Geometry of Keplerian disk systems and bounds on masses of their components

TL;DR

This paper studies how self-gravity in Keplerian accretion disks affects their rotation, showing that neglecting disk mass can lead to overestimating the central mass, with implications for accurately determining system parameters.

Contribution

It provides new insights into how disk self-gravity influences rotation speeds and bounds on central mass estimates in accreting disk systems.

Findings

Self-gravity increases disk rotation speed beyond Keplerian predictions.

Strictly Keplerian formulas overestimate central mass in massive disks.

Disk geometry significantly affects the impact of self-gravity.

Abstract

We investigate accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation -- its rotational frequency is larger than that given by the well known strictly Keplerian formula that takes into account the central mass only. Thus determination of central mass in systems with massive disks requires great care -- the strictly Keplerian formula yields only an upper bound. The effect of self-gravity depends on geometric aspects of disk configurations. Disk systems with a small (circa $10^{-4}$) ratio of the innermost radius to the outermost disk radius have the central mass close to the upper limit, but if this ratio is of the order of unity then the central mass can be smaller by many orders of magnitude from this bound.