1. Why are Massive Black Holes Small in Disk Galaxies ?
Nozomu KAWAKATU
Center for Computational Physics, University of Tsukuba
Collaborator
Masayuki UMEMURA (University of Tsukuba)
Formation of the First Generation of Galaxies: Strategy for the Observational Corroboration of Physical Scenarios, 3-4 September 2003, Niigata University, Niigata, Japan

2. INTRODUCTION Recent high resolution observations of galactic centers
¶ Supermassive BHs have been thought to be the central engine of AGNs.
linear relation
(Kormendy & Richstone 1995; Richstone et al. 1998; Magorrian et al. 1998; Gebhardt et al. 2000; Ferrarese & Merritt 2000; Merritt & Ferrarese 2001; McLure & Dunlop 2002)
¶ BH mass doesn’t correlate with the disk components.
MBH [M ]
(Kormendy & Gebhardt 2001)
Formation of SMBHs
Physical relation!
Formation of Bulges
Lbulge [L ]
Richstone et al.1998

3. It has not been clarified physically
The MBH in disk galaxies are smaller than that in elliptical galaxies ! ¶　 10
Galactic Bulge
(Salucci et al. 2000; Sarzi et al. 2001; Ferrarese 2002; Baes et al. 2003)
¶ MBHs do form in some pure disks 8
log MBH
e.g., NGC 4395 6
(using MBH　-σ relation)
Disk galaxies 4
(Filipenko & Ho 2003) 10 11 12 13
log Mgalaxy
Salucci et al. 2000
It has not been clarified physically
why the BH mass is smaller in disk !!

4. Theoretical Model for SMBH formation
The physics on the angular momentum transfer is requisite !
“ Radiation drag (Poynting-Robertson effect) “
A potential mechanism to extract angular momentum in a spheroidal system
Total accreted mass onto “massive dark object” (MDO) in optically thick regime
:total luminosity of the bulge
“Radiation drag efficiency is determined by the total number of photons”
< Previous Works >
¶ The BH-to-bulge mass ratio is determined by the energy conversion efficiency of nuclear fusion from hydrogen to helium, i.e.,
(Umemura 2001)
¶ The inhomogeneity of ISM helps the radiation drag to sustain the maximal efficiency.
(Kawakatu & Umemura 2002 )
ISM is observed to highly inhomogeneous in active star-forming galaxies !
¶ The radiation drag model can account for the mass ratio observed quantitatively, taking account of the realistic chemical evolution.
(Kawakatu, Umemura & Mori )

5. - Geometrical Dilution -
Radiation drag
- Geometrical Dilution -
(Umemura et al. 1997,1998; Ohsuga et al. 1999)
Spherical System
Disk-like System
low drag efficiency
Observationally, the mass ratio of BH to galaxy is smaller than
We have the question "why small BH in disk galaxy?"
In the radiation drag model, if the system is spherical system, the emitted photon are effectively consumed with in the system. The drag efficiency is high.
On the other hand, a large fraction of photons can escape from a disk-like system.The drag efficiency is low.
In practice, we estimate the effect quantitatively.
high drag efficiency
However, quantitative details are not clear !

6. This Work We disclose the physical reasons
We built up a simple model of the bulge-disk system and accurately solve the 3D radiation transfer in the bulge-disk system in an optically-thick and inhomogeneous ISM.
To elucidate the relation between the morphology of host galaxies and the angular momentum transfer efficiency due to the radiation drag
We disclose the physical reasons
why BHs are smaller in disk galaxies!

7. Model
The difference of morphology is expressed by changing the bulge fraction (fbulge).
•　Spatial distribution
•　Rotational velocity
DM：　NFW profile
rigid rotation
Stars & ISM：　
　Bulge: Hernquist’s profile
　Disk:　exponential profile
rotation valance
•　Star Formation History
Salpeter-type initial mass function
•　Mass-to-Size relation
SFR is proportional to the fractional gas mass.
( bulge:tSF=108yr, disk: tSF=109yr)
•　Optically thick & inhomogeneous ISM
Size of gas clouds : 100pc
Optical depth of a gas cloud:1, 10, 100

