arXiv subjects

Kotaro Fujisawa

Publications and source records attributed to Kotaro Fujisawa.

At least 37 records · Page 2Linked to original sources

arXiv2022

Magnetic field sustained by the elastic force in neutron star crusts

We investigate the magneto--elastic equilibrium of a neutron star crust and magnetic energy stored by the elastic force. The solenoidal motion driven by the Lorentz force can be controlled by the magnetic elastic force, so that conditions for the magnetic field strength and geometry are less restrictive. For equilibrium models, the minor solenoidal part of the magnetic force is balanced by a weak elastic force because the irrotational part is balanced by the dominant gravity and pressure forces. Therefore, a strong magnetic field may be confined in the interior, regardless of poloidal or toroidal components. We numerically calculated axially symmetric models with the maximum shear--strain, and found that a magnetic energy $> 10^{46}$ erg can be stored in the crust, even for a normal surface dipole-field-strength ($<10^{13}$ G). The magnetic energy much exceeds the elastic energy ($ 10^{44} -10^{45}$ erg). The shear--stress spatial distribution revealed that the elastic structure is likely to break down near the surface. In particular, the critical position is highly localized at a depth less than 100 m from the surface.

astro-ph.HE↗

arXiv2021

Magneto-elastic equilibrium of a neutron-star crust

We examine the equilibrium of a magnetized neutron-star-crust. We calculate axially symmetric models in which an elastic force balances solenoidal motion driven by a Lorentz force. A large variety of equilibrium models are allowed by incorporating the elastic shear deformation; in addition, toroidal-magnetic-field dominated models are available. These results remarkably differ from those in barotropic fluid stars. We demonstrate some models wherein the magnetic energy exceeds the elastic energy. The excess comes from the fact that a large amount of magnetic energy is associated with the irrotational part of the magnetic force, which is balanced with gravity and pressure. It is sufficient for equilibrium models that the minor solenoidal part is balanced by a weak elastic force. We find that the elasticity in the crust plays an important role on the magnetic-field confinement. Further, we present the spatial distribution of the shear-stress at the elastic limit, by which the crust-fracture location can be identified. The result has useful implications for realistic crust-quake models.

astro-ph.HE↗

arXiv2020

Evolution of magnetic deformation in neutron star crust

In this study, we examine the magnetic field evolution occurring in a neutron star crust. Beyond the elastic limit, the lattice ions are assumed to act as a plastic flow. The Ohmic dissipation, Hall drift, and bulk fluid velocity driven by the Lorentz force are considered in our numerical simulation. A magnetically induced quadrupole deformation is observed in the crust during the evolution. Generally, the ellipticity decreases as the magnetic energy decreases. In a toroidal-field-dominated model, the sign of the ellipticity changes. Namely, the initial prolate shape tends to become oblate. This occurs because the toroidal component decays rapidly on a smaller timescale than the poloidal dipole component. We find that the magnetic dipole component does not change significantly on the Hall timescale of $\sim 1$Myr for the considered simple initial models. Thus, a more complex initial model is required to study the fast decay of surface dipoles on the abovementioned timescale.

astro-ph.HE↗

arXiv2019

The optically thick rotating magnetic wind from a massive white dwarf merger product

WD J005311 is a newly identified white dwarf (WD) in a mid-infrared nebula. The spectroscopic observation indicates the existence of a neon-enriched carbon/oxygen wind with a terminal velocity of $v_{\infty,\rm obs}\sim 16,000\,\rm km\,s^{-1}$ and a mass loss rate of $\dot M_{\rm obs}\sim 3.5\times 10^{-6}\,M_\odot$ yr$^{-1}$. Here we consistently explain the properties of WD J005311 using a newly constructed wind solution, where the optically thick outflow is launched from the carbon burning shell on an oxygen-neon core and accelerated by the rotating magnetic field to become supersonic and unbound well below the photosphere. Our model implies that WD J005311 has a mass of $M_* \sim 1.1\mbox{-}1.3\,M_\odot$, a magnetic field of $B_* \sim (2\mbox{-}5)\times 10^7\,\rm G$, and a spin angular frequency of $Ω\sim 0.2\mbox{-}0.5 \,\rm s^{-1}$. The large magnetic field and fast spin support the carbon-oxygen WD merger origin. WD J005311 will neither explode as a type Ia supernova nor collapse into a neutron star. If the wind continues to blow another few kyr, WD J005311 will spin down significantly and join to the known sequence of slowly-rotating magnetic WDs. Otherwise it may appear as a fast-spinning magnetic WD and could be a new high energy source.

astro-ph.SR↗

arXiv2019

New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe.

gr-qc↗

arXiv2018

The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations

We propose a new class of method for solving nonlinear systems of equations, which, among other things,has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extention to the Newton-Raphson(NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

math.NA↗

arXiv2018

Effects of rotation and magnetic field on the revival of a stalled shock in supernova explosions

