arXiv subjects

Hirotada Okawa

Publications and source records attributed to Hirotada Okawa.

At least 19 recordsLinked to original sources

arXiv2026

Implementation of multi-grid Poisson solver in numerical relativity and its application to gravitational collapse of massive star

We develop a new grid-based multi-grid Poisson solver in numerical relativity. We report the performance of the multi-grid Poisson solver in the initial value problems for two-puncture black holes, a static spherical neutron star, a uniformly rotating neutron star in equilibrium, and a gravitationally collapsing massive star. As a demonstration, we conduct a numerical-relativity neutrino-radiation-transfer hydrodynamics simulation of the gravitational collapse of the $9M_\odot$ massive star in Ref.~\cite{Aguilera-Dena:2020mfh} up to the core bounce. During the simulation, we employ the constraint-preserving regird prescription with the newly developed multi-grid Poisson solver to improve the resolution. It shows that the baryonic mass, the Arnowit-Deser-Misner (ADM) mass, and the ADM-like angular momentum are, respectively, preserved with $O(10^{-3})\%$ and $O(10^{-2})$--$O(10^{-1})$\% accuracy.

astro-ph.HE↗

arXiv2026

COSMOS: A numerical relativity code specialized for PBH formation

Primordial black holes (PBHs) are black holes generated in the early universe without having gone through stellar evolution. In the standard formation process, PBHs are formed from super-horizon primordial fluctuations with non-linearly large initial amplitude. In order to simulate the non-linear gravitational dynamics of PBH formation, one has to rely on numerical relativity solvers to approximate the solution of the Einstein equations. COSMOS is a C++ package for solving the Einstein equations in 3+1 dimensions, providing simple tools for the simulation of PBH formation. In order to resolve the collapsing region, non-Cartesian scale-up coordinates and a fixed mesh-refinement procedure are implemented. In COSMOS, a massless scalar field and a perfect fluid with a linear equation of state are implemented as matter fields. To achieve a practically acceptable computational speed, OpenMP is used for the parallelization. COSMOS has no other dependencies, which makes for an easier installation.

gr-qc↗

arXiv2026

Dynamics of Binary System around a Supermassive Black Hole :Binary Scattering and Eccentric vZLK Oscillations

We study the dynamics of a binary orbiting a supermassive black hole (SMBH), focusing on both binary scattering in unbound orbits and eccentric von Zeipel-Lidov-Kozai (vZLK) oscillations in bound orbits. The motion is described in a local inertial frame in Kerr spacetime, where tidal effects are encoded in the Riemann curvature. For unbound (parabolic and hyperbolic) orbits, we identify four scattering regimes-adiabatic, tidally affected, chaotic, and disruptive-depending on the binary semi-major axis. As the binary becomes softer, tidal interactions near periapsis lead to strong eccentricity excitation, large changes in the orbital parameters, and eventually chaotic behavior or tidal disruption, with a sensitive dependence on the argument of periapsis. For eccentric bound (elliptic) orbits, the vZLK mechanism differs qualitatively from the standard one, although the $z$-component of the angular momentum in the local inertial frame remains approximately conserved. The evolution proceeds on a dynamical timescale and exhibits step-like changes driven by repeated periapsis passages, which can be interpreted as a sequence of scattering events. We refer to this behavior as scattering-type vZLK oscillations. The rotation of the SMBH also modifies the oscillation profiles, although its effect is less significant than the dependence on the initial orbital parameters. These results suggest a unified picture of periapsis-driven tidal dynamics in galactic nuclei.

gr-qc↗

arXiv2026

Bifurcated Impact of Neutrino Fast Flavor Conversion on Core-collapse Supernovae Informed by Multi-angle Neutrino Radiation Hydrodynamics

In this {\it Letter}, we present a compelling and robust argument for the roles of neutrino fast flavor conversion (FFC) in the explosion mechanism of core-collapse supernova (CCSN), combining the {\it multi-angle} FFC subgrid model rooted in quantum kinetic theory with the multi-dimensional four-species Boltzmann neutrino radiation hydrodynamics. Employing various progenitor masses and the nuclear equations of states, we find that the effect of FFC on CCSN explosion is bifurcated depending on the progenitors. For the lowest-mass progenitor, FFC facilitates the shock revival and enhances the explosion energy, whereas for higher-mass progenitors its impact is inhibitory. We identify the mass accretion rate as the key determinant governing this bifurcation. When the mass accretion rate is low (high), the contribution of FFC to neutrino heating becomes positive (negative), because the heating efficiency enhancement via FFC-driven spectral hardening of electron-type neutrinos dominates over (is outweighed by) the concurrent reduction in neutrino luminosity. Our results further highlight the limitations of approximate neutrino transport, and demonstrate that a multi-angle treatment is essential for accurately capturing FFC effects; otherwise, FFCs are missed and even generated spuriously.

