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Ramesh Narayan (McClintock, Shafee, Remillard, Davis, Li)

Ramesh Narayan (McClintock, Shafee, Remillard, Davis, Li). GRS 1915+105: An. Extreme Kerr Hole. Black Holes are Extremely Simple. Mass: M Spin: a * =a/M (J=a * GM 2 /c) (Electric Charge: Q ). Many BH masses have been measured Obvious next frontier: Measure BH spin (much harder)

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Ramesh Narayan (McClintock, Shafee, Remillard, Davis, Li)

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  1. Ramesh Narayan (McClintock, Shafee, Remillard, Davis, Li) GRS 1915+105: An Extreme Kerr Hole

  2. Black Holes are Extremely Simple • Mass: M • Spin: a*=a/M (J=a*GM2/c) • (Electric Charge: Q) Many BHmasses have been measured Obvious next frontier: Measure BHspin (much harder) Beyond that: Test the Kerr Metric (even harder)

  3. Innermost Stable Circular Orbit (ISCO) • In GR, stable circular orbits are allowed only down to an innermost radius RISCO (effect of strong gravity) • RISCO/M depends on a* (quite a large effect) • An accretion disk terminates at RISCO, and gas falls freely onto the BH inside this radius • Disk emission has a ‘hole’ of radius RISCO at center • If we measure the size of the hole we will obtain a*

  4. Measuring the Radius of a Star • Measure the flux F received from the star • Measure the temperature T (from spectrum) • Then, assuming blackbody radiation: • F and T give solid angle of star • If we know distance D,we directly obtain R R

  5. Measuring the Radius of the Disk Inner Edge • We want to measure the radius of the ‘hole’ in the disk emission • Same principle as before • From F and T get solid angle of hole • Knowing D and i get RISCO • From RISCO and M get a* Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006);… RISCO

  6. Estimates of Spin Obtained with this Method

  7. How to Get Reliable Results? • Should have good estimates of M, D, i • Should include all relativistic effects (Doppler beaming, grav. redshift, ray deflections, Li et al. 2005:KERRBB) • The system should be in the high soft state: thermal blackbody radiation, with very little power-law (>90% of the flux in the thermal component) • Deviations from blackbody (parameter f) should be estimated via a disk atmosphere model • Need accurate theoretical profiles of disk flux F(R) and temperature T(R)

  8. GRS 1915+105 in the High Soft State Gierlinski & Done (2002) Kubota et al. (2004)

  9. Spectral Hardening Factor • Disk emission is not a perfect blackbody • Spectral temperature T of the emitted radiation is generally larger than effective temperature: T=f Teff • Using disk atmosphere model, can estimate f (Shimura & Takahara 1995; Davis et al. 2006) • Results are robust, provided most of the viscous energy is released below the photosphere (it is not necessary to know exact vertical profile, value of ) • Safe assumption in high soft state

  10. Viscous Energy Dissipation Profile • Well-known result for an idealized thin Newtonian disk with zero torque at inner edge (analogous results for PW or GR disk) • Completely independent of viscosity  !!

  11. However,… • The theoretical model makes a critical assumption: torque vanishes at the inner edge (ISCO) of the disk (Shakura & Sunyaev 1973) • Afshordi & Paczynski (2003) say this is okay for a thin disk, but not for a thick disk • Krolik, Hawley,et al. say there is always substantial torque at ISCO, and energy generation inside ISCO Gierlinski et al. (1999)

  12. Torque vs Disk Thickness • Hydrodynamic height-integrated -disk model with full dynamics (radial velocity, pressure, sonic radius, non-Keplerian,…) • For H/R < 0.1 (L<0.3LEdd), good agreement with idealized thin disk model • Less good at large  but still pretty good • Bottom line: stick to low luminosities: L < 0.3LEdd Shafee et al. (2007)

  13. GRS 1915+105 Spin Estimate • Limiting ourselves to L<0.3LEdd, we obtain a robust result: a*=0.98—1.0 • Insensitive to how we model the power-law tail • Insensitive to , torque • Insensitive to uncertainties in M, D, i • Can explain discrepancy with Middleton et al. (2006) McClintock et al. (2006)

  14. Estimates of Spin

  15. Discussion • All four a* values are between 0 and 1(!!) • Spins of XRB BHs evolve very little via accretion  BHs are born with a wide range of spin values • GRS 1915+105 (a*  1) is a near-extreme Kerr BH – any connection to its relativistic jets? • Was GRS 1915+105 a GRB when it was formed? • Other methods of estimating spin (QPOs) could be calibrated using the present method • Would also test the Kerr metric… • Can we estimate spins of Supermassive BHs?

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