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AGN host galaxy mass function in COSMOS: is AGN feedback responsible for the mass-quenching of galaxies? PDF

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Astronomy&Astrophysicsmanuscriptno.HGMF_Bongiorno cESO2016 (cid:13) January12,2016 AGN host galaxy mass function in COSMOS: is AGN feedback responsible for the mass-quenching of galaxies? A.Bongiorno,⋆1,A.Schulze,2 A.Merloni,3 G.Zamorani,4 O.Ilbert,5 F.LaFranca,6 Y.Peng,7 E.Piconcelli,1 V. Mainieri,8 J.D.Silverman,2 M.Brusa,9,4 F.Fiore,1 M.Salvato,3 N.Scoville10 1 INAF-OsservatorioAstronomicodiRoma,viaFrascati33,00040MonteporzioCatone,Italy; 2 KavliInstituteforthePhysicsandMathematicsoftheUniverse,TodaiInstitutesforAdvancedStudy,theUniversityofTokyo, 6 Kashiwa,Japan277-8583(KavliIPMU,WPI); 1 3 Max-Planck-InstitutfuerExtraterrestrischePhysik(MPE),Postfach1312,85741Garching,Germany; 0 4 INAF-OsservatorioAstronomicodiBologna,viaRanzani1,40127Bologna,Italy; 2 5 AixMarseilleUniversité,CNRS,LAM(Laboratoired’AstrophysiquedeMarseille)UMR7326,13388,Marseille,France; 6 DipartimentodiMatematicaeFisica,UniversitàRomaTre,viadellaVascaNavale84,00146Roma,Italy; n 7 CavendishLaboratory,UniversityofCambridge,19J.J.ThomsonAve.,CambridgeCB30HE,UK; a 8 EuropeanSouthernObservatory,Karl-Schwarzschild-str.2,85748GarchingbeiMuenchen,Germany; J 9 DipartimentodiFisicaeAstronomia,UniversitàdiBologna,vialeBertiPichat6/2,40127Bologna,Italy; 9 10 CaliforniaInstituteofTechnology,MC249-17,1200EastCaliforniaBoulevard,Pasadena,CA91125 ] ReceivedSeptember15,1996;acceptedMarch16,1997 A G ABSTRACT . h Weinvestigatetheroleofsupermassiveblackholesintheglobalcontextofgalaxyevolutionbymeasuringthehostgalaxystellarmass p function(HGMF)andthespecificaccretionratei.e.,λ ,distributionfunction(SARDF)uptoz 2.5with 1000X-rayselected - SAR ∼ ∼ o AGNfromXMM-COSMOS.Usingamaximumlikelihoodapproach,wejointlyfitthestellarmassfunctionandspecificaccretionrate r distributionfunction,withtheX-rayluminosityfunctionasanadditionalconstraint.OurbestfitmodelcharacterizestheSARDFasa t doublepower-lawwithmassdependentbutredshiftindependentbreakwhoselowλ slopeflattenswithincreasingredshiftwhile s SAR a thenormalizationincreases.Thisimpliesthat,foragivenstellarmass,higherλSARobjectshaveapeakintheirspacedensityatearlier [ epochcomparedtothelowerλSARones,followingandmimickingthewellknownAGNcosmicdownsizingasobservedintheAGN luminosityfunction.ThemassfunctionofactivegalaxiesisdescribedbyaSchechterfunctionwithaalmostconstantM andalow ∗⋆ 1 massslopeαthatflattenswithredshift.Comparedtothestellarmassfunction,wefindthattheHGMFhasasimilarshapeandthat,up v tolog(M /M ) 11.5theratioofAGNhostgalaxiestostarforminggalaxiesisbasicallyconstant( 10%).Finally,thecomparison 1 oftheAG⋆NH⊙GM∼Ffordifferentluminosityandspecificaccretionratesub-classeswiththephenom∼enological modelpredictionby 9 Pengetal.,2010forthe“transient”population,i.e.galaxiesintheprocessofbeingmass-quenched,revealsthatlow-luminosityAGN 0 donotappeartobeabletocontributesignificantlytothequenchingandthatatleastathighmasses,i.e. M > 1010.7M ,feedback ⋆ 2 fromluminousAGN(logL &46[erg/s])mayberesponsibleforthequenchingofstarformationinthehostgalaxy. ⊙ bol 0 . Keywords. Galaxies:active,Galaxies:fundamentalparameters,Galaxies:evolution 1 0 6 11. Introduction off of both processes. While the physical scales of interest (a : fewpc)cannotbedirectlyresolvedinthese modelsandin cur- vSuper-massiveblackhole(SMBH)growth,nuclearactivity,and rent numerical simulations (e.g. Sijackietal. 2015), they usu- igalaxyevolution,havebeenfoundtobecloselyrelated.Infact, X allyproposethepresenceofanenergeticAGN-drivenfeedback, overthelast15years,thediscoveryoftightcorrelationsbetween i.e.astrongwindoriginatedfromtheAGNthatdepositstheen- rgalaxiesandtheircentralnucleiproperties(seeKormendy&Ho a ergy released by the accretion process within the host galaxy 2013,and references therein) as well as similar evolutionary (Faucher-Giguère&Quataert2012). Thismechanismisableto trends between the growth histories of SMBHs and galaxies linkblackholegrowthandstarformationandshutoffbothpro- (e.g.Boyle&Terlevich1998;Marconietal.2004),haveestab- cessesinaself-regulatedmanner.However,itisstillunclearand lished anew paradigmin whichActiveGalactic Nuclei(AGN) observationallynotproven,whetherAGNdrivenfeedbackpro- are key players in the process of galaxy formation and evo- cesses do indeed have an effect on the global propertiesof the lution. Several theoretical models (e.g. Somervilleetal. 2001; galaxy population, in particular in suppressing the star forma- Granatoetal. 2004; Monaco&Fontanot 2005; Springeletal. tion(SF)intheirhostgalaxiesheatingand/orpushingawaythe 2005;Crotonetal.2006;Hopkinsetal.2006;Schawinskietal. gaswhichisformingstars. 2006;Cen&Chisari2011)havebeendevelopedtoexplainthis co-evolution,and to find the mechanism responsiblefor the si- Star formation quenching via some mechanism is required multaneousfuellingofthecentralBHandtheformationofnew alsotopreventtheovergrowthofmassivegalaxies,hostedinthe starsinthehostgalaxy,aswellasthequasi-simultaneousshut- mostmassivedark-matterhaloes(e.g.Read&Trentham2005). Such a “mass quenching” mechanism, irrespective of its phys- ⋆ E-mail:[email protected] (OAR) ical origin,would suppressthe growthof massive galaxiesand Articlenumber,page1of15 A&Aproofs:manuscriptno.HGMF_Bongiorno explain the steep decline of the galaxy mass function above a givencharacteristic mass. While supernovafeedbackis noten- ergeticenoughinthismassregime,acentralAGNwouldbean efficientmechanism. ToinvestigatesucharoleforAGN,detailedstudiesonsin- gleobjectshavebeenperformedtosearchforsignaturesofAGN feedback. Massive outflows on several kpc scales have been observed in a few cases (Cano-Díazetal. 