1. Growth of massive black holes in dusty clouds: impacts of relative velocity between dust and gas
Shohei Ishiki (Hokkaido University),
Takashi Okamoto (Hokkaido University),
Hidemobu Yajima (Tukuba University)
Collaborato

2. 1. Introduction dust ~1Gyr radiation SMBH seed 10 5 𝑀 ☉ SMBH 10 9 𝑀 ☉
gas
accretion
~1Gyr
(e.g. Mortlock et al. 2011)
radiation
BH becomes massive by accreting the gas. Then, why do we have to study the gas accretion onto the blackhole? Many researchers believe that
by gas accretion onto the SMBH seed, SMBH is created. However, for example, Mortlock find the SMBH in the early universe, earlier than 1Gyr, z 7.
Forming 10^9 Msun at a redshift of z7 by gas accretion is very difficutl. Its’s because, when gas accrete to BH, gas forms the accretion dist arround BH.
Accretion disk emit the strong radiation and prevents gas to accrete to the BH. In addition, if there is the dust,
Because radiation pressure efficently works on dust, affects the accretion onto BH.
From now, I shortly shows the evidence of the existence of dust in the early universe and the effect of radiation pressure on dusty gas.
SMBH seed 10 5 𝑀 ☉
SMBH 𝑀 ☉

3. 1. Introduction Existence of dust around SMBH in the early universe
Extinction curve of quasar at z=6.2
Salpeter IMF
Existence of dust around SMBH in the early universe
Recent observation suggested the existence of a large amount of dust around SMBH in the early universe (e.g. Maiolino et al. 2004; z≈6.2).
This black thick solid line the extinction curve observed by Maiolino. X-axies is one/ lambda and y is extionction.
Other lines are extinction curve derived by theoretical model. Dust formation by supernova exprosion. This four extinction is derived by assuming the Salpeter IMF and
This line is derived by single supernova. As yuu can see, observed extinction curve and matches well with is theoretical model.
Therefore, they concluded that this result shows the existence of dust around SMBH in the early universe.
Maiolino et al. (2004)

4. 1D radiation hydrodynamics
1. Introduction
Yajima et al. (2017) shows that radiation pressure suppress the dusty gas accretion onto BH.
1D radiation hydrodynamics BH
Now we see the existence of dust near the black hole in the early universe. Next, we are going to see the effect of dust.
Yajima put the BH in the centre of the gas cloud. Cloud is consists of H, He, and Dust. By doing the !D radiation hydrodymics simulations,
They show that radiaiton pressure supress the dusty gas accretion onto BH. This is one of the result they did in their paper.
Xaid is the initial condition of number nensity of the gas and yaxis is the BH luminosity devided by Eddington luminosity.
Red dot result is the solar metalicity case and black line is the 0 metalicity reslut. In their simulations. they assume the solar metal—dust mass ratio,
As you can see, if the amount of dust is large, since radiation pressure have a strong influence on dust, radiation pressure supress the dusty gas accretion.
H, He, Dust

5. 1. Introduction
Yajima et al. (2017) assumed that dust and gas are completely coupled. ?
In their simulation, howeve, assumed that dust and gas are completely coupled.
Therefore, we can not get the effect of relative velocity between dust and gas on dusty gas accretion.
The effect of relative velocity between dust and gas

6. 1. Introduction We investigate
the impacts of relative motion of dust and gas on the accretion rate onto BH
Therefore, we .

7. 1D radiation hydrodynamics
2. Method & Model
1D radiation hydrodynamics
Relative velocity between
dust and gas
(Ishiki et al. 2018)
IMBH
𝑀 BH = 𝑀 ☉
Same as in Yajima et al., We do the !d radiaiton hydrodynamics. We put the IMBH in the center of the gas cloud.
Gas cloud is consisit of H, He, and Graphite In addition we consider the effect of relative velocity between dust and gas on gas accretion onto BH,
H, He, Graphite;
𝑛 H =10, 30, 100 cm −3

8. 2. Method 1D radiation transfer 1D Hydrodynamics (Ishiki et al. 2018)
scheme: SLAU2 (Kitayama & Shima 2013)
dust drag force: Coulomb drag force
Collisional drag force
(Draine & Salpeter 1979)
dust charge: primary electron emission
Augar electron emission
secondary electron emission
electron and ion collision
(Weingartner & Draine 2001),
(Weingartner et al. 2006)
In my simulations, we solve 1D radiation transfer and 1D hydrodynamics. In order to derive the
relative velocity we use the code which I made in other paper.
Sheme is slau2 . In order to derive therelative velocity, we consider the effecct of these dust dragfore.
In order toget the coulomb drag force, we consider the effect of following dust charge.

9. 2. Method Dust Graphite size 0.1, 0.01 micron
ratio n0.1: n0.01 = 1:102.5
We assume the very simplified dust modeel in my simulaiton.
In erder to get the MW like extinction curve, we assme this number ratio.

10. 2. Method Chemical reactions Heating and cooling
Collisional ionization
Recombination
Dielectronic recombination
Heating and cooling
photoionization heating
collisional ionization cooling
dielectronic recombination cooling
collisional excitation cooling
bremsstrahlung cooling
inverse Compton cooling
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.

11. 3. Result density: 10, 30, 100 c m −3 BH mass: 10 5 M ☉
𝜂 (𝐿=𝜂 𝑀 𝑐 2 ): 0.1, 0.3
Z: , 1.0 Z ☉
Dust-to-metal: solar
In my simulation, I put a radiation source in the center of spherically symmetric gas distribution. A spectrum of the radiation source is the spectrum of blackbody at or PEGASE.2 which is the spectrum of a cluster of stars. I solve the chemistry of gas consists of H, He and dust.

