  The most commonly used definition of halo formation is the time when a halo's
most massive progenitor first contains at least half the final mass of its
parent. Reasonably accurate formulae for the distribution of formation times of
haloes of fixed mass have been available for some time. We use numerical
simulations of hierarchical gravitational clustering to test the accuracy of
formulae for the mass at formation. We also derive and test a formula for the
joint distribution of formation masses and times. The structure of a halo is
expected to be related to its accretion history. Our tests show that our
formulae for formation masses and times are reasonably accurate, so we expect
that they will aid future analytic studies of halo structure.

Astrophysics