8. Treatment of the radiation tranfser
Clumpy ISM Model
Treatment of the radiation tranfser
We calculate the radiation fields by the direct integration of the radiation transfer.
Opacity : dust in clumpy gas clouds

9. Basic Equations The Eq.of Ang.Mom.Transfer Mass Accretion Rate
： mass extinction due to dust opacity
Radiation Flux
Radiation Drag
radiation energy density
radiation flux
radiation stress tensor
The gain and loss of total angular momentum are determined.
Mass Accretion Rate
Angular Momentum Extraction
From this reason, we adopt the clumpy ISM model.
The basic equation is this.
This equation is the equation of angular momentum transfer.
The first term is the radiation flux, the second term represents the radiation drag.
So, the gain and loss of total angular momentum are
determined.
The mass accretion is expressed as this.
Total mass of the ISM
Estimate for MDO mass

10. Result.1: Morphology-to-radiation drag efficiency
Hubble Type
Sd,Sm Sc Sb Sa S0 E
10-3
Almost constant
mass ratio
10-4
Radiation drag efficiency is reduced
as fbulge is smaller (factor 20) .
Pure disk
0.1 1

11. Why the small in disk galaxies？
Radiation drag efficiency: the total number of photons emitted from stars and absorbed by clouds during the whole history of the galaxy
large
small
The number of photons escaped from the system
Disk components dominant
large
small
Effect of absorption in the optically-thick disk
The distribution of the ISM is closer to uniform
Difference between the velocity of a star and a ISM is closer to zero.

12. Result.2-1: Comparison with the observations
Hubble Type
Sd,Sm Sc Sb Sa S0 E ×
Normal spiral and barred galaxies
Sy1 (Errors of BH fraction:factor 3)
Sy2 ▲
NLSy1
NGC3245
NGC4151
our prediction ( upper limit is AGN activity)
10-3
M81
NGC5548
M31
NGC3783
NGC1023
MBH / Mgalaxy
Fairall 9
Mrk509
NGC4258
IC4329A
NGC3516
NGC4593
10-4
3C120
Galaxy
(NLSy1)
NGC7469
Mrk590
(Starburst-Sy1)
NGC4945
(NLSy1)
NGC4051
NGC7457
NGC1068
(NLSy1)
0.1 1
NGC4395 (pure disk)

13. Result.2-2: Comparison with the observations
Hubble Type
Sd,Sm Sc Sb Sa S0 E
NGC4258
M31
NGC7457
NGC4151
NGC3245
IC4329A
Fairall 9
NGC1023
NGC3783
NGC5548
Mrk509
10-3
NGC4945
M81
MBH / Mbulge
NGC1068
3C120
Galaxy
(NLSy1)
NGC4593
NGC3516
our prediction ( upper limit is AGN activity)
10-4
NGC4051
Mrk590
NGC7469
(NLSy1)
(Starburst-Sy1)
(NLSy1) ×
Normal spiral and barred galaxies
Sy1
Sy2 ▲
NLSy1
0.1 1

14. Result.3 Ellipticity-to-radiation drag efficiency
Morphology Type E7 E6 E5 E4 E3 E2 E1 E0
10-2
Observational Data (Marconi & Hunt 2003)
“Drag efficiency decrease as the axis ratio is smaller (factor 3).” b a
MBH / Mbulge
10-3
our prediction ( upper limit is AGN activity)
10-4
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Axis ratio (b/a)

15. Conclusions
By assuming a simple model of a galactic bulge and disk, we have investigated the relation between the morphology of host galaxies and the radiation drag efficiency. In a clumpy ISM and an aspherical system, we have accurately solved 3D radiation transfer to calculate the radiation drag force by the rotating stars.
１．The radiation drag efficiency is sensitively dependent on the morphology of host galaxies. The disk galaxies have almost twenty times as small BHs as elliptical ones.
＜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.
２．If only the bulge in a disk galaxy is taken, the BH-to-bulge mass ratio is about
It turns out that the formation of MBH is not basically determined by the disk components, but bulge components.
This is consistent with the recent observational results!!
３. For the same reason, the mass ratio could be lower than for a flattened bulge.
Our model predicts the mass ratio correlates with the ellipticity of the galactic bulge.