ｽﾗｲﾄﾞﾀｲﾄﾙなし

Why Massive Black Holes
are Small in Disk Galaxies ?
Nozomu KAWAKATU
Center for Computational Physics, University of Tsukuba
Collaborator
Masayuki UMEMURA
Center for Computational Physics, University of Tsukuba
Formation of the First Generation of Galaxies: Strategy for the Observational Corroboration of Physical
Scenarios, 2-5 December 2003, Niigata University, Niigata, Japan
Contents
• Introduction
Recent observational results ( BH mass-to-bulge mass correlation )
Angular momentum transfer problem for supermassive black holes
• Physical mechanism for formation of Supermassive Black Holes
Radiation drag (Poynting-Robertson) effect
• Basic Equation
Equation of angular momentum transfer
Treatment for extinction by dusty gas
• Model for Disk galaxies
• Results
Relationship between the final BH mass and bulge-to-disk ratio of host galaxy
• Summary
Introduction
Recent high quality observations of galactic centers
1) BH mass-to-galaxy mass ratio is considerably smaller than 0.002 for Disk.
(Salucci et al. 2000; Sarzi et al. 2001; Ferrarese 2002; Baes et al. 2003)
2) BH mass-to-galaxy mass ratio is reduced by more than an order of
magnitude with a smaller bulge-to-disk ratio.
10-2
× Normal spiral and barred galaxies
Sy1
Sy2 ▲ NLSy1
10-3
10-4
10-5
0.03
0.1
1
M bulge M galaxy
3) BH mass-to-bulge mass ratio lies at a level of 0.001,
which is similar to that found in elliptical galaxies.
(e.g., Kormendy & Richstone 1995)
10-2
10-3
ellipticals
10-4
× Normal spiral and barred galaxies
10-5
0.03
Sy1
Sy2 ▲ NLSy1
0.1
M bulge M galaxy
Formation of SMBHs
1
= Formation of Bulges
Physical relation!
Summary of observational results in galactic centers
Elliptical Galaxies
Disk Galaxies
M BH M galaxy
M BH M galaxy  0.002
0.002
( M BH M bulge  0.002)
It has not been clear
why the BH mass is smaller in disk physically!!
SMBH Formation: Angular Momentum Problem
The physics on the angular momentum transfer is essential !
Hydrodynamical Mechanisms for Ang. Mom. Transfer
( From galactic scale to BH horizontal scale )
1) Gravitational torque by a bar or non-axisymmetric mode
But, this mechanism is effective only beyond ~ 1kpc.
(Wada & Habe 1995, Fukuda 1998)
2) Turbulent viscosity
But, the timescale is longer than the Hubble time in galactic scale !
(e.g. A galactic disk cannot shrink via turbulent viscosity.)
12
1
1


j

M
T




12
10
tvis

3

10
yr
R
  4 
kpc

  11
 cs2
 0.1   10 M   10 K 
3) Radiation drag (present work)
theoretical upper limit:  M BH M galaxy max  0.007
(Umemura 2001)
The timescale is shorter than the Hubble time in galactic scale.
tdrag
1
1
 L   Z 
c R
2
7

 8.6 10 yr  12
R
 

kpc
 L
10
L
Z

 

2
2
Radiation Drag – Poynting-Robertson Effect –

Lab.Frame
Lab.Frame
< Re-emission process >
 t v
p
c c
< Absorption process >
E  t
v0
“radiation drag”
m0 v
m
m 0c 2  t  mc 2
m 0v0  mv
v < v0
Matter slowdowns !
v finaal
mfinal
E  t
mc 2  t  m finalc 2
mv  m finalv final 
t v
c c
mfinal  m0 , v final  v
In practice, optically thin surface layer is stripped by radiation drag,
and loses angular momentum (Sato-san talks in details).
Radiation Drag efficiency in galactic bulges
Optically thick regime
“Radiation drag efficiency is determined by the total number of photons ”
M BH

Lbulge
c
2
dt
Lbulge :total luminosity of the bulge
1) The BH-to-bulge mass ratio is basically determined by the energy conversion
efficiency of nuclear fusion from hydrogen to helium, i.e., 0.007. (Umemura 2001)
2) The inhomogeneity of ISM helps the radiation drag to sustain the maximal efficiency.
(Kawakatu & Umemura 2002 )
covering factor O(1)
ISM is observed to highly inhomogeneous in active star-forming galaxies !
3) By incorporating the realistic chemical evolution, we predicted M BH M bulge
0.002 .
(Kawakatu, Umemura & Mori 2003 )
Radiation drag
- Geometrical Dilution (Umemura et al. 1997,1998; Ohsuga et al. 1999)
Spherical System
Disk-like System
low drag efficiency
high drag efficiency
However, the details are not clear quantitatively !
This Work
We investigate the efficiency of radiation drag in disk galaxies.
We solve the 3D radiation transfer in an inhomogeneous ISM.
To investigate the relation between the morphology of host galaxies and
the angular momentum transfer efficiency due to the radiation drag
We have disclosed the physical reasons
why the BHs are smaller in disk galaxies!
Model
1
The difference of morphology is expressed by
changing “ bulge fraction (fbulge)” (. Mgalaxy  1011 M )
f bulge  M bulge M galaxy
0.5
Inhomogeneous ISM
covering factor is unity.
h  0.01rdisk  0.1rdisk
“disk scale height “
fbulge
0.03
Basic Equations
The Eq.of Ang.Mom.Transfer
1 d  rv    
 F  (E  P )v
r dt
c
c
Radiation Flux Radiation Drag
  nd d g ： mass extinction due to dust opacity
E　: radiation energy density F  : radiation flux P : radiation stress tensor
The gain and loss of total angular momentum is regulated by this equation.
The contribution of the radiation from distant stars is essential to radiation drag
since these stars have different velocities from absorbing clouds.
Treatment of the radiation tranfser
All radiative quantities are determined by radiation from stars diluted by dusty ISM.
We calculate the radiation fields by the direct integration of the radiation transfer.
opacity : dust in clumpy gas clouds

b
dF r j ,0
rc
dF r j ,0 e-
N
N
N
j 1
j 1
j 1
F   dF0, j e  , E   dE0, j e  , P   dP0, j e 

