arXiv subjects

Hajime Sotani

Publications and source records attributed to Hajime Sotani.

At least 55 records · Page 3Linked to original sources

arXiv2021

Neutron star asteroseismology and nuclear saturation parameter

Adopting various unified equations of state (EOSs), we examine the quasinormal modes of gravitational waves from cold neutron stars. We focus on the fundamental ($f$-), 1st pressure ($p_1$-), and 1st spacetime ($w_1$-) modes, and derive the empirical formulae for the frequencies and damping rate of those modes. With the resultant empirical formulae, we find that the value of $η$, which is a specific combination of the nuclear saturation parameters, can be estimated within $\sim 30 \%$ accuracy, if the $f$-mode frequency from the neutron star whose mass is known would be observed or if the $f$- and $p_1$-mode frequencies would be simultaneously observed, even though this estimation is applicable only for the low-mass neutron stars. Additionally, we find that the mass and radius of canonical neutron stars can be estimated within a few per cent accuracy via the simultaneous observations of the $f$- and $w_1$-mode frequencies. We also find that, if the $f$-, $p_1$-, and $w_1$-mode frequencies would be simultaneously observed, the mass of canonical neutron stars can be estimated within $2\%$ accuracy, while the radius can be estimated within $1\%$ for the neutron star with $M\ge 1.6M_\odot$ or within $0.6\%$ for the neutron star with $M\ge 1.4M_\odot$ constructed with the EOS constrained via the GW170817 event. Furthermore, we find the strong correlation between the maximum $f$-mode frequency and the neutron star radius with the maximum mass, between the minimum $w_1$-mode frequency and the maximum mass, and between the minimum damping rate of the $w_1$-mode and the stellar compactness for the neutron star with the maximum mass.

astro-ph.HE↗

arXiv2020

Estimating the nuclear saturation parameter via low-mass neutron star asteroseismology

We examine the fundamental ($f$-) and the 1st pressure ($p_1$-) mode frequencies in gravitational waves from cold neutron stars constructed with various unified realistic equations of state. With the calculated frequencies, we derive the empirical formulae for the $f$- and $p_1$-mode frequencies, $f_f$ and $f_{p_1}$, as a function of the square root of the stellar average density and the parameter ($η$), which is a combination of the nuclear saturation parameters. With our empirical formulae, we show that by simultaneously observing the $f$- and $p_1$-mode gravitational waves, when $1.5\lesssim f_{p_1}/f_f\lesssim 2.5$ (which corresponds to neutron star models with the mass of $\lesssim 0.9M_\odot$), one could estimate the value of $η$ within $\sim 10\%$ accuracy, which makes a strong constraint on the EOS for neutron star matter. In addition, we find that the maximum $f$-mode frequency is strongly associated with the minimum radius of neutron star. That is, if one would observe a larger frequency of the $f$-mode, one might constrain the upper limit of the minimum neutron star radius.

astro-ph.HE↗

arXiv2020

Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology

The relativistic Cowling approximation, where the metric perturbations are neglected during the fluid oscillations, is often adopted for considering the gravitational waves from the protoneutron stars (PNSs) provided via core-collapse supernova explosions. In this study, we evaluate how the Cowling approximation works well by comparing the frequencies with the Cowling approximation to those without the approximation. Then, we find that the behavior of the frequencies with the approximation is qualitatively the same way as that without the approximation, where the frequencies with the approximation can totally be determined within $\sim 20\%$ accuracy. In particular, the fundamental mode with the Cowling approximation is overestimated. In addition, we also discuss the damping time of various eigenmodes in gravitational waves from the PNSs, where the damping time for the PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite different from that for cold neutron stars, but it is more or less similar to that for cold neutron stars in the later phase. The damping time is long enough compared to the typical time interval of short-Fourier transformation that often used in the analysis, and that ideally guarantees the validity of the transformation.

astro-ph.HE↗

arXiv2020

Gravitational wave asteroseismology for low-mass neutron stars

The fundamental ($f$-) mode gravitational waves from cold low-mass neutron stars are systematically studied with various equations of state (EOSs) characterized by the nuclear saturation parameters, especially focusing on the phenomena of the avoided crossing with the first pressure ($p_1$-) mode. We find that the $f$-mode frequency and the average density for the neutron star at the avoided crossing can be expressed as a function of the parameter, $η$, which is the specific combination of the nuclear saturation parameters. Owing to these relations, we can derive the empirical formula expressing the $f$-mode frequency for a low-mass neutron star, whose central density is larger than that for the neutron star at the avoided crossing, as a function of $η$ and the square root of the stellar average density, $x$. On the other hand, we also derive the empirical formula expressing the $f$-mode frequency for a neutron star, whose central density is less than that for the neutron star at the avoided crossing, as a function of $x$ independently of the adopted EOS. Furthermore, adopting the empirical formula of $x$ as a function of $η$ and $u_c$, which is the ratio of the stellar central density to the saturation density, we can also rewrite our empirical formula for the $f$-mode frequency to a function of $η$ and $u_c$. So, by observing the $f$-mode gravitational wave from a low-mass neutron star, whose mass or gravitational redshift is known, one could evaluate the values of $η$ and $u_c$, which enables us to severely constrain the EOS for neutron star matter.

