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 matterand 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 thecosmic star formation history, thebulk of galaxy’s stellar mass wereformed through active star formation.
!
Galaxy clustering:
A powerful method to study theconnection between galaxies andtheir 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

44h M1 ¼ 4:74 " 1013 h#1 M$ and varying values of " (left) and with " ¼ 0:89 and varyingrve) and the one-halo contribution (lower curve). The dotted curve shows the two-haloentical in the other models. In all models, the parameter Mmin is adjusted to keep the spaceand equation (XX) can be written as

1h2h
Pgg (k) = Pgg(k) + Pgg
andequation(XX)
canbewrittenasand equation (XX) can be written as
wwgga
1h
2h
Our
follow the (10)analytical(Z(k)==PP1hgg(k)+calculations+PP2hgg(k)(k)PPgggg(k)(k)(10)(ZggBosch etgg al. (2013), which uses the halin ofclosely tracks the predictions of semianalytic models and SPH
lim
Tinker et frameworkal. (2008),inwhich
defines a⟨N
Ourcalculationscalculationsfollow
followthe
theanalyticalanalyticalvandenden
he fitsimulations (Kauffman et al. 1999; Benson et al. 2000; Seljak
Ourframeworkinvan⟨N
ハローモデルは観測をよく記述する
collapsedregionwithan averagedens
Scoccimarro
et al. 2001;asBerlind et al. 2003) in which theBosch et al. (2013), which
nthat(XX)2000;
canbe written
whereMisahalo
mass
above
w
uses
thehalomassfunction
from
min
sa
Bosch
etal.
(2013),
which
uses
thehalomassfunction
from
sa
0:93.
width climbs steadily from nearest-integer at hN i % 1 toTinker et al. (2008), which then
the thisbackgroundmatter density
ofedefines
halotransition
as aa sphericallyspherically
andissmoo
et al. (2008), galaxy
which defines
aa halo
aso thePoisson at high N, with the transition halfway complete Tinker
atemlarge-scalehalobiasofTinker
etal.
(2collapsed
regionwithanaveragedensity
200times
greater
1h2hsuthehN i % 4. We again find that we can fit the data nearly as wellcollapsed(10)region with(Zhenan averagedensity
200 timesWhen
greater we su
P(k)=P(k)+P(k)etal.
2007).
cgg
gg slight changes to thethen the background matter density
its empiricaldependence
1:9).
as with our baselinegg
model, with only
ofthe
thescale
Universe,andthe
theof Tinkc
thenthebackgroundmatterdensityofUniverse,
andoints
hN iM parameters. We are also able to fit wp ðrp Þ well using thelarge-scale halo bias ofmodified
at smallscale(den andBosch
etce
limitedsampleofgalaxies,
itis
Tinkeretal.
(2010,for∆=200)
carlarge-scale halo bias of Tinker et al. (2010, for ∆ = 200) andonecoThe
one-halois expressed
as toaitsempiricalempirical
scaledependence
dependenceofTinker
Tinkeral.term(2005)
thattions
follow the analytical framework invan
denscaleh#1⟨Ncen |M⟩
goes
to1
at
highhaloitsofetetal.
(2005)
thatisis mastofrom central-satellite
and from satellite
data.
modifiedatsmallscale(denBoschetal.
2013).
amodifiedatsmallscale(denBoschetal.
2013).
asfrom2(2013), which uses the halo mass function
sampleconsideredinthisstudy
isr! ¼by theassamehalos
asThe
one-haloterm
isexpressedasumofcontributions
The one-halo term is expressed as a sum of contributions.hese(2008),
which
definesahalo
asaspherically! pairs
fromcentral-satellite
central-satelliteand
andfrom
fromsatellite-satellite
satellite-satellite
pairshosted
hostedemissionline, i.e.,1 highly
star-formn atfromdnbythethesamehalos
halosasas sumptionP1hthat
33&gionwithanaveragedensity200
