Collisional interaction limits between dark matters and baryons in `cooling flow' clusters

Presuming weak collisional interactions to exchange the kinetic energy between dark matter and baryonic matter in a galaxy cluster, we re-examine the effectiveness of this process in several `cooling flow' galaxy clusters using available X-ray observations and infer an upper limit on the heavy dark matter particle (DMP)$-$proton cross section $\sigma_{\rm xp}$. With a relative collisional velocity $V-$dependent power-law form of $\sigma_{\rm xp}=\sigma_0(V/10^3 {\rm km s^{-1}})^a$ where $a\leq 0$, our inferred upper limit is \sigma_0/m_{\rm x}\lsim 2\times10^{-25} {\rm cm}^2 {\rm GeV}^{-1} with $m_{\rm x}$ being the DMP mass. Based on a simple stability analysis of the thermal energy balance equation, we argue that the mechanism of DMP$-$baryon collisional interactions is unlikely to be a stable nongravitational heating source of intracluster medium (ICM) in inner core regions of `cooling flow' galaxy clusters.Comment: 8 pages, 2 figures, MNRAS accepte

General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks

We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) in the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein-de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.Comment: 21 pages, 15 figures, accepted for publication on New Astronom

Adiabatic Perturbations in Homologous Conventional Polytropic Core Collapses of a Spherical Star

We perform a non-radial adiabatic perturbation analysis on homologous conventional polytropic stellar core collapses. The core collapse features a polytropic exponent $\Gamma=4/3$ relativistic gas under self-gravity of spherical symmetry while three-dimensional perturbations involve an adiabatic exponent $\gamma$ with $\gamma\neq\Gamma$ such that the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ buoyancy frequency ${\cal N}$ does not vanish. With proper boundary conditions, we derive eigenvalues and eigenfunctions for different modes of oscillations. In reference to stellar oscillations and earlier results, we examine behaviours of different modes and the criterion for instabilities. The acoustic p$-$modes and surface f$-$modes remain stable. For $\gamma<\Gamma$, convective instabilities appear as unstable internal gravity g$^{-}-$modes. For $\gamma>\Gamma$, sufficiently low-order internal gravity g$^{+}-$modes are stable, whereas sufficiently high-order g$^{+}-$modes, which would have been stable in a static star, become unstable during self-similar core collapses. For supernova explosions, physical consequences of such inevitable g$-$mode instabilities are speculated.Comment: 5 pages, 4 figures, accepted for publication in MNRA

Intermediate-Mass Black Holes in Globular Clusters

There have been reports of possible detections of intermediate-mass black holes (IMBHs) in globular clusters (GCs). Empirically, there exists a tight correlation between the central supermassive black hole (SMBH) mass and the mean velocity dispersion of elliptical galaxies, "pseudobulges" and classical bulges of spiral galaxies. We explore such a possible correlation for IMBHs in spherical GCs. In our model of self-similar general polytropic quasi-static dynamic evolution of GCs, a criterion of forming an IMBH is proposed. The key result is M(BH) = L o^1/(1-n) where M(BH) is the IMBH mass, o is the GC mean stellar velocity, L is a coefficient, and 2/3 < n < 1