Theoretical astrophysics and plasma physics at RPC

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.

Abstract:

The advent of time domain astronomy is revolutionizing our understanding of the Universe. Programs such as the Catalina Real-time Transient Survey (CRTS) or the Palomar Transient Factory (PTF) surveyed millions of objects for several years, allowing variability studies on large statistical samples. The inspection of $\approx$250k quasars in CRTS resulted in a catalogue of 111 potentially periodic sources, put forward as supermassive black hole binary (SMBHB) candidates. A similar investigation on PTF data yielded 33 candidates from a sample of $\approx$35k quasars. Working under the SMBHB hypothesis, we compute the implied SMBHB merger rate and we use it to construct the expected gravitational wave background (GWB) at nano-Hz frequencies, probed by pulsar timing arrays (PTAs). After correcting for incompleteness and assuming virial mass estimates, we find that the GWB implied by the CRTS sample exceeds the current most stringent PTA upper limits by almost an order of magnitude. After further correcting for the implicit bias in virial mass measurements, the implied GWB drops significantly but is still in tension with the most stringent PTA upper limits. Similar results hold for the PTF sample. Bayesian model selection shows that the null hypothesis (whereby the candidates are false positives) is preferred over the binary hypothesis at about $2.3\sigma$ and $3.6\sigma$ for the CRTS and PTF samples respectively. Although not decisive, our analysis highlights the potential of PTAs as astrophysical probes of individual SMBHB candidates and indicates that the CRTS and PTF samples are likely contaminated by several false positives.

Abstract:

Collisional relaxation describes the stochastic process with which a self-gravitating system near equilibrium evolves in phase space due to the fluctuating gravitational field of the system. The characteristic timescale of this process is called the relaxation time. In this paper, we highlight the difference between two measures of the relaxation time in globular clusters: (i) the diffusion time with which the isolating integrals of motion (i.e. energy E and angular momentum magnitude L) of individual stars change stochastically and (ii) the asymptotic timescale required for a family of orbits to mix in the cluster. More specifically, the former corresponds to the instantaneous rate of change of a star's E or L, while the latter corresponds to the timescale for the stars to statistically forget their initial conditions. We show that the diffusion timescales of E and L vary systematically around the commonly used half-mass relaxation time in different regions of the cluster by a factor of ~10 and ~100, respectively, for more than 20% of the stars. We define the mixedness of an orbital family at any given time as the correlation coefficient between its E or L probability distribution functions and those of the whole cluster. Using Monte Carlo simulations, we find that mixedness converges asymptotically exponentially with a decay timescale that is ~10 times the half-mass relaxation time.