astro-ph.HE↗

arXiv2025

Dynamical von Zeipel-Lidov-Kozai Oscillations of a Binary on a Spherical Orbit around a Rotating Supermassive Black Hole

We study the dynamics of a binary system orbiting a rotating supermassive black hole (SMBH). Using Fermi-Walker transport, we construct a local inertial reference frame in the Kerr spacetime and set up a Newtonian binary system. Assuming the binary moves on a spherical orbit with constant radius around the black hole, we derive the equations of motion governing its dynamics. We focus on von Zeipel-Lidov-Kozai (vZLK) oscillations, which arise when the binary is compact and its initial inclination exceeds a critical angle. In our previous work on a circular orbit in the equatorial plane, we found that for hard binary systems, these oscillations in eccentricity and inclination follow a regular pattern, whereas in soft binaries, they exhibit chaotic behavior with irregular periods and amplitudes, yet remain stable. In this study, we extend our analysis to a spherical orbit in the Kerr background. The libration of the binary's orbit in the latitudinal direction affects the vZLK oscillations: as the libration angle increases, the oscillation period shortens, and the maximum eccentricity grows, particularly when the oscillations become chaotic. Notably, when the binary is sufficiently soft yet remains stable, the oscillation period is reduced to the dynamical timescale rather than the secular timescale. This effect arises due to the interaction between the SMBH spin and the binary's angular momentum. As the Kerr rotation parameter increases or the radius of the spherical orbit decreases, both the enhancement of maximum eccentricity and the reduction in oscillation period become more pronounced.

gr-qc↗

arXiv2024

Systematic local simulations of fast neutrino flavor conversions with scattering effects

We investigate the dynamics of fast neutrino flavor conversions (FFCs) in the one-dimensional (1D) and zero-dimensional (0D) models, in which spatial advection is considered and ignored, respectively. In this study, we employ snapshots obtained by our self-consistent, realistic Boltzmann-neutrino-radiation-hydrodynamics simulations. We show that the FFC growth rate is considerably larger in the 1D model than in the 0D model, as expected from the previous linear analysis results. We find that the momentum space dimension does not significantly influence the neutrino transition probability in 1D models. On the other hand, in the 0D model without collisions, the FFC depends on the momentum space, and the azimuthal angle dependence breaks the periodicity of the FFC. Our study demonstrates that collisional instability can lead to further flavor conversions on a long time scale in 1D models after the asymptotic state of FFC has been reached. Such an effect should be taken into consideration when the fast and collisional flavor instabilities coexist.

hep-ph↗

arXiv2023

Chaotic von Zeipel-Lidov-Kozai Oscillations of Binary System around Rotating Supermassive Black Hole

In this paper, we investigate the dynamics of a binary system that orbits a rotating supermassive black hole. Our approach employs Fermi-Walker transport to construct a local inertial reference frame, and to set up a Newtonian binary system. We consider a scenario in which a circular geodesic observer is positioned around a Kerr black hole, and thereby derive the equations of motion governing the binary system. To eliminate the interaction terms between the center of mass (CM) of the binary and its relative coordinates, we introduce a small acceleration for the observer. This adjustment leads to the CM closely following the observer's orbit, deviating from a circular geodesic. Here, we first focus on elucidating the stability conditions in a hierarchical triple system. Subsequently, we discuss the phenomenon of von Zeipel-Lidov-Kozai (vZLK) oscillations, which manifest when the binary system is compact and the initial inclination exceeds a critical angle. In hard binary systems, these oscillations exhibit regular behavior, while in soft binary systems, they exhibit a chaotic character, characterized by irregular periods and amplitudes, albeit remaining stable. Additionally, we observe an orbital flip under circumstances of large initial inclination. As for the motion of the CM, we observe deviations from a purely circular orbit that transform into stable yet chaotic oscillations characterized by minute amplitude variations.

