Dark matter concentrations in galactic nuclei according to polytropic models

We calculate the radial profiles of galaxies where the nuclear region is self-gravitating, consisting of self-interacting dark matter (SIDM) with $F$ degrees of freedom. For sufficiently high density this dark matter becomes collisional, regardless of its behaviour on galaxy scales. Our calculations show a spike in the central density profile, with properties determined by the dark matter microphysics, and the densities can reach the `mean density' of a black hole (from dividing the black-hole mass by the volume enclosed by the Schwarzschild radius). For a galaxy halo of given compactness ($\chi=2GM/Rc^2$), certain values for the dark matter entropy yield a dense central object lacking an event horizon. For some soft equations of state of the SIDM (e.g. $F\ge6$), there are multiple horizonless solutions at given compactness. Although light propagates around and through a sphere composed of dark matter, it is gravitationally lensed and redshifted. While some calculations give non-singular solutions, others yield solutions with a central singularity. In all cases the density transitions smoothly from the central body to the dark-matter envelope around it, and to the galaxy's dark matter halo. We propose that pulsar timing observations will be able to distinguish between systems with a centrally dense dark matter sphere (for different equations of state) and conventional galactic nuclei that harbour a supermassive black hole.Comment: MNRAS accepted, 24 pages, 12 figure

The Centaurus A Northern Middle Lobe as a Buoyant Bubble

We model the northern middle radio lobe of Centaurus A (NGC 5128) as a buoyant bubble of plasma deposited by an intermittently active jet. The extent of the rise of the bubble and its morphology imply that the ratio of its density to that of the surrounding ISM is less than 10^{-2}, consistent with our knowledge of extragalactic jets and minimal entrainment into the precursor radio lobe. Using the morphology of the lobe to date the beginning of its rise through the atmosphere of Centaurus A, we conclude that the bubble has been rising for approximately 140Myr. This time scale is consistent with that proposed by Quillen et al. (1993) for the settling of post-merger gas into the presently observed large scale disk in NGC 5128, suggesting a strong connection between the delayed re-establishment of radio emission and the merger of NGC 5128 with a small gas-rich galaxy. This suggests a connection, for radio galaxies in general, between mergers and the delayed onset of radio emission. In our model, the elongated X-ray emission region discovered by Feigelson et al. (1981), part of which coincides with the northern middle lobe, is thermal gas that originates from the ISM below the bubble and that has been uplifted and compressed. The "large-scale jet" appearing in the radio images of Morganti et al. (1999) may be the result of the same pressure gradients that cause the uplift of the thermal gas, acting on much lighter plasma, or may represent a jet that did not turn off completely when the northern middle lobe started to buoyantly rise. We propose that the adjacent emission line knots (the "outer filaments") and star-forming regions result from the disturbance, in particular the thermal trunk, caused by the bubble moving through the extended atmosphere of NGC 5128.Comment: 38 pages, 13 figures, submitted to ApJ; a version with higher resolution figures is available at http://www.mso.anu.edu.au/~saxton/papers/cena.pd

Scaling law in target-hunting processes

We study the hunting process for a target, in which the hunter tracks the goal by smelling odors it emits. The odor intensity is supposed to decrease with the distance it diffuses. The Monte Carlo experiment is carried out on a 2-dimensional square lattice. Having no idea of the location of the target, the hunter determines its moves only by random attempts in each direction. By sorting the searching time in each simulation and introducing a variable $x$ to reflect the sequence of searching time, we obtain a curve with a wide plateau, indicating a most probable time of successfully finding out the target. The simulations reveal a scaling law for the searching time versus the distance to the position of the target. The scaling exponent depends on the sensitivity of the hunter. Our model may be a prototype in studying such the searching processes as various foods-foraging behavior of the wild animals.Comment: 7 figure