arXiv subjects

Hajime Sotani

Publications and source records attributed to Hajime Sotani.

At least 37 records · Page 2Linked to original sources

arXiv2024

Magnetar QPOs and neutron star crust elasticity

The crust region is a tiny fraction of neutron stars, but it has a variety of physical properties and plays an important role in astronomical observations. One of the properties characterizing the crust is the elasticity. In this review, with the approach of asteroseismology, we systematically examine neutron star oscillations excited by crust elasticity, adopting the Cowling approximation. In particular, by identifying the quasi-periodic oscillations observed in magnetar flares with the torsional oscillations, we make a constraint on the nuclear saturation parameters. In addition, we also discuss how the shear and interface modes depend on the neutron star properties. Once one detects an additional signal associated with neutron star oscillations, one can get a more severe constraint on the saturation parameters and/or neutron star properties, which must be a qualitatively different constraint obtained from terrestrial experiments, and help us to complementarily understand astrophysics and nuclear physics.

astro-ph.HE↗

arXiv2024

Universality in supernova gravitational waves with proto-neutron star properties

Gravitational wave signals from core-collapse supernovae are one of the important observables for extracting the information of dense matter. To extract the properties of proto-neutron stars produced via core-collapse supernovae by asteroseismology, we perform a linear perturbation analysis using data obtained from two-dimensional numerical simulations. We employ 12 and 20 solar-mass progenitors and compare two different treatments of gravity. One is a general relativistic one with a conformal flatness condition and the other is an effective gravitational potential mimicking the Tolman-Oppenheimer-Volkoff solution. We discuss how the frequencies of the proto-neutron star oscillations corresponding to the gravitational wave signals in the simulations depend on the proto-neutron star properties. In our models, we find that the gravitational wave frequencies of the proto-neutron stars determined with the Cowling approximation can be expressed to very good approximation as a function of the proto-neutron star average density almost independently of the progenitor mass, treatment of gravity in the simulations, and the interpolations in the simulations. On the other hand, if one considers the gravitational wave frequencies as a function of the surface gravity of proto-neutron stars, such a relation appears sensitive to the treatment of gravity and other numerical details in the simulations. Thus, the average density of proto-neutron stars seems more suitable for universally expressing the supernova gravitational wave frequencies, instead of the surface gravity.

astro-ph.HE↗

arXiv2024

Shear oscillations in neutron stars and the nuclear symmetry energy

The shear and interface modes excited inside the neutron star due to the presence of elasticity depend on the properties of both the crust and core region. To examine how such eigenfrequencies depend on the neutron star properties, we solve the eigenvalue problem by adopting the relativistic Cowling approximation. Then, we confirm that the number of the interface modes excited in the star is generally equivalent to the number of the interface where the shear modulus discontinuously becomes zero, but we also find that the number of interface modes becomes smaller than that of the interface for the stellar model with lower or higher value of the slope parameter $L$. Furthermore, we derive the empirical relations for expressing the shear modes and one of the interface modes ($i_1$-mode in the text), which is the mode whose amplitude becomes dominant at the interface between the crust and envelopes and at the interface between the phases of slablike and cylindrical nuclei. At the end, we also show the possibility of identifying the higher QPO frequencies observed in GRB 200415A with the shear oscillations, as an alternative possibility instead of the torsional oscillations.

astro-ph.HE↗

arXiv2023

Universality in quasinormal modes of neutron stars with quark-hadron crossover

We examine the gravitational wave frequencies of the fundamental ($f$-) and 1st pressure ($p_1$-) modes excited in the neutron star models constructed with the quark-hadron crossover (QHC) type equations of state (EOS). We find that the $f$-mode frequencies with QHC EOS basically are smaller and the $p_1$-mode frequencies with QHC EOS are larger than those with hadronic EOS, focusing on the neutron star model with a fixed mass. We also find that the universality in the $f$-mode frequencies multiplied by the stellar mass as a function of the stellar compactness or as a function of the dimensionless tidal deformability, which is derived with various hadronic EOSs, can keep even with QHC EOS. That is, using these universal relations, one cannot distinguish QHC EOS from hadronic EOSs. Instead, using the relations one can extract the stellar radii whose evolution from low to high mass neutron stars can differentiate QHC from hadronic EOSs. On the other hand, we find that the $p_1$-mode frequencies multiplied by the stellar mass with QHC EOS significantly deviate in a certain mass range from the corresponding empirical relations derived with various hadronic EOSs, with which one may distinguish QHC EOS from hadronic EOSs.

