Halo collapse: virialization by shear and rotation in dynamical dark-energy models. Effects on weak-lensing peaks

The evolution of the virial overdensity $\Delta_{\rm vir}$ for $\Lambda$CDM and seven dynamical dark-energy models is investigated in the extended spherical collapse model (SCM). Here the virialization process is naturally achieved by introducing shear and rotation instead of using the virial theorem. We generalise two approaches proposed in the literature and show that, regardless of the dark-energy model, the new virialization term can be calibrated on the peculiar velocity of the shell as measured from Einstein-de Sitter simulations. The two virialization recipes qualitatively reproduce the features of the ordinary SCM, i.e., a constant $\Delta_{\rm vir}$ for the EdS model and time-variation for dark-energy models, but without any mass dependence. Depending on the actual description of virialization and on the dark-energy model, the value of $\Delta_{\rm vir}$ varies between 10 and 40 percent. We use the new recipes to predict the surface-mass-density profile of dark matter haloes and the number of convergence density peaks for LSST- and Euclid-like weak lensing surveys.