2012; Feruglioetal. 2010;Crescietal.2015a;Feruglioetal.2015),butuptonowthe evidencethatsuchoutflowsareindeedresponsibleforsuppress- ingstar formationintheregionoftheoutflowiscircumstantial (Cano-Díazetal. 2012; Crescietal. 2015a,b). Further progress can be made through statistical studies of the properties of ac- tivegalaxies(e.g.,SFR)comparedtonormalgalaxies.However, results have been often contradictory, i.e. some authors found that AGN mainly lie above or on the Main Sequence (MS) of galaxies (Santinietal. 2012; Mullaneyetal. 2012), while oth- ers(Bongiornoetal.2012;Mullaneyetal.2015)foundtheSFR of AGN hosts to be lower than the average MS galaxies, as expected by the models including AGN feedback. Bundyetal. Fig.1.BivariatedistributionfortheanalyzedhardX-rayselectedsam- (2008)comparedthestarformationquenchingratewiththerate pleintheM λ planecolor-codeddependingontheredshiftbins. atwhichAGNactivityistriggeredingalaxies,andshowedthat ⋆− SAR Thehorizontalandverticaldashedlinescorrespondstothelowerlimit these two quantities agree over a range of masses. They inter- cutsappliedinM andλ . ⋆ SAR pretthisasaphysicallinkbetweenthesetwophenomenawhich howeverdonotdirectlyimplyacausallink. In fact, irrespective of AGN feedback, an essential pre- requisite to understandthe role ofblack holeactivity in galaxy ing. In particular, we test whether the AGN population can be evolutionistohaveaaccurateandunbiasedcensusoftheAGN associated and/or be responsible for mass quenching using the population an its relation to the properties of their host galax- modelpredictionfrom Pengetal. (2010) for the mass function ies. The former is basically provided by the AGN luminosity ofthe‘transientpopulation”(i.e.galaxiesintheprocessofbeing function, which is now well established over a wide range of mass-quenched). redshift and luminosity (Uedaetal. 2014; Buchneretal. 2015; The paperis organizedasfollows:InSec. 2 we presentthe Airdetal.2015;Miyajietal.2015;Silvermanetal.2008).Deep X-rayselectedsampleweareusing.Sec3 presentsthemethod X-ray surveys established a trend of AGN downsizing, i.e. the used to derive the specific accretion rate distribution function most luminous AGN have the peak in their space density at andthe AGN hostgalaxymass function(Sec. 3.2 and 3.3) and earlier times than lower luminosity AGN (Uedaetal. 2003; theirresults(Sec.3.4).InSec4,weaddressthequestionofthe Hasingeretal. 2005), which is also seen in optical surveys linkbetweenAGNandstarformationquenchingbycomparing (Bongiornoetal.2007;Croometal.2009).Thistrendissimilar theAGNhostgalaxymassfunction,computedfordifferentsub- tothe downsizingin thegalaxypopulation(Cowieetal. 1996), samples, with the model prediction for quenching galaxies by wherethemostmassivegalaxiesbuildtheirmassatearliertimes Pengetal.(2010). thanlowermassgalaxies. Throughout this paper, a standard cosmology (Ωm=0.3, Ω =0.7andH =70kms 1 Mpc 1)hasbeenassumed.Thestel- Linking black hole growth to their host galaxies, re- λ 0 − − quires the study of their stellar mass function and/or the ac- larmassesaregiveninunitsofsolarmassesforaChabrierIMF tive fraction or duty cycle of AGN occurrence in galaxies (Chabrier2003). of given stellar mass (e.g. Bundyetal. 2008; Xueetal. 2010; Georgakakisetal.2011;Airdetal.2012;Bongiornoetal.2012; 2. TheSample Lussoetal. 2012). Most of these studies define AGN activity abovea certain X-ray luminosity thresholdand found the frac- The AGN sample considered here has been extracted from tion of AGN at given L to increase with stellar mass. How- theXMM-COSMOSpoint-likesourcecatalogue(Hasingeretal. X ever, this may lead to a biased view, since AGN at different 2007; Cappellutietal. 2009) whose optical identifications and masses cover different ranges of Eddington ratios for a given multiwavelengthpropertieshavebeenpresentedby Brusaetal. luminosityrangeandAGNhavebeenfoundtoshowawidedis- (2010). The catalog contains 1800 X-ray sources detected tributionofEddingtonratios(e.g.Kauffmann&Heckman2009; above flux limits of 5 10 16∼, 3 10 15 and 7 10 15 erg − − − Schulze&Wisotzki 2010). In fact, Airdetal. (2012) showed cm 2s 1 in the [0.5-2]∼ke×V, [2- 10∼] k×eV and [5-1∼0]×keV bands, − − thattheintrinsicdistributionofspecificaccretionratesatz < 1 respectively. followsapowerlaw,whoseshapedoesnotevolvewithredshift, Our analysis is based on objects that have been detected in independentofstellarmass.Thisresulthasbeenconfirmedand thehard[2-10]keVband.TherestrictiontoahardX-rayselected extendedouttoz<2.5byBongiornoetal.(2012). sample is chosen since the soft bandcan be affected by obscu- In this work, we build upon the aforementioned studies of rationthatcanleadtoaredshift-dependentincompleteness(i.e. AGNhostsbyestablishingthebivariatedistributionfunctionof fluxlimitedsurveyspickupmoreobscuredobjectsathigherred- stellarmassandspecificaccretionrateforahardX-rayselected shift,seee.g.Gillietal.2010).However,thisbandmaystillsuf- AGN sample over the redshift range 0.3 < z < 2.5. We use fersfromincompletenessduetoheavilyobscuredandCompton the derived AGN host galaxy stellar mass function to test the Thick(CT, log(N ) > 24[cm 2]) AGN, whose detectionprob- H − hypothesisofAGNfeedbackasdriverofstarformationquench- abilityisstronglyreducedbecausetheintrinsicemissioncanbe Articlenumber,page2of15 A.Bongiornoetal.:AGNHostGalaxyMassFunction significantlysuppressedduetorepeatedComptonscatteringand 1032erg/s/M . The latter criterionis motivatedby the require- photoelectricabsorption. ment of havin⊙g a clear cut in λ above which we define the SAR Outofthefull 1800sources,weidentifyafinalsampleof AGN as active (see below). The chosen minimum λ value SAR ∼ 927 hard X-ray selected AGN in the redshiftrange 0.3<z<2.5. corresponds to the lowest observed value in our intermediate All hard X-ray sources have accurate photometric redshifts redshift bin and furthermorecorrespondsapproximately to 1% (Salvatoetal. 