Pulsars, transients and relativistic astrophysics

Abstract:

The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes' distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this process for a system of bodies with similar semimajor axes and eccentricities. We extend the previous model of Roupas et al. (2017) by accounting for the multipole moments beyond the quadrupole, which dominate the interaction for radially overlapping orbits. Nevertheless, we find no qualitative differences between the behavior of the system with respect to the model restricted to the quadrupole interaction. The equilibrium distribution resembles a counterrotating disk at low temperature and a spherical structure at high temperature. The system exhibits a first order phase transition between the disk and the spherical phase in the canonical ensemble if the total angular momentum is below a critical value. We find that the phase transition erases the high order multipoles, i.e. small-scale structure in angular momentum space, most efficiently. The system admits a maximum entropy and a maximum energy, which lead to the existence of negative temperature equilibria.

Abstract:

The recent discovery of gravitational waves has opened new horizons for physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and LISA, promise to shed light on black holes of every size from stellar mass (SBH) sizes up to supermassive black holes which reside in galactic nuclei. The intermediate mass black hole (IMBH) family has not been detected beyond any reasonable doubt neither directly nor indirectly. Recent analyses suggest observational evidence for the presence of IMBHs in the centers of two Galactic globular clusters. In this paper, we investigate the possibility that globular clusters were born with a central IMBH, which undergo repeated merger events with SBHs in the cluster core. By means of a semi-analytical method, we follow the evolution of the primordial cluster population in the galactic potential and the Gravitational Wave (GW) mergers of the binary IMBH-SBH systems. Our models predict $\approx 1000$ IMBHs within $1$ kpc from the Galactic Center. Our results show that the IMBH-SBH merger rate density changes from $\mathcal{R}\approx 1000$ Gpc$^{-3}$ yr$^{-1}$ beyond $z\approx 2$ to $\mathcal{R}\approx 1-10$ Gpc$^{-3}$ yr$^{-1}$ at $z\approx 0$. The rates at low redshifts may be significantly higher if young massive star clusters host IMBHs. The merger rates are dominated by IMBHs with masses between $10^3$ and $10^4\,\mathrm{M}_{\odot}$. Currently there are no LIGO/VIRGO upper limits for GW sources in this mass range, but our results show that at design sensitivity these instruments may detect these IMBH-SBH mergers in the coming years. \textit{LISA} and the Einstein Telescope will be best suited to detect these GW events. The inspirals of IMBH-SBH systems may also generate an unresolved GW background.