astro-ph.HE↗

arXiv2023

Shear and interface modes in neutron stars with pasta structures

We carefully examine the shear and interface modes, which are excited due to the presence of crust elasticity, in neutron stars with pasta structures, adopting the relativistic Cowling approximation. We find that the shear modes are independent of the presence of the cylindrical-hole and spherical-hole nuclei at least up to a few kilohertz, while the interface modes strongly depend on the presence of the cylindrical-hole and spherical-hole nuclei. In addition, we find empirical relations for the interface mode frequencies multiplied by the stellar mass and for the shear mode frequencies multiplied by the stellar radius. These relations are expressed as a function of the stellar compactness almost independently of the stiffness in a higher-density region inside the neutron star, once one selects the crust equation of state. Thus, if one would simultaneously observe the shear and interface modes from a neutron star, one might extract the neutron star mass and radius with the help of the constraint on the crust stiffness obtained from terrestrial experiments.

astro-ph.HE↗

arXiv2023

Impacts of the direct URCA and Superfluidity inside a Neutron Star on Type-I X-Ray Bursts and X-Ray Superbursts

We investigate the impacts of neutrino cooling mechanism inside the neutron star (NS) core on the light curves of type-I X-ray bursts and X-ray superbursts. From several observations of NS thermal evolution, physical processes of fast neutrino cooling, such as the direct Urca (DU) process, are indicated. They significantly decrease the surface temperature of NSs, though the cooling effect could be suppressed by nucleon superfluidity. In the present study, focusing on the DU process and nucleon superfluidity, we investigate the effects of NS cooling on the X-ray bursts using a general-relativistic stellar-evolution code. We find that the DU process leads find the longer recurrence time and the higher peak luminosity, which could be obstructed by the neutrons superfluidity. We also apply our burst models to the comparison with {\it Clocked burster} GS 1826$-$24, and to the recurrence time of superburst triggered by carbon ignition. These effects are significant within a certain range of binary parameters and uncertainty of the NS equation of state.

astro-ph.HE↗

arXiv2023

Empirical neutron star mass formula based on experimental observables

We derive the empirical formulae expressing the mass and gravitational redshift of a neutron star, whose central density is less than threefold the nuclear saturation density, as a function of the neutron-skin thickness or the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $, especially focusing on the 8 Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within $ \approx 10 \, \% $ errors with our formulae, while the neutron star radius is also expected within a few $\%$ errors by combining the derived formulae. Owing to the resultant empirical formulae, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of $ {}^{208} \mathrm{Pb} $ than the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $.

nucl-th↗

arXiv2022

Merger and post-merger of binary neutron stars with a quark-hadron crossover equation of state

Fully general-relativistic binary-neutron-star (BNS) merger simulations with quark-hadron crossover (QHC) equations of state (EOSs) are studied for the first time. In contrast to EOSs with purely hadronic matter or with a first-order quark-hadron phase transition (1PT), in the transition region QHC EOSs show a peak in sound speed, and thus a stiffening. We study the effects of such stiffening in the merger and post-merger gravitational (GW) signals. Through simulations in the binary-mass range $2.5 < M/M_{\odot} < 2.75$, characteristic differences due to different EOSs appear in the frequency of the main peak of the post-merger GW spectrum ($f_2$), extracted through Bayesian inference. In particular, we found that (i) for lower-mass binaries, since the maximum baryon number density ($n_{\rm max}$) after the merger stays below $3\text{--}4$ times the nuclear-matter density ($n_0$), the characteristic stiffening of the QHC models in that density range results in a lower $f_2$ than that computed for the underlying hadronic EOS and thus also than that for EOSs with a 1PT, (ii) for higher-mass binaries, where $n_{\rm max}$ may exceed $4\text{--}5 n_0$ depending on the EOS model, whether $f_2$ in QHC models is higher or lower than that in the underlying hadronic model depends on the height of the sound-speed peak. Comparing the values of $f_2$ for different EOSs and BNS masses gives important clues on how to discriminate different types of quark dynamics in the high-density end of EOSs and is relevant to future kilohertz GW observations with third-generation GW detectors.

