arXiv subjects

Shoichi Yamada

Publications and source records attributed to Shoichi Yamada.

At least 37 records · Page 2Linked to original sources

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

Quantum synchro-curvature masers and their application to neutron stars

We explore the possibility of synchro-curvature maser in the magnetosphere of neutron stars (NSs). Unlike previous studies, we employ relativistic quantum mechanics, solving the Dirac equation for an electron in helical magnetic fields and calculating the radiative transition rates perturbatively. Assuming that the curvature of magnetic-field lines is much larger than the Larmor radius, we utilize adiabatic spinor rotations to obtain the wave functions of an electron. We classify the electron states further either by the spin operator projected on the magnetic field or by the helicity operator. We then evaluate numerically the true absorption rates accounting for the induced emission for some parameter values typical to the outer gaps of different types of NSs. We show that maser is indeed possible for a range of parameters. We will also present the dependence on those parameters systematically. We finally give a crude estimate of the amplification factor in the outer gap of NSs, which seems to favor millisecond pulsars as the host of maser emissions.

astro-ph.HE↗

arXiv2021

Deep Learning of the Eddington Tensor in the Core-collapse Supernova Simulation

We trained deep neural networks (DNNs) as a function of the neutrino energy density, flux, and the fluid velocity to reproduce the Eddington tensor for neutrinos obtained in our first-principles core-collapse supernova (CCSN) simulations. Although the moment method, which is one of the most popular approximations for neutrino transport, requires a closure relation, none of the analytical closure relations commonly employed in the literature captures all aspects of the neutrino angular distribution in momentum space. In this paper, we developed a closure relation by using the DNN that takes the neutrino energy density, flux, and the fluid velocity as the input and the Eddington tensor as the output. We consider two kinds of DNNs: a conventional DNN named a component-wise neural network (CWNN) and a tensor-basis neural network (TBNN). We found that the diagonal component of the Eddington tensor is reproduced better by the DNNs than the M1-closure relation especially for low to intermediate energies. For the off-diagonal component, the DNNs agree better with the Boltzmann solver than the M1 closure at large radii. In the comparison between the two DNNs, the TBNN has slightly better performance than the CWNN. With the new closure relations at hand based on the DNNs that well reproduce the Eddington tensor with much smaller costs, we opened up a new possibility for the moment method.

astro-ph.HE↗

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

General Relativistic Effects on Hill Stability of Multi-Body Systems I: Stability of Three-Body Systems Containing a Massive Black Hole

We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and applied to planetary systems. We focus in this paper on the three-body problem and extend the Newtonian analyses to the general relativistic regime in the post-Newtonian approximation. The approximate sufficient condition for the relativistic Hill stability of three-body systems is derived analytically and its validity and usefulness are confirmed numerically. In fact, relativity makes the system more unstable than Newtonian mechanics in the sense of the Hill stability as expected by our theoretical prediction. The criterion will be useful to analyze the results of large-scale N-body simulations of dense environments, in which the stability of three-body sub-systems is important.

gr-qc↗

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↗

arXiv2020

Simulations of the Early Post-Bounce Phase of Core-Collapse Supernovae in Three-Dimensional Space with Full Boltzmann Neutrino Transport

We report on the core-collapse supernova simulation we conducted for a 11.2 M progenitor model in three-dimensional space up to 20 ms after bounce, using a radiation hydrodynamics code with full Boltzmann neutrino transport. We solve the six-dimensional Boltzmann equations for three neutrino species and the three-dimensional compressible Euler equations with Furusawa and Togashi's nuclear equation of state. We focus on the prompt convection at 10 ms after bounce and investigate how neutrinos are transported in the convective matter. We apply a new analysis based on the eigenvalues and eigenvectors of the Eddington tensor and make a comparison between the Boltzmann transport results and the M1 closure approximation in the transition regime between the optically thick and thin limits. We visualize the eigenvalues and eigenvectors using an ellipsoid, in which each principal axis is parallel to one of the eigenvectors and has a length proportional to the corresponding eigenvalue. This approach enables us to understand the difference between the Eddington tensor derived directly from the Boltzmann simulation and the one given by the M1 prescription from a new perspective. We find that the longest principal axis of the ellipsoid is almost always nearly parallel to the energy flux in the M1 closure approximation whereas in the Boltzmann simulation it becomes perpendicular in some transition regions, where the mean free path is 0.1 times the radius. In three spatial dimensions, the convective motions make it difficult to predict where this happens and to possibly improve the closure relation there.

