General Polytropic Self-gravitating Cylinder Free-fall and Accreting Mass String with a Chain of Collapsed Objects

Abstract

We present a theoretical model framework for general polytropic (GP) hydrodynamic cylinder under self-gravity of infinite length with axial uniformity and axisymmetry. For self-similar dynamic solutions, we derive valuable integrals, analytic asymptotic solutions, sonic critical curves, shock conditions, and global numerical solutions with or without expansion shocks. Among others, we investigate various dynamic solutions featured with central free-fall asymptotic behaviours, corresponding to a collapsed mass string with a sustained dynamic accretion from a surrounding mass reservoir. Depending on the allowed ranges of a scaling index a < -1, such cylindrical dynamic mass accretion rate could be steady, increasing with time and decreasing with time. Physically, such a collapsed mass string or filament would break up into a sequence of sub-clumps and segments as induced by gravitational Jeans instabilities. Depending on the scales involved, such sub-clumps would evolve into collapsed objects or gravitationally bound systems. In diverse astrophysical and cosmological contexts, such a scenario can be adapted on various temporal, spatial and mass scales to form a chain of collapsed clumps and/or compact objects. Examples include the formation of chains of proto-stars, brown dwarfs and gaseous planets along molecular filaments; the formation of luminous massive stars along magnetized spiral arms and circum-nuclear starburst rings in barred spiral galaxies; the formation of chains of compact stellar objects such as white dwarfs, neutron stars, and black holes along a highly condensed mass string. On cosmological scales, one can perceive the formation of chains of galaxies, chains of galaxy clusters or even chains of supermassive and hypermassive black holes in the Universe including the early Universe. All these chains referred to above include possible binaries.