Mass Estimate of Black Hole Candidates GRS
1758-258 and GX339-4 Based on a Transition
Layer Model of the Accretion Disk and a Search
for X-ray Jets in GRS 1758-258
Nathan D. Bezayiff, David M. Smith
University of California Santa Cruz
Santa Cruz Institute for Particle Physics Seminar May 23, 2006
GX 339-4 and GRS 1758-258 are
Low Mass X-Ray Binary Systems
I.
Companion Star is smaller than or equal to our sun.
II.
Roche Lobe is the most common type of accretion.
III. If the point where the gravitational attraction between the two
stars is equal (Inner Lagrange Point) occurs near the surface of
the Companion Star, matter will be stripped from the Companion
Star into an Accretion Disc that forms around the Compact
Object.
IV. Matter falling into the black hole converts about half its
graviational binding energy to radiation via viscosity; the other
half will be released near the surface of the star.
Companion Star
Jets 
Compact Object
↑
Accretion Disc
Gravitational Attraction Between
Both Stars equal
From http://lheawww.gsfc.nasa.gov/~still/research/corr.html
Motivation For Development of the Transition
Layer Model to Determine the Mass of Black
Holes
1.
In a Low-Mass X-Ray Binary System, no knowledge of any
of the parameters of the companion are required.
2.
The parameters required to determine the mass of a black
hole only depend on the Energy Spectrum Power Law Index
and Power Density Quasi Periodic Oscillation Frequency.
3.
GRS 1758-258, 1E 1740.7-2942, and GX 339-4 are black
holes where companion information does not exist. Hence
their mass must be determined by another method.
4.
May help to classify objects as neutron stars or black holes
easier. If saturation of the Power-Law Indices is observed,
the object is a black hole. If no saturation of the Power-Law
Indices are observed, the object may be a neutron star.
Proportional Counter Array of Rossi X-Ray Timing
Explorer Provides Timing, Energy Spectra
Energy range: 2 - 60 keV
Energy resolution: < 18% at 6
keV
Time resolution: 1 microsec
Spatial resolution: collimator with
1 degree FWHM
Detectors: 5 proportional
counters
Collecting area: 6500 square cm
Layers: 1 Propane veto; 3
Xenon, each split into two; 1
Xenon veto layer
First, Get the Power Law Index
↑
Power Law Component
Interstellar
Absorption
Residuals
Normalized counts/sec/keV
Obtaining the PLI and QPO from a given observation for GRS 1758-25
Channel Energy (keV)
↓
Power Density [(Rms/Mean)^2/Hz]
Obtain the Quasi Periodic Oscillation Frequency
in the Power Density Spectra
QPO
Frequency (Hz)
Power Law Index
(PLI) Power Law Index-Quasi Periodic Oscillation
(QPO) curve
↑
Harmonic Pair?
Quasi-Periodic Oscillation (QPO) freq (Hz)
TRANSITION LAYER MODEL (VERY BASIC)
1. The Optical Depth (τ) is related to the accretion rate (dM/dt)
2. The Power Law Index, G is related to the Optical Depth,τ.
3. The Power Law Index is related to dM/dt
4. The QPO frequency is related to the Transition Layer Outer
Radius
(33 kB)
5. The Transition Layer is Related to dM/dt
6. Thus, sine both G and n are both related to dM/dt,
they are related to each other.
QuasiPeriodic Oscillation Correlations of two black holes related by
shift in QPO frequency, n2=(m1/m2) n1
Best Fit Mass GRS 1758-258
2.3 ±.00m
GRS 1915 + 105
GRS 1758-258
1. The Fit is Poor and the Curve is the Wrong
Shape
2. There are two more free parameters
we can adjust A, d. They are found
from the relation between t and the
Reynold’s number g, t=A gd.
3. We Can Allow A, d, and the mass to
Vary
and fit them freely for the Black Hole
as
1. If we assume GRS 1758-258 and GRS1915+105 have
the
same t=A gd (A=1.0, d = 1.25) then the best fit mass is
m=2.3±.0m
3. If t(g) is different for GRS 1758-258, our best fits have
A=1.0, d is 0.95), and the best fit mass is
m=9.3+.05-3.3m
A, d are clearly important in the shift between QPO-PLI Correlations
from one black hole to another. A, d, and the mass are not orthogonal.
Below, curve families of A, m, d.
“Mass” varies
A, δ constant
“A” varies
Mass, δ constant
“δ” varies
A, mass constant
Reduced chi square space for GX339-4 One of A,m,d is held constant at best
fit
parameters.
δ,Constant, Mass-A varied
A constant, M- δ varied
δ
A
Mass (M)
Mass constant, δ-A varied
δ
A
Mass (M )
Power Law Index
Transition Layer Model More Complicated for GX 339-4
Quasi-Periodic Oscillation (QPO) freq (Hz)
Power Law Index
GX 339-4 Blue Count Rate > 500 cts/sec Red < 500
Cts/sec
Blue 2002 Outburst, Red is 2004, 2003, 2005 Outburst
Quasi-Periodic Oscillation (QPO) freq (Hz)
Power Law Index
GX 339-4 Low, Best Fit Parameters
A= 0.75, Mass=2.68M, δ=1.6
2.05 ± 0.0 M
Quasi-Periodic Oscillation (QPO) freq (Hz)
Power Law Index
GX 339-4 High, Best Fit Parameters
A=0.65, Mass=2.35 M, δ=2.35
2.66 +0.04 – 0.05 M
Quasi-Periodic Oscillation (QPO) freq (Hz)
CONCLUSIONS FOR TRANSITION LAYER
MODEL
1. Certain parameters need to be better
constrained in the TL model, i.e., A, d,
saturation
2. We’d like to do the analysis considering the
other harmonics as the fundamental frequency.