astro-ph.HE↗

arXiv2020

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.

gr-qc↗

arXiv2020

Dimension dependence of numerical simulations on gravitational waves from protoneutron stars

We examine the eigenfrequencies of gravitational waves from the protoneutron stars (PNSs) provided via the core-collapse supernovae, focusing on how the frequencies depend on the dimension of numerical simulations especially for the early phase after core bounce. As expected, we find that the time evolution of gravitational wave frequencies depends strongly on the dimension of numerical simulation as well as the equation of state for high density matter. Even so, we find that the fundamental frequency as a function of PNS average density and the ratio of the specific eigenfrequencies to the fundamental frequency as a function of PNS properties are independent of the dimension of the numerical simulations, where the dependence of the equation of state is also very weak in this early postbounce phase. Thus, one can safely discuss the gravitational wave frequencies of the PNSs as a function of the PNS average density or compactness even with the frequencies obtained from the one dimensional simulations. We also provide phenomenological relation between the compactness and average density as well as the relation among the $f$-, $p$-, and $g$- mode frequencies.

astro-ph.HE↗

arXiv2020

Light curves from highly compact neutron stars with spot size effect

We systematically examine light curves from a single hot spot on a slowly rotating neutron star with very high compactness, where the so-called invisible zone does not exist. In particular, we adopt three different shapes of hot spot and take into account the finite size effect of hot spot on the light curves. Then, we find that the brightening of flux occurs when the hot spot with small area crosses the opposite side to the observer, where the brightening becomes stronger as the area of hot spot decreases. Since this brightening happens only when a part of hot spot crosses the opposite side to the observer, one may constrain the neutron star geometry, i.e., the combination of an inclination angle, angle between the rotational axis and normal vector at the center of hot spot, and the opening angle of hot spot, if the brightening would be observed. In addition, by counting such a brightening in the light curves, one may know how many narrow bands of hot spot and/or spots with small area cross the opposite side to the observer.

astro-ph.HE↗

arXiv2019

Determination of properties of protoneutron stars toward black hole formation via gravitational wave observations

We examine the frequencies of the fundamental ($f$-) and the gravity ($g_i$-) mode in gravitational waves from accreting protoneutron stars (PNSs) toward black hole formation. For this purpose, we analyze numerical results of gravitational collapse of massive stars for two different progenitors with three equations of state. We adopt profiles of central objects obtained from the numerical simulations by solving general relativistic neutrino-radiation hydrodynamics under the spherical symmetry. Using a series of snapshots as a static configuration at each time step, we solve the eigenvalue problem to determine the specific frequencies of gravitational waves from the evolving PNSs with accretion from core bounce to black hole formation by the relativistic Cowling approximation. We find that the frequency of the $f$-mode gravitational waves can be expressed as a function of the average density of the PNS at each time step almost independently of the progenitor models in accord with the previous studies on ordinary PNSs. We also find that the ratio of the $g_1$-mode frequency to the $f$-mode frequency is insensitive to the progenitor, but strongly depends on the compactness of the PNSs. Having a simultaneous observation of the $f$- and $g_1$-mode gravitational waves, it would provide the information of the average density and compactness of PNS, which can reconstruct the evolution of mass and radius of the PNSs as a constraint on the equation of state at high densities. Furthermore, we show that the highest average density of the PNS with the maximum mass can be estimated with the detection of the $f$-mode gravitational waves together with the help of the neutrino observations.

astro-ph.HE↗

arXiv2019

Finite size effects on the light curves of slowly-rotating neutron stars

An important question when studying the light curves produced by hot spots on the surface of rotating neutron stars is, how might the shape of the light curve be affected by relaxing some of the simplifying assumptions that one would adopt on a first treatment of the problem, such as that of a point-like spot. In this work we explore the dependence of light curves on the size and shape of a single hot spot on the surface of slowly-rotating neutron stars. More specifically, we consider two different shapes for the hot spots (circular and annular) and examine the resulting light curves as functions of the opening angle of the hot spot (for both) and width (for the latter). We find that the point-like approximation can describe light curves reasonably well, if the opening angle of the hot spot is less than $\sim 5^\circ$. Furthermore, we find that light curves from annular spots are almost the same as those of the full circular spot if the opening angle is less than $\sim 35^\circ$ independently of the hot spot's width.

