextinction 0.45 0.73 ±0.24 Barris & Tonry (2006) bydust,anditisalsoreasonablethatthedegreeofextinc- 0.47 0.42 ±0.06 Neill et al. (2006) tionevolveswithredshiftsreflectinggalaxyevolution. We 0.5 0.48 ±0.17 Tonry et al. (2003) treat E(B V)CC as a free parameter for all high-z CC 0.55 0.54 ±0.10 Pain et al. (2002) SNe in the−analysis of the GOODS, SDF-SNS, and SSS 0.55 2.04 ±0.38 Barris & Tonry (2006) data. Ontheotherhand,weincludethelocalCCSNrate 0.65 1.49 ±0.31 Barris & Tonry (2006) densityofCappellaroetal.(1999)inourlikelihoodanaly- 0.75 1.78 ±0.34 Barris & Tonry (2006) sis. ComparingtheCCSNlightcurvesusedinCappellaro ± etal.(1999)withthoseunreddened,theextinctionimplic- Data for CC SNe itlyincludedinthisestimateisE(B V) 0.2. Therefore, − ∼ 0.01 0.43 0.17∗ Cappellaro et al. (1999) ifwesetE(B V)CC 0.2,itmeansthatthereis noevo- Note: the rate d±ensities are corrected for the cosmological lution for the−mean ex∼tinction of CC SNe. Instead, if we parametersusedinthiswork. getahighervalueofE(B V) bythelikelihoodanaly- CC ∗Theoriginalvaluehasbeencorrectedbyusingamorerecent sis,itmeansthataheavie−rmeanextinctionofCCSNe at estimate of the local B-band luminosity density, ρ=(1.03+ highredshiftsthaninthelocaluniverseisrequired. Wedo 1.76z)×108L⊙Mpc−3 (Botticellaetal.2007). notincludeotherCCSNratedensitydata(e.g.,Botticella et al. 2007) than that of Cappellaro et al., because it is difficult to test evolutionary models of E(B V) by an − analysis including various rate density data at different