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SMBH Spherically Symmetric Accretion regulated by
Violent Star Formation Feedback
Sergiy Silich
Filiberto Hueyotl-Zahuantitla & Guillermo Tenorio-Tagle
INAOE, Puebla, Mexico
The mounting evidence for violent nuclear star formation in Seyfert galaxies
has led us to consider the hydrodynamics of the matter reinserted by massive
stars through strong stellar winds and supernovae, under the presence of a central massive BH. Here we show that in most cases there is a bimodal solution
strongly weighted by the location of the stagnation radius (R_ST). Matter reinserted within the stagnation volume is to be accreted by the BH while its outer
counterpart would composed a star cluster wind. The mechanical power of the
latter, ensures that there is no accretion of the ISM into the BH and thus the BH
accretion and its luminosity is regulated by the star formation feedback. The
location of the stagnation radius is a function of three parameters: the BH
mass, the mechanical power (or mass) of the star formation event and the size
of the burst of star formation. We construct a self-consistent, stationary solution and calculate the accretion rates and BH luminosities and show that in the
case of massive burst of star formation, the BH luminosity highly exceeds the
predictions from the Bondi accretion theory.
The model
Young nuclear starbursts prevent through
their super winds the accretion of interstellar matter from the bulges and disks
of their host galaxies onto the central BHs.
In such cases the BHs are fed with the
matter injected by numerous stellar winds
and SNe explosions occurring inside young
stellar clusters.
The accretion rate and the BH luminosity
are then defined by the stagnation radius,
Rst , which separates the central zone,
where the injected matter falls onto the
BH, from the outer zone, where the star
cluster wind is formed.
Stellar cluster
ISM
.
Msc - the star cluster mass deposition rate,
Rsc - the star cluster radius
Main equations and Boundary Conditions
where qm and qe are the SB mass and energy deposition rates, respectively;
uw , ρw and Pw are the velocity, density and thermal pressure in the flow;
Q is the cooling rate, M(r) is the stellar mass inside radius r and M BH is
the BH mass.
The proper integral curve is selected by the location of two sonic points:
the inner one must be located at the star cluster center and the outer one at
the star cluster surface.
The Hydrodynamic Solution
Velocity
Number density
MSC = 108 Msol
MBH = 108 Msol
RSC = 40 pc
Rst = 2.7pc
Temperature
The threshold mechanical luminosity
Cooling cannot compete with gravity.
The critical luminosity does not exist.
Radiative cooling defines the stagnation radius
MBH = 108Msol
The gravitational pull
of the central BH and
strong radiative cooling
compete in defining the
value of the stagnation
radius.
The threshold line separates clusters evolving
in the strongly radiative,
thermally unstable regime
from those whose stagnation radius is defined by
the gravitational pull of
the central BH.
BH defines the stagnation radius
BH accretion rates
MBH = 108 Msol
RSC = 40 pc
Our model
Bondi
The comparison of our semi-analytic results with Bondi
accretion rates.
BH accretion luminosities
RSC = 10 pc
RSC = 30 pc
RSC = 40 pc
The normalized luminosity of a 108Msol
BH embedded into stellar cluster of
different mass. The various curves
consider different star cluster sizes.
The normalized luminosity of a 108Msol
BH embedded into compact (RSC = 3pc)
stellar clusters with different masses.
Conclusions
We suggest that in the case of composite AGN/starburst galaxies the
super-winds driven by a central young stellar cluster prevent the accretion
of the ISM from the host galaxies onto the central BH. In such cases the BH
luminosity is defined by the fraction of mass reinserted by stellar winds and
supernovae within the stagnation volume.
We found a threshold mechanical luminosity. This luminosity separates, in
the SC mass – BH mass – SC radius parameter space, systems evolving in
the strongly radiative, thermally unstable regime from those whose inner
structure is dominated by the gravitational pull of the central BH.
The classic, Bondi’s accretion theory shows a good agreement with our
model only in the case of low mass clusters. One has to use our results
in order to estimate the accretion rates and BH luminosities in the case
of more energetic (LSC > 0.1 Lcrit) clusters.
In the case of extended clusters the BH luminosities fall well below the
Eddington limit. However, the accretion luminosity grows rapidly for
more compact clusters and for very compact ones can approach the
Eddington limit.