第2回銀河進化研究会 2015年6月4-6日 名古屋大学 Connection between dark matter and star-forming galaxies at z~1.6 in COSMOS 柏野 大地|名古屋大学 J. SilvermanIPMU; S. MoreIPMU; COSMOS team Motivation In what environment were galaxies formed at the peak epoch?! What is their fate? The epoch z=1-3 is a peak era of the cosmic star formation history, the bulk of galaxy’s stellar mass were formed through active star formation. ! Galaxy clustering: A powerful method to study the connection between galaxies and their host dark matter halos. Bolshoi simulation FMOS-COSMOS survey Redshift Near-IR spectroscopy at z 1.6 Mapping galaxy 3D distribution More than 1100 spec-z beyond z>1 Small scales traced by multiple exp. Wide range of the MS (SFR≳10M yr1) mapped by long exp. ( 4-5hrs) Preliminary Comoving distance [h-1Mpc] Preliminary 44 h M1 ¼ 4:74 " 1013 h#1 M$ and varying values of " (left) and with " ¼ 0:89 and varying rve) and the one-halo contribution (lower curve). The dotted curve shows the two-halo entical in the other models. In all models, the parameter Mmin is adjusted to keep the space and equation (XX) can be written as 1h 2h Pgg (k) = Pgg (k) + Pgg and equation (XX) can be written as and equation (XX) can be written as ww g ga 1h 2h Our follow the (10) analytical(Z (k)==PP1hgg (k)+calculations +PP2hgg(k) (k) PPgggg(k) (k) (10) (Z ggBosch et gg al. (2013), which uses the ha li n of closely tracks the predictions of semianalytic models and SPH lim Tinker et framework al. (2008),inwhich defines a⟨N Ourcalculations calculationsfollow followthe theanalytical analytical vanden den he fit simulations (Kauffman et al. 1999; Benson et al. 2000; Seljak Our framework in van ⟨N ハローモデルは観測をよく記述する collapsed region with an average dens Scoccimarro et al. 2001;as Berlind et al. 2003) in which theBosch et al. (2013), which nthat(XX)2000; can be written where M is a halo mass above w uses the halo mass function from min sa Bosch et al. (2013), which uses the halo mass function from sa 0:93. width climbs steadily from nearest-integer at hN i % 1 toTinker et al. (2008), which then the this background matter density ofe defines halotransition as aa spherically spherically and is smoo et al. (2008), galaxy which defines aa halo as o the Poisson at high N, with the transition halfway complete Tinker at em large-scale halo bias of Tinker et al. (2 collapsed region with an average density 200 times greater 1h 2h su the hN i % 4. We again find that we can fit the data nearly as well collapsed(10) region with(Zhen an average density 200 timesWhen greater we su P (k) = P (k) + P (k) et al. 2007). c gg gg slight changes to thethen the background matter density its empirical dependence 1:9). as with our baselinegg model, with only ofthe thescale Universe, andthe theof Tinkc then the background matter density of Universe, and oints hN iM parameters. We are also able to fit wp ðrp Þ well using thelarge-scale halo bias of modified at small scale (den and Bosch etce limited sample of galaxies, it is Tinker et al. (2010, for ∆ = 200) car large-scale halo bias of Tinker et al. (2010, for ∆ = 200) and one co The one-halo is expressed as to a itsempirical empirical scaledependence dependence ofTinker Tinker al.term (2005) that tions follow the analytical framework in van denscale h#1 ⟨Ncen |M⟩ goes to 1 at high halo its of etetal. (2005) that isis mas to from central-satellite and from satellite data. modified at small scale (den Bosch et al. 2013). a modified at small scale (den Bosch et al. 2013). as from 2(2013), which uses the halo mass function sample considered in this study