Journal Article

Where is a Marginally Stable Last Circular Orbit in Super-Critical Accretion Flow?

Ken-ya Watarai and Shin Mineshige

in Publications of the Astronomical Society of Japan

Published on behalf of Astronomical Society of Japan

Volume 55, issue 5, pages 959-965
Published in print October 2003 | ISSN: 0004-6264
Published online October 2003 | e-ISSN: 2053-051X | DOI:
Where is a Marginally Stable Last Circular Orbit in Super-Critical Accretion Flow?

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  • Astrometry and Celestial Mechanics
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Impressed by a widespread misunderstanding of the issue, we return to the old question concerning the location of the inner edge of the accretion disk around a black hole. We recall the fundamental results obtained in the 1970’s and 1980’s by Warsaw and Kyoto research groups that proved, in particular, that the inner edge does not coincide with the location of the innermost stable Keplerian circular orbit. We give some novel illustrations of this particular point and of some other fundamental results obtained before. To investigate the flow dynamics of the inner edge of an accretion disk, we carefully solved the structure of the transonic flow and plotted the effective potential profile based on the angular-momentum distribution calculated numerically. We showed that the flow does not have a potential minimum for accretion rates, [math] (with [math] being the Eddington luminosity and [math] being the speed of light). This property is realized even for relatively small viscosity parameters (i.e., [math]), because of the effect of the pressure gradient. In conclusion, an argument based on the last circular orbit of a test particle cannot give a correct inner boundary of the super-critical flow, and the inner edge should be determined in connection with radiation efficiency. The same argument can apply to optically thin ADAF. The interpretation of the observed QPO frequencies should be re-considered, since the assumption of a Keplerian rotation velocity can grossly over–or underestimate the disk rotation velocity, depending on the magnitude of the viscosity.

Keywords: accretion, accretion disks; black holes; X-rays: stars

Journal Article.  5088 words.  Illustrated.

Subjects: Astrometry and Celestial Mechanics ; Astronomy and Astrophysics

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