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Dependence of Multi-Transonic Accretion on Black Hole Spin
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  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 P. Barai, GSU

  2. Contents • Introduction & Motivation • What are we doing? • Our system formulations • Results • Conclusions P. Barai, GSU

  3. Mach number Accretion flow Subsonic: M < 1 Supersonic: M > 1 Transonic: crosses M = 1 Transition Smooth -- Sonic point Discontinuous -- Shock Multi-transonic flow  3 sonic points Introduction P. Barai, GSU

  4. 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 Motivation P. Barai, GSU

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

  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 P. Barai, GSU

  7. Notations Gravitational Radius Black Hole Spin / Kerr Parameter = a 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 P. Barai, GSU

  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 P. Barai, GSU

  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 >> infall) • Effect of Viscosity     Flow behavior as function of  provides information on viscous transonic flow P. Barai, GSU

  10. Metric & Others • Kerr metric in equatorial plane of BH (Novikov & Thorne 1973) • Angular velocity,  • Normalization: • 4th Component of velocity: P. Barai, GSU

  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 P. Barai, GSU

  12. Conserved Quantities • Specific energy (including rest mass) • Mass accretion rate • Entropy accretion rate P. Barai, GSU

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

  14. Sonic Point Quantities P. Barai, GSU

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  16. Results • For some [P4] -- get 3 sonic points on solving eqn • rout > rmid > rin • rout, rin : X-type sonic points • rmid : O-type sonic pt (unphysical – no steady transonic soln passes thru it) • Multitransonic Accretion: (rin) > (rout) • Multitransonic Wind : (rin) < (rout) • General astrophysical accretion  Flow thru rout • Flow thru rinpossible 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 P. Barai, GSU

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  18. E- Multi-Transonic Space For Different  P. Barai, GSU

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  20. Variation of E- Multi-Transonic Space for Change in Kerr Parameter, a P. Barai, GSU

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  22. 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 We found: At higher values of angular momentum multi-transonicity is more common for retrograde flow Angular Momentum P. Barai, GSU

  23. Important Conclusion: Differentiating Accretion Properties of Co & Counter Rotation of Central Black Hole P. Barai, GSU

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  27. Prograde Accretion Flow Multi-transonic regions at lower value of  Retrograde Accretion Flow Multi-transonicity much more common Covers higher value of angular momentum () Differentiating Pro & Retro-Grade Flows P. Barai, GSU

  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 P. Barai, GSU

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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 P. Barai, GSU

  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 P. Barai, GSU

  33. Thank You All P. Barai, GSU

  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 P. Barai, GSU

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