Press–Schechter formalism

Summary

The Press–Schechter formalism predicts how many dark matter halos of each mass exist in the universe at a given time. It starts from a Gaussian linear density field and smooths it on the scale that contains the mass $M$. Every region whose linear overdensity exceeds the threshold $\delta_c \approx 1.686$ of the spherical collapse model counts as collapsed. William Press and Paul Schechter introduced it in 1974. It gives an analytic halo mass function that is still the starting point of more accurate fits.