  2 1   b rc 

2 12
 ：the optical depth for all intervening clouds
along the light ray
  gas rc :optical depth of a gas cloud
Angular momentum transfer in an Inhomogeneous ISM
Total angular momentum loss rate
J

Nc
r (F  F

c
rot
i 1
i
i
drag
i
)
( Nc:Number of clouds)
Mass Accretion Rate
J
M g  M g
J
Angular Momentum Extraction
Total mass of the ISM
Estimate for BH mass
t0
t0
0
0
M BH   M g dt   
J
M g dt
J
( t0:Hubble time; J: total angular momentum )
Result.1: BH mass-to-morphology relation
Hubble Type
Sc
Sb
Sd
Sa
S0
E
M BH M bulge
Almost constant
10-3
h  0.1rdisk
h  0.04rdisk
h  0.01rdisk
10-4
～1/20
～1/50
10-5
0.03
M BH M galaxy
M BH M galaxy
h  0.1rdisk
h  0.1rdisk
h  0.04rdisk
h  0.04rdisk
h  0.01r
h  0.01rdisk disk
M BH M galaxy 103 f bulge
～1/200
0.1
fbulge  Mbulge Mgalaxy
1
Why MBH are small in disk
① & ②galaxies？
③
“radiation”
pole on view
① A number of photons escaped from the system (Surface-to-volume ratio )
② Radiation from disk stars is heavily diminished across the disk (optically thick disk)
③ The velocity difference stars and absorbing clouds becomes closer to zero
(optically thick disk)
Radiation drag cannot work effectively in disk galaxies !
Result.2-1: Comparison with the observations
10-2 ×
Normal spiral and barred galaxies
Sy1
Sy2 ▲ NLSy1
NGC3227
NGC3245
NGC4151
M31
10-3
M81
NGC
1023
NGC4258
NGC3783
Mrk509
NGC4593
NGC4593
Fairall 9
10-4
NGC4395
(Sy2/Starburst)
10-5
0.03
NGC5548
NGC3516
3C120
3C120
Galaxy
NGC7457
NGC7469
NGC7469
Mrk590
Mrk590
(Sy1/Starburst)
(Sy1/Starburst)
(Sy1/Starburst)
Mrk590
NGC1068
NGC1068
NGC1068
(Sy2/Starburst)
NGC4051
(Sy2/Starburst)
(Sy2/Starburst)
Circinus
(Sy2/Starburst)
Circinus
(Sy2/Starburst)
NGC4051
NGC4051
1
0.1
M bulge M galaxy
TheseThis
objects
have
relatively
small BHs
compared
with
the predictions.
trend
is broadly
consistent
with
theoretical
prediction.
Result.2-2: Comparison with the observations
10-2
NGC4258
NGC4395
NGC4395
(Sy2/Starburst)
(Sy2/Starburst)
M31
Fairall 9
M81
NGC1023
NGC4151
NGC3783 NGC5548
NGC5548
Mrk509
10-3
NGC1068
NGC1068
(Sy2/Starburst)
(Sy2/Starburst)
Galaxy
3C120
3C120
NGC4593
NGC4593
NGC3516
NGC3516
Circinus
(Sy2/Starburst)
Circinus
Circinus(Sy2/Starburst)
(Sy2/Starburst)
NGC7457
NGC7457
NGC4051
NGC4051
10-4
10-5
NGC3227
NGC3227
NGC3245
NGC3245
NGC7469
NGC7469
(Sy1/Starburst)
(Sy1/Starburst)
Mrk590
Mrk590
Mrk590
×
×Normal
Normalspiral
spiraland
andbarred
barredgalaxies
galaxies
0.03
Sy1
Sy1
Sy2
▲NLSy1
NLSy1
Sy2 ▲
0.1
M bulge M galaxy
1
Observational
data roughly
agree withbelow
the prediction
.
Sy1
with SB & NLSy1
fall appreciably
0.001 again.
Summary
１．BH-to-galaxy mass ratio decreases with a smaller bulge-to-disk ratio, and is
reduced maximally by two orders of magnitude, resulting in M BH M galaxy  105 .
The present model also predict BH-to-galaxy mass ratio depends on
the disk scale-height (h), M BH M galaxy  103   h / 2rdisk 
＜Physical Reasons＞
• Almost all photons can escape from a disk-like system, owing to the effect of
geometrical dilution.
• The radiation from stars in disk galaxies is considerably reduced in the
optically-thick disk.
• The velocity difference stars and absorbing clouds becomes closer to zero
２．In disk galaxies, the BH-to-bulge mass ratio is about 0.001 .
It turns out that the formation of SMBH is not basically determined by disk
components, but bulge components, consistently observational data.
The BH-to-bulge mass ratio is fundamentally determined by physical
constantε=0.007, regardless of morphology of host galaxies.
Grazie mille!
どうもありがとう
ございました！

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