Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe

We study the evolution of an isolated, spherical halo of self-interacting dark matter (SIDM) in the gravothermal fluid formalism. We show that the thermal relaxation time, $t_r$, of a SIDM halo with a central density and velocity dispersion of a typical dwarf galaxy is significantly shorter than its age. We find a self-similar solution for the evolution of a SIDM halo in the limit where the mean free path between collisions, $\lambda$, is everywhere longer than the gravitational scale height, $H$. Typical halos formed in this long mean free path regime relax to a quasistationary gravothermal density profile characterized by a nearly homogeneous core and a power-law halo where $\rho \propto r^{-2.19}$. We solve the more general time-dependent problem and show that the contracting core evolves to sufficiently high density that $\lambda$ inevitably becomes smaller than $H$ in the innermost region. The core undergoes secular collapse to a singular state (the ``gravothermal catastrophe'') in a time $t_{coll} \approx 290 t_r$, which is longer than the Hubble time for a typical dark matter-dominated galaxy core at the present epoch. Our model calculations are consistent with previous, more detailed, N-body simulations for SIDM, providing a simple physical interpretation of their results and extending them to higher spatial resolution and longer evolution times. At late times, mass loss from the contracting, dense inner core to the ambient halo is significantly moderated, so that the final mass of the inner core may be appreciable when it becomes relativistic and radially unstable to dynamical collapse to a black hole.Comment: ApJ in press (to appear in April), 12 pages. Extremely minor changes to agree with published versio

Fluctuating hydrodynamics of multi-species, non-reactive mixtures

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper

How much larger quantum correlations are than classical ones

Considering as distance between two two-party correlations the minimum number of half local results one party must toggle in order to turn one correlation into the other, we show that the volume of the set of physically obtainable correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388 larger than the volume of the set of correlations obtainable in local deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32 = 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling) theories.Comment: REVTeX4, 6 page