The Dynamics of Black Holes in aGaseous Medium

Andres EscalaYale University/Universidad de Chile

November 2002

Advisors: Paolo Coppi, Richard Larson.

Conclusions.

Outline

Scientific Motivation.

Role of Hydrodynamical Friction in theCoalescence of a Binary SMBH.

Evolution After the End of the HydrodynamicalFriction Regime.

SMBH History in the Context ofGalaxy Formation

Current Galaxy Formation Theory is based on Hierarchical Mergers.

What is the fate of the BH's? Will they also Coalesce?

Such Mergers show aVariety of PhysicalConditions. The easiestdistinction is between gasrich and gas poor mergers.

Steinmetz 02'

Hydrodynamical Friction

FHDF = -4π (G ΜΒΗ)2 ρ vBH-2 F(vBH/CS)

Hydrodynamical Friction

FHDF = -4π (G ΜΒΗ)2 ρ vBH-2 F(vBH/CS)

Ostriker '99

Isothermal Sphere

Non Singular Isothermal Spherein Hydrostatic Equilibrium.

Nsph=400,000

One BH (Mbh= 0.01Mgas) initially

in a circular orbit.

Spiral Shock, v=1.1 cS.

X

Y

Evolution of a Single BHinitially in a circular orbit.Hydrostatic gas sphere.Stellar sphere in dynamical

equilibrium.Stronger decay in the gas

sphere (factor of 2).

Isothermal Sphere

Gas

Stars

Adiabatic Sphere

Adiabatic (n=1.5) Sphere inHydrostatic Equilibrium.Single BH (Mbh= 0.01Mgas)

initially in a circular orbit.

Qualitatively same spiral

feature, v=1.1 cS.

X

Y

Hydrostatic gas sphere.Stellar sphere in dynamical

equilibrium.Transonic regime: stronger

decay in the gas sphere.Subsonic regime: comparable.

Adiabatic Sphere

Gas

Stars

Isothermal Sphere

Binary BH initially in acircular orbit.

Spiral shock, v=1.1 cS.

Non-singular isothermalsphere in hydrostaticequilibrium.

X

Y

Isothermal Sphere

0.020.1 0.06

Evolution of the binary'sseparation.Mbinary/Mgas: 0.02,0.06,0.1.

Tsound=1, orbital period=2.

Adiabatic (n=1.5) sphere inhydrostatic equilibrium.Binary BH in a circular

orbit.

Mbinary= 0.02Mgas

Adiabatic Sphere

Adiabatic Sphere

Evolution of the Binary'sSeparation.Mbinary/Mgas: 0.02,0.06,0.1.

Tsound=2, orbital period=4.The total effect is 2-3 times

weaker than isothermal.

0.02

0.06

0.1

Comparison

0.02

0.06

0.1

0.020.1 0.06

t/tsound

[tsound=0.5 torbital]

t/tsound

Isothermal Adiabatic

Efficient Drag Force.

Drag Force (Ostriker 1999) Mach Number

The RadialProfile of the Mach Number (vrot/CS) is Important.

Isothermal

Adiabatic

Strong Drag

Scaling.

Gas Sphere withMgas=1010MO, r=200pc.

Tsound=1.6 106 yr

A Binary SMBH with Mbh=5 108 MO will reduce itsseparation from 200pc to 3pc in 8 106 yr.

Gravitational Radiation Coalescence Timescale (Peters 64'):

tGR = 0.08 c5a4(G3M123)-1 F(e) = 1011 yr > tHo

Non-singular isothermalsphere in hydrostaticequilibrium.

Futher Evolution

Binary BH with Mbinary =Mgas

Roughly equivalent to theevolution of the binary(0.01Mgas) in sphere insider=0.2

X

Y

Non-singular isothermalsphere in hydrostaticequilibrium.

Evolves from spherical toflattened configuration.

Z

X

Futher Evolution (X-Z Plane)

Z

X

Binary BH with Mbinary =Mgas

Evolution of the binary'sseparation.

Mbinary = Mgas

No signature ofcoalescence stalling.

Futher Evolution

.... Still running

Conclusions

With gas, radial Mach number profile is also important(not just density profile).

In the transonic regime the coalescence timescales areshorter (factors of 2) than the stellar (collisionless) case.

Dissipative nature of gas can produce more condencedconfigurations (shorter timescales).

Instead the coalescence is driven by interaction withcircumbinary envelope. No evidence (yet) of stalling.

When binary BH dominates local gravitational potential,the coalescence is no longer hydrodynamical friction.