is r ! ¼ by theas same halos as The one-halo term is expressed a sum of contributions The one-halo term is expressed as a sum of contributions .hese (2008), which defines a halo as a spherically ! pairs fromcentral-satellite central-satelliteand andfrom fromsatellite-satellite satellite-satellite pairshosted hosted emission line, i.e.,1 highly star-form n at from dn bythe the samehalos halosas as sumptionP1hthat 33 & gion with an average density 200 times greater dM (M, z) by same alln¯2 massive halos h gg (k, z) = f we dM ! g セントラル銀河とサテライト銀河 ra ! ckground matter density of the Universe, and the data " central galaxy clearly does not hol 1 dn ra 1h 1 dn (M, z) in a 1h P (k, z) = dM th gg 2 |M⟩ ⟨N |M⟩ ⟨N P (k, z) = dM (M, z) ⟨N u(k, M, z) + 2 th halo bias of Tinker et al. (2010, for ∆ = 200) and cen sat s gg ¯ n dM completeness, we introduce an add ock2g ¯ n dM in (11) g in #(11) we # l,icity scale dependence of Tinker et al. (2005)""2that is 2 tor f . Although the f should de te 2 inc inc 2 te 2 |M⟩ ⟨N |M⟩ ⟨N |M⟩ M, z) ⟨N u(k, M, z) + u (k, ¯ where n is the mean number density of cen|M⟩ ⟨N sat|M⟩ u(k, M, z) + ⟨N sat|M⟩ u (k, M, z) g sat 2 ⟨Ncen our sat th small scale (den Bosch et al. 2013). assume a constant value for it beca th ered, dn/dM is the halo mass function, ulti(0 サテライト銀河同士 (0 paradenote the HOD, i.e, the average numbe halo term is expressed as a sum of contributions wheren¯n¯gisisthe themean meannumber numberdensity densityof ofgalaxies galaxiesbeing beingconsidconsidwhere to g and to lite galaxies hosted by a halo of mass ered, dn/dM is the halo mass function, ⟨N |M⟩ and ⟨N |M⟩ cen sat l-satellite and from satellite-satellite pairs hostedis the halo mass function, Stellar-to-halo ered, dn/dM ⟨Ncen4.2. |M⟩ and ⟨Nsat |M⟩ at a fo fo 6 3 we assume that the occupation numbers denote the HOD, i.e, the average numbers of central and satelh denote the HOD, i.e, the average numbers of central and satelhalos as are independent, so that ⟨Ncen Nsa litegalaxies galaxiesSatellite hostedby byaaStellar-to-halo halolites ofmass mass M,respectively. respectively. Here mass ratio (SHMR lite hosted halo of M, Here que, that theCentral number of satellite galaxies of a weassume assumethat thatthe theoccupation occupation numbers ofcentrals centrals andsatelsatel! we numbers of and r the ratio of the stellar mass of a central statistics, which is supported both 1 dn lites are independent, so that ⟨N N ⟩ = ⟨N ⟩ ⟨N ⟩, and cenN sat⟩ = ⟨N cen⟩ ⟨N sat⟩, and by ob strilites are independent, so that ⟨Ncen sat cen sat dM (M, z) 2008) and by numerical simulations (K the host halo, encode the efficiency e= the that the number of satellite galaxies of a halo follows Poisson 2 that the number of satellite galaxies of a halo follows Poisson 0 or n ¯g Fig. 3.—Projected dM correlation function statistics,(11) whichisissupported supported both by observations (Yang etal. al.of the for theet M0:1r < #21 sample, Given this assumption, the equation SDSS; al. 2004 into stars towards the amount statistics, which both by observations (Yang et get together with that for the best-fit HOD model, with parameters " ¼ 0:89, #andby 2008)and by numerical numerical simulations simulations (Kravtsov et al. al.that 2004). holds. We also assume number den but M1 ¼ 4:74 " 1013 h#1 M$ , and Mmin ¼ 6:10 " 1012 h#1 M$ . The reduced 2008) (Kravtsov et 2004). 