準解析的銀河形成モデルからBHへの質量降着機構に与えられる制限
白方 光 (北海道大学 M２)- 共同研究者 川勝 望 (呉高専), 和田 桂一 (鹿児島大), 榎 基宏 (東京経済大),岡本 崇 (北海道大), 長島 雅裕 (文教大), 他 ν2GC グループメンバー
AGN銀河の中心1kpc → 1pcスケールでの質量降着機構の理解に向けて @ NAOJ, 2015.12.21 - 22

Semi Analytic (SA)galaxy formation model•

dark haloの形成・進化… N体シミュレーションで与える•

銀河形成・星形成・SMBH成長はモデル化( 解析解, シミュレーションや観測結果の応用)•

cosmological simulationより大きな計算体積,少ない計算時間•個数密度の小さな天体の統計的研究には特に有用※ 長島 雅裕さん (文教大) のスライドより拝借

Semi Analytic (SA)galaxy formation model
Hot gasStandard disk starformation

Cold gasνGC: Nagashima+ 05, ApJ, 634, 26

No. 1, 2009

MOLECULAR GAS DISK STRUCTURES AROUND AGNs

69

(a)

Revealing AGN mechanism
SA modelThe Astrophysical Journal, 794:69 (8pp), 2014 October 10

Next, we consider the light curve of AGNs. The accretionof cold gas during a starburst leads to AGN activity. Following
Kauffmann & Haehnelt (2000, 2002), we assume that a fixed
fraction of the rest mass energy of the accreted gas is radiatedin the B band, and we adopt the B-band luminosity of an AGN
at time t after a major merger as follows:

SA model + Subaru(b)

LB (t) =制限
The Astrophysical Journal, 811:39 (15pp), 2015 September 20

比較

Figure 5. Density distributions on x–y and x–z planes (a) in a high-resolution model H100a and (b) in a low resolution model L100a at t = 4.02 Myr.
(A color version of this figure is available in the online journal.)

Wada+ 09, ApJ, 702, 63

4.2. Effects of X-rays

Izumi+ 15, ApJ, 811, 39

molecular material. The main results of our observations andz > 3, being inconsistent with the downsizing scenario.
It Ris not obvious
what is causing this discrepancy.
3. The highHCN HCO+ and RHCN CS are only found in the
Masters
et al. (submitted to the ApJ) stated that

(5)

where ϵB is the radiative efficiency in the B band, tlife is the
AGN lifetime, and c is the speed of light. In our model,
we allow for super-Eddington accretion. We assume that tlife
scales with the dynamical timescale, tdyn , as expected if theradius of the accretion disk were to scale with the radiusof the host galaxy (Kauffmann & Haehnelt 2000). The AGN
lifetime, tlife , depends on the redshift of the major merger since
−1/2
−1/2
tlife ∝ tdyn ∝ ρgal ∝ ∆vir (z); ∆vir (z) is the ratio of thedark halo density at the redshift
7 of the major merger to thepresent critical density. In order to determine the parameter ϵBand the present AGN lifetime, tlife (z = 0), we chose them tomatch the estimated luminosity function in our model with theobserved B-band luminosity function of AGNs at z = 2. We
obtain ϵB = 0.0055 and tlife (z = 0) = 5.0 × 107 yr.
Some recent SA models include prescriptions for the radiomode AGN feedback. The radio-mode AGN feedback is dueto the radio jet, which is powered by hot gas accretion andinjects energy into hot gas. Since the radio-mode AGN feedback
is a mechanism to quench cooling of hot gas and preventstar formation in massive dark halos, the radio-mode AGN
feedback is expected to explain part of the downsizing evolutionof galaxies (e.g., Croton et al. 2006; Bower et al. 2006).
However, the detailed physics of hot gas heating is still unknown.
Moreover, the radio-mode AGN feedback helps to reproduce theobserved density of massive galaxies but has hardly any effects
on the space density of low-mass galaxies, which are affectedby supernova feedback. Our model does not implement theradio-mode AGN feedback. Instead we take a simple approachto suppress gas cooling as described in Section 2.1. The gas
cooling process is applied only to halos with circular velocity
Vcirc ! Vcut .

Izumi et al.

