Moment Approach for Determining the Orbital Elements of an Astrometric Binary with Low Signal-to-noise Ratio

A moment approach for orbit determinations of an astrometric binary with low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period such as Cyg-X1 and also at a star wobbled by planets. As an exact solution to the nonlinearly coupled equation system, the orbital elements are written in terms of the second and third moments of projected positions that are measured by astrometry. This may give a possible estimation of the true orbit.Comment: 18 pages, 5 figures, 1 table; accepted by PAS

Numerical Simulations of Equatorially-Asymmetric Magnetized Supernovae: Formation of Magnetars and Their Kicks

A series of numerical simulations on magnetorotational core-collapse supernovae are carried out. Dipole-like configurations which are offset northward are assumed for the initially strong magnetic fields together with rapid differential rotations. Aims of our study are to investigate effects of the offset magnetic field on magnetar kicks and on supernova dynamics. Note that we study a regime where the proto-neutron star formed after collapse has a large magnetic field strength approaching that of a ``magnetar'', a highly magnetized slowly rotating neutron star. As a result, equatorially-asymmetric explosions occur with a formation of the bipolar jets. Resultant magnetar's kick velocities are $\sim 300-1000$ km s$^{-1}$. We find that the acceleration is mainly due to the magnetic pressure while the somewhat weaker magnetic tension works toward the opposite direction, which is due to stronger magnetic field in the northern hemisphere. Noted that observations of magnetar's proper motions are very scarce, our results supply a prediction for future observations. Namely, magnetars possibly have large kick velocities, several hundred km s$^{-1}$, as ordinary neutron stars do, and in an extreme case they could have those up to 1000 km s$^{-1}$.Comment: 36 pages, 9 figures, accepted by the Astrophysical Journa