We investigate the black hole (BH) scaling relation in galaxies using a model in which the galaxy halo and central BH are a self-gravitating sphere of dark matter (DM) with an isotropic, adiabatic equation of state. The equipotential where the escape
velocity approaches the speed of light defines the horizon of the BH. We find that the BH mass ($m_bullet$) depends on the DM entropy, when the effective thermal degrees of freedom ($F$) are specified. Relations between BH and galaxy properties arise naturally, with the BH mass and DM velocity dispersion following $m_bulletproptosigma^{F/2}$ (for global mean density set by external cosmogony). Imposing observationally derived constraints on $F$ provides insight into the microphysics of DM. Given that DM velocities and stellar velocities are comparable, the empirical correlation between $m_bullet$ and stellar velocity dispersions $sigma_star$ implies that $7<F<10$. A link between $m_bullet$ and globular cluster properties also arises because the halo potential binds the globular cluster swarm at large radii. Interestingly, for $F>6$ the dense dark envelope surrounding the BH approaches the mean density of the BH itself, while the outer halo can show a nearly uniform kpc-scale core resembling those observed in galaxies.
We investigate the effects of a cD galaxys gravity and AGN heating of the host galaxy cluster. We consider a standard prescription for the hydrodynamics, with the structures determined by mass continuity, momentum and energy conservation equations in
spherical symmetry. The cluster comprises a dark matter halo (DM) and ionised X-ray emitting intracluster gas (ICM), which jointly determine the gravitational potential. The cD galaxy is an additive gravitational potential component. The DM assumes a polytropic equation of state (determined by its microphysics), which could be non-radiative self-interacting particles or more exotically interacting particles. The AGN provides distributed heating, counteracting radiative cooling. Stationary density and velocity dispersion profiles are obtained by numerically integrating the hydrodynamic equations with appropriate boundary conditions. The minimum gas temperature in the cluster core is higher when a cD galaxy is present than when it is absent. The solutions also yield a point-like mass concentration exceeding a minimum mass: presumably the AGNs supermassive black hole (SMBH). Consistency with observed SMBH masses constrains the possible DM equations of state. The constraints are looser when a cD galaxy is present. Distributed (AGN) heating alters cluster global properties, and also reduces the lower limits for the central point-mass, for the preferred DM models in which the dark particles have greater heat capacity than point particles. Eluding these constraints would require dominant non-spherical or anisotropic effects (e.g. bulk rotation, non-radial streaming, asymmetric lumps, or a strong magnetic field).
We investigated the time-dependent radiative and dynamical properties of light supersonic jets launched into an external medium, using hydrodynamic simulations and numerical radiative transfer calculations. These involved various structural models fo
r the ambient media, with density profiles appropriate for galactic and extragalactic systems. The radiative transfer formulation took full account of emission, absorption, re-emission, Faraday rotation and Faraday conversion explicitly. High time-resolution intensity maps were generated, frame-by-frame, to track the spatial hydrodynamical and radiative properties of the evolving jets. Intensity light curves were computed via integrating spatially over the emission maps. We apply the models to jets in active galactic nuclei (AGN). From the jet simulations and the time-dependent emission calculations we derived empirical relations for the emission intensity and size for jets at various evolutionary stages. The temporal properties of jet emission are not solely consequences of intrinsic variations in the hydrodynamics and thermal properties of the jet. They also depend on the interaction between the jet and the ambient medium. The interpretation of radio jet morphology therefore needs to take account of environmental factors. Our calculations have also shown that the environmental interactions can affect specific emitting features, such as internal shocks and hotspots. Quantification of the temporal evolution and spatial distribution of these bright features, together with the derived relations between jet size and emission, would enable us to set constraints on the hydrodynamics of AGN and the structure of the ambient medium.
The kinematics of stars and planetary nebulae in early type galaxies provide vital clues to the enigmatic physics of their dark matter halos. We fit published data for fourteen such galaxies using a spherical, self-gravitating model with two componen
ts: (1) a Sersic stellar profile fixed according to photometric parameters, and (2) a polytropic dark matter halo that conforms consistently to the shared gravitational potential. The polytropic equation of state can describe extended theories of dark matter involving self-interaction, non-extensive thermostatistics, or boson condensation (in a classical limit). In such models, the flat-cored mass profiles widely observed in disc galaxies are due to innate dark physics, regardless of any baryonic agitation. One of the natural parameters of this scenario is the number of effective thermal degrees of freedom of dark matter (F_d) which is proportional to the dark heat capacity. By default we assume a cosmic ratio of baryonic and dark mass. Non-Sersic kinematic ideosyncrasies and possible non-sphericity thwart fitting in some cases. In all fourteen galaxies the fit with a polytropic dark halo improves or at least gives similar fits to the velocity dispersion profile, compared to a stars-only model. The good halo fits usually prefer F_d values from six to eight. This range complements the recently inferred limit of 7<F_d<10 (Saxton & Wu), derived from constraints on galaxy cluster core radii and black hole masses. However a degeneracy remains: radial orbital anisotropy or a depleted dark mass fraction could shift our models preference towards lower F_d; whereas a loss of baryons would favour higher F_d.
We analyse the radial structure of self-gravitating spheres consisting of multiple interpenetrating fluids, such as the X-ray emitting gas and the dark halo of a galaxy cluster. In these dipolytropic models, adiabatic dark matter sits in equilibrium,
while the gas develops a gradual, smooth, quasi-stationary cooling flow. Both affect and respond to the collective gravitational field. We find that all subsonic, radially continuous, steady solutions require a non-zero minimum central point mass. For Mpc-sized halos with 7 to 10 effective degrees of freedom (F2), the minimum central mass is compatible with observations of supermassive black holes. Smaller gas mass influxes enable smaller central masses for wider ranges of F2. The halo comprises a sharp spike around the central mass, embedded within a core of nearly constant density (at 10-10^2.5kpc scales), with outskirts that attenuate and naturally truncate at finite radius (several Mpc). The gas density resembles a broken power law in radius, but the temperature dips and peaks within the dark core. A finite minimum temperature occurs due to gravitational self-warming, without cold mass dropout nor needing regulatory heating. X-ray emission from the intracluster medium mimics a beta-model plus bright compact nucleus. Near-sonic points in the gas flow are bottlenecks to allowed steady solutions; the outermost are at kpc scales. These sites may preferentially develop cold mass dropout during strong perturbations off equilibrium. Within the sonic point, the profile of gas specific entropy is flatter than s r^{1/2}, but this is a shallow ramp and not an isentropic core. When F2 is large, the inner halo spike is only marginally Jeans stable in the central pc, suggesting that a large non-linear disturbance could trigger local dark collapse onto the central object.
We investigate the hydrodynamics of accretion channelled by a dipolar magnetic field (funnel flows). We consider situations in which the electrons and ions in the flow cannot maintain thermal equilibrium (two-temperature effects) due to strong radiat
ive loss, and determine the effects on the keV X-ray properties of the systems. We apply this model to investigate the accretion shocks of white dwarfs in magnetic cataclysmic variables. We have found that the incorporation of two-temperature effects could harden the keV X-rays. Also, the dipolar model yields harder X-ray spectra than the standard planar model if white dwarf is sufficiently massive (>~1M_sun). When fitting observed keV X-ray spectra of magnetic cataclysmic variables, the inclusion of two-temperature hydrodynamics and a dipolar accretion geometry lowers estimates for white-dwarf masses when compared with masses inferred from models excluding these effects. We find mass reductions <~9% in the most massive cases.
