Properties of AGNs predicted froma semi-analytic model of galaxy formation
Hikari SHIRAKATA (Hokkaido Univ.)

arXiv: 1802.02169

Collaborators: T. Okamoto (Hokkaido), T. Kawaguchi(Onomichi),
M. Nagashima (Bunkyo), T. Oogi (IPMU), and ν2GC members
5th galaxy evolution workshop @ Ehime University (2018/06/06-08)

Introduction (1/2)• Growth timescale of SMBHs,and triggering mechanisms of AGNs

Their effects aredegenerate to each other?

(‘frequency’ of AGN activities)
quiescent / active

quiescent / active

timetime

7 yr (e.g. Yu & Tremaine 2002)
Growthtimescale(QSOs):~10• How about less luminous (LX < 1044 erg/s) AGNs?
How is this timescale determined? (physical processes)• Triggering mechanisms of AGNs?
"2Introduction (2/2)
Hirschmann+12• Hirschmann +12 (with an SA model)
mergers only:
underestimate lessluminous AGNs
disc instabilities play a role.
(but with simple modelling)10

accretion timescale ~ Salpeter timescale• Only one solution?

12log(Lbol /L )No. Other possible scenario exists.

"3142
ν GC (1/4)
N-body simulations (Ishiyama+ 15)
Publications of the Astronomical Society of Japan (2015), Vol. 67, No. 4

Minimum halo mass:

Fig. 1. Mass resolution versus simulation volume of recent large cosmological N-body simulations. The mass resolution of each simulationis corrected, as the cosmological parameters of all simulations are thesame as those we chose. The number of particles along the three dashedlines is constant. Circles show simulations based on the Planck cosmology. The six filled circles are the ν 2 GC simulations. The four opengray circles denote four of the five Dark Sky Simulations (DSS: Skillman(1.37 - 87.9)×108 Msun

Downloaded from http://pasj.oxfordjournals.

simulation with 16384 MPI (Message Passing Interface) tasks, in which eight OpenMP threads ran inparallel. The calculation time was 50–60 s per stepwith global and adaptive timesteps. The total CPU
time and memory consumed were 11 million CPU hr(1.38 million node hr) and about 50 TB. At z = 0, themaximum CPU and memory imbalances are about 3% and25%. The relatively large imbalance of memory consumption ensured nearly ideal load balance.
The data set 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, a total of 46 output redshifts
was selected, as the time interval is proportional to thetypical dynamical time of the halos. The corresponding
logarithmic redshift interval "log (1 + z) is 0.02–0.03.
Moreover, five data sets at high redshifts of z = 8.15, 10.0,12.9, 16.2, and 20.0 were stored. For the ν 2 GC-H1 andν 2 GC-H2 simulations, the 46 output redshifts from z = 7.54
2GC-L-1Mpc)(1120hwereνidenticalto thoseof the first
three simulations. Furthermore, from z = 12.5 to z = 7.54, 10 data sets with aconstant logarithmic redshift interval of "log (1 + z) = 0.02
and two data sets at high redshifts of z = 16.2, 20.0 werestored. Thus there is a total of 58 time slices for the ν 2 GCH1 and ν 2 GC-H2 simulations. For the ν 2 GC-H3 simulation, the output redshifts were identical to those of the "4ν 2 GC-H1 and ν 2 GC-H2 simulations, and 22 data sets were

61-4

2
ν GC (2/4)
SMBH growth (mergers and/or DI)
Mergers and/or disc instability
Vmax
Dynamical friction< ✏DI,crit
1/2
Random collision (GMdisc /rds )(Efstathiou+ 82)(Hopkins+09)- Including bulge potential
5% of the disc → bulge

Starburst (bulge)
Normal SF (disc)
SMBH growth
Accreted gas mass:
Macc = fBH M⇤,burst
SMBH-SMBH coalescence
Mseed = 103 M"5model AGN luminosity functions
observed AGN LFs. In this paper,2GC(3/4)
Eq. 30 νincludes
the angularmo-cal bands despite suﬃciently larg
We calculate the AGN bolometricluminosity,, froavoid
this uncertainty, L
wecompaboltionsweby using“absorption-correcaccretion rate (Eq. 29). Hereafter
definethe bolokeV) (see also Sec. 2.4.5).