2011) while half (581/927) have secure spectro- ofEddingtonwhichwechoseinthefollowingasourminimum scopicredshifts. thresholdto defineanactiveblackhole,consistentwithstudies oftype–1AGN(Schulzeetal.2015).Afterapplyingtheselim- its,oursampleisreducedto877AGNwith0.3<z<2.5. 2.1.X-rayluminosities,hostgalaxystellarmassesand specificaccretionrates 3. TheAGNHostGalaxyMassFunctionand Rest-frame,intrinsicX-ray[2-10]keVluminositiesforthefinal sample have been derived from the observed hard X-ray flux. specificaccretionratedistributionfunction FollowingLaFrancaetal.(2005),weconvertedtheobserved[2- InordertoderivetheAGNhostgalaxymassfunction(HGMF) 10]keVfluxestotheintrinsic[2-10]keVluminosities,foreach and the specific accretion rate distribution function (SARDF), AGN with a given measured N , by applying a K-correction H we have to account for various selection effects in our flux- computedbyassuminganintrinsicX-rayspectrumwithapho- limited AGN sample. This requiresa carefulassessment of the ton index Γ=1.8, an exponential cut-off at E=200 keV and, a incompletenessfunction. photoelectricabsorptioncorrespondingtotheobservedN col- H In fact, completeness in L does not directly ensure umndensity.The[2-10]keVluminosityisgivenby: X completeness in M . As previously reported, AGN show a ⋆ Lrf =F 4πD2K(z,N ) (1) wide range of Eddington ratios (Kauffmann&Heckman 2009; [2−10]keV [2−10]keV L H Schulze&Wisotzki2010),andthusalsoawiderangeofLX/M⋆ (λ ), with a distributionfalling below the correspondingEd- where D is the luminosity distance and K(z,N ) is the term SAR L H dingtonlimitapproximatelyfollowinga power-lawdistribution which accountsforthe K-correctionand absorptioncorrection. (Airdetal.2012;Bongiornoetal.2012). The absorbingcolumndensity N forour sample hasbeen de- H rivedasinMerlonietal.(2014).Forthebrightestsources(above AluminositycompleteAGNsamplewillbebiasedtowards 200pncountsinthe0.5-10keV bandofXMM-Netwton)N is high mass BHs and high galaxy mass i.e. since an AGN with H obtainedfromthefullspectralanalysisofMainierietal.(2011), low Eddington ratio will be included in the sample only if its which is available for 195/927 of the AGN. For the remain- MBHishighenoughtobeabovethegivenluminosity(LX)limit, ing sources, NH is estimated in a statistical fashion, by assess- given the relation between MBH-M⋆, a bias towards high-mass ingthevalueofthe‘observed’spectralslopefromthehardness blackholesinducesabiastowardhigh-massgalaxies.Thiseffect ratio and assessing the value of the ’observed’ spectral slope has to be carefully taken into account when building a galaxy drawn from a normal distribution with mean and dispersion of masscompletesamplestartingfromanX-rayflux-limitedAGN Γ = 1.8 0.2. While this estimate shows a significant scat- sample. int ± ter, thereare noapparentsystematic biases, as demonstratedin Merlonietal.(2014).Thereforetheseestimatescanberobustly 3.1.Incompletenessfunction usedforthestatisticalstudiesasperformedinthispaper. Host galaxy stellar masses have been derived in Our corrections for incompleteness account for three effects: Bongiornoetal. (2012) using a two-component (AGN and (1) the X-ray sensitivity function; (2) the absorption correc- galaxy)SEDfittingtechnique.Wereferthereadertothispaper tion f(N L ,z);and (3)the stellar mass completenessdown H X | foradetaileddescriptionofthemethod. to our threshold in units of specific accretion rate logλ = SAR Following Airdetal. (2012) and Bongiornoetal. (2012) 32[erg/s/M ]. we define “specific accretion rate” λ L /M (see also The first⊙selection effect to consider is the position depen- SAR X ⋆ ≡ Brusaetal.2009;Georgakakisetal.2014)asadirectlymeasur- dentX-rayfluxlimitbasedonthesensitivitymapcomputedby able quantity which can be regarded as a proxy for the black Cappellutietal. (2009). Theabsorptioncorrectionaccountsfor hole growth rate relative to the stellar mass of the host galaxy, the sourceswhich have been missed in the sample due to their M˙ /M , after taking into account the (luminosity dependent) highcolumndensityN .ForthiscorrectionweusetheN distri- BH ⋆ H H bolometric correction (e.g. Marconietal. 2004; Lussoetal. butionasafunctionofzandL publishedbyUedaetal.(2014) X 2012) and a radiative efficiency factor. It is also related to the basedonseveralX-rayAGNsurveys(seetheireq.(5)and(6)). SMBH’s Eddingtonratio,λ = L /M , applyingthe bolo- We integrate over the N distribution between 20 < logN < Edd bol BH H H metric correction factor and the scaling relationship between 24, i.e. we do not include Compton thick AGN in our HGMF blackholemassandhoststellarmass. Assumingasanapprox- determination.ThefractionofCTAGNisstilluncertainandthe imation a mean bolometric correction k =25 (Marconietal. N distributionabovelogN =24ispoorlyknown(Uedaetal. bol H H 2004;Lussoetal.2012)andaconstanthoststellartoblackhole 2014;Buchneretal.2015;Airdetal.2015).Thecontributionof massratioof500(Marconi&Hunt2003;Häring&Rix 2004), CT AGN to the AGN space density is expected to lie between logλ =34[erg/s/M ]approximatelycorrespondstotheEd- 10 40%(Gillietal.2007;Treisteretal.2009;Vignalietal. SAR dingtonlimit,whilelogλ⊙ =32[erg/s/M ]wouldgive1%of ∼2014;−Buchneretal.2015;Lansburyetal.2015).Thesetwocor- SAR Eddington.ThebivariatedistributionM -λ⊙ fortheanalyzed rectionsappliedtothefluxlimitedsampleresultinaluminosity ⋆ SAR sample is shown in Fig. 1 where differentcolorscorrespondto completesample. differentredshiftrangesaslabeled. As describedabove, we additionallysuffer from significant For the determination of the mass function, we further re- incompleteness due to the fact that a broad range of M can ⋆ strict our