We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that describe approximately accretion flows through a standing shock wave and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the 2-dimensional (2D) steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star has rotation and/or magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force and the critical luminosity is modified.In fact we find that the critical luminosity is reduced by about 50% - 70% for rapid rotations and about 20% - 50% for strong toroidal magnetic fields, depending on the mass accretion rate. These results may be also interpreted as an existence of the critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will revive for a given combination of mass accretion rate and neutrino luminosity.

astro-ph.HE↗

arXiv2016

Rotational equilibria by Lagrangian variational principle: toward multi-dimensional stellar evolutions

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.

astro-ph.HE↗

arXiv2016

Hyperbolic Self-Gravity Solver for Large Scale Hydrodynamical Simulations

A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly corresponds to the weak field limit of the Einstein equations in general relativity, and as long as the gravitation propagation speed is taken to be larger than the hydrodynamical characteristic speed, the results agree with solutions for the Poisson equation. The solutions almost perfectly agree if the domain is taken large enough, or appropriate boundary conditions are given. Our new method can not only significantly reduce the computational time compared with existent methods, but is also fully compatible with massive parallel computation, nested grids and adaptive mesh refinement techniques, all of which can accelerate the progress in computational astrophysics and cosmology.

astro-ph.IM↗

arXiv2015

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

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.

astro-ph.SR↗

arXiv2015

Magnetic field configurations of a magnetar throughout its interior and exterior -- core, crust and magnetosphere

We obtained the magnetic field configurations, including both poloidal and toroidal components, throughout the interior and exterior of magnetars using a realistic equation of state. We divided the magnetized star into the hydromagnetic equilibrium core, Hall equilibrium crust and twisted force-free magnetosphere. We systematically and simultaneously calculated these regions under various boundary conditions using the Green function relaxation method, and noted the following interesting characteristics of these numerical results. First, the strength and structure of core magnetic fields affect the crustal magnetic fields. Second, the current sheet on the core-crust interface affects both internal and external magnetic field configurations. Third, the twisted magnetosphere makes a cross-point of magnetic field lines, such as X-point geometry, in the magnetosphere. The X-point geometry appears and disappears according to the strength of the twisted field in the magnetosphere or the core-crust boundary conditions. Our results mean that both Hall magnetohydrodynamics secular evolution and magnetospheric dynamical evolution are deeply affected by conditions of another region and the core-crust stress of magnetars.

astro-ph.HE↗

arXiv2015

Magnetized stars with differential rotation and a differential toroidal field

We have succeeded in obtaining magnetized equilibrium states with differential rotation and differential toroidal magnetic fields. If an internal toroidal field of a proto-neutron star is wound up from the initial poloidal magnetic field by differential rotation, the distribution of the toroidal magnetic field is determined by the profile of this differential rotation. However, the distributions of the toroidal fields in all previous magnetized equilibrium studies do not represent the magnetic winding by the differential rotation 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 localized and concentrated near the rotational 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.

astro-ph.HE↗

arXiv2015

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

We have analyzed magnetized equilibrium states and showed a condition for appearance of the prolate and the toroidal magnetic field dominated stars by analytic approaches. Both observations and numerical stability analysis support that the magnetized star would have the prolate and the large internal toroidal magnetic fields. In this context, many investigations concerning magnetized equilibrium states have tried to obtain the prolate and the toroidal dominant solutions, but many of them have failed to obtain such configurations. Since the Lorentz force is a cross product of current density and magnetic field, the prolate shaped configurations and the large toroidal magnetic fields in stars require a special relation between current density and the Lorentz force. We have analyzed simple analytical solutions and found that the prolate and the toroidal dominant configuration require non force-free toroidal current density that flows in the opposite direction with respect to the bulk current within the star. Such current density results in the Lorentz force which makes the stellar shape prolate. Satisfying this special relation between the current density and the Lorentz force is a key for appearance of the prolate and the toroidal magnetic field dominated magnetized star.

astro-ph.HE↗

arXiv2014

A Novel Formulation by Lagrangian Variational Principle for Rotational Equilibria: Toward Multi-Dimensional Stellar Evolutions

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 $O(10^{-4})$ 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.

astro-ph.SR↗

arXiv2014

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

Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal and toroidal magnetic fields are obtained numerically. Because of the mixed components of the magnetic field, the underlying stationary and axisymmetric spacetimes are no longer circular. These configurations are computed from the full set of the Einstein-Maxwell equations, Maxwell's equations and from 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 highly deformed magnetized rotating compact stars.

astro-ph.HE↗

arXiv2013

Prolate stars due to meridional flows

We have shown analytically that shapes of incompressible stars could be prolate if appropriate meridional flows exist. Although this result is strictly valid only if either the meridional flow or the rotation is absent and the vorticity is associated uniformly with meridional flow, this implies that perpendicular forces against centrifugal and/or magnetic forces might play important roles within stars. A consequence of the presence of meridional flows might be to decrease stellar oblateness due to centrifugal and/or magnetic fields.

astro-ph.SR↗

arXiv2013

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

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 meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields 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 stationary structures of the toroidal gaseous configurations around central point masses in the framework 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 poloidal magnetic fields are apt to elongate the density contours in a certain direction depending 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 stationary 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.

astro-ph.HE↗

arXiv2013

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 $φ$-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.

astro-ph.HE↗