Dependence of MultiTransonic Accretion on Black Hole Spin

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Dependence of Multi-Transonic Accretion on Black
Hole Spin

• Paramita Barai
• Graduate Student, Physics Astronomy
• Georgia State University
• Atlanta, GA, USA
• 06/29/2005

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Contents

• Introduction Motivation
• What are we doing?
• Our system formulations
• Results
• Conclusions

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Introduction

• Mach number
• Accretion flow
• Subsonic M lt 1
• Supersonic M gt 1
• Transonic crosses M 1

• Transition
• Smooth -- Sonic point
• Discontinuous -- Shock
• Multi-transonic flow ? 3 sonic points

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Motivation

• BH inner boundary condition Supersonic flow at
  Event Horizon (EH)
• Far away from EH subsonic
• Hence BH accretion is essentially transonic
• Except cases where already supersonic initially
• Multi-transonic flow ? Shock Formation

• Transonic Flow is relevant in various
  astrophysical situations
• Black Hole (BH) or Neutron Star (NS) accretion
• Collapse / Explosion of stars
• Solar / Stellar winds
• Formation of protostars galaxies
• Interaction of supersonic galactic (or
  extragalactic) jets with ambient medium

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Draw fig in board

• BH spin angular momentum of accreting matter
  directions
• Show prograde retrograde accretion flow
  explicitly (or, co counter rotating BH)

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Highlights

• Study variation of dynamic and thermodynamic
  properties of accretion flow very close to event
  horizon their dependence on spin of BH
• Found Higher shock formation possibility in
  retrograde accretion flow (i.e. BH spin is
  opposite to rotation of accreting matter) as
  compared to prograde flow

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• What do we do?
• Formulate solve conservation equations
  governing general relativistic, multi-transonic,
  advective accretion flow in Kerr metric
• Calculate flow behavior very close (? 0.01 rg) to
  event horizon as function of a
• Can be done at any length scale

• Notations
• Gravitational Radius
• Black Hole Spin / Kerr Parameter a

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Describing Our System

• No self-gravity, no magnetic field
• Units G c MBH 1
• Boyer-Lindquist coordinates ( )
• Observer frame corotating with accreting fluid
• ? Specific angular momentum of flow -- aligned
  with a
• Stationary axisymmetric flow
• Euler Continuity eqns
• Polytropic equation of state
• K specific entropy density
• ? adiabatic index, n polytropic index

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Our System

• Specific proper flow enthalpy, h
• Polytropic sound speed, as
• Frame dragging neglected
• Weak viscosity limit
• Very large radial velocity close to BH ?
  Timescale (viscous gtgt infall)
• Effect of Viscosity ? ? ? ? Flow behavior as
  function of ? provides information on viscous
  transonic flow

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Metric Others

• Kerr metric in equatorial plane of BH (Novikov
  Thorne 1973)
• Angular velocity, ?
• Normalization
• 4th Component of velocity

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Accretion Disk

• Vertically integrated model (Matsumoto et al.
  1984)
• Flow in hydrostatic equilibrium in transverse
  direction
• Equations of motion apply to equatorial plane of
  BH
• Thermodynamic quantities vertically averaged over
  disk height
• Calculate quantities on equatorial plane
• 1-dimensional quantities, vertically averaged
• Disk height, H(r) from Abramowicz et al. 1997

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Conserved Quantities

• Specific energy (including rest mass)
• Mass accretion rate
• Entropy accretion rate

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Quantities at Sonic Point

• Radial fluid velocity
• Sound speed
• Quadratic eqn for (du/dr)c

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Sonic Point Quantities
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Results

• For some P4 -- get 3 sonic points on solving
  eqn
• rout gt rmid gt rin
• rout, rin X-type sonic points
• rmid O-type sonic pt (unphysical no steady
  transonic soln passes thru it)
• Multitransonic Accretion ?(rin) gt ?(rout)
• Multitransonic Wind ?(rin) lt ?(rout)
• General astrophysical accretion ? Flow thru rout
• Flow thru rin possible only in case of a shock
• If supersonic flow thru rout is perturbed to
  produce entropy ?(rin) ?(rout), it joins
  subsonic flow thru rin forming a standing shock
• Shock details from GR Rankine-Hugoniot conditions
  

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E-? Multi-Transonic Space For Different ?
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Variation of E-? Multi-Transonic Space for Change
in Kerr Parameter, a
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Angular Momentum

• We found
• At higher values of angular momentum
  multi-transonicity is more common for retrograde
  flow

• Weakly rotating flows, found in several physical
  situations
• Detached binary systems fed by accretion from OB
  stellar winds
• Semidetached low-mass non-magnetic binaries
• Supermassive BHs fed by accretion from slowly
  rotating central stellar clusters
• Turbulence in standard Keplerian accretion disk

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Important Conclusion Differentiating Accretion
Properties of Co Counter Rotation of Central
Black Hole
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Differentiating Pro Retro-Grade Flows

• Prograde Accretion Flow
• Multi-transonic regions at lower value of ?

• Retrograde Accretion Flow
• Multi-transonicity much more common
• Covers higher value of angular momentum (?)

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Terminal Behavior of Accretion Variables

• Terminal value of accretion variable, A
• A? A (at r? re ?)
• Integrate flow from rc down to r? ? get A?
• Studied variation of A? with a ? BH spin
  dependence of accretion variables very close to
  event horizon
• Can be done for any r? ? dependence of flow
  behavior on BH spin at any radial distance from
  singularity

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Discussion Summary

• Study dependence of multi-transonic accretion
  properties on BH spin at any radial distance /
  accretion length scale
• Very close to event horizon
• Possible shock location
• Found non-trivial difference in the accretion
  behavior for co counter rotating BH
• Prograde flow (co-rotating BH) low ?
• Retrograde flow (counter-rotating BH) high ?
  greater shock formation possibility

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Astrophysical Implications

• Preliminary step towards understanding how BH
  spin affects astrophysical accretion and related
  phenomenon
• Shock waves in BH accretion disks must form
  through multi-transonic flows
• Study of the post shock flow helpful in
  explaining
• Spectral properties of BH candidates
• Cosmic (galactic extragalactic) jets powered by
  accretion (formation dynamics)
• Origin of Quasi Periodic Oscillations in galactic
  sources

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Thank You All
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Observational Consequences

• Debate Determining BH spin from observations
• Most popular approach study of skew shaped
  fluorescent iron lines
• Our approach presents the potential to deal with
  this problem
• We predict behavior of flow properties
• For hot, low-? prograde accretion flow high-?
  retrograde flow

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