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

Mass and Mean Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges

Growing evidence indicate supermassive black holes (SMBHs) in the mass range of $M_{\rm BH}$$\sim 10^6-10^{10}M_{\odot}$ lurking in central bulges of many galaxies. Extensive observations reveal fairly tight power laws of $M_{\rm BH}$ versus the mean stellar velocity dispersion $\sigma$ of the host bulge. The dynamic evolution of a bulge and the formation of a central SMBH should be physically linked by various observational clues. In this contribution, we reproduce the empirical $M_{\rm BH}-\sigma$ power laws based on a self-similar general polytropic quasi-static bulge evolution and a sensible criterion of forming a SMBH surrounding the central density singularity of a general singular polytropic sphere (SPS) \cite{loujiang2008}. Other properties of host bulges and central SMBHs are also examined. Based on our model, we discuss the intrinsic scatter of the $M_{\rm BH}-\sigma$ relation and a scenario for the evolution of SMBHs in different host bulges.Comment: 8 pages, 2 figures, accepted for publication in the Proceedings of Science for VII Microquasar Workshop: Microquasars and Beyon

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density N which travels at a relevant radial group speed Cg. The wave energy surface density ℰ and the wave angular momentum surface density J are related to N by ℰ=ωN and J=mN respectively, where ω is the angular frequency in an inertial frame of reference and the integer m, proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discusse