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

The criterion of supernova explosion revisited: the mass accretion history

By performing neutrino-radiation hydrodynamic simulations in spherical symmetry (1D) and axial symmetry (2D) with different progenitor models by Woosley & Heger (2007) from 12 $M_{\odot}$ to 100 $M_{\odot}$, we find that all 1D runs fail to produce an explosion and several 2D runs succeed. The difference in the shock evolutions for different progenitors can be interpreted by the difference in their mass accretion histories, which are in turn determined by the density structures of progenitors. The mass accretion history has two phases in the majority of the models: the earlier phase in which the mass accretion rate is high and rapidly decreasing and the later phase with a low and almost constant accretion rate. They are separated by the so-called turning point, the origin of which is a change of the accreting layer. We argue that shock revival will most likely occur around the turning point and hence that its location in the $\dot M$-$L_\nu$ plane will be a good measure for the possibility of shock revival: if the turning point lies above the critical curve and the system stays there for a long time, shock revival will obtain. In addition, we develop a phenomenological model to approximately evaluate the trajectories in the $\dot M$-$L_\nu$ plane, which, after calibrating free parameters by a small number of 1D simulations, reproduces the location of the turning point reasonably well by using the initial density structure of progenitor alone. We suggest the application of the phenomenological model to a large collection of progenitors in order to infer without simulations which ones are more likely to explode.Comment: 17 pages, 24 figures, 2 tables; accepted for publication in Ap