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Dependence of MultiTransonic Accretion on Black Hole Spin

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Title: Dependence of MultiTransonic Accretion on Black Hole Spin


1
Dependence of Multi-Transonic Accretion on Black
Hole Spin
  • Paramita Barai
  • Graduate Student, Physics Astronomy
  • Georgia State University
  • Atlanta, GA, USA
  • 06/29/2005

2
Contents
  • Introduction Motivation
  • What are we doing?
  • Our system formulations
  • Results
  • Conclusions

3
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

4
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

5
Draw fig in board
  • BH spin angular momentum of accreting matter
    directions
  • Show prograde retrograde accretion flow
    explicitly (or, co counter rotating BH)

6
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

7
  • 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

8
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

9
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

10
Metric Others
  • Kerr metric in equatorial plane of BH (Novikov
    Thorne 1973)
  • Angular velocity, ?
  • Normalization
  • 4th Component of velocity

11
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

12
Conserved Quantities
  • Specific energy (including rest mass)
  • Mass accretion rate
  • Entropy accretion rate

13
Quantities at Sonic Point
  • Radial fluid velocity
  • Sound speed
  • Quadratic eqn for (du/dr)c

14
Sonic Point Quantities
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16
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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18
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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22
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

23
Important Conclusion Differentiating Accretion
Properties of Co Counter Rotation of Central
Black Hole
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27
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 (?)

28
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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31
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

32
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

33
Thank You All
34
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

35
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