sample in stellar mass M and specific accretion rate be associated to a given luminosity L . To accountfor this ef- ⋆ X λ , applyingthe followingcuts:M > 109.5 M andλ > fect in the HGMF, we need to include an additional term to SAR ⋆ SAR ⊙ Articlenumber,page3of15 A&Aproofs:manuscriptno.HGMF_Bongiorno Table1.BestfitmodelparametersandtheirerrorsforthebivariatedistributionfunctionofstellarmassandSAR(eq.7).Theparametersdenoted withan arekeptfixedduringthefit. ∗ f (M ,z)fromeq.10 f (λ )fromeq.11 f (z)fromeq.12 ⋆ ⋆ λSAR SAR z log(Ψ ) logM [M ] α logλ k logM γ k γ p p z ∗ ⋆∗ ∗SAR,0 λ ⋆,0 1,0 γ 2 1 2 0 ⊙ -6.86 10.99 0.24 33.8 -0.48 11.0 -1.01 0.58 -3.72 5.82 2.36 1.1 ∗ ∗ ∗ +/-0.01 +/-0.03 +0.07 – +0.03 – +0.02 +0.02 +0.09 +0.12 +0.08 – 0.06 0.03 0.02 0.02 0.09 0.13 0.08 − − − − − − − 0.3<z<0.8 0.8<z<1.5 1.5<z<2.5 ]⊙35 M / s / g 34 r e [ R A λS33 g o l 32 9.5 10.0 10.5 11.0 11.5 12.0 9.5 10.0 10.5 11.0 11.5 12.0 9.5 10.0 10.5 11.0 11.5 12.0 log M [M ] log M [M ] log M [M ] ∗ ⊙ ∗ ⊙ ∗ ⊙ Fig.2.BivariatedistributionfunctionΨ(M ,λ ,z),forourbestfittingparametricmodel,derivedthroughtheMaximumLikelihoodmethod,in ⋆ SAR threeredshiftsbins.Theorangecontoursindicatelinesofconstantspacedensity,from10 10to10 3Mpc 3),separatedbyafactorof10each. − − − the incompleteness function based on the distribution of λ . isgivenby: SAR Using this distribution function, we correct for incompleteness 1 down to a fixed threshold in λ , which we set at logλ = p(M ,λ ,N ,z) = Ψ(M ,λ ,z) (M ,λ ,z,N ) SAR SAR i ⋆ SAR H ⋆ SAR ⋆ SAR H N I 32[erg/s/M ]. The HGMF is therefore defined as the mass functionofa⊙llAGNabovethisλSAR threshold.Themostrigor- f (NH LX,z)dV , (2) ousandselfconsistentapproachtodothisisbydeterminingthe × | dz HGMF and the SARDF simultaneously,e.g. via the maximum where Ψ(M ,λ ,z) is the bivariate distribution function ⋆ SAR likelihoodmethoddescribedinthenextsection. of stellar mass and specific accretion rate that we want to de- rive, (M ,λ ,z,N ) = (L ,z,N ) is the X-ray selection ⋆ SAR H X H I I functiongivenbythesensitivitymapinthe2-10keVbandand f (N L ,z)istheabsorptiondistributionfunction,takenfrom H X 3.2.MaximumLikelihoodmethod Uedae|tal.(2014).WeusetheN estimatespresentedinSec.2.1 H to compute L (and therefore λ ) and f (N L ,z) for our X SAR H X | sample.ThefactorN correspondstothetotalnumberofobjects We here present the methodology of determining the SARDF inthesamplepredictedbythemodelanditisgivenbyintegrat- and the HGMF simultaneously as a bivariate distribution ingoverM ,λ ,N ,andz,i.e. ⋆ SAR H function of stellar mass and specific accretion rate, i.e. Ψ(M ,λ ,z), where Ψ(M ,λ ,z)dlogM dlogλ gives N =% Ψ(M⋆,λSAR,z) (M⋆,λSAR,z,NH) ⋆ SAR ⋆ SAR ⋆ SAR I the space density of AGN with stellar mass host galaxies be- f (N L ,z)dVdlogN dlogλ dlogM dz, (3) tween logM and logM + dlogM and a specific accretion × H | X dz H SAR ⋆ ⋆ ⋆ ⋆ where we integrate over the N distribution between 20 < ratebetweenlogλ andlogλ +dlogλ attheredshiftz. H SAR SAR SAR logN < 24, while our integration ranges in M , λ and z TheHGMF, SARDF andtheX-rayAGNLF(XLF)can bede- H ⋆ SAR are9.5<logM < ,32<logλ < and0.3<z<2.5,as rivedasdifferentmarginalizationsoverthisbivariatedistribution ⋆ SAR ∞ ∞ discussedinSec.2.1. function. We use the maximum likelihood method developed Our sample also contains 12 AGN without M measure- by Schulze&Wisotzki (2010) and extended by Schulzeetal. ⋆ ments,duetopoorqualityphotometry.However,weaccountfor (2015) to compute Ψ(M ,λ ,z). While these works focused ⋆ SAR thesesourcesusingtheirluminosityandredshiftinformationin- on the joint determination of the active black hole mass func- tegratedovertheentiremassrange,i.e. tion andtheEddingtonratiodistributionfunction(usingtype 1 AGN),themethodisimplementedhereforthejointdetermina- tionoftheHGMFandSARDF. p (L ,N ,z)= p (M ,λ ,N ,z)dlogM . (4) j X H j ⋆ SAR H ⋆ Z The technique minimizes the likelihood function S = OurXMM-COSMOSbasedsamplecoversonlyalimiteddy- 2 lnp,wherethe probabilitydistribution p foreachobject namical range in L , narrower than the full range over which i i X − P Articlenumber,page4of15 A.Bongiornoetal.:AGNHostGalaxyMassFunction Fig.3.UpperPanels:TotalAGNHGMFwiththeassociatederrorsinthreeredshiftbinsderivedthroughtheMaximumLikelihood(blackline andgreyshadedarea)andtheV (datapoints)methods.Ineachbinthelowestzfitisreportedforreferencewithadashedline.Theredandthe max bluelinesarethetotalandthestarforminggalaxystellarmassfunctionswiththeassociatederrorsareshowninmagentaandcyanshadedareas) fromIlbertetal.(2013).LowerPanels:RatioofAGNhostgalaxiestothetotal(redline)andthestarforming(blueline)galaxypopulationasa functionofstellarmassinthesameredshiftbins. theXLFiscurrentlydetermined.Thismightleadtodegenerate (5) solutions for the bivariate distribution function, some of which maybeinconsistentwiththeXLF.Ideally,wewouldliketocon- where NM⋆ is the number of AGN with M⋆ measurements in structthe HGMFandSARDF includingdeeperandlargerarea oursampleandNLX isthenumberofAGNwithonlyLX known. surveys,butthisisbeyondthescopeofthepresentwork.Tore- Theabsolutenormalizationofthebivariatedistributionfunction ducethiseffect,weincludeasadditionalobservationaldatathe is then determined by scaling to the total observed number of XLF.Inthisway,weensureconsistencywiththeXLFobserva- objectsinthesample. tions overits fullobservationallydeterminedluminosityrange. Following Airdetal. (2012) and Bongiornoetal. (2012), In particular, we use the binned XLF from Miyajietal. (2015) we first assume that the bivariate distribution function andcomputetheχ2 valueforthecomparisonwiththeXLFim- Ψ(M⋆,λSAR,z)isseparable,i.e.thespecificaccretionratedistri- pliedbytheHGMFandSARDF.Wethenaddthislikelihoodto butionis mass independentand vice versa.Underthis assump- thatofthe