astro-ph.HE↗

arXiv2020

Neutrino transport with Monte Carlo method: I. Towards fully consistent implementation of nucleon recoils in core-collapse supernova simulations

The small energy exchange via nucleon recoils in neutrino-nucleon scattering is now supposed to be one of the important factors for successful explosion of core-collapse supernovae (CCSNe) as they can change neutrino spectra through accumulation of a large number of scatterings. In finite-difference methods employed for neutrino transport in CCSN simulations, we normally can not afford to deploy a large enough number of energy bins needed to resolve this small energy exchange and sub-grid techniques are employed one way or another. In this paper we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by $\sim$15% for heavy-lepton neutrinos and by much smaller quantities for other types of neutrinos in a typical post-bounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the finite-difference methods. In order to mimic the latter calculation, we re-distribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected and depend on the energy-resolution. We also discuss possible implications of our results for the finite-difference methods.

astro-ph.HE↗

arXiv2020

Fast collective neutrino oscillations inside the neutrino sphere in core-collapse supernovae

Neutrinos are believed to have a key role in the explosion mechanism of core-collapse supernovae as they carry most of the energy released by the gravitational collapse of a massive star. If their flavor is converted fast inside the neutrino sphere, the supernova explosion may be influenced. This paper is reporting the results of the extended work of our previous paper. We perform a thorough survey of the ELN crossing in one of our self-consistent, realistic Boltzmann simulations in two spatial dimensions under axisymmetry for the existence of the crossings between $ν_e$ and $\barν_e$ angular distributions, or the electron lepton number (ELN) crossing. We report for the first time the positive detections deep inside the core of the massive star in the vicinity of neutrino sphere at $r$ $\approx$ 16 - 21 km. We find that low values of the electron fraction $Y_e$ produced by convective motions together with the appearance of light elements are critically important to give rise to the ELN crossing by enhancing the chemical potential difference between proton and neutron, and hence by mitigating the Fermi-degeneracy of $ν_e$. Since the region of positive detection are sustained and, in fact, expanding with time, it may have an impact on the explosion of core-collapse supernovae, observational neutrino astronomy and nucleosynthesis of heavy nuclei.

astro-ph.HE↗

arXiv2019

Spatio-temporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the spatial dimension is more than 1. In this study, using the Lefschetz thimble method, we develop a new formalism to give an explicit expression to the asymptotic behavior of linear perturbations. It is not only more mathematically rigorous than the previous theory but also useful practically in its applications to realistic problems, and, as such, has an impact on broad subjects in physics.

math-ph↗

arXiv2019

Fast-pairwise collective neutrino oscillations associated with asymmetric neutrino emissions in core-collapse supernova

We present a linear stability analysis of the fast-pairwise neutrino flavor conversion based on a result of our latest axisymmetric core-collapse supernova (CCSN) simulation with full Boltzmann neutrino transport. In the CCSN simulation, coherent asymmetric neutrino emissions of electron-type neutrinos ($ν_{\rm e}$) and their anti-particles ($\barν_{\rm e}$), in which the asymmetry of $ν_{\rm e}$ and $\barν_{\rm e}$ is anti-correlated with each other, occur at almost the same time as the onset of aspherical shock expansion. We find that the asymmetric neutrino emissions play a crucial role on occurrences of fast flavor conversions. The linear analysis shows that unstable modes appear in both pre- and post-shock flows; for the latter they appear only in the hemisphere of higher $\barν_{\rm e}$ emissions (the same hemisphere with stronger shock expansion). We analyze in depth the characteristics of electron-lepton-number (ELN) crossing by closely inspecting the angular distributions of neutrinos in momentum space. The ELN crossing happens in various ways, and the property depends on the radius: in the vicinity of neutron star, $\barν_{\rm e}$ ($ν_{\rm e}$) dominates over $ν_{\rm e}$ ($\barν_{\rm e}$) in the forward (backward) direction: at the larger radius the ELN crossing occurs in the opposite way. We also find that the non-radial ELN crossing occurs at the boundary between no ELN crossing and the radial one, which is an effect of genuine multi-D transport. Our findings indicate that the collective neutrino oscillation may occur more commonly in CCSNe and suggest that the CCSN community needs to accommodate these oscillations self-consistently in the modelling of CCSNe.

