A Method for Black Hole Mass Determination in Accretion Powered X-Ray Sources

Abstract

We describe a method for the determination of black-hole masses based on information inferred from high-energy spectra. It is required that the spectral energy distribution consist of thermal and Comptonized components. One can then, in principle, infer the depth of the gravitational potential well for sources of known distance. The thermal component is inferred by the integration of a blackbody spectral form over the disk. We assume that the color temperature distribution in the disk has a specific shape given by the Shakura-Sunyaev (1973) disk model which goes to zero at the inner disk radius and at infinity and has a maximum at 4.2 Schwarzchild radii. In this formulation there is only one parameter, the so called color correction factor, relating the apparent temperature to effective temperature which characterizes the thermal emission component. We have made use of improved Galactic black hole binary dynamical mass determinations to derive, in effect, an empirical calibration of this factor. We then present our analysis of observational data for representative objects of several classes; Galactic black hole X-ray binaries, narrow line Seyfert galaxies (NLS1), and ``ultra-luminous'' extragalactic X-ray sources (ULX). We then apply our mass determination calculation and present our results. We argue that this approach can potentially fill a void in the current knowledge of NLS1 and ULX properties, and discuss how a deeper understanding of both classes has relevance to the broader issues of how cosmic black holes, beyond the stellar-mass realm, are formed and what is their overall mass distribution.

15 pages, 3 tables, 6 figures. Accepted for publication in ApJ, 1st of August

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• Probable intermediate mass black holes in NGC4559: XMM-Newton spectral and timing constraints
• Determination of Black Hole Mass in Cyg X-1 by Scaling of Spectral Index-QPO Frequency Correlation
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• Is M82 X-1 Really An Intermediate-Mass Black Hole? X-ray Spectral and Timing Evidence
• XMM-Newton Observations of the Ultraluminous Nuclear X-ray Source in M33
• Radio and X-ray Properties of Relativistic Beaming Models for Ultra-Luminous X-ray Sources
• A Chandra view of NGC 3621: a bulgeless galaxy hosting an AGN in its early phase?
• The Observed Galactic Annihilation Line. Possible Signature of the Cluster for Accreting Small Mass Black Holes
• A variable ultra-luminous X-ray source in the colliding galaxy NGC 7714
• The ultraluminous X-ray source bubble in NGC 5585
• Discovery of a Quasi-Periodic Oscillation in the Ultraluminous X-ray Source IC 342 X-1: XMM-Newton Results
• The slim-disk state of the ultraluminous X-ray source in M83
• NGC 4051: Black hole mass and photon index-mass accretion rate correlation
• MAXI~J1348--630: Estimating the black hole mass and binary inclination using a scaling technique
• On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system
• The 2007 outburst of the X-ray binary XTE J1856+053
• Black hole mass estimates from soft X-ray spectra
• How To Distinguish Neutron Star and Black Hole X-ray Binaries? Spectral index and Quasi-Periodic Oscillation Frequency Correlation