XMM-COSMOSsample.The studyby Miyajietal. tion,thebivariatedistributionfunctionisgivenby: (2015) uses the same N distribution as Uedaetal. (2014) for H Ψ(M ,λ ,z)=Ψ f (λ ,z) f (M ,z) f (z), (6) thedeterminationoftheXLFwhichwealsoemployhere.Over ⋆ SAR ∗ λSAR SAR ⋆ ⋆ z our range in redshift and luminosity, the XLF by Miyajietal. whereΨ isthenormalizationofthebivariatedistributionfunc- ∗ (2015)isconsistentwithotherrecentstudies(Uedaetal.2014; tion, f (λ ,z) is the SAR-term, f (M ,z) is the M -term Buchneretal.2015;Airdetal.2015),thusourresultsarerobust λSAR SAR ⋆ ⋆ ⋆ and f (z)isaredshiftevolutionterm. z againstthespecificchoiceofXLF. However,fortheSAR-term,wealsotestedamass-dependent WecautionthatthefaintendoftheXLFisnotdirectlycon- modelandfoundthismodeltoprovideabetterdescriptionofour strained by our sample: the XLF will also include AGN below data (see AppendixA for more details). The bivariate distribu- our threshold in M and λ , which are not accounted for in ⋆ SAR tionfunctionisthereforewrittenas: ourbivariatedistributionfunctionfit.Thismayleadtoanover- estimateofthespacedensityatlogL <43[erg/s]. X Thetotallikelihoodtominimizeisgivenby: Ψ(M ,λ ,z)=Ψ f (λ ,M ,z) f (M ,z) f (z), (7) ⋆ SAR ∗ λSAR SAR ⋆ ⋆ ⋆ z where f (λ ,M ,z)containsnowalsoadependenceonthe λSAR SAR ⋆ NM⋆ NLX mass. We use this more general parametrization as our default Stot =−2Xi=1 lnpi(M⋆,λSAR,NH,z)−2Xj=1lnpj(LX,NH,z)+χ2(XLFmM)o,⋆d-teelr.mWfe⋆waraentnototepqouianlttooutthethSaAt RthDeFSAanRd-HteGrmMFfλ.SAR and the Articlenumber,page5of15 A&Aproofs:manuscriptno.HGMF_Bongiorno The HGMF and the SARDF are calculated by integrating Table 2. Best fit model parameters for the AGN host galaxy mass Ψ(M ,λ ,z)overλ andover M ,respectively.Tobespe- Schechterfunction,computedinour3redshiftbins. ⋆ SAR SAR ⋆ cific: <z> log(Φ ) logM α ∗M ∗⋆ 0.55 3.83+0.04 10.99+0.03 0.41+0.04 Φ⋆(M⋆,z)= dVddlNogM = 3∞2 Ψ(M⋆,λSAR,z)dlogλSAR − −0.05 −0.03 − −0.04 R 1.15 3.54+0.04 10.99+0.03 0.24+0.04 = 3∞2 Ψ∗ fλSAR(λSAR,M⋆,z) f⋆(M⋆,z) fz(z)dlogλSAR (8) − −0.05 −0.03 − −0.04 R 2.00 3.84+0.04 10.99+0.03 0.03+0.05 and − −0.04 −0.03 − −0.05 ΦλSAR(λSAR,z)= dVddNlogλ = 9∞.5Ψ(M⋆,λSAR,z)dlogM⋆ Table3.Bestfitmodel parametersoftheAGNspecificaccretionrate R doublepower-lawfunction,computedinour3redshiftbins. = 9∞.5Ψ∗ fλSAR(λSAR,M⋆,z) f⋆(M⋆,z) fz(z)dlogM⋆ (9) R In case of separable SAR- and M⋆-terms, as in Eq. 6, the <z> logΦ γ γ logλ SARDF (HGMF) has the same shape as f (f ) and only ∗λ 1 2 ∗SAR theabsolutenormalizationisdeterminedbythλSeARmar⋆ginalisation. 0.55 6.04+0.08 1.35+0.02 3.64+0.10 34.33+0.04 − 0.08 − 0.02 − 0.11 0.04 However,inthemoregeneralcaseofEq.7,thisisnotnecessar- − − − − 1.15 5.22+0.08 1.02+0.02 3.61+0.10 34.32+0.03 ily the case, whichis whythe HGMFandSARDF cannotthen − 0.09 − 0.02 − 0.10 0.03 − − − − beexplicitlyexpressedasanalyticfunctions. 2.00 4.850.08 0.54+0.03 -3.58+0.10 34.30+0.03 Wehereconsiderthefollowingparametricmodelsforthein- − −0.09 − −0.03 −0.10 −0.03 dividualterms:theM -termismodeledusingaSchechterfunc- ⋆ tion: maximum likelihood solution. The quoted uncertainties repre- f⋆(M⋆,z)= M⋆ αe(cid:18)−MM⋆⋆∗ (cid:19). (10) sizeendttohvee1r6alalnodth8e4r%pa-rtailmeeotfetrhseappaarrtafmroemterΨdi.stTrihbeultaiottne,rmisanrgoitndael-- M ! ∗ ⋆∗ terminedbytheMaximumlikelihoodfitandtheirerrorisgiven While a modelwith a low mass slope α evolvingwith redshift by1/√N . tot hasbeenincluded,wefindthatthebestfitparametersareindeed Asmentionedabove,ourbestfitHGMFandSARDFgiven consistentwithnoz-evolutioninα. byEq.8andEq.9cannotbeexpressedassimpleanalyticfunc- TheSAR-termisinsteaddescribedbyadoublepowerlaw: tions, due to the entanglementof M and λ in the SARDF ⋆ SAR term.Forabetterquantitativerepresentationoftheredshiftevo- 1 f (λ ,M ,z)= . (11) lution of HGMF and SARDF and for illustrative purposes, we λSAR SAR ⋆ λSAR −γ1(z)+ λSAR −γ2 provideananalyticapproximationofthetwodistributionfunc- (cid:18)λ∗SAR(M⋆)(cid:19) (cid:18)λ∗SAR(M⋆)(cid:19) tions,evaluatedatthecenterofourthreeredshiftbins.Forthis, ateach redshift,we performeda least-squaresfitto the HGMF wherethe low λ slope γ (z) = γ +k (z z ), with z set SAR 1 1,0 γ 0 0 (computed via Eq. 8) with a standard Schechter function with − at 1.1, and the break logλ (M ) = logλ +k (logM logM⋆,0)withlogM⋆,0 =1∗SA1R. ⋆ ∗SAR,0 λ ⋆ − SnoArRmDalFis(actoiomnpΦut∗Med, vbiraeaEkq.M9)⋆∗wainthdalodwoubmleaspsowsleorpleawα,wainthdntohre- TcohveerastshuemdpotuiobnleopfowaedroluabwleshpaopweeorflatwhefXorLFfλSwARi,thalaloSwcshetcohrtee-r fimtapliasraatmioenteΦrs∗λ,ibnrTeaabk.λ2∗SAaRndan3d. slopesγ1,γ2.Weprovidethebest functionHGMF,asdemonstratedbyAirdetal.(2013).Wefixed thebreakvaluetologλ =33.8[erg/s/M ]tolimitthenum- ∗SAR,0 beroffreeparameters.Thisvalueisclosetot⊙heimpliedEdding- 3.3.Vmaxmethod tonlimit,consistentwiththeapproachinthestudyofAirdetal. Anadditionalconsistencycheckcanbeobtainedbycomputing (2013),andwiththetentativeevidenceforsuchabreakfirstre- theAGNhostgalaxymassfunctionusingtheV method.The max portedinBongiornoetal.(2012). V foreachindividualobjectisgivenby: max Finally, we parameterize the redshift evolution of the nor- malizationofthespacedensityas: zmax dV V (M )= (M ,z) dz (13) max ⋆ ⋆ fz(z)=((11++zz)0p)1p1(cid:16)11++zz0(cid:17)p2 zz>≤zz00 (12) gwihveernebAy(thMe⋆Zt,ozztm)ainlissuAthrveeeyffaercetaidvΩez atirmeaesasthaefiunncoctmiopnleotefnMes⋆safunndcz- wherewefixedz =1.1,motivatedbythebreakredshiftusedin tion.We emphasizeherethattheV (M )valuesusedarenot 0 max ⋆ the LDDE modelin the XLF fromMiyajietal. (2015) and ap- identicaltotheV (L )valuesthatwouldbeusedforthecom- max X proximatelycorrespondingtothecentralredshiftinoursample. putation of the AGN luminosity function. This is because, as The best fit bivariate distribution function Ψ(M ,λ ,z) discussedabove,wehavetoaccountintheincompletenessfunc- ⋆ SAR is shown in Fig. 2 while the best fitting parameters and tion also for the SARDF in addition to the sensitivity function their errors are given in Table 1. We computed the uncer- andtheabsorptioncorrection.Theincompletenessfunctionthus tainties of each parameter using a Markov chain Monte Carlo includesthreetermsandcanbewrittenas: (MCMC) sampling of the likelihood function space, using em- cee(Foreman-Mackeyetal.2013),aPythonimplementationof 24 an Affine Invariant MCMC Ensemble sampler as presented by (M ,z)= ∞ (M ,λ ,z,N ) f (N L ,z) ⋆ ⋆ SAR H H X Goodmanetal.