The strong X-ray continuum emanating from the AGN could
affect the chemical state of the ISM in the central region(Maloney et al. 1996; Meijerink et al. 2007). It is known that thechemical state of theFig.
X-ray
DissociatedRegionis mainly
8.— Constraints
on thefaint-end(XDR)
slope β andthe break∗
M1450. The shaded region shows the parameter spacedetermined by HXmagnitude/n,is where
X-ray1σheating
X is
that
consistentHwiththeainferredconfidence deposition
upper limits on
the quasar
space density
at zgas∼ 5 (Maloneyderived in our etstudy.
dot andrate and n is the number
densityof theal. A1996).
triangle are the results inferred at z ∼ 4 by Ikeda et al. (2011) and
Glikmanet al.the(2011),
respectively.
Notefromthat weestimatethe erAlthough we do notincludeeffectof
X-ray
thenucleus,∗rors of M1450
and the faint-end slope by applying a weighted leasthere we estimate its
potential
usingetoneof ourmodels.
squaresmethod effectwhile Glikmanal. (2011)
estimated
themInby
the STY
maximum-likelihood
methodas(Efstathiou
et al.
Figure 10, we plot applyingafractionofH
andtemperatureafunction
21988).
of HX /n (erg cm3 s−1 ) at randomly selected points in thecomputational box. Here, we assume that the X-ray luminosity
al. 2007),
we plot onlythere
the resultsof theof the AGN is LXBongiorno= 1044eterg
s−1 . Although
is a large
2dF-SDSS LRG and Quasar Survey (2SLAQ; Croom etscatter, for log(HXal.
/n)2009),≃ −24
or smaller,
the molecule
fraction
the Spitzer
Wide-area
Infrared Extragalactic
Legacyand
SurveySiana et2008),and SDSS
increases significantly
the(SWIRE;
temperatureinal.mostregionsiset al. 2006), in order to avoiddata
5−3 with large
less than 100 K. (Richards
Athigh-gasdensities
(∼10
cm
),
large
statistical errors. While most studies at z < 3 suggest(>0.1) H2 fractions
can besustained
therange ofthe
HXsitua/n
consistent
results(i.e., thefor
AGN
downsizing),
tionimpact
is rather ofcontroversial
at z > (Meijerink
3. Recently, thenewvalues, limiting the
XDR
effectsetal.
z ∼ 4 QLF results of the NOAO Deep Wide-Field Survey2007). This is partly
becausethefreeelectrons
associated
with(NDWFS) and the Deep Lens Survey (DLS) are reported
by Glikman
et al. H(2011).
Interestingly,
results
ionization processes
help to form
the H−the
route
andof
2 throughGlikman et al. (2011) suggest constant or higher numalso because H2 formation
scaleswithdensitysquared.
Still,
ber densities of low-luminosity QSOs at z > 3, whileforour−26
HX /n significantlyCOSMOS
larger result
than 10, gas
is mostly
atomicassuggestsa continuous
decreaseof these
Figure 6. Evolution of molecular gas fraction fH2 in high-resolution models
fromz ∼ 2 to z ∼ 5.
(H10a and H100a) and low resolution models (L10a, L100a and L100c)
expected (Maloneyobjects
etal.
1996).
Our result is consistent with the downsizing AGN
recalculating from the high-resolution runs at t = 2.5 Myr.
These results suggest
XDR chemistrychangedis-atevolutionthat
suggestedby previousmay
quasarsurveyslower-zanboth
in theopticaland X-ray(e.g., X-ray
Croom
tribution of H2 around
AGN,
if we
explicitly
includeet al. 2009; Ueda et al. 2003; Hasinger et al. 2005).
from the nucleus in
the following
sense.
The
H2rms
abundanceisa clumpy torus plus
a central thick disk model from mid-IR
et ∼2
al. kpc(2010)
the Thefaint
endof (1σ)the QLF
Figure 6. Integrated intensity maps of (a) CO(3–2), (b) HCN(4–3), (c) HCO+(4–3), and (d) CS(7–6), inWillott
the central
regionreportedof NGC 7469.
noises−1 has−1a Seyfert 2
indeedrobustinabut<isthegasobservations using areVLTIofCircinus,which
atclumpyzCO(3–2)∼ 6 medium,
although
a XDR
large
bar
for the0.20, 0.06, 0.06, and 0.06 Jy beam km s in (a)–(d), respectively. Note that we could not observe
emission at there
VLSR
4900
km s−1error
owingtemperato ourfaintest
magnitude
bincasebecauseone ofquasarwasobservational
the displayed
mapgeometry
is incompleteand(southeast partis deﬁcient).
molecularknots
are marked
as A–Fthe CO(3–2)
map forture
shouldSome
risebright
relativetothePDR
by ainonly
factor∼5
nucleus. Although thesize is setting;thus,
smaller (∼2pc), theThebeamsz ∼ 6(∼0space−22
is lower(positions A–D are the same as the ones marked in Figure 1(a)). The white ﬁlled ellipses indicate thefound.
synthesized
50 density
× 0 40). at
TheMcentral
signs
1450 ∼plus> −26(Meijerink
etlimital.70σ;2007).
all,
X-ray
ionstructures suggestedindicate
by theirhigh-resolution
observationsa 30σ, ...,log
the AGN
position. Contours are(a)−5σ, 3σ, 5σ, (see10σ, 20σ,
and H
130σ;(b)3σ, 5σ,10σ,the20σ,upper
30σ, ...,
and(c) −5σ,
10σ,density
20σ, 30σ,at
X /n −5σ,thanof ourz After
∼3σ,
5 5σ,
space
the
−25
−3 withand Figure
50σ; and (d)3σ, and5σ, respectively.
Negative contours areindicatedheatingby dashed withlines.
See
Section 2andforvelocity
rangesintegrated
same
magnitude
resultis alsoizationforalsoexampleHXthethis/n∼ 10
ergconsistent
cmover.
s−1 ,schematic picture in40σ,
their9) −5σ,is quitesimilarto the models
AGN downsizing evolution. However, the results
is more efficient thethanphotoelectric
emissiondust picture
grains,atpresented here.
of
Glikmanet al. (2011)
require a by
diﬀerent

