Planar infall of CH3OH gas around Cepheus A HW2

Aims: In order to test the nature of an (accretion) disk in the vicinity of Cepheus A HW2, we measured the three-dimensional velocity field of the CH3OH maser spots, which are projected within 1000au of the HW2 object, with an accuracy of the order of 0.1km/s. Methods: We made use of the European VLBI Network (EVN) to image the 6.7GHz CH3OH maser emission towards Cepheus A HW2 with 4.5 milli-arcsecond resolution (3au). We observed at three epochs spaced by one year between 2013 and 2015. During the last epoch, on mid-march 2015, we benefited from the new deployed Sardinia Radio Telescope. Results: We show that the CH3OH velocity vectors lie on a preferential plane for the gas motion with only small deviations of 12+/-9 degrees away from the plane. This plane is oriented at a position angle of 134 degrees east of north, and inclined by 26 degrees with the line-of-sight, closely matching the orientation of the disk-like structure previously reported by Patel et al.(2005). Knowing the orientation of the equatorial plane, we can reconstruct a face-on view of the CH3OH gas kinematics onto the plane. CH3OH maser emission is detected within a radius of 900au from HW2, and down to a radius of about 300au, the latter coincident with the extent of the dust emission at 0.9mm. The velocity field is dominated by an infall component of about 2km/s down to a radius of 300au, where a rotational component of 4km/s becomes dominant. We discuss the nature of this velocity field and the implications for the enclosed mass. Conclusions: These findings bring direct support to the interpretation that the high-density gas and dust emission, surrounding Cepheus A HW2, trace an accretion disk.Comment: 9 pages, 4 figures, 2 tables, accepted by Astronomy & Astrophysic

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

We consider a periodic self-adjoint pseudo-differential operator $H=(-\Delta)^m+B$, $m>0$, in $\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in \bx, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schr\"odinger operator with a periodic magnetic potential in all dimensions.Comment: 61 page

Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials

We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.Comment: Corrected versio