(2010).Weuseduniformpriorsforourfreepa- I Z20 ZλSARmIin | rametersandinitilisedtheMCMC"walkers"aroundthebestfit f (λ ,M ,z)dlogλ dlogN (14) × λSAR SAR ⋆ SAR H Articlenumber,page6of15 A.Bongiornoetal.:AGNHostGalaxyMassFunction Fig.4.UpperPanels:TheSAR-termsplitintothreeredshiftbinsanddescribedasadoublepower-lawwithamassdependentλ asineq.11. SAR∗ LowerPanels:SARDFderivedthroughtheMaximumLikelihoodmethodbyintegratingthebivariatedistributionfunctionoverM (eq.8).The ⋆ shadedareaincludestheerrorsontheparameters. where (M ,λ ,z,N ) = (L ,z,N ) is the X-ray selec- fitM -dependentSAR-termdeterminedabove(Eq.11),normal- ⋆ SAR H X H ⋆ I I tion function given by the sensitivity map in the [2-10] keV izedwithinlogλ > 32[erg/s/M ],whichagaindefinesour SAR band, f (N L ,z)istheabsorptiondistributionfunctionfrom lowerintegrationlimit. ⊙ H X | Uedaetal.(2014)and fλSAR(λSAR,M⋆,z)istheSARDFtermin The AGN Host Galaxy Mass Function is thus computedin ΨλSAR(M⋆,λSAR,z). The latter term is requiredfor the mass de- threeredshiftbinsas: pendentincompletenessfunction (M ,λ ,z,N )inaddition ⋆ SAR H I totheonesneededforthecomputationoftheluminositydepen- dentincompletenessfunction (L ,z). X While the V method hIas the advantage of providing a 1 Nobj 1 max Φ(M )= (15) non-parametricestimateoftheAGNhostgalaxymassfunction, ⋆ ∆logM V ithasthedisadvantagesthatitrequiresaspecificassumptionfor ⋆ Xi=1 max the SARDF term and, furthermore, it does not include the ad- ditionalconstraintsfromthe AGN XLF, which,due to the lim- andthebinnedvaluesareshowninFig.3,togetherwiththeMax- ited luminosity range probed by our sample, makes the results imumlikelihoodresult. Theerrorbarsare determinedbyboot- less robust in particular at the low mass end, where we only strappingofthesamplewiththeirVmax(M⋆)values. probe a limited range in λ . On the contrary, the maximum Asshowninthefigure,weoverallfindagoodagreementbe- SAR likelihoodprovidesa parametricestimate ofthe mass function, tweentheV binnedAGNHGMFandtheAGNHGMFbased max anddeterminestheHGMFandSARDFsimultaneouslyandself- onthemaximumlikelihoodmethod.Thisconfirmstheadopted consistently.ThereforeweonlyusetheV methodasaconsis- parametricmodelinthemaximumlikelihoodapproachandver- max tencycheck.Forthefunction f we assumethebest ifiestherobustnessofourresults. λSAR(λSAR,M⋆,z) Articlenumber,page7of15 A&Aproofs:manuscriptno.HGMF_Bongiorno Fig. 5. Left Panel: Redshift evolution of the SARDF space density for different λ , i.e. magenta: log(λ )=32[erg/s/M ] ( 1% Edd); green: log(λ )=32.5[erg/s/M ] ( 3% Edd); yellow: log(λ )=33[erg/s/M ] ( 1SA0R% Edd); red: log(λ S)A=R33.5[erg/s/M ⊙] ( ∼30% Edd); blue:log(λ SA)R=34.0[erg/s/M ]⊙( ∼Edd);andblack:log(λ S)=AR34.5[erg/s/M ]⊙(>∼Edd).CentralPanel:ReSdAsRhiftevolutionoft⊙heH∼GMFspace densityforSdAiRfferentM .Right⊙Pan∼el:RedshiftevolutionofStAhReXLFspacedens⊙ityfordifferentL byMiyajietal.(2015). ⋆ X 3.4.Results The best fit HGMF (black line in Fig. 3) is well described byaSchechterfunctionwithconstantM andalowmassslope ∗⋆ In the upper panles of Fig. 4, we show the SAR-term f α flattening with redshift (i.e. α = 0.41 in the first redshift (Eq. 11), described by a double power-law with mass depλλeSAnR- bin, 0.24inthesecondand 0.03in−thethirdone;seeEq.2). dent, butredshiftindependentbreakλ . The SARDF, shown Wec−omparetheAGNHGMF−withthetotalgalaxystellarmass ∗SAR inthelowerpanelsofthesamefigure,isobtainedbyintegrating function (red curve and shaded magenta region) and the star thebivariatedistributionfunction(includingtheabovefunction) forminggalaxy mass function (blue curve and shaded cyan re- overM .TheSARDFcanbedescribedbyadoublepower-law gion)byIlbertetal.(2013).Wenotethat,atlog(M /M )>11.5, ⋆ ⋆ whoselowλ characteristicslopeflattensfrom-1.35to-0.54 the HGMF but also the total and SF galaxymass func⊙tionsare SAR fromthelowesttothehighestredshiftbin.Theoverallnormal- not well constrained by the data (see Fig. 1) due to the lim- izationφ onthe contraryincreasesforincreasingredshift(see ited volume sampled in both cases. This regionis indicated by ∗λ Tab.3).Theincreasingnormalizationwithredshiftwasalready thedashedlinesinFig.3.Furthermore,inthehighestz-binthe notedinAirdetal.(2012)andBongiornoetal.(2012).Inthose galaxy mass function of Ilbertetal. (2013) shows an upturn at works,the specific accretionrate distributionwas parametrized lowmasses,capturedintheirdoubleSchechterfunctionmodel, with a single power law over the full redshift range, but al- which is not captured in our more restricted single Schechter ready Bongiornoetal. (2012) noticed the presence of a break function model for the HGMF. Our data do not allow to con- abovelogλ > 34[erg/s/M ].Furthermore,Airdetal.