Kotaro Fujisawa

Coexistence of oppositely flowing multi-φ currents: key to large toroidal magnetic fields within stars

We will show the importance of coexistence of oppositely flowing

A versatile numerical method for obtaining structures of rapidly rotating baroclinic stars: self-consistent and systematic solutions with shellular-type rotation

\varphi

Equilibrium solutions of relativistic rotating stars with mixed poloidal and toroidal magnetic fields

-currents for magnetized stars to sustain strong toroidal magnetic fields within the stars by an- alyzing stationary states of magnetized stars with surface currents which flow in the opposite direction with respect to the bulk currents within the stars. We have imposed boundary conditions for currents and toroidal magnetic fields to vanish outside the stars. It is important to note that these boundary conditions set an upper limit for the total current within the stars. This upper limit for the total current results in the presence of an upper limit for the magnitude of the energy for the toroidal magnetic fields of the stars. If the stars could have the toroidal surface currents which flow in the opposite directions to the internal toroidal currents, the positively flowing inter- nal toroidal currents can become stronger than the upper limit value of the current for configurations without surface toroidal currents. Thus the energies for the toroidal magnetic fields can become much larger than those for the magnetized stars with- out surface toroidal currents. We have also analyzed the same phenomena appearing in spherical incompressible stars for dipole-like magnetic fields with or without sur- face toroidal currents by employing the zero-flux-boundary method. We have applied those configurations with surface toroidal currents to magnetars and discussed their flares through which magnetic helicities could arise outside the stellar surfaces.

Counter effects of meridional flows and magnetic fields in stationary axisymmetric self-gravitating barotropes under the ideal MHD approximation: Clear examples - toroidal configurations

This paper develops a novel numerical method for obtaining structures of rapidly rotating stars based on a self-consistent field scheme. The solution is obtained iteratively. Both rapidly rotating barotropic and baroclinic equilibrium states are calculated self-consistently using this method. Two types of rotating baroclinic stars are investigated by changing the isentropic surfaces inside the star. Solution sequences of these are calculated systematically and critical rotation models beyond which no rotating equilibrium state exists are also obtained. All of these rotating baroclinic stars satisfy necessarily the Bjerknes-Rosseland rules. Self-consistent solutions of baro-clinic stars with shellular-type rotation are successfully obtained where the isentropic surfaces are oblate and the surface temperature is hotter at the poles than at the equator if it is assumed that the star is an ideal gas star. These are the first self-consistent and systematic solutions of rapidly rotating baroclinic stars with shellular-type rotations. Since they satisfy the stability criterion due to their rapid rotation, these rotating baroclinic stars would be dynamically stable. This novel numerical method and the solutions of the rapidly rotating baroclinic stars will be useful for investigating stellar evolution with rapid rotations.

Magnetized stars with differential rotation and a differential toroidal field

Department of Earth Science and Astronomy, Graduate School of Arts and Sciences,University of Tokyo, Komaba 3-8-1, Meguro, 153-8902 Tokyo, Japan(Dated: October 16, 2014)Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal andtoroidal magnetic fields are obtained numerically. Because of the mixed components of the magneticfield, the underlying stationary and axisymmetric spacetimes are no longer circular. These configu-rations are computed from the full set of the Einstein-Maxwell equations, Maxwell’s equations andfrom first integrals and integrability conditions of the magnetohydrodynamic equilibrium equations.After a brief introduction of the formulation of the problem, we present the first results for highlydeformed magnetized rotating compact stars.

A novel formulation by Lagrangian variational principle for rotational equilibria: towards multidimensional stellar evolutions

We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meri dional flows under the ideal MHD approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic field s act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stat ionary structures of the toroidal gaseous configurations around central point masses in the fr amework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the p oloidal magnetic fields are apt to elongate the density contours in a certain direction depend ing on the situation. Therefore the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the station ary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems.

Prolate stars due to meridional flows

We have succeeded in obtaining magnetised equilibrium states with differential rotation and differential toroidal magnetic fields. If an internal toroidal field of a pr oto-neutron star is wound up from the initial poloidal magnetic field by differen tial rotation, the distribution of the toroidal magnetic field is determined by the profile of thi s differential rotation. However, the distributions of the toroidal fields in all previous magn etised equilibrium studies do not represent the magnetic winding by the differential rotatio n of the star. In this paper, we investigate a formulation of a differential toroidal magnetic field that represents the magnetic field wound up by differential rotation. We have developed two functional forms of differential toroidal fields which correspond to a v-constant and a j-constant field in analogy to differential rotations. As the degree of the differential becomes very high, the toroidal magnetic field becomes highly localised and concentrated near the rot ational axis. Such a differential toroidal magnetic field would suppress the low- T/|W| instability more efficiently even if the total magnetic field energy is much smaller than that of a non- differential toroidal magnetic field.

Hyperbolic Self-Gravity Solver for Large Scale Hydrodynamical Simulations

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of

Appearance of the prolate and the toroidal magnetic field dominated stars: Analytic approach

O(10^{-4})

Rotational equilibria by Lagrangian variational principle: Towards multidimensional stellar evolutions

in the Virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.