astro-ph.HE↗

arXiv2022

Neutron star mass formula with nuclear saturation parameters for asymmetric nuclear matter

Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $η\equiv (K_0L^2)^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by $η_τ\equiv (-K_τL^5)^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matter, $K_τ$, and derive the empirical relations for the neutron star mass and gravitational redshift as a function of $η_τ$ and the normalized central number density. With these empirical relations, one can evaluate the mass and gravitational redshift of the neutron star, whose central number density is less than threefold the saturation density, within $\sim 10\%$ accuracy, and the radius within a few \% accuracies. In addition, we discuss the neutron star mass and radius constraints from the terrestrial experiments, using the empirical relations, together with those from the astronomical observations. Furthermore, we find a tight correlation between $η_τ$ and $η$. With this correlation, we derive the constraint on $K_τ$ as $-348\le K_τ\le -237$ MeV, assuming that $L=60\pm 20$ and $K_0=240\pm 20$ MeV.

nucl-th↗

arXiv2022

Effects of finite sizes of atomic nuclei on shear modulus and torsional oscillations in neutron stars

The shear modulus of neutron star matter is one of the important properties for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear symmetry energy. In practice, when one identifies the quasi-periodic oscillations from a neutron star, where the magnetic effect is negligible, with crustal torsional oscillations, the finite-size effect can be more significant at frequencies higher than $\sim 100$ Hz.

nucl-th↗

arXiv2022

Accuracy of one-dimensional approximation in neutron star quasi-normal modes

Since the eigenfrequency of gravitational waves from cold neutron stars becomes a complex number, where the real and imaginary parts respectively correspond to an oscillation frequency and damping rate, one has to somehow solve the eigenvalue problem concerning the eigenvalue in two-dimensional parameter space. To avoid this bother, one sometimes adopts an approximation, where the eigenvalue is in one-dimensional parameter space. In this study, first, we show the accuracy of the zero-damping approximation, which is one of the one-dimensional approximations, for the fundamental and 1st pressure modes. But, this approximation is not applicable to the spacetime mode, because the damping rate of the spacetime mode is generally comparable to the oscillation frequency. Nevertheless, we find the empirical relation for the ratio of the imaginary part to the real part of the eigenfrequency, which is expressed as a function of the steller compactness almost independently of the adopted equations of state for neutron star matter. Adopting this empirical relation, one can express the eigenfrequency in terms of just the real part, i.e., the problem to solve becomes an eigenvalue problem with a one-dimensional eigenvalue. Then, we find that the frequencies are estimated with good accuracy even with such approximations even for the 1st spacetime mode.

gr-qc↗

arXiv2022

New constraints on the neutron-star mass and radius relation from terrestrial nuclear experiments

The determination of the equation of state (EOS) for nuclear matter has been one of the biggest problems in nuclear astrophysics, because the EOS is essential for determining the properties of neutron stars. To constrain the density-dependence of the nuclear symmetry energy, several nuclear experiments, e.g., reported by the S$π$RIT and PREX-II collaborations, have recently been performed. However, since their uncertainties are still large, additional constraints such as astronomical observations must be crucial. In addition, it is interesting to see the effect of their reported value on neutron star properties. In this study, focusing on the relatively lower density region, we investigate the allowed area of the neutron-star mass and radius relation by assuming the constraints from S$π$RIT and PREX-II. Each region predicted by these experiments is still consistent with the allowed area constrained by the various astronomical observations. Our results show that terrestrial nuclear experiments must provide further constraints on the EOS for neutron stars, complementing astronomical observations.

nucl-th↗

arXiv2022

Neutron star mass formula with nuclear saturation parameters

We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determined with the specific equation of state. Since our empirical formulas directly connect the neutron star mass and radius to the nuclear saturation parameters, one can discuss the neutron star properties with the specific values of nuclear saturation parameters constrained via nuclear experiments.

