Mass-ratio distribution of extremely low-mass white dwarf binaries

Knowing the masses of the components of binary systems is very useful to constrain the possible scenarios that could lead to their existence. While it is sometimes possible to determine the mass of the primary star, for single-lined spectroscopic binaries it is not trivial to have good estimates of the mass of the secondary. If a large enough sample of such binaries is available, it is possible, however, to use statistical methods to determine the mass ratio distribution, and thus, the secondary mass distribution. Recently, Andrews et al. (2014) studied the mass distribution of companions to extremely low-mass white dwarfs, using a sample of binaries from the ELM WD Survey. I reanalyse the same sample, using two different methods: in the first one, I assume some functional form for the mass distribution, while in the second, I apply an inversion method. I show that the resulting companion-mass distribution can be as well approximated by either a uniform distribution or a Gaussian distribution. The mass ratio distribution derived from the inversion method, without assuming any a priori functional form, shows some additional fine-grain structure, although, given the small sample, it is difficult to claim that this structure is statistically significant. I conclude that it is not possible yet to fully constrain the distribution of the mass of the companions to extremely low-mass white dwarfs, although it appears that the probability to have a neutron star in one of the systems is indeed very small.Comment: A&A Letters, in pres

Parallax and masses of alpha Centauri revisited

Context. Despite the thorough work of van Leeuwen (2007), the parallax of alpha Centauri is still far from being carved in stone. Any derivation of the individual masses is therefore uncertain, if not questionable. And yet, that does not prevent this system from being used for calibration purpose in several studies. Aims. Obtaining more accurate model-free parallax and individual masses of this system. Methods. With HARPS, the radial velocities are not only precise but also accurate. Ten years of HARPS data are enough to derive the complement of the visual orbit for a full 3D orbit of alpha Cen. Results. We locate alpha Cen (743 mas) right where Hipparcos (ESA 1997) had put it, i.e. slightly further away than derived by Soderhjelm (1999). The components are thus a bit more massive than previously thought (1.13 and 0.97 Msun for A and B respectively). These values are now in excellent agreement with the latest asteroseismologic results.Comment: 4 pages, 3 figures, accepted in Astronomy & Astrophysic

Connes-Chern character for manifolds with boundary and eta cochains

We express the Connes-Chern character of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off pa- rameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression involves higher eta cochains and their b-analogues. The corresponding pairing formulae with relative K-theory classes capture information about the boundary and allow to derive geometric consequences. As a by-product, we show that the generalized Atiyah-Patodi-Singer pairing introduced by Getzler and Wu is necessarily restricted to almost flat bundles.Comment: 98 pages, 6 figures; major revision, accepted for publication in the Memoirs of the AM

Mimicking complex dislocation dynamics by interaction networks

Two-dimensional discrete dislocation models exhibit complex dynamics in relaxation and under external loading. This is manifested both in the time-dependent velocities of individual dislocations and in the ensemble response, the strain rate. Here we study how well this complexity may be reproduced using so-called Interaction Networks, an Artificial Intelligence method for learning the dynamics of complex interacting systems. We test how to learn such networks using creep data, and show results on reproducing individual and collective dislocation velocities. The quality of reproducing the interaction kernel is discussed