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

Santa Cruz Institute for Particle Physics Seminar May 23, 2006

Nathan D. Bezayiff, David M. SmithUniversity of California Santa Cruz

GX 339-4 and GRS 1758-258 areLow 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.

From http://lheawww.gsfc.nasa.gov/~still/research/corr.html

Companion Star

Compact Object

Jets

Accretion DiscGravitational Attraction Between

Both Stars equal

↑

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

Obtaining the PLI and QPO from a given observation for GRS 1758-258

Power Law Component

↓

↑

InterstellarAbsorption

First, Get the Power Law Index

Channel Energy (keV)

Res

idua

ls

Nor

mal

ized

cou

nts/

sec/

keV

Obtain the Quasi Periodic Oscillation Frequency in the Power Density Spectra

Frequency (Hz)

Pow

er D

ensi

ty [

(Rm

s/M

ean)

^2/H

z]

QPO

(PLI) Power Law Index-Quasi Periodic Oscillation (QPO) curve

Pow

er L

aw I

ndex

Quasi-Periodic Oscillation (QPO) freq (Hz)

Harmonic Pair?↑

                  

                  (33 kB)

TRANSITION LAYER MODEL (VERY BASIC)

1. The Optical Depth (τ) is related to the accretion rate (dM/dt)

2. The Power Law Index, 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

5. The Transition Layer is Related to dM/dt

6. Thus, sine both and 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, 2=(m1/m2) 1

Best Fit Mass GRS 1758-258 2.3 ±.00m

GRS 1758-258

GRS 1915 + 105

1. The Fit is Poor and the Curve is the Wrong Shape

2. There are two more free parameters we can adjust A, They are found from the relation between and the Reynold’s number =A

3. We Can Allow A, and the mass to Vary and fit them freely for the Black Hole as done for GRS 1915+105 (TF04)

1. If we assume GRS 1758-258 and GRS1915+105 have the same =A (A=1.0, = 1.25) then the best fit mass is

m=2.3±.0m

3. If () is different for GRS 1758-258, our best fits have

A=1.0, is 0.95), and the best fit mass is m=9.3+.05-3.3m

A, are clearly important in the shift between QPO-PLI Correlationsfrom one black hole to another. A, , and the mass are not orthogonal. Below, curve families of A, m, .

“δ” varies

A, mass constant

“Mass” varies “A” varies

Mass, δ constantA, δ constant

Reduced chi square space for GX339-4 One of A,m,d is held constant at best fit parameters.

Mass (M)

δ

A constant, M- δ varied

δ

A

Mass constant, δ-A varied

δ,Constant, Mass-A varied

A

Mass (M )

Transition Layer Model More Complicated for GX 339-4

Pow

er L

aw I

ndex

Quasi-Periodic Oscillation (QPO) freq (Hz)

GX 339-4 Blue Count Rate > 500 cts/sec Red < 500 Cts/secBlue 2002 Outburst, Red is 2004, 2003, 2005 Outburst

Pow

er L

aw I

ndex

Quasi-Periodic Oscillation (QPO) freq (Hz)

GX 339-4 Low, Best Fit ParametersA= 0.75, Mass=2.68M, δ=1.6

Quasi-Periodic Oscillation (QPO) freq (Hz)

Pow

er L

aw I

ndex

2.05 ± 0.0 M

GX 339-4 High, Best Fit ParametersA=0.65, Mass=2.35 M, δ=2.35

Pow

er L

aw I

ndex

Quasi-Periodic Oscillation (QPO) freq (Hz)

2.66 +0.04 – 0.05 M

CONCLUSIONS FOR TRANSITION LAYER MODEL

1. Certain parameters need to be better constrained in the TL model, i.e., A, , 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 saturation are required to support this prediction.

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 1758-258.

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

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

Chandra Satellite

Raw Data From HRC-I

GRS 1758-258 Observation 2718

Each Pixel is 0.13“

Fit Gaussians to Slices, Look For Unusual Standard Deviations

Heindl Astrophys J. 578,2 L125Slice Angle (Degrees)

Poi

nt S

prea

d F

unct

ion

Sig

ma

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 North Lobe

Signal/Noise 0.72 1.47Ratio

Counts/Area 1.07 1..34

% of GRS 1758 7.66e-3 % 9. 6e-3 %Core Brightness

Needed for 3-Sigma Detection

Counts/Area 1.18 1..39 % of GRS 1758 8.45e-3 % 9. 9e-3 %Core Brightness

Finally, We Took Azimuthal Slices Around GRS 1758-258

|

18 “arcsecs |

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

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.

Merged Data; Roll Angle=90°

Merged Data; Roll Angle=270°

Expected Signals if GRS 1758-258 Was Similar to Other Black Holes

)/)(/(_ GRSBHBHGRSBHExpectedGRS DDRRJJ

)/( __ PSBHPSGRSBHGRS FFFF

What Would The Size of the Jet Be?

What Would The Flux of the Jet Be?

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/ continuous

GRS_jet_flux WebPimms cts/ Could weX-Ray Jet Flux ergs/sec/cm^2 cts/sec arcsec^2 detect this?

H1743-322 1.32e-14 9.55e-5 1.55 No Cygnus X-3 3.27e-12 0.023 95.8 Yes XTE J1550-564 5.21e-13 3.76e-3 139.5 Yes M87 6e-8 452.7 1.6e16 Yes Radio Jet Flux

H1743-322 ~e-17 7.23e-8 1.0e-3 No Cygnus X-3 2.46e-12 0.018 75.18 Yes XTE J1550-564 1.73e-13 1.23e-3 45..92 Yes M87 (no radio data)

Persistent=appeared in all observations, continuous=connected to central source, ejected=separated from central source

Conclusions For X-Ray Jet Search of GRS 1758-258

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.