OneDimensional Accretion Disk Model with Inflow Outflow

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One-Dimensional Accretion Disk Model with Inflow
- Outflow

• By
• Truong Le Peter Becker
• Oct. 31, 2001
• George Mason University
• School of Computational Science

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Outline

• Observational Driven
• Accretion Disk
• (1) Models, (2) Descriptions, and (3) Flows
• Hydrodynamics Equations Describe Accretion
  Inflow-Outflow
• 4 Conservation Equations
• 8 Dynamical Equations
• Boundary Conditions
• Inner boundary conditions
• Sonic point boundary conditions
• Outer boundary conditions
• Numerical Flow Solutions
• ADAF Inflow (Narayan etal. 1997 )
• Comparison between ADAF and ADAF Acceleration
• Conclusion
• Future Works
• Final Thought

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Observational Driven

• What are these objects?
• AGN
• Quasars, QSOs, Radio Galaxies, Seyfert Galaxies,
  and BL Lac Objects
• Why do we bother to study these objects?
• Interesting and they are objects which predicted
  by Einstien General Theory of Relativity and also
  they may contain information relating to the
  understanding of the universe.
• What do we observed from these objects?
• Highly collimated jets
• Multiple wavelengths emission
• What is the power house for these objects?
• Black hole
• What mechanism produces these jets? Where is the
  jet originated? What processes produce these
  multiple wavelengths emission ? And why do some
  objects produce jets while other do not?

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Thin Accretion Disk Models

• Cooling-Dominated Flows describe the viscous
  heating of the gas is balanced by local radiative
  cooling.
• Thin accretion disk model was first developed by
  Shakura Sunyaev (1973), Novikov Thorne (1973)
  to study black holes in binary systems
• Global models of thin accretion disk developed by
  Paczynski Bisnovatyi-Kogan (1981), Muchotrzeb
  Paczynski (1992) which include effects such as
  the radial pressure and radial energy transfer to
  study transonic accretion flows around black
  holes.
• Advection-Dominated Flows describe the radiative
  cooling is very inefficient and most of the
  dissipated energy is advected into the black
  hole.
• Global models Advection-Dominated Accretion
  Flows developed by Begelman (1978), Begelman
  Meier (1982) and Narayan, Kato Honma (1997) to
  study the properties of global solutions,
  concentrating on the nature of the flow near the
  black hole
• Advection-Dominated Flows with Outflow have also
  suggested that outflow is possible based on the
  Bernoulli number.
• Global models Advection-Dominated Inflow-Outflow
  Solution (ADIOS) developed by Blandford
  Begelman (1999).
• Global models Relativistic Advection-Dominated
  Inflow-Outflow Solutions (RADIOS) modified by
  Becker, Subrammanian Kazanas (2001)

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Accretion Disk Description

• Suppose matter is going around a mass M in a
  nearly circular orbit of radius r.
• Balancing gravitational force against centrifugal
  force, we find the angular velocity to be
• Now consider a gaseous disk varies in accordance
  with the angular description W.
• Such a variation of angular velocity would imply
  the existence of velocity shear within the disk
• Due to the action of viscosity, we then expect
  angular momentum to be transferred from the
  faster-moving inner regions of the disk to the
  slower-moving outer regions.
• As the material in an inner layer loses angular
  momentum, it moves inward in a spiral path.
• Hence it is viscosity which determines the rate
  of radial inflow of matter and therefore the rate
  at which the gravitational potential energy is
  converted into other forms.
• If the gas had no viscosity, then the material in
  the disk would keep on going in circular orbits
  and there would be no release of gravitational
  energy after the formation of the disk.

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Accretion Disk Flows

• Since the gas will be radially accelerated toward
  the black hole, undergoing a transition from
  subsonic to supersonic speed, a full description
  of the flow forces that the pressure and inertial
  terms be included in the radial equation motion,
  the viscosity be included in the angular equation
  of motion, and the energy transport by advection
  be included in the energy equation.
• Also, because we are interested in the outflow
  solution as well as the inflow solution, we need
  to include the outflow of mass, angular momentum
  and energy in the dynamical equations.

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What model(s) do we need to consider?
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Conservation Equations
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Conservation Equations
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Dynamical Equations
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Dynamical Equations
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Dynamical Equations
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What do I got so far?
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Boundary Conditions
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Boundary Conditions
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Narayan et al. (1997) Solution

• To obtain Narayan et al.(1997) solution, we
  assume that there is no outflow by taking the
  escaping times to infinity.
• Once we did that our equations confirm their
  dynamical equations as well as their
• numerical solutions.

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ADAF-Inflow Numerical Solutions

• Case 1 a.1, gg1.5, Jg2.6, Qc10-4,
  K00.00734, rC6.132, rgC2.001

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ADAF-InflowNumerical Solutions

• Case 2 a.001, gg1.5, J3.767 , Qc10-4,
  K00.0000708, rC4.22, rgModify2.001

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ADAF with Outflowtoy model
Mdot
T_esc
Q
J
r
r
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ADAF Case1
U/U_r
U,U_r
Rho,rho_r
Rho/rho_r
r
r
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ADAF with Acceleration Case 1
U,U_r
U/U_r
Rho,rho_r
Rho/rho_r
r
r
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So, why is the crossing?
Energy Rate Density Ratio
Energy Rate density
Timescale SSM
Timescale SSM2nd FA
r
r
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What do I got now?
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Conclusions

• (1) we have shown that our numerical solutions
  are the same as
• Narayan et al. (1997)
• (2) the Advection-Dominated Accretion Flows
  (ADAF) model provides the
• picture of how gases flow near the
  vicinity of a black hole
• (3) we have successfully incorporate the outflow
  part to the toy model and the
• results are promising.
• (4) From the toy model, we have shown that the
  specific angular momentum (J)
• and the mass accretion rate (\dotM) have to
  be large at far infinity and slowly decrease as
  materials begin to escape.
• (6) we have shown that the energy transporting
  rate per unit mass (Q)
• is increasingly positive as material
  transport toward the sonic point, which is
• one of the criterial for outflow.
• (7) Physical Model ADAF Acceleration
  problem???
• Crossing between total and relativistic energy
  density
• Relativistic energy density is higher than the
  total energy density

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Future Works

• Exploring the free parameters space and see what
  we get.
• Solving the energy transport equation. We want to
  use the results obtain from the integration to
• Obtain the energy distribution function
• Obtain the temperature profile
• Check against our results from the dynamical
  equations
• Using this model, we want to fit it with the
  observed data and see what we can come up with.

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Final Thought