Collapse of an isothermal sphere

An isothermal sphere initially at hydrostatic equilibrium is marginally stable against small perturbations. In analogy to a Jeans' cloud (constant density) there exist a critical radius R_crit which separates the stable and the unstable solutions (Bonnor-Ebert). A description of the problem including 1D numerical simulations can be found in P.N. Foster and R.A. Chevalier, ApJ 416 (1993) 303. The setup can be found in 'isothermal_sphere'.



The initial density profile was slightly enhanced off the hydrostatic solution to get the isothermal sphere collapsed. Note that the critical radius R_crit = 6.451. For this simulations the cut-off radius was R_max = 15.



The initial density profile (max. 8 levels of refinement)




and initial temperature profile
c_amb = 25. c_sph




resolution study



The relevant energies in the low resolution simulations start to oscillate after the collaps of the sphere. Note, in this case (r_max = 5) the local (minimal) Jeans length is only 0.64 of the grid spacing. The code stops right after the core formation reporting a non-convergence error in the rieman solver.



Time evolution of the radial density profile
delta_t ~ 0.5 t_J




Time evolution of the radial velocity








2D slice through density showing also the refinement block structure




2D slice through temperature

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