ϵB Macc c2
exp(−t/tlife ),
tlife

相補的

• Although we discover the type-2 quasar at z ∼5.07, no type-1 quasars at z ∼ 5 are identified
through the follow-up spectroscopic observation.

10-8(M1450 )
-22
-23
-24
-25
0

1

2

z

3

4

5

The cold gas in a galaxy is depleted over time by star formation.
Moreover, the hot gas cooling process is suppressed in massive
dark halos. Therefore, the amount of the cold gas accreted onto
SMBH decreases with cosmic time. Figure 3 shows the redshift
evolution of the logarithmic mean of the ratio of cold gas mass
(Mcold ) to stellar mass (Mstar ) for galaxies with MB < −18. Thisshows that the mass fraction of cold gas mass in a galaxy decreases with time and that massive galaxies with massive black
holes have a smaller cold gas fraction than less massive galaxies with less massive black holes. Therefore, at low redshifts,
a major merger does not necessarily trigger a luminous AGN
because the luminosity of AGNs is proportional to the cold gas
mass of accreted onto SMBHs. As a result, the space densityof luminous AGNs decreases quickly. In addition, Enoki et al.
(2004) showed that at z " 1, a dominant process for the mass
growth of SMBHs is due to black hole coalescence and not due
to gas accretion, since the cold gas decreases with time.
As described in Section 2.2, we allow for super-Eddington
accretion. Although we do not calculate bolometric luminosity
Lbol , observational studies have indicated that Lbol is smaller
than 10LB . Therefore, adopting Lbol = 10LB , we can obtainthe upper limit of the number fraction of super-Eddington AGN(Lbol /LEdd > 1) from the B-band Eddington ratio (LB /LEdd ),which can be calculated in our model. As shown in Figure 4(a),the 90th percentiles of LB /LEdd is less than unity at z < 1 andlarger than unity at 1 < z < 4, which results in the fractionof the super-Eddington AGN of less than 10% at z < 1 and10 ∼ 15% at 1 < z < 4. The maximum values of LB /LEdd also
indicate that the maximum Eddington ratio is less than 10 atz < 1 and 10 ∼ 80 at 1 < z < 4. The median of the Eddington
ratios of AGNs and the fraction of high Eddington ratio AGNs
(log[LB /LEdd ] > −1) decrease with cosmic time. These results

Ikeda+ 12, ApJ, 756, 160

6. SUMMARY

10-7

Figure 2. Redshift evolution of the AGN space density. Orange, blue, red, andblack lines are space density of AGN with M1450 = −22, −23, −24, and −25,
respectively. Solid lines show model results. Symbols with error bars linearly
connected with dashed lines are observations: 2SLAQ and SDSS (circles; Croom
et al. 2009); GOODS (triangles; Fontanot et al. 2007); and COSMOS (filledsquares; Ikeda et al. 2011, 2012).
(A color version of this figure is available in the online journal.)

3. EVOLUTION OF AGN SPACE DENSITY

In order to examine the faint end of the QLF at z ∼ 5,
we select photometric candidates of quasars at z ∼ 5 in
the COSMOS field. The main results of this study are:

