Spectrum of a relativistic accretion disk around a spinning black hole

BHSPEC is a spectral fitting model which has been implemented as a additive table model for the Xspec Spectral Fitting Package. It consists of a large grid of tabulated artificial spectra which are used to fit data via interpolation. Currently, the model is comprised of multiple files which cover different, but overlapping, regions of parameter space.

Our method for generating the artificial spectra is described in detail in Davis et al. (2005, ApJ, 621, 372) and Davis & Hubeny (submitted to ApJ). The spectra are based on fully relativistic accretion disk models similar to the KERRBB model already implemented in Xspec. The main difference between KERRBB and BHSPEC is the treatment of the emission at disk surface. KERRBB utilizes a color-corrected blackbody prescription with either isotropic emission or an analytic limb darkening profile. BHSPEC uses stellar atmospheres-like calculations of disk annuli to self-consistently calculate the vertical structure and radiative transfer. The spectra from these calculations are tabulated in the parameters of interest and then used to calculate the spectra at a given radius via interpolation.

The BHSPEC model is parameterized as follows: (note that parameters and their ordering may vary slightly from file-to-file)

  • log(M/Msun), the mass of the black hole in units of solar masses.

  • log(L/Ledd), the luminosity of the accretion disk as a fraction of the Eddington luminosity for completely ionized H (Ledd=1.3*10^38 (M/Msun) erg/s. Here L=eta*Mdot*c^2 where the efficiency, eta, is determined by the position of the last stable circular orbit in the Kerr spacetime.

  • cos(i), the cosine of the inclination of the accretion disk relative to the plane of the sky.

  • a/M, the dimensionless spin of the black hole.

  • log(alpha), the dimensionless variable in the Shakura & Sunyaev (1973) prescription for the midplane accretion stress tau_{r phi}=alpha*P, where P is the total pressure at the disk midplane. Currently the model is tabulated for only two values of alpha: 0.1 and 0.01. We recommend keeping this parameter fixed at log(alpha)=-1 or -2, the values for which the spectra were tabulated.

  • K, the model normalization. K is related to the source distance D via K=(10 kpc/D)^2

The table model files available are bhspec.fits.gz and bhspec2.fits.gz. One first file considers black hole spins (a/M) extending from 0 - 0.8 for alpha=0.1 and 0.01 (alpha is the standard 'anamalous viscocity' parameter). The other file covers a larger range of spin (a/M from 0 - 0.99), but only for alpha=0.01. This partitioning is needed because the disk annuli of high spin, low alpha models do not converge.


Keith Arnaud, Lab. for High Energy Astrophysics, NASA/Goddard Space Flight Center

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Last modified: Thursday, 09-Feb-2006 10:28:52 EST