(2013) strainsuchanupturnforourAGNsample,whichwouldrequire SAR arguedforabreakinthespeci⊙ficaccretionratedistributiontobe alargersample,andprobablyadeeperfluxlimitforthegalaxies consistentwiththeXLF. includinglowerluminosityAGN. While these previous studies do not report a change in the TheratioofAGNHGMFovertotalgalaxymassfunctionis shapeofthespecificaccretionratedistributionwithredshift,we shownbytheredlineandtheshadedmagentaareainthelower find a SARDF clearly flattening towards higher redshift. It is panelsofFig.3.Suchratioindicatestheactivefractionorduty importantto note that, comparedto the aforementionedworks, cycle of AGN activity in the galaxypopulation,if we consider therearesomedifferences.First,herewedeterminetheSARDF, AGNwithlogλSAR > 32( 1%Eddington)whichcorresponds ∼ i.e. the absolute space density as a function of λ , while the tothedefinitionofanAGNassumedinthispaper. SAR previousstudies present pAGN(λSAR M⋆), i.e. the AGN fraction We find a redshift evolution in the mass dependenceof the | in the galaxy population. Furthermore, we account for obscu- activefraction.AtM =1010M ,theactivefractionisapproxi- ⋆ ration by integration over the NH distribution, which generally matelyconstantat 10%,while⊙at M⋆ = 1011.5M itincreases steepensourlowλSAR slope. over our three reds∼hift bins from 3% to 8%⊙ to 20%. ∼ ∼ ∼ TheworkbyAirdetal.(2012)isrefersto0.2<z<1.0,and This trend is in qualitative agreement with the results for the thus it did not cover a sufficiently large redshift range to con- SMBHmassdependenceoftheactivefractionoftheblackhole strainthisshapeevolution.ThesampleusedinBongiornoetal. mass function, presented in Schulzeetal. (2015). This could (2012) is instead similar and largely overlaps the one used in be related to the redshift evolution of the gas reservoir avail- this study. A more accurate analysis of the sample used in able to fuel the AGN, since in high redshift galaxies a greater Bongiornoetal. (2012) could indeedrevealthe redshiftdepen- amount of gas can be responsible for triggering AGN activity dence of the specific accretion rate, which was not included (Tacconietal.2010). in the parametric model presented in Bongiornoetal. (2012), TheratioofAGNHGMFtothestarformingmassfunction duetothesimplersinglepower-lawparametrisation.Finally,we (shown by the blue line in the lower panels of Fig. 3) traces modelthebivariatedistributionfunctionofλ andM andnot the averagerelation between star formingand AGN activity as SAR ⋆ onlytheSARDFandincludeadditionalinformationontheXLF. a function of stellar mass. It extends the well known average WediscusstheeffectofthelatterinmoredetailintheAppendix. agreement between star formation rate density and black hole Articlenumber,page8of15 A.Bongiornoetal.:AGNHostGalaxyMassFunction 0.3<z<0.8 0.8<z<1.5 1.5<z<2.5 -4 -5 -6 -7 -4 -5 -6 -7 10 11 12 10 11 12 10 11 12 Fig. 6. Total AGN HGMF in three redshift bins derived through the Maximum Likelihood (black line) and compared with the AGN HGMF fordifferentAGNsubsamplesin(upperpanels)luminosities,i.elog(L )<43[erg/s](magenta);log(L )>43[erg/s](cyan),log(L )>43.5[erg/s] X X X (green),log(L )>44[erg/s](red),andlog(L )>44.5[erg/s](blue);and(lowerpanels)specificaccretionratesλ ,i.e.,logλ >32.5[erg/s/M ] X X SAR SAR (magenta);logλ >33[erg/s/M ](cyan),logλ >33.5[erg/s/M ](green),andlogλ >34[erg/s/M ](red). ⊙ SAR SAR SAR ⊙ ⊙ ⊙ accretion density (e.g. Marconietal. 2004) to its stellar mass sizing behaviour (e.g. Uedaetal. 2003; Hasingeretal. 2005; dependence.Overallwe find a weaker redshiftevolutionin the LaFrancaetal. 2005; Bongiornoetal. 2007; Silvermanetal. shape of this ratio than for the active fraction, where the ratio 2008).Fortheλ dependence,weseethathigherλ objects SAR SAR staysalmostconstantover1010 < M <1011M ,themassrange (logλ > 33.5[erg/s/M ])haveapeakintheirspacedensity ⋆ SAR tracing the bulk of the population,in all three⊙redshiftbins. At at an earlier cosmic epoch⊙comparedto the lower λ objects SAR thehighmassendforz > 0.8theAGN/SFgalaxyratioandfor (logλ <33.5[erg/s/M ]),i.e.alsoshowingacleardownsiz- SAR z > 1.5 also the active fraction appear to increase with stellar ingtrend.The M depende⊙nce,based onthe HGMF, also indi- ⋆ mass.Futurestudieswillberequiredtoconfirmordisprovethe catesadownsizingtrend,withAGNinlowerstellarmassgalax- realityofthistrend. iesshowingasteeperdeclineintheirspacedensitytowardshigh redshift than higher stellar mass galaxies, but less pronounced The redshift evolution of the SARDF and HGMF allows than what is seen in the SARDF. This suggests that the down- a more detailed look at the AGN downsizing behaviour, i.e. sizing in the AGN luminosity function is due to the combina- the luminosity-dependent evolution, seen in the XLF out to tionofa(weak)mass-dependentevolutionoftheHGMFandthe z 2.5. They probe the more physically meaningful quan- ∼ strongerevolutionoftheSARDF. tities stellar mass and specific accretion rate distribution, and by inference relate to black hole mass and Eddington ratio. In InFig.6upperpanels,weshowtheAGNHGMFfordiffer- Fig.5 we showtheglobaltrendoftheredshiftevolutionofthe ent luminosity sub-classes, i.e. log(L ) <43[erg/s] (magenta), X space density in bins of λ (left panel), M (central panel) log(L ) >43[erg/s] (cyan), log(L ) >43.5[erg/s] (green), SAR ⋆ X X and L (right panel). The L dependence, based on the XLF log(L ) >44[erg/s] (red), and log(L ) >44.5[erg/s] (blue). As X X X X from Miyajietal. (2015) shows the well known AGN down- expected the high mass end is dominated by luminous AGN Articlenumber,page9of15 A&Aproofs:manuscriptno.HGMF_Bongiorno (logL > 43[erg/s]),while the low mass bins are mainly pop- thetransientphasecorrespondstotheactivefeedback/blow-out X ulated by low luminosity objects (logL < 43[erg/s]) whose phase i.e. the gas depletion time-scale associated with the out- X contribution above log(M /M ) 11 is negligible. Our defini- flow. Current observations suggest this time-scale to be of the ⋆ tion threshold of logL /M >⊙ 3∼2 directly excludes any AGN orderof1 10 107yr(Maiolinoetal.2007;Feruglioetal.2010; X ⋆ withlogL <43[erg/s]aboveM >1011M .Thisalsoimplies Ciconeet−al.2×014).Finally,sSFR(M ,z)istheevolvingspecific X ⋆ ⋆ thatwhenapplyinganAGNdefinitionbyalu⊙minositythreshold, starformationrate.Hereweconsidertherecentmeasurementof asusuallydone,youwilltendtofindanactivefractionincreas- thesSFRfromLillyetal.