2 ter into the host halos. Behroozi 2 !2 for this two-parameter fit is !2 =dof ¼ 0:93, while the reduced2!2 for the and ⟨N ies follows an NFW (Navarro et al. 1 2 |M⟩ |M⟩ ⟨N |M⟩ M, z) u(k, M, z) + u (k, Given this assumption, the equation ⟨N N − 1⟩ = ⟨N ⟩ 2 sat sat sat sat fit shown by the solid line in Fig. 1sat power-law is ! =dof ¼ 6:12. The lower Given this assumption, the equation ⟨N N − 1⟩ = ⟨N ⟩ sat sat sat pairs the mass relations a halo center, with the mass-concentrati panel shows the data and model prediction divided by this best-fit power law. holds.We Wealso alsoassume assume thatstellar-to-halo number density ofsatellite satellite galaxpenholds. that number density of galax- 射影相関関数 Galaxy clustering Our galaxy sample Parent sample (SED-selected): #3567! KAB<23.5 Mstar>109.8Msun Predicted f(Ha)>4e−17 erg/s/cm2! Observed galaxies: #1284! Spec-z sample: #551 15% of parent sample for clustering analysis Measuring correlation function Projected correlation function! 銀河の固有速度の影響を最小化する。 ! ! ! Landy & Szalay's (1983) estimator: ! ! Two difficulties • OH airglow and masks on radial selection • The fiber-allocation system of FMOS Effects of OH airglow and masks on radial selection: Weight function taking into account the OH line positions constructed by noise spectra Data Random FMOS noise spectrum Redshift Effects of the fiber-allocation system of FMOS causing suppression of finding close pairs and nasty clusterings on the 2D distribution + ◇◇ Fiber home positions Allocated fibers (for dummy positions) ● Observed galaxies (dummy positions) ◆ Out-of-order Fibers for guide stars ● ■ Correction with angular correlation — weighting “DD” terms Parent sample Observed sample Parent Observed Validity check by mocks! from Bolshoi simulation sub-halo catalog Results Evolution of correlation length A. Durkalec et al.: The evolution of clustering length, bias and halo mass at 2<z<5 14 1014 This work ★ VUDS Limited in luminosity EROs BzK LBGs 10 20 15 1310 13 -1Mpc] r0 [h r0 [h-1 Mpc] 10 10 { Preliminary VUDS 5 ★ ★ 12 10 0 1 Mhalo= 12 110011 ★ 11 1010 1010 0 0 1 2 3 4 5 redshift z Redshift z Fig. 5. Correlation length r as a function of redshift from various surveys of different types of objects. Black stars indicate the measurements obtained from this work in three redshift ranges.Durkalec Different colours indicateet different populations targeted al.galaxy 2014 by using various techniques, as indicated in the upper right corner. Open symbols indicate measurements based on photometric 0 Error estimate from Jackknife data, while filled symbols are for measurements from spectroscopic data. Blue: LBG galaxies (Foucaud et al. 2003, Ouchi et al. 2004, Adelberger et al. 2005, Kashikawa et al. 2006, Savoy et al. 2011, Bielby et al. 2013, Barone-Nugent et al. 2014). Orange: BzK galaxies (Blanc et al. 2008, Hartley et al. 2010, McCracken et al. 2010, Lin et al. 2012). Green: Galaxy samples from surveys limited in luminosity (Norberg et al. 2002, Coil et al. 2006, Le F`evre et al. 2005, Pollo et al. 2006, Zehavi et al. 2011, Marulli et al. 2013, Skibba et al. 2009). Red: EROs or massive red galaxies (Daddi et al. 2003, Zehavi et al. 2005a, Brown et al. 2008). The five solid curves show the correlation length of dark halos with different minimum masses, as labelled. larly in z=[2,2.9] where it is an excellent representation of the data. For the highest redshift bin z=[2.9,5] the fit is not as good. This is mainly due to the more noisy measurement of the correlation function in this redshift range. The three HOD parameters, the minimum halo mass Mmin , the satellite occupation halo mass M , and the high halo mass Mmin , has comparable value for the z ∼ 2.5 and z ∼ 3.5 samples. The satellite occupation mass M1 is noticeably higher in the higher