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Dependence of Multi-Transonic Accretion on Black Hole Spin

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##### Dependence of Multi-Transonic 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 P. Barai, GSU**Contents**• Introduction & Motivation • What are we doing? • Our system formulations • Results • Conclusions P. Barai, GSU**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**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**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**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**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**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**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**Metric & Others**• Kerr metric in equatorial plane of BH (Novikov & Thorne 1973) • Angular velocity, • Normalization: • 4th Component of velocity: P. Barai, GSU**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**Conserved Quantities**• Specific energy (including rest mass) • Mass accretion rate • Entropy accretion rate P. Barai, GSU**Quantities at Sonic Point**• Radial fluid velocity • Sound speed • Quadratic eqn for (du/dr)c P. Barai, GSU**Sonic Point Quantities**P. Barai, GSU**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**E- Multi-Transonic Space For Different **P. Barai, GSU**Variation of E- Multi-Transonic Space for Change in Kerr**Parameter, a P. Barai, GSU**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**Important Conclusion: Differentiating Accretion Properties**of Co & Counter Rotation of Central Black Hole P. Barai, GSU**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**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**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**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**Thank You All**P. Barai, GSU**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