nucl-th↗

arXiv2021

Gravitational wave asteroseismology on cooling neutron stars

We examine the gravitational wave frequencies from neutron stars during thermal evolution, adopting the relativistic Cowling approximation. We particularly focus on the neutron star models, in which the direct Urca (rapid cooling process) does not work, without the superfluidity and superconductivity. For such models, the cooling curve hardly depends on the equation of state (EOS) as well as the mass of neutron star, while we show that the gravitational wave frequencies strongly depend on the both properties. Then, we find that the frequencies of the fundamental and the 1st pressure mode multiplied with the stellar mass are well expressed as a function of the stellar compactness almost independently of the EOS. We also find that the frequency of the 1st gravity mode in later phase of the thermal evolution is strongly correlated with the stellar compactness. In addition, we derive the empirical formula estimating the threshold mass for the onset of the direct Urca inside the neutron star as a function of the nuclear saturation parameter. This formula will give us a constraint on the neutron star properties, if it would be observationally found that the direct Urca occurs (or does not work) inside the neutron star.

gr-qc↗

arXiv2021

Universal relation for supernova gravitational waves

Using the numerical simulation data for two-dimensional core-collapse supernova, we examine the protoneutron star (PNS) asteroseismology with the relativistic Cowling approximation. As shown in the previous study, the gravitational wave signals appearing in the numerical simulation can be well identified with the gravity (fundamental) oscillation in the early (later) phase before (after) the avoided crossing between the gravity and fundamental oscillations. On the other hand, the time evolution of supernova gravitational waves strongly depends on the PNS models, such as the progenitor mass and the equation of state for dense matter. Nevertheless, we find that the fundamental and gravity mode frequencies according to the gravitational wave signals appearing in the numerical simulations can be expressed as a function of the protoneutron star average density independently of the PNS models. Using the average density, we derive the empirical formula for supernova gravitational wave frequency. In addition, we confirm that the dependence of the PNS surface density on the PNS average density is almost independent of the PNS models and also discuss how the different treatment of the non-uniform matter in the equation of state affects the observables.

astro-ph.HE↗

arXiv2021

Universal relations between the quasinormal modes of neutron star and tidal deformability

Universal relations independently of the equation of state (EOS) for neutron star matter are valuable, if they exist, for extracting the neutron star properties, which generally depend on the EOS. In this study, we newly derive the universal relations predicting the gravitational wave frequencies for the fundamental ($f$), the 1st pressure ($p_1$), and the 1st spacetime ($w_1$) modes and the damping rate for the $f$- and $w_1$-modes as a function of the dimensionless tidal deformability. In particular, with the universal relations for the $f$-modes one can predict the frequencies and damping rate with less than $1\%$ accuracy for canonical neutron stars.

gr-qc↗

arXiv2021

Avoided crossing in gravitational wave spectra from protoneutron star

The ramp up signals of gravitational waves appearing in the numerical simulations could be important signals to estimate parameters of the protoneutron star (PNS) at supernova explosions. To identify the signals with PNS oscillations, we make a linear perturbation analysis and compare the resultant eigenfrequencies with the ramp up signals obtained via the two-dimensional numerical simulations. Then, we find that the ramp up signals correspond well to the $g_1$-mode in the early phase and to the $f$-mode, to which the $g_1$-mode is exchanged via the avoided crossing. We also confirm that the $f$- and $g_1$-modes are almost independent of the selection of the PNS surface density in the later phase after core bounce. In addition, we successfully find that the fitting formula of $g_1$- and $f$-modes, which correspond to the ramp up signals in the numerical simulation, as a function of the PNS average density. That is, via the direct observation of the gravitational waves after supernova explosion, one could extract the time evolution of the PNS average density by using our fitting formula.

astro-ph.HE↗

arXiv2021

Stability of the protoneutron stars toward black hole formation

We examine the protoneutron star (PNS) stability in this study by solving the radial oscillation equations. For this purpose, we adopt the numerical results of massive PNS toward the black hole formation obtained by spherically symmetric numerical simulations for core-collapse supernova with general relativistic neutrino-radiation hydrodynamics. We find that the PNSs are basically stable in their evolution against the radial perturbations, while the PNS finally becomes unstable before the apparent horizon appears inside the PNS. We also examine the gravitational wave frequencies from PNS with the relativistic Cowling approximation. Then, we derive the empirical formula for the $f$-mode frequency, which weakly depends on the PNS models. This kind of universality tells us the PNS property, which is a combination of the PNS mass and radius in this study, once one would observe the $f$-mode gravitational waves.

astro-ph.HE↗