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The observation of a population of massive black hole binaries (MBHBs) is key for our complete understanding of galaxy mergers and for the characterization of the expected gravitational waves (GWs) signal. However, MBHBs still remain elusive with only a few candidates proposed to date. Among these, SDSSJ143016.05+230344.4 ('tick-tock' hereafter) is the only candidate with a remarkably well sampled light curve showing a clear reduction of the modulation period and amplitude over three years of observations. This particular feature has been recently claimed to be the signature of a MBHB that is about to merge. In this paper, we provide an optical follow-up of the tick-tock source using the Rapid Eye Mount (REM) telescope. The decreasing luminosity observed in our follow up is hardly explained within the binary scenario. We speculate about an alternative scenario that might explain the observed light curve through relativistic Lense-Thirring precession of an accretion disc around a single massive black hole., 9 pages, 2 figure, accepted for publication in MNRAS

The study of the interaction of a massive black hole binary with its gaseous environment is crucial in order to be able to predict merger rates and possible electromagnetic counterparts of gravitational wave signals. The evolution of the binary semi-major axis resulting from this interaction has been recently debated, and a clear consensus is still missing, also because of several numerical limitations, i.e. fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc. Using on-the-fly particle-splitting in the 3D meshless code gizmo, we achieve hyper-Lagrangian resolution, which allows us to properly resolve the dynamics inside the cavity, and in particular for the first time the discs that form around the two components of a live binary surrounded by a locally isothermal gaseous circumbinary disc. We show that the binary orbit decays with time for very cold and very warm discs and that the result of the interaction in the intermediate regime is strongly in uenced by the disc viscosity as this essentially regulates the fraction of mass contained in the discs around the binary components as well as the fraction that is accreted by the binary. We find the balance between these two quantities to determine whether the binary semi-major axis decreases with time., 8 pages, published in ApJL

Giant outbursts of Be/X-ray binaries may occur when a Be-star disc undergoes strong eccentricity growth due to the Kozai-Lidov (KL) mechanism. The KL effect acts on a disc that is highly inclined to the binary orbital plane provided that the disc aspect ratio is sufficiently small. The eccentric disc overflows its Roche lobe and material flows from the Be star disc over to the companion neutron star causing X-ray activity. With N-body simulations and steady state decretion disc models we explore system parameters for which a disc in the Be/X-ray binary 4U 0115+634 is KL unstable and the resulting timescale for the oscillations. We find good agreement between predictions of the model and the observed giant outburst timescale provided that the disc is not completely destroyed by the outburst. This allows the outer disc to be replenished between outbursts and a sufficiently short KL oscillation timescale. An initially eccentric disc has a shorter KL oscillation timescale compared to an initially circular orbit disc. We suggest that the chaotic nature of the outbursts is caused by the sensitivity of the mechanism to the distribution of material within the disc. The outbursts continue provided that the Be star supplies material that is sufficiently misaligned to the binary orbital plane. We generalise our results to Be/X-ray binaries with varying orbital period and find that if the Be star disc is flared, it is more likely to be unstable to KL oscillations in a smaller orbital period binary, in agreement with observations., Accepted for publication in MNRAS

Type I outbursts in Be/X-ray binaries are usually associated with the eccentricity of the binary orbit. The neutron star accretes gas from the outer parts of the decretion disk around the Be star at each periastron passage. However, this mechanism cannot explain type I outbursts that have been observed in nearly circular orbit Be/X-ray binaries. With hydrodynamical simulations and analytic estimates we find that in a circular orbit binary, a nearly coplanar disk around the Be star can become eccentric. The extreme mass ratio of the binary leads to the presence of the 3:1 Lindblad resonance inside the Be star disk and this drives eccentricity growth. Therefore the neutron star can capture material each time it approaches the disk apastron, on a timescale up to a few percent longer than the orbital period. We have found a new application of this mechanism that is able to explain the observed type I outbursts in low eccentricity Be/X-ray binaries., 6 pages, 4 figures, Accepted for publication in ApJL

We investigate the misalignment of the circumbinary disk around the binary HD 98800 BaBb with eccentricity $e\simeq 0.8$. \cite{Kennedy2019} observed the disk to be either at an inclination of $48^{\circ}$ or polar aligned to the binary orbital plane. Their simulations showed that alignment from $48^\circ$ to a polar configuration can take place on a shorter timescale than the age of this system. We perform hydrodynamical numerical simulations in order to estimate the cavity size carved by the eccentric binary for different disk inclinations as an independent check of polar alignment. Resonance theory suggests that torques on the inner parts of a polar disk around such a highly eccentric binary are much weaker than in the coplanar case, indicating a significantly smaller central cavity than in the coplanar case. We show that the inferred inner radius (from carbon monoxide measurements) of the accretion disk around BaBb can exclude the possibility of it being mildly inclined with respect to the binary orbital plane and therefore confirm the polar configuration. This study constitutes an important diagnostic for misaligned circumbinary disks, since it potentially allows us to infer the disk inclination from observed gas disk inner radii., Comment: Accepted for publication in ApJL

In this paper we will review some recent developments in the theory of Tidal Disruption Events (TDE). In particular, we discuss how recent work has led to a reconsideration of the time evolution of the debris of the disrupted star, which in turn determines the lightcurve of the event. We discuss the efforts being currently made to understand how an accretion disc forms around these objects. Finally, we discuss whether we can expect these systems to undergo rigid precession as a consequence of the Lense–Thirring torques produced by a spinning black hole.