Self-gravitating fluid dynamics, instabilities, and solitons - art. no. 084005

This work studies the hydrodynamics of self-gravitating, compressible, isot hermal fluids. We show that the hydrodynamic-evolution equations are scale covariant in the absence of viscosity. Then, we study the evolution of the time-dependent fluctuations around singular and regular isothermal spheres. We linearize the fluid equations around such stationary solutions and deve lop a method based on the Laplace transform to analyze their dynamical stab ility. We find that the system is stable below a critical size (X similar t o9.0 in dimensionless variables) and unstable above; this criterion is the same as the one found for the thermodynamic stability in the canonical ense mble and it is associated with a center-to-border density ratio of 32.1. We prove that the value of this critical size is independent of the Reynolds number of the system. Furthermore, we give a detailed description of the se ries of successive dynamic instabilities that appear at larger and larger s izes following the geometric progression X(n)similar to 10.7(n), n=1,2,.... Then, we search for exact solutions of the hydrodynamic equations without viscosity, we provide analytic and numerical axisymmetric soliton-type solu tions. The stability of exact solutions corresponding to a collapsing filam ent is studied by computing linear fluctuations. Radial fluctuations growin g faster than the background are found for all sizes of the system. However , a critical size (X similar to4.5) appears, separating a weakly from a str ongly unstable regime.