times
greaterdM(M,z)
by
samealln̄2 massive
halos
hgg (k, z) =f wedM!
g
セントラル銀河とサテライト銀河
ra!
ckgroundmatter density of the Universe, andthedata"
centralgalaxyclearly
does
nothol1dnra
1h1dn (M, z)
in a1hP(k,z)
=dM
thgg
2|M⟩
⟨N|M⟩
⟨NP(k,z)=dM(M,z)⟨Nu(k,M,z)+2thhalobias
ofTinkeretal.
(2010,for∆=200)
andcensatsggn̄dM
completeness,
weintroduce
anadd
ock2gn̄dMin(11)
gin#(11)
we#l,icity
scale dependence of Tinker et al. (2005)""2thatis2
torf.
Althoughthefshould
dete2incinc
2te2|M⟩⟨N|M⟩⟨N|M⟩M,z)⟨Nu(k,M,z)+u(k,wheren̄
isthemeannumberdensityofcen|M⟩ ⟨N sat|M⟩ u(k, M, z) + ⟨N
sat|M⟩ u (k, M, z)g sat
2 ⟨Ncenoursat
th
small
scale
(denBoschetal.
2013).
assumeaconstant
value
for
it
beca
th
ered,
dn/dM
is
the
halo
mass
function,ulti(0サテライト銀河同士(0paradenote
theHOD,i.e,
theaveragenumbe
halo
term is expressed as a sum of contributions
wheren̄n̄gisisthe
themeanmeannumber
numberdensity
densityof
ofgalaxies
galaxiesbeingbeingconsidconsidwheretogandtolitegalaxies
hostedbyahalo
ofmass
ered,
dn/dM
is
thehalomassfunction,
⟨N
|M⟩
and
⟨N|M⟩
censatl-satellite
and from satellite-satellite pairs
hostedis the halo mass function,
Stellar-to-haloered, dn/dM⟨Ncen4.2.
|M⟩ and⟨Nsat |M⟩at afofo
6 3
we
assumethat
theoccupation
numbers
denotetheHOD,i.e,theaverage
numbers
ofcentralandsatelhdenote the HOD, i.e, the average numbers of central and satelhalos
asare independent,
sothat⟨Ncen Nsa
litegalaxies
galaxiesSatellite
hostedby
byaaStellar-to-halo
halolites
ofmassmass
M,respectively.
respectively.
Here
mass
ratio
(SHMR
litehosted
haloofM,
Here
que,
that
theCentral
numberof satellite
galaxies of a
weassume
assumethat
thatthetheoccupation
occupation
numbers
ofcentrals
centrals
andsatelsatel!
we
numbers
ofand
r theratioofthestellarmass
ofa
centralstatistics,
which
issupported
both
1dn
lites
are
independent,
sothat⟨NN⟩=⟨N⟩⟨N⟩,
andcenN sat⟩ = ⟨N cen⟩ ⟨N sat⟩, and by ob
strilites are independent, so that ⟨Ncen
satcensatdM(M,z)
2008)
andby
numerical
simulations(Kthehosthalo,
encodetheefficiencye=thethatthenumberofsatellite
galaxiesof
ahalo
follows
Poisson2
that
thenumberofsatellite
galaxiesofahalo
follows
Poisson0 or n̄dMstatistics,(11)whichisissupported
supported
bothbyobservations
(Yang
etal.
al.of theFig. 3.—Projected correlation function
for theet
M0:1r
< #21
sample,gGiventhisassumption,
theequation
SDSS;
al.
2004
intostars
towards
theamountstatistics,
which
bothbyobservations(Yangetgettogether with that for the best-fit HOD model, with parameters " ¼ 0:89,#andby
2008)andby numericalnumerical simulations
simulations(Kravtsovet al.
al.that2004).
holds. We
also assume
number denbut
M1 ¼ 4:74 " 1013 h#1 M$ , and Mmin ¼ 6:10 " 1012 h#1 M$ . The reduced2008)(Kravtsovet2004).
2ter
intothehosthalos.
Behroozi
2!2 for this two-parameter fit is !2 =dof ¼ 0:93, while the reduced2!2 for theand ⟨N
iesfollows
anNFW(Navarroet al. 12|M⟩|M⟩⟨N|M⟩M,z)u(k,M,z)+u(k,Giventhisassumption,
theequation⟨NN−1⟩
=
⟨N
⟩
2
sat
sat
sat
sat fit shown by the solid line in Fig. 1sat
power-lawis ! =dof ¼ 6:12. The lower
Given this assumption,
theequation⟨NN−1⟩
=
⟨N
⟩
sat
sat
sat
pairs
themassrelations
ahalo center,withthe mass-concentrati
panel shows the data and model prediction divided by this best-fit power law.
holds.We
Wealsoalsoassume
assumethatstellar-to-halo
numberdensityofsatellite
satellite
galaxpenholds.
thatnumberdensityofgalax-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
DataRandom

