Re-examination of several key aspects of an earlier model analysis on cylinder hydrodynamics under self-gravity

Abstract

In several astrophysical and cosmological contexts, long dynamic filamentary structures emerge ubiquitously in observations and numerical simulations. For theoretical understanding, such filaments may be idealized as self-similar hydrodynamic cylinders under self-gravity of infinite length with axisymmetry and axial uniformity. We review and present analytical results of such a self-similar dynamic cylinder, including asymptotic solutions both towards the symmetry axis and at large radii, asymptotic solution just outside a dynamically expanding central void cylinder and a dimensional energy conservation equation. We introduce a velocity potential and derive cylindrical Bernoulli relations in similarity forms. Besides, the sonic critical curve (SCC) for γ=1 is treated and examined. A thorough classification of the SCC of this kind is done. Most importantly, intrinsic invariance of the general polytropic dynamic cylinder emerges when γ=1, which builds connections among individual self-similar solutions of the same kind. We re-examine several key aspects of the study by Holden et al. (2009) and find that some of their results and conclusions to be misleading and incomplete. We pinpoint the sources of their errors and offer our correct results. Finally, we numerically compute self-similar solutions with a central free-fall behaviour as well as solutions that go across either the upper or the lower branch of the SCC once and show the corresponding global solution profiles.