gr-qc↗

arXiv2023

Dynamics of Binary System around Supermassive Black Hole

We discuss motion of a binary system around a supermassive black hole. Using Fermi-Walker transport, we construct a local inertial reference frame and set up a Newtonian binary system. Assuming a circular geodesic observer around a Schwarzschild black hole, we write down the equations of motion of a binary. Introducing a small acceleration of the observer, we remove the interaction terms between the center of mass (CM) of a binary and its relative coordinates. The CM follows the observer's orbit, but its motion deviates from an exact circular geodesic. We first solve the relative motion of a binary system, and then find the motion of the CM by the perturbation equations with the small acceleration. We show that there appears the Kozai-Lidov (KL) oscillations when a binary is compact and the initial inclination is larger than a critical angle. In a hard binary system, KL oscillations are regular, whereas in a soft binary system, oscillations are irregular both in period and in amplitude, although stable. We find an orbital flip when the initial inclination is large. As for the motion of the CM, the radial deviations from a circular orbit become stable oscillations with very small amplitude.

gr-qc↗

arXiv2023

Threshold of Primordial Black Hole Formation in Nonspherical Collapse

We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal super-horizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for the large amplitude of perturbations expected for PBH formation.

gr-qc↗

arXiv2022

Protoneutron Star Convection Simulated with a New General Relativistic Boltzmann Neutrino Radiation-Hydrodynamics Code

We investigate the protoneutron star (PNS) convection using our newly developed general relativistic Boltzmann neutrino radiation-hydrodynamics code. This is a pilot study for more comprehensive investigations later. As such, we take a snapshot of a PNS at 2.3 seconds after bounce from a 1D PNS cooling calculation and run our simulation for $\sim160\,\mathrm{ms}$ in 2D under axisymmetry. The original PNS cooling calculation neglected convection entirely and the initial condition is linearly unstable to convection. We find in our 2D simulation that convection is instigated there indeed and expands inward after being full-fledged. The convection is then settled to a quasi-steady state in $\sim100\,\mathrm{ms}$, being sustained by the negative $Y_e$ gradient, which is in turn maintained by neutrino emissions. It enhances the luminosities and mean energies of all species of neutrinos compared to 1D. Taking advantage of the Boltzmann solver, we analyze the possible occurrence of the neutrino fast flavor conversion (FFC). We found that FFC is likely to occur in the regions, where $Y_e$ is lower, and that the growth rate can be as high as $\sim 10^{-1}\,{\mathrm{cm}^{-1}}$.

astro-ph.HE↗

arXiv2022

A Lagrangian construction of rotating stars

We present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian description, i.e., we solve the force-balance equations to find the spatial positions of fluid elements endowed individually with a mass, specific entropy and angular momentum. The system of nonlinear equations obtained by finite-differencing the basic equations are solved with the W4 method, which is a new multi-dimensional root-finding scheme of our own devising. We augment it with a remapping scheme to avoid distortions of the Lagrangian coordinates. In this first one of a series of papers, we will give a detailed description of these methods initially. We then present the results of some test calculations, which include the construction of both rapidly rotating barotropic and baroclinic equilibrium states. We gauge their accuracies quantitatively with some diagnostic quantities as well as via comparisons with the counterparts obtained with an Eulerian code. For a demonstrative purpose, we apply the code to a toy-model cooling calculation of a rotating white dwarf.

astro-ph.SR↗

arXiv2022

Primordial black hole formation from massless scalar isocurvature

We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wavenumber $k$; $\sim\exp(-k^2R^2)$, where $R$ is the radial coordinate. We find that a PBH is formed for a sufficiently large amplitude of the scalar field profile. Nevertheless, we find that the late time behavior of the gravitational collapse is dominated by the dynamics of the fluid but not by the scalar field, which is analogous to the PBH formation from an adiabatic perturbation in the radiation-dominated universe.

gr-qc↗

arXiv2022

Principal-Axis Analysis of the Eddington Tensor for the Early Post-Bounce Phase of Rotational Core-Collapse Supernovae

Using full Boltzmann neutrino transport, we performed two-dimensional (2D) core-collapse supernova simulations in axisymmetry for two progenitor models with 11.2M and 15.0M both rotational and non-rotational. We employed the results obtained in the early post-bounce phase (t < 20 ms) to assess performance under rapid rotation of some closure relations commonly employed in the truncated moment method. We first made a comparison in 1D under spherical symmetry, though, of the Eddington factor p defined in the fluid rest frame (FR). We confirmed that the maximum entropy closure for the Fermionic distribution (MEFD) performs better than others near the proto-neutron star surface, where p < 1/3 occurs, but does not work well even in 1D when the phase space occupancy satisfies e < 0.5 together with p < 1/3, the condition known to be not represented by MEFD. For the 2D models with the rapid rotation, we employed the principal-axis analysis of the Eddington tensor. We paid particular attention to the direction of the longest principal axis. We observed in FR that it is aligned neither with the radial direction nor with the neutrino flux in 2D, particularly so in convective and/or rapidly rotating regions, the fact not accommodated in the moment method. We repeated the same analysis in the laboratory frame (LB) and found again that the direction of the longest principal axis is not well reproduced by MEFD because the interpolation between the optically thick and thin limits is not very accurate in this frame.