3. GRS 1758-258 appears to be the type of black
hole that the transition layer model may apply
to.
4. The Transition Layer Model predicts a possible
neutron star mass for GX 339-4. Better fits and
Part II: Search For X-Ray Jets in
GRS 1758-258
Motivation For X-Ray Jet Search For
GRS 1758-258
1. Persistent Radio Jets Have
Been Seen in GRS 1758258.
2. A Persistent Extension Has
Been Seen in Cygnus X-3.
3. Might GRS 1758-258 have
X-ray jets too?
Extension
The Chandra HRC-I is excellent for
Imaging X-Ray Sources
1. 0.13” per pixel Resolution
Chandra Satellite
2. Large uniform field of view
(31 x 31 arc minutes)
3. Large uniform field of view (31
x 31 arc minutes)
4. High time resolution over the
entire field of view (16
microseconds)
5. Low background (4 x 10^-6
cts/s/arcsec)
High Resolution Camera HRC-I
Raw Data From HRC-I
GRS 1758-258 Observation 2718
Each Pixel is 0.13“
Point Spread Function Sigma
Fit Gaussians to Slices, Look For
Unusual Standard Deviations
Slice
Angle
(Degrees)
Heindl Astrophys J. 578,2 L125
Gaussian Fits of Slices Through Center Yield No
X-Ray Jets
1E 1740.7-2942
♦
GRS 1758-258
X
Cygnus X-3
AR Lacertae
■
▲
Radio Jets Have Been Seen in GRS 1758-258.
Thus, We Looked For X-Ray Jets in Radio Centers
No Jets Found In Regions Corresponding
To, or Perpendicular To Radio Jets
South Lobe
Signal/Noise
Ratio
Counts/Area
0.72
1.07
% of GRS 1758 7.66e-3 %
Core Brightness
North Lobe
1.47
1..34
9. 6e-3 %
Needed for 3-Sigma Detection
Counts/Area
% of GRS 1758
Core Brightness
1.18
8.45e-3 %
1..39
9. 9e-3 %
Finally, We Took Azimuthal Slices
Around GRS 1758-258
We Found An Extension . . .
Signal/Noise
Counts in
Counts/Area
12.2 arcsec^2 region
136 Degrees
4.07
200
16.4
316 Degrees
2.90
177
14.5
Avg Background ----
126
10.3
…But It Is A Detector Artifact
Merged Data;
Roll Angle=270°
Merged Data;
Roll Angle=90°
1.The spacecraft orientation is 90 or 270 degrees. If the extension was real, it should be present
no matter how I orient the Satellite.
2. Upon rotating the satellite, the extension rotates also, so the extension must be part of the
satellite.
3. From the Chandra Handbook, a “ghost” artifact, a secondary image, appears on one side of
every source, due to the Saturation of the High Gain Amplifiers. The brightness of the
ghost image is reported to be 0.1% of the source.
4. The fake jet is about 0.01% of the brightness of the center of the source.
5. Thus we conclude the extension is an artifact of the satellite.
Expected Signals if GRS 1758-258
Was Similar to Other Black Holes
What Would The Size of the Jet Be?
J GRS _ Expected  J BH ( RGRS / RBH )( DBH / DGRS )
What Would The Flux of the Jet Be?
FGRS  FBH ( FGRS _ PS / FBH _ PS )
BH= Black Hole GRS is being compared to, PS=Point Source or Central Compact Region,
R=Radius, D=Distance to compact object, J=size of Jet in Arcsecs, F=Flux of Jet in
ergs/sec/cm^2
Black Holes Most Similar to GRS 1758-258
XTE J1550-564
H1743-322
Cygnus X-3
M87
GRS 1758-258
width
X
height
comments
H1743-322
1.88
X
1.88
ejected
Cygnus X-3
5.88
X
2.35
persistent/
continuous
XTE J1550-564
5.1
X
2.55
ejected
M87 (with BH mass scaled)
1.48E-4 X
1.4E-5
persistent/
continuous
M87 (without BH mass scake)
44,470 X
4,447
persistent/
Persistent=appeared in all observations, continuous=connected to central source, ejected=separated
continuous
from central source
X-Ray Jet Flux
GRS_jet_flux
ergs/sec/cm^2
H1743-322
Cygnus X-3
XTE J1550-564
M87
1.32e-14
3.27e-12
5.21e-13
6e-8
WebPimms
cts/sec
cts/
arcsec^2
Could we
detect this?
9.55e-5
0.023
3.76e-3
452.7
1.55
95.8
139.5
1.6e16
No
Yes
Yes
Yes
7.23e-8
0.018
1.23e-3
1.0e-3
75.18
45..92
No
Yes
Yes
Radio Jet Flux
H1743-322
Cygnus X-3
XTE J1550-564
M87 (no radio data)
~e-17
2.46e-12
1.73e-13
Conclusions For X-Ray Jet Search of GRS 1758258
1. No Jets Were Found With Chandra
Observations.
2. If GRS 1758-258 Was Similar to Black Holes
M87, Cygnus X-3, or XTE J1550-564, We
Should Have Seen X-Ray Jets Based on
Rough Estimates. If GRS 1758-258 is More
Similar to H1743-322, We Would Not Have
Seen X-Ray Jets.
3. The Extension We Found Was a Property of
the Chandra HRC-I Detector.