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