Sourav Mitra¹, Girish Kulkarni^1,2, J. S. Bagla^1,3 and Jaswant K. Yadav^4
1Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India
²Max-Planck Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
³Indian Institute of Science Education and Research (Mohali), Sector 81, S A S Nagar, Manauli PO, Mohali 140306, Punjab, India
⁴Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul 130722, South Korea

Abstract. We derive an estimate of the rate of formation of dark matter haloes per unit volume as a function of the halo mass and redshift of formation. Analytical estimates of the number density of dark matter haloes are useful in modeling several cosmological phenomena. We use the excursion set formalism for computing the formation rate of dark matter haloes. We use an approach that allows us to differentiate between major and minor mergers, as this is a pertinent issue for semi-analytic models of galaxy formation. We compute the formation rate for the Press-Schechter and the Sheth-Tormen mass function. We show that the formation rate computed in this manner is positive at all scales. We comment on the Sasaki formalism where negative halo formation rates are obtained. Our estimates compare very well with N-body simulations for a variety of models. We also discuss the halo survival probability and the formation redshift distributions using our method.

Keywords: cosmology: large scale structure of the Universe -- galaxies: formation -- galaxies: evolution -- galaxies: haloes

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