Unbeamed tidal disruption events at hard X-rays

Owing to their thermal emission, tidal disruption events (TDEs) were regularly detected in the soft X-rays and sometimes in the optical. Only a few TDEs have been detected at hard X-rays: two are high redshift beamed events, one of which occurred at the core of a nearby galaxy, and the most recent one is of a different nature, involving a compact object in the Milky Way. The aims of this work are to obtain a first sample of hard X-ray-selected unbeamed TDEs, to determine their frequency and to probe whether TDEs usually or exceptionally emit at hard X-ray energies. We performed extensive searches for hard X-ray flares at positions in over 53000 galaxies, up to a distance of 100 Mpc in the Swift BAT archive. Light curves were extracted and parametrized. The quiescent hard X-ray emission was used to exclude persistently active galactic nuclei. Significant flares from non-active galaxies were derived and checked for possible contamination. We found a sample of nine TDE candidates, which translates into a rate of $2 \times 10^{-5}\,{\rm galaxy}^{-1}\,{\rm yr}^{-1}$ above the BAT detection limit. This rate is consistent with those observed by XMM-Newton at soft X-rays and in the optical from SDSS observations, and is as expected from simulations. We conclude that hard X-ray emission should be ubiquitous in un-beamed TDEs and that electrons should be accelerated in their accretion flow.Comment: accepted for publication in A&A; 14 pages, 6 figures, 2 table

Global surfaces of section for Reeb flows in dimension three and beyond

We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic inequalities. Applications to topology and celestial mechanics are also presented.Comment: 33 pages, 3 figures. This is an extended version of a paper written for Proceedings of the ICM, Rio 2018; in v3 we made minor additional corrections, updated references, added a reference to work of Lu on the Conley Conjectur

Fast finite-energy planes in symplectizations and applications

We define the notion of fast finite-energy planes in the symplectization of a closed 3-dimensional energy level $M$ of contact type. We use them to construct special open book decompositions of $M$ when the contact structure is tight and induced by a (non-degenerate) dynamically convex contact form. The obtained open books have disk-like pages that are global surfaces of section for the Hamiltonian dynamics. Let $S \subset \R^4$ be the boundary of a smooth, strictly convex, non-degenerate and bounded domain. We show that a necessary and sufficient condition for a closed Hamiltonian orbit $P\subset S$ to be the boundary of a disk-like global surface of section for the Hamiltonian dynamics is that $P$ is unknotted and has self-linking number -1.Comment: 73 pages, some minor corrections made. To appear in Transactions of the American Mathematical Societ