10-6

Enoki+ 14, ApJ, 794, 69

In Figure 2, we present the redshift evolution of AGN spacedensity.
Solidquasarlines areresultsof our SA model and symbols
Fig. 9.— The redshift evolutionof thespace
denwith lighterror bars
connected
sity.
Red, green, blue, magenta,
blue,linearlyorange,black, with dashed lines are resultsofobservations(Croometal.
2009;
purple lines are the space density of quasars with M1450 = Fontanot et al. 2007; Ikeda−20, −21, −22, −23, −24, −25, −26,
−27, 2012).
respectively.
et andal. 2011,
In orderFilled
to compare the model result withsquares, open circles, filled circle,observations,and open triangles
denotethewe convert
the absoluteB-band magnitude (MB )results of diﬀerent quasar surveys,into
as thedescribed
intheupper-leftabsolute AB magnitude at 1450 Å (M1450 ) using theside of the panel (see the main text for details). For the comparempirical relation given by Shen & Kelly (2012). Our SA
ison, the results of COSMOS and previous surveys are connectedmodel
can qualitatively
reproduce the downsizing trend of theby the dashed lines while the resultsof NDWFS& DLS (Glikman
AGN space
et al. 2011) are connected by the dottedlines.density evolution. While our model overproduces
the space density of faint AGNs (i.e., M1450 > −24) at z " 1, it
is consistent with the results of GOODS (Fontanot et al. 2007)
Consequently, we cannot explain
this discrepancy
due
to 2012) at z # 3.
and COSMOS(Ikeda et al.
2011,
the diﬀerence of the quasar selection
criteria.weTherefore
In the following,
will discuss the physical reasons responit remains important that wesible
searchlow-luminosity
for thefor
AGN
downsizing trend predicted by our SA model.
quasars at high redshift in otherfields andderivethe their mass through cold gas
In our model,
SMBHs
assemblefaint end of the QLF. We also
plotduring
the quasar
space and through the coalescenceaccretiona major mergerof the twofields
SMBHs
themselves. et
At high redshifts, since galaxies
density measured in the GOODS(Fontanot
generally
contain a larger
al. 2007) in Fig. 9, whichis consistent
withamountboth of cold gas, a large amount of
the
cold
gas
fuel
is
providedforresults from Glikman et al. (2011) and COSMOSbeing accreted onto a SMBH.

due to its large uncertainty. Further observations of
low-luminosity quasars in a wider survey area are crucial
to derive firm constraints on the scenarios of the quasar
evolution, especially at z > 4.

2SLAQ & SDSSCOSMOS
GOODS

10-5

Φ [ Mpc-3 mag-1]

Simulation + ALMA

Enoki et al.

4

AGN & SMBH model in
SA models•

SMBHへのガス降着トリガー- 銀河合体- 銀河disk 不安定・bar (optional)- haloのhot gasの直接降着 (optional)•~kpc → ~100-10 pc スケールへのガス降着- 特に何も考えない(バルジのガスの一部が即時的にSMBHに降着する)- 簡単にモデル化されたgas reservoirを経由

2.1
BHsectionaccretion
the next
we will mainly focus on a single aspect of MOR GANA
, namely
the modelling
BH theaccretion
and AGN
feedbackThe
model
for accretionof gasofonto
BH follows
Granatoet al.
(see
Monaco&Fontanot2005;
Fontanot
et
al.
2006,
for
a
complete(2004), and starts from the assumption that the main bottleneck isoverviewof thisgiven
by thelossapproach).
of angular momentum, necessary for the gas tomass of an unstable disc goes into the bulge component. C
Hopkins
Quataert(2011),
calibrated
results
flowing &into
the bulge
can thenaccreteononto
the from
BH asnumdesimulations.
In allcases,wewheneveran unstabledisc ofcontainabove. In what
follows
will discuss
the impact
varyi
gas,
a fractionof it will be made available to accrete onto th
on our
final results.
powering an AGN. In MORGANA, we assume that, when thebility criterion is met, a fixed fraction (fDI = 0.5) of the bar
2.2 of
AGN-triggered
winds
mass
an unstable discgoes into the bulge component. Co
flowing
into thecan
bulge
can thenaccreteamountonto theofBH
as desc
AGN activity
injecta relevantenergyi
above.
In
what
follows
we
will
discusstheimpactofvaryininter-stellar medium, favouring the triggering of a massiveon
final
ticourwind
thatresults.
halts the star formation episode ultimately resp

