Analytical approach to the mass distribution function of subhalos and cold fronts in galaxy clusters

We construct an analytical model of the mass distribution function (MDF) of subhalos in a galaxy cluster in the context of the cold dark matter theory. Our model takes account of two important effects: the high density of the precluster region and the spatial correlation of initial density fluctuations. For subhalos with small masses, the MDF that our model predicts is in between the Press-Schechter (PS) MDF and a conditional MDF as an extension of the PS formalism. We compare the results of our model with those of numerical simulations. We find that our model predictions are consistent with the mass and velocity distribution functions of subhalos in a cluster obtained by numerical simulations. We estimate the probability of finding large Xray subhalos that often have cold fronts. The observed large X-ray subhalos and cold fronts may not always be the result of cluster mergers but may instead be internal structures in clusters.