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

Ramesh Narayan
(McClintock, Shafee,
Remillard, Davis, Li)
Black Holes are
Extremely Simple
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Mass: M
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Spin: a*=a/M (J=a*GM2/c)
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(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)
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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
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Measure the flux F received from the star
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Measure the temperature T (from spectrum)
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Then, assuming blackbody radiation:
L  4 D 2 F  4 R 2 T 4
2
F
R
  =
4
D

T
 
R
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F and T give solid angle of star
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If we know distance D, we directly obtain R
Measuring the Radius of the
Disk Inner Edge
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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
R
Knowing D and i
get RISCO
From RISCO and M get a*
ISCO
Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006);
McClintock et al. (2006); Davis et al. (2006);…
Estimates of Spin Obtained
with this Method
System
GRO J1655-40
4U1543-47
GRS 1915+105
LMC X-3
a*
Reference
0.65-0.75 Shafee et al. (2006)
0.7-0.8
0.98-1.0
<0.26
Shafee et al. (2006)
McClintock et al. (2006,
astro-ph/0606076)
Davis et al. (2006)
How to Get Reliable Results?
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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
Gierlinski & Done (2002)
Kubota et al. (2004)
Spectral Hardening Factor
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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
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Well-known result for an idealized thin
Newtonian disk with zero torque at inner
edge (analogous results for PW or GR disk)
1/ 2

 Rin  
4
4  Rin 
F ( R)   Teff (r )   Teff* 
 1  
 
 R    R  
T ( R)  f Teff ( R)
3
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Completely independent of viscosity  !!
However,…
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The theoretical model makes
a critical assumption: torque
vanishes at the inner edge
(ISCO) of the disk (Shakura &
Sunyaev 1973)
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Afshordi & Paczynski (2003)
say this is okay for a thin disk,
but not for a thick disk
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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
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Hydrodynamic heightintegrated -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
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Limiting ourselves to
L<0.3LEdd, we obtain a
robust result:
a*=0.98—1.0
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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 Spin
System
GRO J1655-40
4U1543-47
GRS 1915+105
LMC X-3
a*
Reference
0.65-0.75 Shafee et al. (2006)
0.7-0.8
0.98-1.0
<0.26
Shafee et al. (2006)
McClintock et al. (2006,
astro-ph/0606076)
Davis et al. (2006)
Discussion
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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
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Would also test the Kerr metric…
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Can we estimate spins of Supermassive BHs?