AGN & SMBH model in
SA models•

flow onto a putative accretion disc. As soon as a galaxy is formed,
theassumes that it contains a seed BH of 103 M⊙ . The first
2.1 model
BH accretion
step in the loss of angular momentum is connected to the same proThe model
for accretionof gas ontothat
thebring
BH follows
Granatoet al.
cesses(mergers,
disc instabilities)
gas to thespheroidal(2004), and thisstartsfrom the assumptionthat themainbottleneckiscomponent;
assumption
links BH growth
with
bulge
formation
given bythe history
loss of ofangularmomentum,
foristhegas tofor BH accretion. In the AGN feedback model included ineventsin thethe model
galaxy. necessary
Further loss
triggered
flow
onto
a
putativeaccretion
disc.
As
soon
as
a
galaxyisformed,GANA, the onset of suchdramatic events is supposed to beby other physical processes (i.e. turbulence, magnetic
fields or radi2.2
AGN-triggered
winds
3
the
model
assumesthatitcontains
a
seed
BH
of
10
M
.
The
first
the interplay between stellar and AGN feedback, as descr
ation drag) that are related to star formation in the bulge⊙(Umemura
AGN
activity
can injecta relevant
amountofofa massive
energy int
step
in
the
loss
of
angularmomentumisconnected
to
the
same
proMonaco& Fontanot(2005).
The triggeringw2001). This results in the building up of a reservoir of low anguinter-stellar
medium,favouringthetriggeringofamassive
cesses(mergers,
disc
instabilities)
that
bring
gas
to
the
spheroidal
pable of removing all cold gas from the host bulge, is sublar momentum gas with mass MRS . Its evolution is regulated bytic
windthat halts The
the starultimately
respo
component; this assumption+ links BH−growth with bulge formation
three
conditions.
firstformation
conditionepisode
is motivatedby thethegrowth and loss rates (ṀRS and ṀRS respectively). The growthfor BH accretion. In the AGN feedback model included inevents in the history of the model galaxy. Further loss is triggered
expectation that AGN radiation is able to evaporate somerate is taken to be proportional to some power of the bulge star
GANA , the onset of such dramatic events is supposed to be dby other physical processes (i.e. turbulence, magnetic fields or radiof cold gas for each M⊙ of accreted mass. Whenever the eformation rate (φB ):the interplay between stellar and AGN feedback, as describ
ation drag) that are
relatedtostarformation
in
the
bulge
(Umemura!
"α−1tion rate overtakes the star formation rate, the inter-stellar m
Monaco& Fontanot (2005). The triggering of a massive win
2001).
This
results
inthebuildingupofareservoiroflow
anguφB+isexpected
to thicken and cause the percolation of all SupeṀ= fBH φB gas with mass−1M . Its, evolution is regulated by
(1)
pable
of
removing
all cold gas from the host bulge, is subj
larRSmomentum
RS
100M⊙+yr
remnants into a galaxy-wide super-bubble, that can be acce−
three conditions. The first condition is motivated by the theor
growth and loss rates (ṀRS and ṀRS respectively). The growthby radiation pressure from the AGN. The second condition r
+
where
=gas
1 be
refersto the Umemura(2001) ofrelation
usedstarin
expectationthat AGN radiation is able to evaporate some 5
rate is α
taken
toproportional
to some power
therate:
bulge
Ṁ
母銀河→
reservoirへのinﬂow
RS that energy needed to sweep out all the inter-stellar medium
Granatoet rateal. (2004),
of cold gas for each M⊙ of accreted mass. Whenever the eva
formation(φB ): while α = 2 corresponds to a model
host bulge is not greater than the available energy from thewhere the loss of!angular momentum"α−1 is due by cloud encounterstion rate overtakes the star formation rate, the inter-stellar me
The third condition is that the BH is accreting in a radiative
φB is a free parameter, whose value affects+(Cattaneoetal.
2005).
f
BH
isexpected
to thicken
and cause the percolation of all Super
ṀRS = fBH φB
,
(1)
φ
bulge
SFR
B:
−1
cient
way,
i.e.
more
than
onesuper-bubble,
percent of its that
Eddington
the normalization of100M
the final⊙ yrMbh -Msph relation, as it regulates theremnants into a galaxy-wide
can be limit.
accel
In
Fontanotetal.
(2006),
weshowedthat
AGN-trtotal
into the(2001)
reservoir
duringused
galaxyby radiation pressure from the AGN. The second condition rewhereamountα = of1 coldrefersgasto flowing
the Umemura
relationinwinds
are aneeded
key ingredientthe evolutionof thevolution.
gas in thereservoir
onto tothea BH
at a
that
energyto sweepto
outreproduce
all the inter-stellar
mediumGranato etTheal. (2004),
while
α =then2 accretes
corresponds
model
luminosity
function and the space density of bright quasars i
rateregulated
byoftheviscosityof the accretion
disc(Granato
et al.
host− bulge is not greater than the available energy from the
where
the
loss
angularmomentum
is
due
by
cloud
encountersgas
reservoir→ SMBHへのaccretion rate: ṀThe
GANA: therefore,
weiswillconsiderinRSthird2004):
conditioninisthis
thatpaper
the BH
accretingin amodels
radiativel(Cattaneo et al. 2005). fBH is a free parameter, whose value affects
this mechanism.
In thanparticular,
we willrefer
to the MORGA
$
#
$
cient
way, i.e. more
one percent
of itsEddington
limit.
3 #Mbh -M
3/2 relation,
1/2
the−normalization of theσfinalasitregulates
the
sph
MRS
MBH
B
sion
labelled“drywinds”,
which
implies
using
a
high
value
Ṁ
= ṀBHof=cold
0.001
1reservoir+(2)
In
Fontanotet al. (2006),
we showed that AGN-trig
σvelocity
dispersion
B: bulge
RS amounttotal
gasGflowing
intotheduringgalaxyMBH
MRS
with winds
actually
limiting
the BH masses.
It is worth
winds
are a keyingredient
to reproduce
the evolutionof theevolution. The gas in the reservoir then accretes onto the BH at athat AGN-triggeredwinds
notdensity
necessary
to reproducethwhere σB is the 1D velocity dispersion of the bulge and MBH isluminosity
function andthe arespaceof bright
quasars inrate regulated by the viscosity of the accretion disc (Granato et al.
Mal.,
MORGANA. In
model
without
winds,incl
hosph: relation
the BH mass. This term is also capped at the Eddington limit.
(Fontanot et2015, inMNRAS,
453,
4112)
GANA
therefore,
inthis paper
wea willconsidermodels2004):
the mechanism.
Mbh -Msph In
relation
is mainly
determined
the mec
A key role in the feeding of the central BH is played by thethisparticular,
we willrefer to thebyMORGAN
$
$
3 #
3/2 #
1/2
σ available
MRS in the spheroidal
MBH component
that labelledregulates“drythe winds”,
accretion
ontoimplies
the BH,usingratherthanvalueby feeactual− amount of cold gas
sion
which
a higho
ṀRS= ṀBH = 0.001 B
1+(2)
basedwinds
self-regulation.
We referreaderto Fontanot
et al.n
G formation
MBH events. A comprehensive
MRS
as a consequence of bulge
diswithactually limiting
thetheBH
masses.
It is worth~kpc → ~100-10 pc スケールへのガス降着- 特に何も考えない- 簡単にモデル化されたgas reservoirを経由
例えば…

