selfgravitating

Self-gravitating refers to a system in which the gravitational field is generated by the system's own mass distribution, rather than by external sources. In astronomy, many structures are self-gravitating across scales, including stars, stellar clusters, planets and planetary systems, molecular clouds, accretion disks, and galaxies.

The gravitational potential is described by Poisson's equation ∇^2Φ = 4πGρ, with dynamical evolution determined by the density ρ, pressure P, and velocity field. In hydrostatic equilibrium, dP/dr = -ρ dΦ/dr. For a bound, quasi-static system, the virial theorem 2K + U = 0 relates kinetic energy K to gravitational energy U. Self-gravity tends to drive contraction unless countered by pressure, rotation, or internal energy.

Key concepts include the Jeans criterion for gravitational collapse: collapse occurs when mass exceeds the Jeans mass M_J ∝ (T^3/ρ)^{1/2} (up to constants). In disk systems, stability is often assessed with Toomre's Q parameter; Q < 1 indicates gravitational instability. Dynamical, or free-fall, times t_dyn ~ (Gρ)^-1/2 characterizes the timescale of collapse or relaxation.

Examples: self-gravity shapes the evolution of molecular clouds into stars, planetary systems through accretion, and galaxies through their disk and halo dynamics. Numerical modeling combines gravity with hydrodynamics or collisionless dynamics, solving Poisson's equation; N-body and SPH methods are common.