Transcript BH Spin

MEASURING SPIN
PARAMETERS OF
STELLAR-MASS
BLACK HOLES
Ramesh Narayan
Spin: Fundamental
Property of a Black Hole

Mass: M

Spin: a* (J=a*GM2/c)

Charge: Q (~0)
From the point of view of BH physics, the
spin of a BH is very fundamental
Importance in Astrophysics





Free energy associated with BH spin may
be responsible for relativistic jets
BH spin values give a handle on angular
momenta of progenitor stars
Gamma-ray bursts and BH spin?
SMBH spin and galaxy merger history
BH spin affects gravitational wave signals
Mass is Easy, Spin is Hard





Mass can be measured in the Newtonian limit using test
particles (e.g., stellar companion) at large radii
Spin has no Newtonian effect
To measure spin we must be in the regime of strong
gravity, where General
Relativity operates
Need test particles at
small radii
So we must use
the gas in the
accretion disk…
Estimating Black Hole Spin

X-Ray Continuum Spectrum 

Relativistically Broadened Iron Line –

Quasi-Periodic Oscillations
Our Team
Jeff McClintock
Ramesh Narayan
Charles Bailyn, Shane Davis, Lijun Gou,
Akshay Kulkarni, Li-Xin Li, Jifeng Liu, Jon McKinney,
Jerry Orosz, Bob Penna, Mark Reid, Ron Remillard,
Rebecca Shafee, Danny Steeghs, Manuel Torres,
Jack Steiner, Sasha Tchekhovskoy, Yucong Zhu
Innermost Stable Circular
Orbit (ISCO)




RISCO/M depends
on the value of a*
If we can measure
RISCO, we will
obtain a*
Note factor of 6
variation in RISCO
Especially sensitive
as a*1
The Basic Idea
Accretion disk has a dark central “hole” with no radiation
Measure radius of hole by estimating area of the bright inner disk
Measuring the Radius of a Star

Measure the flux F received from the star

Measure the temperature T* (from spectrum)
L*  4 D F  4 R  T
2
2
*
4
*
R
F
 

D
 T*4
2
*
2
R*  D

L1/2
 37.5 *2

T*
R*
 cgs 
Measuring the Radius of the
Disk Inner Edge

We want the radius of the “hole” in the disk emission

Same principle as for a star


From X-ray data we obtain
FX and TX   (bright)
Knowing distance D and
inclination i we get RISCO
(geometrical factors)
RISCO
RISCO
(some

From RISCO/M we get a*

Need to be careful: focus on Thermal Dominant (TD) data
Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006);
Davis et al. (2006); Liu et al. (2007); Gou et al. (2009,2010); Steiner et al. (2010)…

Ldisk
3GMM
F ( R) 
8 R3
GM M

2Rin

Rin 
4
1



T


eff ( R )
R 

1/4
Rin 
 Rin  
Teff ( R)  T* 

 1 
R 
 R  
3/4
1/4
 3GMM 
T*  
, Teff,max  0.4879T*
3 
 8 Rin 
L1/2
Rin  15.4 2disk  cgs 
Teff,max
ShakuraSunyaev
model
Rin=6M
Note that the result does not depend on the details of the
‘viscous’ stress ( parameter)
A Test of the
Blackbody
Assumption




H1743-322
For a blackbody, L scales as T4 Kubota, Done et al. (2002,…)
(Stefan-Boltzmann Law)
McClintock et al. (2008)
BH accretion disks vary a lot in
their luminosity
If a disk is a perfect blackbody,
L should exactly as T4
Good, but not perfect…
L  A T
4
f = Tcol/Teff
H1743-322
Tin4
Davis et al. (2005, 2006)
After including the
color correction, we get
an excellent L-T4 trend
f
Spectral hardening factor
Conclusion:
Thermal State is
very good for
quantitative
modeling
4
Teff
f
General Relativistic Disk Model:
Novikov & Thorne (1973)
L(r) peaks at a
different radius for
each value of the
dimensionless BH
spin parameter a*
Therefore, the
observed spectrum
depends on a*
This is what enables
us to estimate a*
from observations
Summary of the Method





We fit the X-ray continuum spectrum
We include all relativistic effects
We focus on “good data” (TD), where the
emission is mostly blackbody so that we
can model the spectrum reliably  
To convert “solid angle” measurement to
an estimate of RISCO, we measure
independently D, i
Then, knowing M, we calculate RISCO/M,
and thus obtain an estimate of a*
L / LEdd
LMC X-3: 1983 - 2009
LMC X-3
Thick Disk
L / LEdd
LMC X-3: 1983 - 2009
Hard State
LMC X-3
Rin
L / LEdd
LMC X-3: 1983 - 2009
LMC X-3
Steiner et al. (2010)
403 spectra (assuming M=10M, i=67o)
New Result: XTE J1550-564
(Steiner, Reis et al. 2010)