AGN & SMBH model in
SA models

なぜ gas reservoir を考える必要があるか?
- BHに降着するまでに, ガスは持っていた角運動量の99.9999%を捨てないといけない- 近傍で明るいAGNがモデルの中で出来すぎ,
SMBH成長史を正しくモデル化できない
10−3

10−3

model
Ueda+ 14model
Ueda+ 14

- AGN放射を吸収するトーラス状の構造が示唆されている. しかしSAでは無視されている10−4

Φ [h3 Mpc−3 dex−1 ]10−4

Φ [h3 Mpc−3 dex−1 ]

•

10−5
10−6
10−7
10−8

43

44
45
46
log LX (2 − 10keV) [erg s−1 ]

10−6
10−7

z~2

42

10−5

47

10−8

z~0

42

43

44
45
46
log LX (2 − 10keV) [erg s−1 ]47

AGN & SMBH model in SA
models
これまでのνGC

母銀河に存在するダストによる減光だけで,
AGNLFのbright end は~2等暗くなる→ 銀河合体からSMBHに数dynamical time以上の遅れがあれば観測と矛盾しなくなる

CND導入によって実現!?

Φ[h3 Mpc−3 mag−1 ]ガス降着が始まるまでに

10−4

10−5

w/o dust (E14 model)
with dust (E14 model)
νdelay = 1
νdelay = 3
Croom+09
from X-ray obs.

10−6

10−7
-27

-26

-25
-24
MB − 5 log h

-23

-22

Shirakata+ 2015, MNRAS, 450, L6

This work•

最小限のフリーパラメータで, SMBH周辺の構造(= gas reservoir) をモデル化したい•

gas reservoirのシミュレーションモデルはたくさんあるが, 銀河形成の枠組みの中でモデルの現実性を議論するのは難しい•

SAを使って, gas reservoirが銀河形成の枠組みの中で果たす役割を調べる
今回はKawakatu & Wada (2008), ApJ, 681, 73 をベースに用いた.

2
ν GC: an SA model•

元々のモデル: Nagashima+ 05, ApJ, 634, 26 &Enoki+ 03, PASJ, 55, 133“Numerical Galaxy Catalogue (νGC)”•

アップデート: Makiya+ Submitted to PASJ
“New Numerical Galaxy Catalogue (ν2GC)”銀河モデルのアップデート•

SMBH・AGN モデルアップデート: HS+ in prep.

