Globular Cluster Core Collapse (2D)

Cluster Setup

Star count 900

Heavy-star fraction 18%

Relaxation rate (time speed) 1.0×

Core State

Core radius r꜀/r꜀₀

1.00

Core density ρ꜀/ρ꜀₀

1.0×

Elapsed time

0.00 T_rh

Binary bounces

Phase

Contracting

How it works

A self-gravitating star cluster has negative heat capacity: as the core loses kinetic energy to two-body gravitational encounters, it must contract and heat up further to stay virialised, which only speeds up further heat loss. Left unchecked this runs away — the gravothermal catastrophe (Lynden-Bell & Wood 1968; Cohn 1980).

Two-body relaxation also drives mass segregation: encounters push the system toward energy equipartition, so heavier stars sink toward the centre while lighter stars are flung to larger orbits — modelled here per star as an inward pull scaled by its mass relative to the mean.

Core collapse (self-similar phase):
  d(r꜀)/dt ≈ -k / r꜀²   →   r꜀(t) ≈ (r꜀₀³ - 3k·t)^(1/3)
Relaxation time (Spitzer 1987):
  T_rh ∝ N / ln(N) · r_h³ᐟ² / (G·M)¹ᐟ²

Real clusters don't collapse to a point: once the core is dense enough, three-body encounters bind hard binary stars, which release orbital energy into the core on each subsequent encounter (Heggie 1975). That energy input reverses the contraction, the core re-expands, cools, and collapses again — repeating as gravothermal oscillations (Bettwieser & Sugimoto 1984). Toggle "Binary heating" off to see the unphysical runaway collapse this mechanism prevents in real clusters.

This 2D build projects the same radial collapse law top-down: every star keeps its 3D simulator's radius and inward "pull" formula, just flattened onto a plane, so the core-radius and density numbers you see here are the identical physics — only the rendering is 2D. Drag the cluster view to pan and scroll to zoom; the strip chart below plots r꜀/r꜀₀ and the density multiplier live against elapsed relaxation time.

Star count — number of stars rendered; larger clusters relax more slowly in reality (T_rh ∝ N/ln N), shown here as a visual density change.
Heavy-star fraction — share of high-mass stars; more of them means stronger, faster mass segregation into the core.
Relaxation rate — compresses the (very long, real) relaxation-time clock into a watchable animation speed.
Binary heating — toggles the stabilising energy source that turns runaway collapse into oscillation.

Light stars Heavy stars (segregating) Halo boundary

drag to pan · scroll to zoom