Some improvements to the spherical collapse model

I study the joint effect of dynamical friction, tidal torques and cosmological constant on clusters of galaxies formation. I show that within high-density environments, such as rich clusters of galaxies, both dynamical friction and tidal torques slows down the collapse of low-ν peaks producing an observable variation in the time of collapse of the perturbation and, as a consequence, a reduction in the mass bound to the collapsed perturbation. Moreover, the delay of the collapse produces a tendency for less dense regions to accrete less mass, with respect to a classical spherical model, inducing a biasing of over-dense regions toward higher mass. I show how the threshold of collapse is modified if dynamical friction, tidal torques and a non-zero cosmological constant are taken into account and I use the Extended Press Schecter (EPS) approach to calculate the effects on the mass function. Then, I compare the numerical mass function given in Reed et al. (2003) with the theoretical mass function obtained in the present paper. I show that the barrier obtained in the present paper gives rise to a better description of the mass function evolution with respect to other previous models (Sheth & Tormen 1999 (hereafter ST), Sheth & Tormen 2002 (hereafter ST1)).