(2013,eq.(2)): ingwith mass, consistentwith previouswork(e.g.Bundyetal. 2008;Xueetal.2010;Airdetal.2012;Silvermanetal.2009). Inthelowerpanels,weinsteadshowthetotalAGNHGMFin sSFR(M,z)=0.07 M⋆ β(1+z)3Gyr 1 forz<2 λSAR binsi.e., logλSAR> 32.5[erg/s/M ] (magenta),logλSAR> 1010.5M ! − 33[erg/s/M ] (cyan), logλ > 33.5[e⊙rg/s/M ] (green), and ⊙ logλSAR> 34⊙[erg/s/M ] (rSeAdR). Overall, the ma⊙ss distributions sSFR(M,z)=0.30 M⋆ β(1+z)5/3Gyr−1 forz>2 ofAGNofdifferentspe⊙cificaccretionratehaveasimilarshape, 1010.5M ! ⊙ only mildly affected by the M dependence in our SARDF ⋆ model. (17) withβ 0.1. 4. Themassfunctionofgalaxiesintheprocessof ∼− Starting from the star-forminggalaxymass function (green beingmass-quenched line in Fig. 7), we then derive, using the above equations, the According to the model described in Pengetal. (2010), the predicted mass function of the transient, i.e. “in the process of quenchingprocess,i.e.theprocesswhichleadstothetransition being mass-quenched”, population. Given the uncertainties on from star-forming to passive galaxies, independentof its phys- thevalueofτtrans weshowinFig.7thepredictionsforarange ical origin, can be describedby two differentmodes:mass and of τtrans = 1 10 107; the blue solid line is for τ = 5 107 environment quenching, whose differential effects on the frac- whiletheblue−dash×edlinescorrespondto1 107yrand1 ×108yr × × tionofpassive/redgalaxiesareseparable. (lowerandupperboundary,respectively). In Pengetal. (2010) paper, it is speculated that the envi- To test whether AGN can be responsible for the mass- ronment quenching occur in satellite galaxies, while the mass quenching of galaxies, we chose to restrict our analysis to the quenching could reflect a feedback mechanism related to star- mostluminousobjects.Theoryindeedpredictsthatthecapabil- formation or AGN. In a subsequent paper, Pengetal. (2012) ity of AGN outflows of perturbing the ISM depends on AGN confirmtheexpectationontheenvironmentquenchingasdueto luminosityasL1/2(Mencietal.2008)andthatgalaxy-scaleout- Bol satellitegalaxies,studyingthemassfunctionofcentralandsatel- flowsareenergy-driven,i.e.,theirmechanicalenergyispropor- lite galaxies.Herewe wantto testwhetherthemassquenching tionaltotheAGNluminosity(Zubovas&King2012).Thissce- processcanbelinkedtoAGNfeedback. narioissupportedbyobservationsthatfindthatthemomentum The strength of the Pengetal. (2010) approach is that this rateofkpc-scaleoutflows(Sturmetal.2011;Ciconeetal.2014; phenomenological model is based on simple observational in- Feruglioetal. 2015) is 10 20L /c, i.e. the more lumi- Bol ≥ − puts, which allow one to successfully reproduce many of the noustheAGNis,themorepowerfuloutflowsareproduced.This features of the galaxy population. Moreover,the model is able meansthattheAGN-drivenfeedbackmechanismshouldbecome togiveaclearpredictionforthemassfunctionofthegalaxiesin increasingly more efficient in halting the star-formation in the the process of being mass-quenchedand the inter-relationships hostgalaxyforhigherAGNluminosities. between the Schechter parametersfor star-formingand passive In Fig. 7 we compare the prediction for the mass function galaxies. of mass quenchingtransient objects with the HGMF of the to- The mass function of the transient population can be de- talpopulation,i.e.logλ > 32,andofdifferentsub-samples. SAR scribedbyasingleSchechterfunctionwithparameters(seeeq. We test the agreement using sub-samples applying in addition (28)ofPengetal.2010): different cuts on either L or λ , as shown in Fig. 6. We X SAR do not consider more complicated cuts or for example a lumi- M =M ∗⋆,trans ∗⋆,blue nositydependenttransitiontime-scale,whichcouldimprovethe αs,trans =αs,blue+(1+β) agreementbetweenthetwomassfunctions,inordertokeepthe Φ =Φ sSFR(M ,z) τ comparisonas simple as possible.We find thatthe class of ob- ∗trans ∗blue ⋆ |M∗ trans (16) jects that best reproduces, in terms of both shape and normal- where M⋆∗,blue, αs,blue and Φ∗blue are the parameters of the ization,theexpectedmassfunctionare:logLX >43.8+00..43[erg/s] Schechter function which describes the star-forming galaxy (red solid line and yellow shaded area) at 0.3 < z <− 0.8, and mass function and β is the exponent in the power law relation logL > 44 0.5[erg/s]at0.8 < z < 2.5.Reducingthethresh- X ± that links the specific star formation rate (sSFR) and the stel- old in L leads to a space density in the HGMF higher than X lar mass (see Eq. 17). Here we use the data for star-forming theexpectedforthe"transient"objectsatthelowmassend.On galaxiesfromIlbertetal. (2013),andforcethefitwitha single the contrary, specific accretion rate based sub-samples do not Schechterfunction.Thisparametricchoiceisrequiredtousethe seemtoreproducetheexpectedmassfunctionparticularlywell. modelfitsprovidedbyPengetal.(2010)withasingleSchechter Thisisbecause,withinthePengetal.(2010)model,fora con- functionas starting MF. Thisintroducessome uncertaintieses- stant τ , the fractionaldensity of the "transition" population trans pecially with respect to slope of the high-mass end, which is stronglydecreasesatlowmasses:onlyveryfewlow-massgalax- themostdifficultpartofthestellarMFtobeconstrained,aswe iesexperiencequenchingatanyredshift.Ontheotherhand,the will point out later in this section. The value τ is the pe- poluationofAGNaboveanygivenλ thresholdincreasesto- trans SAR riod of time the “transient” signatureis visible, and is notcon- wardslowstellarmasses(seethebottompanelofFig.6):rapidly strained by the Pengetal. (2010) model. Here, we assume that growinghighEddingtonratioobjectscanbefoundingalaxiesof Articlenumber,page10of15

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