2
ν GC N-bodyN体シミュレーション: Ishiyama+ 15, PASJ, 67, 61
The ν 2 GC Simulations

No. ]generated by a publicly available code, 2LPTic1 , using second-order Lagrangian perturbation theory (e.g.,
Crocce et al. 2006). The adopted cosmological parameters were based on an observation of the cosmic microwave background obtained by the Planck satellite(Planck Collaboration et al. 2013), namely, Ω0 = 0.31,Ωb = 0.048, λ0 = 0.69, h = 0.68, ns = 0.96, and σ8 = 0.83.
To calculate the transfer function, we used the online version2 of CAMB (Lewis et al. 2000). All simulations began
at z = 127.
Simulations were performed by GreeM3 (Ishiyama et al.
2009a; Ishiyama et al. 2012), a massively parallel TreePM
code, on the K computer at the RIKEN Advanced
Institute for Computational Science, and Aterui supercomputer at Center for Computational Astrophysics,
CfCA, of National Astronomical Observatory of Japan.
To accelerate the calculation of the tree force, we used
the the Phantom-GRAPE library4 (Nitadori et al. 2006;
Tanikawa et al. 2012; Tanikawa et al. 2013) with support
for the HPC-ACE architecture of the K computer and
AVX instruction set extension to the x86 architecture.
The dataset of the particles was stored at 51 time slices
from z = 20 to z = 0 for the ν 2 GC-L, ν 2 GC-M, and ν 2 GC-S
simulations. From z = 7.54, total 46 output redshifts wereselected, as the time interval is proportional to the typical6

Ishiyama et al.

[Vol. ,

Dark matter distribution in the largest ν 2 GC-L simulation at z=0. The background image shows a projected region with

Fig. 2.
a thickness of 45 h−1 Mpc and a side length of 1120 h−1 Mpc. An enlargement of the largest halo is shown in the central image witha thickness of 45 h−1 Mpc and a side length of 140 h−1 Mpc. The bottom right panel is a close-up of the largest halo.

106

corrected mass resolution [h-1M⊙]

•

3
20483

40963

81923

ν2GC-H2 ν2GC-H3

107

Millennium-II

ds14-g-200-2048

ν2GC-H1
ds14-g-400-2048
SMDPL

108

BolshoiP

BolshoiWhite+10

Q-Continuum2

ν GC-M2

ν GC-L2

ν GC-Sds14-g-800-4096

109

Millennium

MDPL

Planck

ds14-g-1600-4096

WMAP
1010
105

Millennium-XXL
Horizon

106

107

108

109

1010

1011

Box size [(Mpc/h)3]Ishiyama+ 15, PASJ, 67, 61

2ν GC AGN model••gas reservoirスケールへのガス降着トリガーは銀河合体のみを考える.
Hopkins+ 2009, MNRAS, 691, 1168 をベースにして,銀河合体でbulgeに分配される星・ガス量を計算

2
ν GC AGN model
M2

M1
M0,bulge = M1,bulge + fVR M1,disk + M2
M0,disk = (1.0 − fVR )M1,disk

MIN(M1,disk , M2 )fVR =M1,disk

M2/M1 > 0.1 の場合に有効.
大きい方の銀河円盤のうち~ M2の質量がviolent relaxationを受けてbulgeへ.

starburst
cold gas(bulge)BH growth ∆MBH = fBH ∆M∗,burst= 0.007

2
ν GC AGN model
74•

KAWAKATU & WADA

gas reservoir = CircumNuclear Disk (CND) モデル
銀河から降着したガスが ~ 100pc スケールに溜まる (CND形成)↓

CND内で星形成↓

超新星爆発が作る乱流でガスの角運動量を抜く↓

SMBHへ降着Fig. 1.—Schematic picture for a model of SMBH growth linked with the change of physical state in the circumnuclear disk supported by the turbulent p

Kawakatu
Wada(2008)
Fig.i.e.,1r > rc , where rc
explosions, where rin and rout are the inner radius and the outer radius, respectively. Star symbols
represent &the region
wherestars can form,by the Toomre criterion (see x 2.2). Here, MBH , Mg , ṀBH , Ṁ* , and Ṁsup are the mass of the SMBH, the gas mass, the stellar mass, the BH growth rate, therate, and the mass supply rate from the host galaxy, respectively. [See the electronic edition of the Journal for a color version of this figure.]2
ν GC AGN model
1. 銀河からCNDへのガス供給
2. CNDが不安定状態ならSMBHへ

from host galaxy
Msup = fBH ∆M∗,burst

ガス降着を起こすmode(i) CND全体が不安定(降着率が高い)mode(ii) 一部不安定 (外側)
(降着率が低め)

CND
rCND

SMBH

2
ν GC AGN modelfrom host galaxy2
ΣCND,gas = MCND,gas /πrCND

cs −1/2 −3/2
Σcrit (r) = G
r(MBH + 3MCND,gas )πMsup = fBH ∆M∗,burst

Σcrit (rCND ) < ΣCND,gas のときCND不安定.
Σcrit (rin ) < ΣCND,gas

mode (i)Σcrit (rin ) ≥ ΣCND,gas

mode (ii)rCND = αrbulge rin: resolution limit (0.1pc)

α = 0.01

CND
rCND

SMBH

2
ν GC AGN model•

mode(i)3
rCND
ṀBH = 3παSN ηESN C∗ Σgas,CND (rCND )GMBHC∗ = ΣSFR /Σgas,CND
log ΣSFR /[M⊙ yr−1 kpc−2 ]= 1.42 × log ΣCND,gas /[M⊙ pc−2 ] − 3.83 +0.9
(Daddi+ 10, ApJL, 714, L118)ULIRG等のKS relationがCNDに適用できると仮定•

mode (ii)
ṀBH = 21!

rCND
h(rCND )"!

