Gravitational collapse of conventional polytropic cylinder
Abstract
In reference to general polytropic and conventional polytropic hydrodynamic cylinders of infinite length with axial uniformity and axisymmetry under self-gravity, the dynamic evolution of central collapsing mass string in free-fall dynamic accretion phase is re-examined in details. We compare the central mass accretion rate and the envelope mass infall rate at small radii. Among others, we correct mistakes and typos of Kawachi & Hanawa (KH hereafter) and in particular prove that their key asymptotic free-fall solution involving polytropic index γ in the two power exponents is erroneous by analytical analyses and numerical tests. The correct free-fall asymptotic solutions at sufficiently small \hat{r} (the dimensionless independent self-similar variable) scale as {∼ } -|ln \hat{r}|^{1/2} in contrast to KH's ∼ -|ln \hat{r}|^{(2-γ )/2} for the reduced bulk radial flow velocity and as {∼ } \hat{r}^{-1}|ln \hat{r}|^{-1/2} in contrast to KH's {∼ } \hat{r}^{-1} |ln \hat{r}|^{-(2-γ )/2} for the reduced mass density. We offer consistent scenarios for numerical simulation code testing and theoretical study on dynamic filamentary structure formation and evolution as well as pertinent stability properties. Due to unavoidable Jeans instabilities along the cylinder, such collapsing massive filaments or strings can further break up into clumps and segments of various lengths as well as clumps embedded within segments and evolve into chains of gravitationally collapsed objects (such as gaseous planets, brown dwarfs, protostars, white dwarfs, neutron stars, black holes in a wide mass range, globular clusters, dwarf spheroidals, galaxies, galaxy clusters and even larger mass reservoirs etc.) in various astrophysical and cosmological contexts as articulated by Lou & Hu recently. As an example, we present a model scheme for comparing with observations of molecular filaments for forming protostars, brown dwarfs and gaseous planets and so forth.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- July 2017
- DOI:
- 10.1093/mnras/stx465
- Bibcode:
- 2017MNRAS.468.2771L
- Keywords:
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- gravitation;
- hydrodynamics;
- plasmas;
- planets and satellites: rings;
- stars: formation;
- ISM: clouds