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 Lane-Emden equation, describing the hydrostatic equilibrium of a self-gravitating sphere with a logatropic equation of state. We present approximate analytic solutions for the small radius behavior of the non-singular 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, non-singular solution. Using both an exact (numerical) and the approximate analytic solution, we apply Bonnor’s stability criterion, and determine the stability of the non-singular solution of the logatropic, self-gravitating sphere.
| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional Autónoma de México, Instituto de Astronomía
2017
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| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0185-11012017000200020 |
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