redshift bin compared to the lower redshift sample, although the errors are quite large. These uncertainties are related to the weak one-halo term signal in the correlation function for the higher redshift measurement. + ⟨Nsat |M1 ⟩ ⟨Nsat |M2 ⟩ u(k, M1 , z)u(k, M2 , z) Phh (k|M1 , M2 , z) where Phh (k|M1 , M2 , z) describes the power-spectrum (12)of halos of masses M1 and M2 , which is calculated from the nonlinearPhh matter (Smith et al. 2003) andofthe where (k|M1power , M2 , z)spectra describes the power-spectrum ha-scaledependent halo bias also is accounts for from the halo los of masses M M2and , which calculated the exclusion non1 and (see van den Bosch et al.(Smith 2013).et al. 2003) and the scalelinear matter power spectra Nowhalo we bias parametrize halo occupation dependent and alsothe accounts for the halodistribution exclusion for (seeour vanstudy den Bosch al.emitting 2013). galaxies. The mean distribution using et Hα Halo occupation distribution! Now wenumber parametrize the halo occupation for of the of central galaxies is givendistribution by ' distribution our study using Hα emitting &galaxies. The mean ( ) *+ 2 ! 1 log(M/Mmin ) of the number of central galaxieslog(M/M is given min by) ⟨Ncen |M⟩ = Fg (1−Fs ) exp − +F 1 + erf s 2 & ' σlog M*+ 2σlog ( 2 ) 2M ! log(M/Mmin ) 1 log(M/M min ) (13) High mass comp. ⟨Ncen |M⟩ = Fg (1−Fs ) exp − +Fs 1 + erf Gaussian comp. 2 σlog M above has a central log Mwhich the2halo !where Mmin is a halo mass 2σ (smoothed step function) galaxy and this transition is smoothed by the scatter (13)σlog M *+ ) a * we consider complete massα Geach+12; GALFORM !(Zhen et al.1 (2007).) When log(M/Mmin ) M limited ⟨Nsat |M⟩sample = 1 +oferfgalaxies, it is reasonable to assume (14) that 2 σlog M M1 HOD modeling ! MCMC fitting! To avoid overfitting, some parameters are fixed: Fg=0.6, Fs=0.1, σlogM=0.6, α=1 Only two free parameters: Mmin, M1 +0.2 logMmin=12.50 −0.15 +0.47 logM1=12.50 −0.24 HOD modeling logM1/Msun Preliminary Preliminary logMmin/Msun Fate of z 1.6 star-forming galaxies A. Durkalec et al.: The evolution of clustering length, bias and halo mass at 2<z<5 Log <Mh> [h-1 Msun] 15 Kim et al. (2013) Blake et al. (2008) Wake et al. (2008) Sawangwit et al. (2011) Abbas et al. (2010) Coupon et al. (2012) Zehavi et al. (2011) Bielby et al. (2010) This work VUDS 14 13 12 <Mh>=(3.2 1.5) 1012 h1Msun Galaxy bias: beff=2.1 0.2 11 0 1 2 redshift z 3 Durkalec et al. 2014 4 Fig. 7. The evolution of the number-weighted average host halo mass given by Eq. 10 for the three redshift ranges analysed in this study. The red filled circles indicate mass estimations from VUDS. Black and grey symbols represent the results of previous work based on spectroscopic and photometric surveys respectively. The solid black lines indicate how a host halo of a given mass M0 at z = 0 evolves with redshift, according to the model given by van den Bosch (2002). The solid red line represents the halo mass evolution derived using Eq. 21, with the HOD parameters obtained from the best-fit HOD model at a redshift z ∼ 3. The dashed red line is using the HOD best-fit parameters for z ∼ 2.5. VUDS galaxies with a typical L⋆ luminosity are likely to evolve Summary 551個のFMOS spec-z 星形成銀河の射影相関関数を測定した! ✓ ファイバー観測による影響を補正 ✓ N-bodyモックカタログにより妥当性を検証 rp~0.2-1 h−1Mpc に優位な1-halo termを検出 相関長 r0=5 h−1Mpc ▶︎ Mhalo~1012.5 h−1Msun at z~1.6 HODモデルでフィットし、average halo mass (=3.2x1012 h−1Msun), effective galaxy bias (b=2.1) を推定 ✓ ハロー質量進化トラックに載せると、z=0で LogMhalo/h−1Msun~13.5-14 ✓ HODモデルの検証の必要あり
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