Critically Rotating Polytropic Cylinders

Abstract

Observations indicate that interstellar molecular clouds can often be approximated by rotating (polytropic) cylinders. The two limiting configurations -the homogeneous and the isothermal cylinder-are used to obtain analytical solutions valid, at least qualitatively, for the whole range 0 n 1 of permitted polytropic indices. The radius of critically rotating, infinitely long polytropic cylinders has a flat minimum at polytropic index n ¼ 0:854, becoming infinite in the two limiting cases n ¼ 0 and 1. The ratio between the radii of critically rotating and nonrotating polytropic cylinders decreases strongly from 1 if n ¼ 0 to 1.52 if n ¼ 2:04, afterward increasing slowly to exp (1/2) ¼ 1:65 if n ¼ 1. Natural polytropic variables are presented in the Appendix. Subject headingg s: equation of state -hydrodynamics -ISM: kinematics and dynamics

Prestellar cores: initial orbit and boundary

“…The filaments can be modeled by isothermal (polytropic) cylinders (Lada et al 2007, p. 10;McKee and Ostriker 2007, p. 583;Oproiu and Horedt 2008). Overdense, gravitationally bound or unbound regions in these filaments are called clumps.…”

On the equilibrium of rotating filaments

“…Concerning hypothesis (ii), and after the pioneering work of Robe (1968), there has been a number of publications devoted to the study of equilibrium and stability of rotating filaments (see e.g. Hansen et al 1976;Inagaki & Hachisu 1978;Robe 1979;Simon et al 1981;Veugelen 1985;Horedt 2004;Kaur et al 2006;Oproiu & Horedt 2008). However, this body of knowledge has not been recently used to constrain properties of observed filaments in molecular clouds.…”