astro-ph.HE↗

arXiv2022

Singularity-Avoiding Multi-Dimensional Root-Finder

We proposed in this paper a new method, which we named the W4 method, to solve nonlinear equation systems. It may be regarded as an extension of the Newton-Raphson~(NR) method to be used when the method fails. Indeed our method can be applied not only to ordinary problems with non-singular Jacobian matrices but also to problems with singular Jacobians, which essentially all previous methods that employ the inversion of the Jacobian matrix have failed to solve. In this article, we demonstrate that (i) our new scheme can define a non-singular iteration map even for those problems by utilizing the singular value decomposition, (ii) a series of vectors in the new iteration map converges to the right solution under a certain condition, (iii) the standard two-dimensional problems in the literature that no single method proposed so far has been able to solve completely are all solved by our new method.

math.NA↗

arXiv2022

A novel formulation for the evolution of relativistic rotating stars

We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own devising, in which we solve force balance equations to seek for the positions of fluid elements assigned to the grid points, instead of the ordinary Eulerian formulation. Unlike previous works in the literature, we do not employ the first integral of the Euler equation, which is not obtained by an analytic integration in general. We assign a mass, specific angular momentum and entropy to each fluid element in contrast to the previous methods, in which the spatial distribution of the angular velocity or angular momentum is specified. Those distributions are determined after the positions of all fluid elements (or grid points) are derived in our formulation. We solve the large system of algebraic nonlinear equations that are obtained by discretizing the time-independent Euler and Einstein equations in the finite-elements method by using our new multi-dimensional root-finding scheme, named the W4 method. To demonstrate the capability of our new formulation, we construct some rotational configurations both barotropic and baroclinic. We also solve three evolutionary sequences that mimic the cooling, mass-loss, and mass-accretion as simple toy models.

gr-qc↗

arXiv2021

ECO-spotting: looking for extremely compact objects with bosonic fields

Black holes are thought to describe the geometry of massive, dark compact objects in the universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how compact can self-gravitating solutions be. We discuss theories with a well-posed initial value problem, consisting in either a single self-interacting scalar, vector or both. We focus on spherically symmetric solutions, investigating the influence of self-interacting potentials into the compactness of the solutions, in particular those that allow for flat-spacetime solutions. We are able to connect such stars to hairy black hole solutions, which emerge as a zero-mass black hole. We show that such stars can have light rings, but their compactness is never parametrically close to that of black holes. The challenge of finding black hole mimickers to investigate full numerical-relativity binary setups remains open.

gr-qc↗

arXiv2021

Multidimensional Boltzmann Neutrino Transport Code in Full General Relativity for Core-collapse Simulations

We develop a neutrino transfer code for core-collapse simulations, that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the six dimensional phase space. The code is an extension of our special relativistic code coupled to a Newtonian hydrodynamics code, which is currently employed for core-collapse supernova simulations. In order to demonstrate our code's capability to treat general relativistic effects, we conduct some tests: we first compute the free streaming of neutrinos in the Schwarzschild and Kerr spacetimes and compare the results with the geodesic curves; in the Schwarzschild case we deploy not only a 1-dimensional grid in space under spherical symmetry but also a 2-dimensional spatial mesh under axisymmetry in order to assess the capability of the code to compute the spatial advection of neutrinos; secondly, we calculate the neutrino transport in a fixed matter background, which is taken from a core-collapse supernova simulation with our general relativistic but spherically symmetric Boltzmann-hydrodynamics code, to obtain a steady neutrino distribution; the results are compared with those given by the latter code.

astro-ph.HE↗

arXiv2020

The Boltzmann-radiation-hydrodynamics Simulations of Core-collapse Supernovae with Different Equations of State: the Role of Nuclear Composition and the Behavior of Neutrinos

Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the different strength of the prompt convection and the later neutrino-driven convection. The protoneutron star seen in the FS model is more compact than that in the LS model because the existence of multinuclear species softens the EOS. For the behavior of neutrinos, we examined the flux and the Eddington tensor of neutrinos. In the optically thick region, the diffusion of neutrinos and the dragging by the motion of matter determine the flux. In the optically thin region, the free-streaming determines it. The Eddington tensor is compared with that obtained from the M1-closure relation. The M1-closure scheme overestimates the contribution from the velocity-dependent terms in the semitransparent region.

astro-ph.HE↗