astro-ph.HE↗

arXiv2019

A new possibility of the fast neutrino-flavor conversion in the pre-shock region of core-collapse supernova

We make a strong case that the fast neutrino-flavor conversion, one of the collective flavor oscillation modes, commonly occurs in core-collapse supernovae (CCSNe). It is confirmed in the numerical data obtained in realistic simulations of CCSNe but the argument is much more generic and applicable universally: the coherent neutrino-nucleus scattering makes the electron lepton number (ELN) change signs at some inward direction and trigger the flavor conversion in the outward direction in the pre-shock region. Although the ELN crossing is tiny and that is why it has eluded recognition so far, it is still large enough to induce the flavor conversion. Our findings will have an important observational consequences for CCSNe neutrinos.

astro-ph.HE↗

arXiv2019

Possible early linear acceleration of proto-neutron stars via asymmetric neutrino emission in core-collapse supernovae

In this {\it Letter}, we present the result of an axisymmetric CCSN simulation conducted with appropriate treatments of neutrino transport and proper motions of proto-neutron star (PNS), in which a remarkable PNS acceleration is observed in association with asymmetric neutrino emissions by the time of $300$ms after bounce. We find that these asymmetric neutrino emissions play important roles in the acceleration of PNS in this phase. The correlation between the PNS proper motion and the asymmetric ejecta is similar to that in the neutron star (NS) kick of hydrodynamic origin. Both electron-type neutrinos ($ν_{\rm e}$) and their anti-particles ($\barν_{\rm e}$) have $\sim 10\%$ level of asymmetry between the northern and southern hemispheres, while other heavy-leptonic neutrinos ($ν_x$) have much smaller asymmetry of $\sim 1 \%$. The emissions of $\barν_{\rm e}$ and $ν_x$ are higher in the hemisphere of stronger shock expansion whereas the $ν_{\rm e}$ emission is enhanced in the opposite hemisphere: in total the neutrinos carry some linear momentum to the hemisphere of the stronger shock expansion. The asymmetry is attributed to the non-spherical distribution of electron-fraction ($Y_e$) in the envelope of PNS. Although it is similar to LESA (lepton-emission self-sustained asymmetry), the $Y_e$ asymmetry seems to be associated with the PNS motion: the latter triggers lateral circular motions in the envelope of PNS by breaking symmetry of the matter distribution there, which are then sustained by a combination of convection, lateral neutrino diffusion and matter-pressure gradient. Our findings may have an influence on the current theories on the NS kick mechanism although long-term simulations are required to assess their impact on the later evolution.

astro-ph.HE↗

arXiv2019

Three-Dimensional Boltzmann-Hydro Code for core-collapse in massive stars III. A New method for momentum feedback from neutrino to matter

We present a new method for neutrino-matter coupling in multi-dimensional radiation-hydrodynamic simulations of core-collapse supernova (CCSN) with the full Boltzmann neutrino transport. The development is motivated by the fact that the accurate conservation of momentum is required for reliable numerical modelings of CCSN dynamics including a recoil of proto-neutron star (PNS). The new method is built on a hybrid approach, in which we use the energy-momentum tensor of neutrinos to compute the momentum feedback from neutrino to matter in the optically thick region while we employ the collision term in the optically thin region. In this method we utilize a general relativistic description of radiation-hydrodynamics with angular moments, which allows us to evaluate the momentum feedback from neutrino to matter without inconsistency with our Boltzmann solver. We demonstrate that the new method substantially improves the accuracy of linear momentum conservation in our CCSN simulations under reasonable angular resolutions in momentum space, alleviating the difficulty in giving the diffusion limit precisely with the discrete ordinate (Sn) method. It is the first-ever demonstration that the PNS kick can be handled directly and properly in multi-dimensional radiation-hydrodynamic simulations with the full Boltzmann neutrino transport.

astro-ph.HE↗

arXiv2019

Linear Analysis of Fast-Pairwise Collective Neutrino Oscillations in Core-Collapse Supernovae based on the Results of Boltzmann Simulations