12. Time averaged BH Luminosity Eddington Luminosity
3. Result Time averaged BH luminosity
𝐿=𝜂 𝑀 𝑐 2
Red: relative velocity
Black: completely coupled
𝜂=0.3
𝜂=0.1
×2.7
×10
×3.2
Time averaged BH Luminosity Eddington Luminosity
𝑍=1.0 𝑍 ☉
The decoupling of dust from gas promotes the gas accretion onto BH.
First, x-axis is distance from radiation source and y-axis is number density of H, and large size dust-small size dust mass ratio.
Difference of Cloud number is the strength of radiation from radiation source. Right Cloud has more strong radiation compare with left Cloud.
From this results, large dust is selectively removed from HII regions.
Then why is large dust removed from HII regions?
Constant radaitive efficiency
𝑍=0.1 𝑍 ☉
Number density of gas

13. 3. Result
Why does the decoupling of dust from gas promote the gas accretion onto BH?
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.

14. 3. Result Spatial distribution of dust grains
𝑛 H =100 c m −3 ,
Z=1.0 Z ☉ , 𝜂=0.1
𝑛 H =10 c m −3 ,
Z=1.0 Z ☉ , 𝜂=0.1
𝑛 H =100 c m −3 ,
Z=1.0 Z ☉ , 𝜂=0.3
gas
dust 0.1 micron
dust 0.01 micron
t=5.0 Myr
Dust-to-gas mass ratio near BH becomes small.
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.
The effect of radiation pressure on dusty gas accretion becomes weaker.
The decoupling of dust from gas promotes the gas accretion onto BH.

15. Time averaged BH Luminosity Eddington Luminosity
3. Result Time averaged BH luminosity
𝐿=𝜂 𝑀 𝑐 2
Red: relative velocity
Black: completely coupled
𝜂=0.3
𝜂=0.1 ?
Time averaged BH Luminosity Eddington Luminosity
𝑍=1.0 𝑍 ☉
First, x-axis is distance from radiation source and y-axis is number density of H, and large size dust-small size dust mass ratio.
Difference of Cloud number is the strength of radiation from radiation source. Right Cloud has more strong radiation compare with left Cloud.
From this results, large dust is selectively removed from HII regions.
Then why is large dust removed from HII regions?
𝑍=0.1 𝑍 ☉
Number density of gas

16. Time averaged BH Luminosity Eddington Luminosity
3. Result Time averaged BH luminosity
Red: relative velocity
Black: completely coupled
Blue: analytical estimate Z=1.0 𝑍 ☉
Green: analytical estimate Z=0.1 𝑍 ☉
Gray: analytical estimate Z=0.0 𝑍 ☉
𝐿=𝜂 𝑀 𝑐 2
𝜂=0.3
𝜂=0.1
Time averaged BH Luminosity Eddington Luminosity
𝑍=1.0 𝑍 ☉
Analytical estimate shows almost same accretion rate between 𝜂=0.1, 𝑍=0.1 𝑍 ☉ and 𝜂=0.1, 𝑍=0.0 𝑍 ☉ .
First, x-axis is distance from radiation source and y-axis is number density of H, and large size dust-small size dust mass ratio.
Difference of Cloud number is the strength of radiation from radiation source. Right Cloud has more strong radiation compare with left Cloud.
From this results, large dust is selectively removed from HII regions.
Then why is large dust removed from HII regions?
𝑍=0.1 𝑍 ☉
Number density of gas

17. How about Spectral Energy Distribution (SED) at IR wavelengths?
3. Result
How about Spectral Energy Distribution (SED) at IR wavelengths?
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.

18. 3. Result Temperature of dust: Radiative equilibrium
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.

19. 3. Result SED: IR re-emission from dust
𝑛 H =100 c m −3 ,
Z=1.0 Z ☉ , 𝜂=0.3
SED
Magenta: Relative velocity
Black: Initial dust-to-gas mass ratio
gas
dust 0.1 micron
dust 0.01 micron
×0.1
Magenta: Relative velocity
Black: Initial D/g
This Magenda solid line is the sed of IR re-emission from dust when we use the spatial distribution of dust I get from my simulation result.
This is the spatial distribution of gas and dust and magent dust temperature we use to plot the sed.
As same as before, black..
The black dashded line of SED and dust temperature is the result when we assume the initial uniform dust-to-gas mass ratio in our simulations.
I mean that black dashed line is the SED that we do not use these dust number de sity, but I use initial uniform dust-to-gas mass ratio.
Since radiation pressure hot 10^3 K dust from near BH, SED at 10 microm becomes smaller than 1 order.
For this reason, we should be careful the dust-to-gas mass ratio.
∼10 3 K
Dust
Temperature
Radiation pressure removes high temperature dust.

20. 4. Summary
The decoupling of dust from gas promote the gas accretion onto BH.
The dust-to-gas mass ratio significantly changes in HII regions because of the strong radiation pressure.
The decoupling of dust from gas affects SED at IR wavelengths.

22. 3. Result Spatial distribution of dust grains
𝑛 H =100 c m −3 ,
Z=1.0 Z ☉ , 𝜂=0.1
𝑛 H =100 c m −3 ,
Z=0.1 Z ☉ , 𝜂=0.1
gas
dust 0.1 micron
dust 0.01 micron
t=5.0 Myr
12. I solve one-dimensional radiation transfer equation including scattering by
the impact parameter method.
Hydro dynamics is solved by a scheme called ASUM+ with second order accuracy in space and time.
In addition, we add the effect of dust drag force including collisional drag and coulomb drag.