FMOS noise spectrum

RedshiftEffects of the fiber-allocation system of FMOS
causing suppression of finding close pairs andnasty 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

ParentObserved

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<5141014

This work ★
VUDS
Limited in luminosity
EROs
BzK
LBGs

1020151310

13-1Mpc]
r0 [hr0 [h-1Mpc]

1010{PreliminaryVUDS

5★ ★

121001
Mhalo=12110011★

111010

1010

00123

4

5

redshift z
Redshiftz
Fig. 5. Correlation length r as a function of redshift from various surveys of diﬀerent types of objects. Black stars indicate themeasurements obtained from this work in three redshift ranges.Durkalec
Diﬀerent colours indicateet
diﬀerent
populations targetedal.galaxy
2014
by using various techniques, as indicated in the upper right corner. Open symbols indicate measurements based on photometric
0Error 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 fromsurveys limited in luminosity (Norberg et al. 2002, Coil et al. 2006, Le Fèvre 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 thedata. 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 thehigher 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 forthe 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 nonlinearPhhmatter(Smithet al. 2003) andofthewhere(k|M1power, M2 , z)spectra
describes
the power-spectrum
ha-scaledependent
halobiasalso isaccounts
for from
the halolos ofmasses M
M2and, whichcalculated
the exclusion
non1 and(seevan denBoschet al.(Smith2013).et al. 2003) and the scalelinear
matterpower
spectraNowhalo
we biasparametrize
halo occupation
dependent
and alsotheaccounts
for the halodistribution
exclusion for(seeourvanstudy
den Boschal.emitting2013). galaxies. The mean distribution
using etHαHalooccupation
distribution!
Nowwenumberparametrize
the halooccupation
forof theof central
galaxies
is givendistribution
by' distribution
our study using Hα emitting &galaxies. The mean()*+2!
1log(M/Mmin )of the number of central galaxieslog(M/Mis given minby)⟨Ncen |M⟩ = Fg (1−Fs ) exp −+F
1+erf
s2&'σlog M*+2σlog
( 2 )
2M!
log(M/Mmin )1log(M/Mmin )(13)
Highmasscomp.
⟨Ncen |M⟩ = Fg (1−Fs ) exp−+Fs 1 + erf
Gaussiancomp.
2σlog Mabove
has a central
log Mwhich the2halo!where Mmin is a halo mass 2σ(smoothedstep function)
galaxy and this transition is smoothed by the scatter(13)σlog M*+ ) a *we consider
completemassαGeach+12; GALFORM!(Zhen et al.1 (2007).) Whenlog(M/Mmin )M
limited⟨Nsat |M⟩sample=1 +oferfgalaxies, it is reasonable to assume(14) that
2σlog 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 modelinglogM1/Msun

Preliminary

Preliminary

logMmin/MsunFate of z~1.6 star-forming galaxies
A. Durkalec et al.: The evolution of clustering length, bias and halo mass at 2<z<5Log <Mh> [h-1 Msun]

15Kim 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

141312<Mh>=(3.2 1.5) 1012 h­1Msun
Galaxy bias: beﬀ=2.1 0.2

11012
redshift z3Durkalec et al. 2014

4Fig. 7. The evolution of the number-weighted average host halo mass given by Eq. 10 for the three redshift ranges analysed inthis 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 halomass 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 (=3.2x1012h−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