General polytropic hydrodynamic cylinder under self-gravity

Abstract

ABSTRACT For filamentary clouds on various scales obeying general polytropic (GP) equation of state, their hydrodynamic collapses, expansions, and shocks are investigated. Our cylindrical model is axisymmetric, infinitely long with axial uniformity and involves Newtonian gravity. For such GP cylinders, we explore various analytical and numerical similarity solutions. Based on a singular hydrostatic solution, we derive a quasi-static asymptotic dynamic solution approaching the axis. There, we also derive the asymptotic cylindrical free-fall solution for polytropic index γ ≤ 1 and show the absence of such solutions for γ > 1. We find new asymptotic solutions for expanding cylindrical central voids with no matter inside, and examine the asymptotic expansion solutions to higher orders far from the axis. We classify the sonic critical curve (SCC) into three (or five) types and analyse their properties. The asymptotic behaviors of the SCC towards the axis and infinity are examined. Examples are shown for solutions crossing the SCC twice with the global features of cylindrical envelope expansion or contraction with core collapses. We numerically construct new types of global similarity solutions with or without outgoing shocks. For γ > 1, a shock is necessary to connect the inner and outer parts. The collapse and fragmentation of massive filaments or strings may give clues and implications to the formations of chains of stellar objects, chains of black holes, chains of galaxies or even chains of galaxy clusters in proper astrophysical and cosmological contexts.