M=9.100.61, D=4.380.5, i=74.73.8
(Orosz et al. 2010)
Spin estimate from continuum fitting:
a* ~ 0.35 (90% cl: -0.11, +0.71)
Spin estimate from iron line fitting:
a* ~ 0.55 (1 limits: 0.33, 0.70)
Combined spin estimate:
a* = 0.49 (1 limits: 0.29, 0.62)
XTE J1550-564: Outburst Light Curve 1998-1999
X-ray continuum spectral fits and residuals for a TD (“gold”) and
an SPL (“silver”) observation
Estimates of disk inner edge Rin and BH spin parameter a* from all
suitable TD (“gold”) and SPL/Intermediate (“silver”) observations
Combined
Fe line method
CF Method:
Includes errors
in M, D, I
Probability distribution of spin of J1550 (Steiner et al. 2010)
BH Spin Measurements via
Continuum-Fitting
Source Name
BH Mass (M)
BH Spin (a*)
A0620-00
6.3—6.9
0.10 ± 0.20
LMC X-3
5.9—9.2
~0.25
XTE J1550-564
8.5—9.7
0.50±0.20
GRO J1655-40
6.0—6.6
0.70 ± 0.05
M33 X-7
14.2—17.1
0.77 ± 0.05
4U1543-47
7.4—11.4
0.80 ± 0.05
LMC X-1
9.0—11.6
0.92 ± 0.06
GRS 1915+105
10—18
0.99 ± 0.01
Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu
et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)
A Major Issue

NT model assumes that the
torque vanishes at the ISCO
(Shakura & Sunyaev 1973)

But magnetic fields could
produce significant torque at
and inside the ISCO (Krolik
1999; Gammie 1999)

Afshordi & Paczynski (2003),
Shafee et al. (2008) showed
that the effect is not important
for a THIN hydrodynamic disk

But what about an MHD disk?
3D GRMHD Simulations of
Thin Accretion Disks





Shafee et al. (2008), Penna
et al. (2010)
Self-consistent MHD
simulations (HARM: Gammie,
McKinney & Toth 2003)
All GR effects included
h/r ~ 0.05 — 0.08 (thin!!)
Very few other thin disk
simulations: Reynolds &
Fabian (2008); Noble, Krolik
& Hawley (2009, 2010)
a*=0
a*=0, 0.7, 0.9, 0.98
Kulkarni et al. (2010)
a*=0.9; i=15o, 45o, 75o
a*=0, 0.7, 0.9; i=75o
Modeling Error Due to Deviations
From the Novikov-Thorne Model
a*=0
a*=0.7
a*=0.9 a*=0.98
i=15o
0.04
0.72
0.90
0.985
i=45o
0.06
0.73
0.91
0.986
i=75o
0.17
0.80
0.93
0.991
Kulkarni et al. (2010)

The systematic error due to assuming the NT model is less than the
statistical error due to measurement uncertainties
The simulated disks correspond to L/LEdd ~ 0.5
Measurements are, however, made using data at L  0.3 LEdd

 True systematic errors will be less than the above values


BH Spin Measurements via
Continuum-Fitting
Source Name
BH Mass (M)
BH Spin (a*)
A0620-00
6.3—6.9
0.10 ± 0.20
LMC X-3
5.9—9.2
~0.25
XTE J1550-564
8.5—9.7
0.50±0.20
GRO J1655-40
6.0—6.6
0.70 ± 0.05
M33 X-7
14.2—17.1
0.77 ± 0.05
4U1543-47
7.4—11.4
0.80 ± 0.05
LMC X-1
9.0—11.6
0.92 ± 0.06
GRS 1915+105
10—18
0.99 ± 0.01
Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu
et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)
Disk
Inclination
Is BH spin aligned
with orbit vector?
We assume this in
order to estimate i
X-ray polarimetry
will help: GEMS
Population synthesis
studies look hopeful
(Fragos et al. 2010)
Li, Narayan & McClintock (2009)
Importance of BH Spin





Of the two parameters, mass and spin,
spin is more fundamental
Mass is merely a scale – just tells us
how big the BH is
Spin fundamentally affects the basic
properties of space-time around a BH
More than simple re-scaling
BH spin may power relativistic jets…
Relativistic Jets in GRS
1915+105
GRS 1915+105 has an extreme
value of spin: a*=0.98-1
Also spectacular relativistic jets
Blobs of material are seen to
flow out with v = 0.92c
Could the relativistic ejections
be connected to the BH spin?
GRS
1915+105
BH Spin Values vs
Relativistic Jets
Source Name
BH Mass (M)
BH Spin (a*)
A0620-00 (J)
6.3—6.9
0.10 ± 0.20
LMC X-3
5.9—9.2
~0.25
XTE J1550-564 (J)
8.5—9.7
0.50±0.20
GRO J1655-40 (J)
6.0—6.6
0.70 ± 0.05
M33 X-7
14.2—17.1
0.77 ± 0.05
4U1543-47
7.4—11.4
0.80 ± 0.05
LMC X-1
9.0—11.6
0.92 ± 0.06
GRS 1915+105 (J)
10—18
0.99 ± 0.01
Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu
et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)
Summary





BH spin measurement by continuum
fitting is now a well-developed technique
Measurement errors are quantifiable
(except for disk inclination)
Systematic model errors are under control
XTE J1550-564: Consistent spin estimates
from continuum-fitting & Fe-line methods
BH spin is perhaps not very important for
relativistic jets…