Dependence of Multi-Transonic Accretion on Black Hole Spin Paramita Barai Graduate Student, Physics & Astronomy Georgia State University Atlanta, GA, USA 06/29/2005 12/24/2018 P. Barai, GSU

Contents Introduction & Motivation Our system formulations Results What are we doing? Our system formulations Results Conclusions 12/24/2018 P. Barai, GSU

Introduction Mach number Accretion flow Transition Subsonic: M < 1 Supersonic: M > 1 Transonic: crosses M = 1 Transition Smooth -- Sonic point Discontinuous -- Shock Multi-transonic flow  3 sonic points 12/24/2018 P. Barai, GSU

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 12/24/2018 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) 12/24/2018 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 12/24/2018 P. Barai, GSU

Can be done at any length scale Notations Gravitational Radius 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 12/24/2018 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 12/24/2018 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 12/24/2018 P. Barai, GSU

Metric & Others Kerr metric in equatorial plane of BH (Novikov & Thorne 1973) Angular velocity,  Normalization: 4th Component of velocity: Just glance thru the eqns (this slide & the 2 next) while giving the talk finally – no need to say in detail .. 12/24/2018 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 Show fig in black-board: showing the disk heights –H/2 to +H/2, 12/24/2018 P. Barai, GSU

Conserved Quantities Specific energy (including rest mass) Mass accretion rate Entropy accretion rate 12/24/2018 P. Barai, GSU

Quantities at Sonic Point Radial fluid velocity Sound speed Quadratic eqn for (du/dr)c 12/24/2018 P. Barai, GSU

Sonic Point Quantities 12/24/2018 P. Barai, GSU

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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 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 Don’t show this slide to audience .. Just remember what is written in the text here .. Show previous fig & say this text in words, showing the fig 12/24/2018 P. Barai, GSU

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E- Multi-Transonic Space For Different  12/24/2018 P. Barai, GSU

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Variation of E- Multi-Transonic Space for Change in Kerr Parameter, a 12/24/2018 P. Barai, GSU

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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 Draw Fig in Black-Board : BH spin (a) in 1 direction, & accretion disk angular momentum is another or same direction depending on if retro or prograde accretion flow 12/24/2018 P. Barai, GSU

Important Conclusion: Differentiating Accretion Properties of Co & Counter Rotation of Central Black Hole 12/24/2018 P. Barai, GSU

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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 () 12/24/2018 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 12/24/2018 P. Barai, GSU

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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 12/24/2018 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 12/24/2018 P. Barai, GSU

Thank You All 12/24/2018 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 12/24/2018 P. Barai, GSU

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