Bence Kocsis

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.

Abstract:

Mergers of stellar-mass black holes on highly eccentric orbits are among the targets for ground-based gravitational-wave detectors, including LIGO, VIRGO, and KAGRA. These sources may commonly form through gravitational-wave emission in high velocity dispersion systems or through the secular Kozai-Lidov mechanism in triple systems. Gravitational waves carry information about the binaries' orbital parameters and source location. Using the Fisher matrix technique, we determine the measurement accuracy with which the LIGO-VIRGO-KAGRA network could measure the source parameters of eccentric binaries using a matched filtering search of the repeated burst and eccentric inspiral phases of the waveform. We account for general relativistic precession and the evolution of the orbital eccentricity and frequency during the inspiral. We find that the signal-to-noise ratio and the parameter measurement accuracy may be significantly higher for eccentric sources than for circular sources. This increase is sensitive to the initial pericenter distance, the initial eccentricity, and component masses. For instance, compared to a 30 Msun-30 Msun non-spinning circular binary, the chirp mass and sky localization accuracy can improve for an initially highly eccentric binary by a factor of ~129 (38) and ~2 (11) assuming an initial pericenter distance of 20 Mtot (10 Mtot).

Abstract:

It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the Universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around ${\cal O}(10) M_\odot$, which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a quantity constructed from the mass-distribution of the merger rate density per unit cosmic time and comoving volume $\mathcal{R}(m_1,m_2)$, $\alpha = -{(m_1+m_2)}^2\partial^2 \ln\mathcal{R}/\partial m_1\partial m_2 $, which universally satisfies $0.97 \lesssim \alpha \lesssim 1.05$ for all binary masses independently of the PBH mass function. This result suggests that the measurement of this quantity is useful for testing the PBH scenario.