An approximate analytic solution and stability criterion for the logatropic sphere
Abstract
A logatropic equation of state (in which the pressure is proportional to the logarithm of the gas density) has been used in models of molecular clouds to mimic turbulent pressure. We explore solutions of the associated logatropic LaneEmden equation, describing the hydrostatic equilibrium of a selfgravitating sphere with a logatropic equation of state. We present approximate analytic solutions for the small radius behavior of the nonsingular solution, and for its large radius convergence to the singular solution. Combining a "small radius" and a "large radius" solution, we obtain an analytic approximation to the full, nonsingular solution. Using both an exact (numerical) and the approximate analytic solution, we apply Bonnor's stability criterion, and determine the stability of the nonsingular solution of the logatropic, selfgravitating sphere.
 Publication:

Revista Mexicana de Astronomia y Astrofisica
 Pub Date:
 October 2017
 Bibcode:
 2017RMxAA..53..477L
 Keywords:

 equation of state;
 ISM: clouds;
 stars: formation