MCND,gasMBH"

h: scale hightResults
MBH - Mbulge relationと z ~ 0 のSMBH mass function

109

10−1

model
Haring & Lix 04
Merrit & Ferrarese 01

dN/d log(MBH [h3 Mpc−3 dex−1 ])1010

MBH [M⊙ ]

•

108
107
106
105 7
10

108

109

1010
Mbulge [M⊙ ]

1011

1012

Shankar+ 04
model (70)

10−2

10−3

10−4

10−5

7

7.5

8

8.5
9
2
log(MBH [M⊙ /h ])

9.5

10

Results
AGN luminosity functions

10−3

model
Ueda+ 14

10−3

z~0

10−5
10−6
10−7
10−8

model
Ueda+ 1410−4
Φ [h3 Mpc−3 dex−1 ]10−4
Φ [h3 Mpc−3 dex−1 ]

•

z~2

10−5
10−6
10−7

42

43

44
45
46
−1
log LX (2 − 10keV) [erg s ]

47

10−8

42

43

44
45
46
−1
log LX (2 − 10keV) [erg s ]47

Results
MBH - MCND,gas relationmode(i)は全く起こらず, 全てmode (ii)で成長.
1010

1010

E
S0
S

108
107
106
105 5
10

E
S0
S

109
MCND,gas [M⊙ ]109
MCND,gas [M⊙ ]

•

107

108
MBH [M⊙ ]

109

1010

107
106

z~0
106

108

1011

105 5
10

z~2
106

107
108
MBH [M⊙ ]

109

1010

Results
Mcnd,gas - mass accretion rate relation
100

model

10
ṀBH [M⊙ /yr]

•

1

0.1

z~0
0.01 510106107
MCND,gas [M⊙ ]

108

109

Problems & Discussion•

モデルの問題
1. CNDで星形成が起きない-> 星形成を起こす条件がCND内縁半径に依存-> BHがactiveでない時の”内縁半径”とは何?
2. AGN光度関数の観測との不一致

Problems & Discussion•

準解析的銀河形成モデルのために欲しい情報
1. CND版 KS relation
2. CND スケール
3. 母銀河からCNDへのガス供給タイムスケール
L120

DADDI ET AL.

Figure 3. Same as Figure 2
dynamical time. The best-fittof 1.14.
(A color version of this figur
Figure 2. SFR density as a function of the gas (atomic and molecular) surface
density. Red filled circles and triangles are the BzKs (D10; filled) and z ∼ 0.5
disks (F. Salmi et al. 2010, in preparation), brown crosses are z = 1–2.3 normal
galaxies (Tacconi et al. 2010). The empty squares are SMGs: Bouché et al.
(2007; blue) and Bothwell et al. (2009; light green). Crosses and filled triangles
are (U)LIRGs and spiral galaxies from the sample of K98. The shaded regions
are THINGS spirals from Bigiel et al. (2008). The lower solid line is a fit tolocal spirals and z = 1.5 BzK galaxies (Equation (2), slope of 1.42), and theupper dotted line is the same relation shifted up by 0.9 dex to fit local (U)LIRGsand SMGs. SFRs are derived from IR luminosities for the case of a Chabrier(2003) IMF.
(A color version of this figure is available in the online journal.)(Daddi+ 10, ApJL, 714, L118) tion timescale at the ga

measured at a higher signal-to-noise ratio. Again, we find thatthe populations are split in this diagram and are not well fit by asingle sequence. Our fit to the local spirals and the BzK galaxies
is virtually identical to the original K98 relation:log ΣSFR /[M⊙ yr−1 kpc−2 ]= 1.42 × log Σgas /[M⊙ pc−2 ] − 3.83.

(2)

The slope of 1.42 is slightly larger than that of Equation (1),with an uncertainty of 0.05. The scatter along the relation is

et al. 2009 use the freelected z = 0.5–2.3 galahalf-light radius. Extra
radius would not affectthe location of normal
from that of local (U)well described by the flog ΣSFR /[M⊙ yr−1 kpc= 1.14 × log Σgwith a slope error ofremarkable difference
to the fact that the nlonger dynamical time(U)LIRGs.
We can test if this
dividing the gas masses

Summary•

SAモデル, ν2GCにKawakatu & Wada 08のCNDモデルを導入している•

局所的シミュレーションや観測から示唆される物理
メカニズムが銀河形成の枠組みの中でどう機能するかを調べる必要がある•(今回の結果には多くの問題があるが) 今後シミュレー
ション・SAモデルの連携はより重要になるだろう