3D self-gravitating gas: rho_t+div m=0, m_t+div(mv)+grad p=−rho gradφ, e_t+div(ev)+p div v=nu|grad u|^2, lapφ=G rho, p=gamma e.
1003, isolated (φ=0 at walls). Warm, mildly super-Jeans cloud collapses gently, forms a core, bounces, rings down.
Centre-row line plots on the z-slice (log scale): density,
temperature, pressure,
|potential|, |∇p|, ρ|∇φ|.
Force balance: where ρ|∇φ| (gravity) overtakes |∇p| (pressure) the gas collapses.
3D threshold Γ>4/3 (gamma>1/3); no black hole (Newtonian).