Polytrope

Abstract: In this paper we present results from a large set of numerical simulations that demonstrate that H2 formation occurs rapidly in turbulent gas. Starting with purely atomic hydrogen, large quantities of molecular hydrogen can be produced on timescales of 1-2 Myr, given turbulent velocity dispersions and magnetic field strengths consistent with observations. Moreover, as our simulations underestimate the effectiveness of H2 self-shielding and dust absorption, we can be confident that the molecular fractions that we compute are strong lower limits on the true values. The formation of large quantities of molecular gas on the timescale required by rapid cloud formation models therefore appears to be entirely plausible. We also investigate the density and temperature distributions of gas in our model clouds. We show that the density probability distribution function is approximately lognormal, with a dispersion that agrees well with the prediction of Padoan and coworkers. The temperature distribution is similar to that of a polytrope, with an effective polytropic index γeff 0.8, although at low gas densities, the scatter of the actual gas temperature around this mean value is considerable, and the polytropic approximation does not capture the full range of behavior of the gas.

Abstract: We report results from the analysis of 21 nearby galaxy clusters, 11 with cooling flow (CF) and 10 without cooling flow, observed with BeppoSAX. The temperature profiles of both CF and non-CF systems are characterized by an isothermal core extending out to ~0.2r180; beyond this radius both CF and non-CF cluster profiles rapidly decline. Our results differ from those derived by other authors, who found either continuously declining profiles or substantially flat profiles. Neither the CF nor the non-CF profiles can be modeled by a polytropic temperature profile, the reason being that the radius at which the profiles break is much larger than the core radius characterizing the gas density profiles. For r > 0.2r180, where the gas can be treated as a polytrope, the polytropic indexes derived for CF and non-CF systems are respectively 1.20 ± 0.06 and 1.46 ± 0.06. The former index is closer to the isothermal value, 1, and the latter to the adiabatic value, . Published hydrodynamic simulations do not reproduce the peculiar shape of the observed temperature profile, probably suggesting that a fundamental ingredient is missing.

Abstract: We examine the effect of primordial dark matter velocity dispersion and/or particle self-interactions on the structure and stability of galaxy halos, especially with respect to the formation of substructure and central density cusps. Primordial velocity dispersion is characterized by a ``phase density'' $Q\ensuremath{\equiv}\ensuremath{\rho}/〈{v}^{2}{〉}^{3/2},$ which for relativistically decoupled relics is determined by particle mass and spin and is insensitive to cosmological parameters. Finite Q leads to small-scale filtering of the primordial power spectrum, which reduces substructure, and limits the maximum central density of halos, which eliminates central cusps. The relationship between Q and halo observables is estimated. The primordial Q may be preserved in the cores of halos and if so leads to a predicted relation, closely analogous to that in degenerate dwarf stars, between the central density and velocity dispersion. Classical polytrope solutions are used to model the structure of halos of collisional dark matter, and to show that self-interactions in halos today are probably not significant because they destabilize halo cores via heat conduction. Constraints on masses and self-interactions of dark matter particles are estimated from halo stability and other considerations.

Abstract: The Einstein–Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43:1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44:1419, 2012) are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars.