An Introduction to Modern Astrophysics · Problem 18.32

Physical Processes in the Solar System — Carroll & Ostlie

Physics — Astrophysics · accretion-disk-black-hole-temperature-wavelength

Problem

Use Eq. (18.19) and Wien's law to make two log-log graphs: (1) the disk temperature, T(r)T(r), and (2) the peak wavelength [λmax⁡(r)][\lambda_{\max}(r)] of the blackbody spectrum, for the accretion disk around the black hole A0620−-00 as a function of the radial position rr. For this system, the mass of the black hole is 3.82 M⊙3.82\,\mathrm{M}_\odot, the mass of the secondary star 0.36 M⊙0.36\,\mathrm{M}_\odot, and the period of the orbit is 0.3226 day. Assume M˙=1014 kg s−1\dot{M} = 10^{14}\text{ kg s}^{-1} (about 10−9 M⊙ yr−110^{-9}\,\mathrm{M}_\odot\text{ yr}^{-1}), and use the Schwarzschild radius, RSR_S (Eq. 17.27), for the radius of the black hole. (On your graph, plot r/RSr/R_S rather than rr.) For a nonrotating black hole, the last stable orbit for a massive particle is at 3RS3R_S, so use this as the inner edge of the disk. Let the outer edge of the disk be determined by Kepler's third law along with Eqs. (18.25) and (18.26). On your log-log graph of λmax⁡\lambda_{\max} vs. r/RSr/R_S, identify the regions of the disk that emit X-ray, ultraviolet, visible, and infrared radiation.

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