Ramesh Narayan

(McClintock, Shafee, Remillard, Davis, Li)

Black Holes are Extremely SimpleBlack Holes are

Extremely Simple Mass: M Spin: a*=a/M (J=a*GM2/c)

(Electric Charge: Q)Many BH masses have been measured

Obvious next frontier: Measure BH spin (much harder)

Beyond that: Test the Kerr Metric (even harder)

Innermost Stable Circular Orbit (ISCO)

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*

Measuring the Radius of a Star

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

2 2 4

2

4

4 4

R F=

D T

L D F R T

R

Measuring the Radius of the Disk Inner Edge

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

Estimates of Spin Obtained with this Method

Estimates of Spin Obtained with this Method

System a* Reference

GRO J1655-40

0.65-0.75

Shafee et al. (2006)

4U1543-47 0.7-0.8 Shafee et al. (2006)

GRS 1915+105

0.98-1.0 McClintock et al. (2006, astro-ph/0606076)

LMC X-3 <0.26 Davis et al. (2006)

How to Get Reliable Results?

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)

GRS 1915+105 in the High Soft

State

GRS 1915+105 in the High Soft

State

Gierlinski & Done (2002) Kubota et al. (2004)

Spectral Hardening Factor

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

Viscous Energy Dissipation Profile

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 !!

3 1/ 24 4 in ineff eff*

eff

( ) ( ) 1

( ) ( )

R RF R T r T

R R

T R f T R

However,…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)

Torque vs Disk Thickness

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)

GRS 1915+105

Spin Estimate

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)

Estimates of SpinEstimates of Spin

System a* Reference

GRO J1655-40

0.65-0.75

Shafee et al. (2006)

4U1543-47 0.7-0.8 Shafee et al. (2006)

GRS 1915+105

0.98-1.0 McClintock et al. (2006, astro-ph/0606076)

LMC X-3 <0.26 Davis et al. (2006)

DiscussionDiscussion 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?