Nakia Carlevaro

I.C.R.A.Net- International Center for Relativistic Astrophysics Network, University of Rome "La Sapienza"

Title:  Viscosity effects on gravitational collapse

Authors:  Nakia Carlevaro, Giovanni Montani

Speaker:  Nakia Carlevaro

Abstract:  We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the

work is to investigate whether the presence of viscous corrections to  the evolution of a collapsing gas cloud influence the top-down fragmentation process. To this end, we generalize the approach presented  by C. Hunter to include in the dynamics of the (uniform and spherically symmetric) cloud the negative pressure contribution associated to the  bulk viscosity phenomenology. Within the framework of a Newtonian approach, we extend to the viscous case either the Lagrangian, either  the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form  $\zeta=\zeta_0\rho^{5/6}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how the adiabatic-like behavior of the gas is deeply influenced by viscous correction when its collapse reaches the extreme regime toward the singularity. In fact, for sufficiently large viscous contributions, density contrasts associated to a given scale of the fragmentation process acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. Since in the non-dissipative case density contrasts diverge, we can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that  in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase; this issue, absent in the non-viscous case, is equivalent to deal with a Jeans length.