Neutrinos are densely populated deep inside the core of massive stars after their gravitational collapse to produce supernova explosions and form compact stars such as neutron stars (NS) and black holes (BH). It has been considered that they may change their flavor identities through so-called fast-pairwise conversions induced by mutual forward scatterings. If that is really the case, the dynamics of supernova explosion will be influenced, since the conversion may occur near the neutrino sphere, from which neutrinos are effectively emitted. In this paper, we conduct a pilot study of such possibilities based on the results of fully self-consistent, realistic simulations of a core-collapse supernova explosion in two spatial dimensions under axisymmetry. As we solved the Boltzmann equations for neutrino transfer in the simulation not as a post-process but in real time, the angular distributions of neutrinos in momentum space for all points in the core at all times are available, a distinct feature of our simulations. We employ some of these distributions extracted at a few selected points and times from the numerical data and apply linear analysis to assess the possibility of the conversion. We focus on the vicinity of the neutrino sphere, where different species of neutrinos move in different directions and have different angular distributions as a result. This is a pilot study for a more thorough survey that will follow soon. We find no positive sign of conversion unfortunately at least for the spatial points and times we studied in this particular model. We hence investigate rather in detail the condition for the conversion by modifying the neutrino distributions rather arbitrarily by hand.

astro-ph.HE↗

arXiv2019

On the Neutrino Distributions in Phase Space for the Rotating Core-collapse Supernova Simulated with a Boltzmann-neutrino-radiation-hydrodynamics Code

With the Boltzmann-radiation-hydrodynamics code, which we have developed to solve numerically the Boltzmann equations for neutrino transfer, the Newtonian hydrodynamics equations, and the Newtonian self-gravity simultaneously and consistently, we simulate the collapse of a rotating core of the progenitor with a zero-age-main-sequence mass of $11.2\,M_\odot$ and a shelluler rotation of $1\,{\rm rad\,s^{-1}}$ at the center. We pay particular attention in this paper to the neutrino distribution in phase space, which is affected by the rotation. By solving the Boltzmann equations directly, we can assess the rotation-induced distortion of the angular distribution in momentum space, which gives rise to the rotational component of the neutrino flux. We compare the Eddington tensors calculated both from the raw data and from the M1-closure approximation. We demonstrate that the Eddington tensor is determined by complicated interplays of the fluid velocity and the neutrino interactions and that the M1-closure, which assumes that the Eddington factor is determined by the flux factor, fails to fully capture this aspect, especially in the vicinity of the shock. We find that the error in the Eddington factor reaches $\sim 20\%$ in our simulation. This is due not to the resolution but to the different dependence of the Eddington and flux factors on the angular profile of the neutrino distribution function, and hence modification to the closure relation is needed.

astro-ph.HE↗

arXiv2019

Linear Analysis of the Shock Instability in Core-collapse Supernovae: Influences of Acoustic Power and Fluctuations of Neutrino Luminosity

This paper is a sequel to Takahashi et al. (2016), in which the authors investigated the influences of fluctuations in pre-shock accreting matter on the linear stability of the standing accretion shock in core-collapse supernovae (CCSNe). If one understands that this was concerning the effect of the outer boundary condition for the post-shock accretion flows, the present paper should be regarded as an investigation on the possible influences of the inner boundary conditions. More specifically, we impose a time-dependent, oscillating condition at the inner boundary, having in mind the injection of acoustic power by an oscillating proto-neutron star. We also consider possible correlations between the inner and outer boundary conditions as invoked in the argument for Lepton-number Emission Self-sustained Asymmetry, or LESA. In this paper, we conduct the linear stability analysis of the standing accretion shock commonly encountered in CCSNe based on Laplace transform. We find that the acoustic power enhances the standing accretion shock instability, or SASI, especially when the luminosity is low. On the other hand, the correlation between the fluctuations of neutrino luminosity at the neutrino sphere has little influences on the instability, changing the amplitudes of eigenmodes only slightly. We further investigate steady solution of perturbation equations, being motivated by LESA, and conclude that not the difference but the sum of the fluxes of electron-type neutrinos and anti-neutrino is the key ingredient to production of the self-sustained steady perturbed configuration.

astro-ph.HE↗