luminosity normalized by the Eddington luminosity
as Edd ⌘ Lbol /LEdd and the accretion rate normali
2.4.4 AGN luminosity
2€€ The Eddingt
Eddington rate ( MEdd = LEdd /c ) as m.
We calculate the AGN bolometr
minosity is defined ascretion rate (Eq. 29). Hereafter

a circumnuclear torus and in thect a simplified and phenomenologmomentum loss in the central renosity normalized by the Edding
4⇡cGmpould continue
beyondthe starburst/LEdd and the accretion ra
SMBH
growth& AGNsLEdd =MBH,Starting time ofLbol
AGN
activity2 ) as m.
"an" The Edd(M=L/cf the accreted gas requires a longer
EddEdd✓T◆
Macct tstart
4πcGm pr momentum in the circumnuclear
LEddlight=c and T are the speed ofandMcrosssecṀBH = whereexp
accretion
rate:
BH,σT
disc . In this region, the gravitatTompson
tacc
acc
scattering, respectively.
Weemploy
thefolwherecandσarethespeedof lT
2
ted by the SMBH. The timescale
Ṁ=L/c
Eddonrespectively.
Edd
relation between Edd and m€ (basedKawaguchi
20
scattering,We empl
e mass of the SMBH. Considering
λEdd and m" (based on Kawaguch! mwhich the mass accretion rate de€ crit 1 11
bolometricluminosity:,
λEdd = +Edd =stability(e.g. Kawakatu& Wada"€ m€ crit ))} 1 + 3.5{11 + 3.5{1 + tanh(log(m/m€ + tanh(log(m/cale wouldbecomelonger for 03)
the(basedon Kawaguchi+
where m" crit is an adjustable param€
wheremisanadjustableparameter,whose valueṁ = ṀBH /Ṁm"Edd" crs timescale would also depend on
Edd = Lcritbol /LEdd
crit ! 16.0. When we set m€ critbe 2.5 . m€ crit . 16.0. We set
10.0and iEq. m33,
has =similar
dependence
he accreted gas and the SMBH.
et al. (2000)
andtoMineshige
et€
case,
has
similardependence
onmthatobEdd
higher, the self-gravity of the acm" crit = 10.0.
by Watarai(2000).
Lbol et al. (2000) and Mineshige
We noteet
thatal.
althoughthe gactively X-ray
and thus(2-10the outeredgeofkeV) luminosity:We note=thatg(Lbol)with time,Lbol (dalthough themonotonicallygas accretion
rateLX
smaller. The dynamical timescale
time. The bolometric luminosity
decreases
monotonicallywithtime,
Lbol does notnece(basedon
Marconi+04)
hence describe tloss as a function
crease monotonicallywith time (Edecrease with time. The bolometricnorm
to MBH ,luminosity
it, on the other hand,
inlowing conditionis satisfied,bolby LEdd , Edd , decrease monotonicallywithtime L(ESince L"6 Edd is proportional to MBH , it, on the other ha◆ gas
λEdd (t)L (tstart )Macc> Edd.

2
ν GC (4/4)
Accretion timescale for 1 accretion event
tacc = ↵bulge tdyn,bulge + tloss
0.58

Considering angular momentum loss in
CND and/or accretion disc:↵BH↵gas
tloss = tloss,0 Macc
MBH

QSOs: tacc ~ 107 yr↵gas =(e.g. Yu & Tremaine 2002)

timescale<latexit sha1_base64="2TXv3fsAm8onHfDqaECnI8T69SA=">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</latexit>~ tdyn, bulge
LX < 1044erg/s: tacc > 108 yr"74.0, ↵BH = 3.5

Results (1/4)
Fiducial model
tacc = αbulge tdyn,bulge

Only the fiducial model
explains observational
tacc ∝ tdyn,haloresults.

"8Results (2/4)• Less luminous AGNs @ z ~ 0 are mainly merger driven
Typically long-lived AGNs(> 109 yr)• Need further comparison
with observations"9Summary• Using ν2GC (a semi-analytic model of galaxy formation), weﬁnd that…
- Faint end slopes of AGN LFs @ z < 1.5 can be explainedby (1) “long-lived, merger-driven” AGNsor (2) “short-lived, disc instability driven” AGNs.
- Eddington ratio distribution function is important tomight solve this discrepancy(but, many uncertainties and free parameters…)
2GC.
Contactus
ifyouareinterestedinusingν•"10Appendix• Star Formation
Rate Density

Appendix• K-band LF(galaxy)Appendix• Bulge size, velocity

Appendix• MBH—Mbulge@z~0Appendix• Active fraction of AGNs @ z~0 (fiducial model)

Appendix• How is the Eddington ratio distribution diﬀerent by tacc?
tacc∝tdyn,bulge

The difference appear@ Lbol/LEdd< 0.01 ← difficult to observe(※ Assuming Type-2 fraction = 0 for model results)

Appendix• Eddington ratio

distribution
at higher redshift