Spherical top-hat collapse model

A uniform overdensity evolves as a separate spherical pressureless region until shell crossing. In an Einstein-de Sitter background, formal collapse has linearly extrapolated threshold ${\delta }_c=(3/5)(3\pi /2{)}^{2/3}\simeq 1.686$. This is distinct from the actual nonlinear density. Virialization and nonspherical tides require further physics.