astro-ph.HE↗

arXiv2019

Astrophysical implications of double-layer torsional oscillations in a neutron star crust as a lasagna sandwich

In the crust of a neutron star, global torsional oscillations could occur in two elastic layers. The outer and inner layers are composed of spherical and cylindrical nuclei and of cylindrical holes (tubes) and spherical holes (bubbles), respectively, while between these two layers, a phase of slab-like (lasagna) nuclei with vanishingly small elasticity is sandwiched. In this work, we update systematic calculations of the eigenfrequencies of the fundamental oscillations in the inner layer by newly allowing for the presence of tubes. We find that the frequencies still depend strongly on the slope parameter of the nuclear symmetry energy, $L$, while being almost independent of the incompressibility of symmetric nuclear matter. We also find that the fundamental frequencies in the inner layer can become smaller than those in the outer layer because the tube phase has a relatively small shear modulus and at the same time dominates the inner layer in thickness. As a result, we can successfully explain not only the quasi-periodic oscillations originally discovered in the observed X-ray afterglow of the giant flare of SGR 1806--20 but also many others recently found by a Bayesian procedure.

astro-ph.HE↗

arXiv2019

Dependence of outer boundary condition on protoneutron star asteroseismology with gravitational-wave signatures

To obtain the eigenfrequencies of a protoneutron star (PNS) in the postbounce phase of core-collapse supernovae (CCSNe), we perform a linear perturbation analysis of the angle-averaged PNS profiles using results from a general relativistic CCSN simulation of a $15 M_{\odot}$ star. In this work, we investigate how the choice of the outer boundary condition could affect the PNS oscillation modes in the linear analysis. By changing the density at the outer boundary of the PNS surface in a parametric manner, we show that the eigenfrequencies strongly depend on the surface density. By comparing with the gravitational wave (GW) signatures obtained in the hydrodynamics simulation, the so-called surface $g$-mode of the PNS can be well ascribed to the fundamental oscillations of the PNS. The frequency of the fundamental oscillations can be fitted by a function of the mass and radius of the PNS similar to the case of cold neutron stars. In the case that the position of the outer boundary is chosen to cover not only the PNS but also the surrounding postshock region, we obtain the eigenfrequencies close to the modulation frequencies of the standing accretion-shock instability (SASI). However, we point out that these oscillation modes are unlikely to have the same physical origin of the SASI modes seen in the hydrodynamics simulation. We discuss possible limitations of applying the angle-averaged, linear perturbation analysis to extract the full ingredients of the CCSN GW signatures.

astro-ph.HE↗

arXiv2018

Systematical study of pulsar light curves with special relativistic effects

We systematically study pulsar light curves, taking into account the special relativistic effect, i.e., the Doppler factor due to the fast spin of the neutron stars, together with the time delay, which comes from the difference of the travel times depending on the position of the spots. For this purpose, first we derive the basic equations with the general expression of the metric for the static, spherically symmetric spacetime, where for simplicity we adopt the pointlike spot approximation for the antipodal spots associated with the magnetic polar cap model. Then, we calculate the light curves from the neutron star models in general relativity, with various angle between rotational and magnetic axes and the inclination angle. As the results, unlike the case for a slowly rotating stellar model, we find that the light curve from a fast rotating stellar model depends not only the stellar compactness but also the stellar radius. We also find that the amplitude of the light curve becomes larger as the stellar radius increases and as the stellar compactness decreases. Thus, via careful observations of the light curves from the rotating neutron star, one would determine the stellar compactness together with the stellar radius, if it rotates fast enough.

astro-ph.HE↗

arXiv2018

Pulse profiles of highly compact pulsars in general relativity

Gravitational light bending by compact stars is an important astrophysical phenomenon. The bending angle depends on the stellar compactness, which is the ratio of stellar mass $M$ to radius $R$. In this paper, we investigate the pulse profile of highly compact rotating neutron stars for which the bending angle exceeds $π/2$. When $M/R > 0.284$ (the bending angle becomes equal to $π/2$ for the stellar model with $M/R=0.284$), such a large bending happens, resulting in that a photon emitted from any position on the stellar surface can reach an observer. First, we classify the parameter plane of inclination angle $i$ and angle $Θ$ between the rotation axis and the normal on the hot spot by the number of photon paths reaching the observer. Then, we estimate the time-dependent flux of photons emitted from two hot spots on the rotating neutron star, associated with the magnetic polar caps, for various combinations of $i$ and $Θ$, and for two values of compactness, assuming that the stellar rotation is not so fast that the frame dragging and the stellar deformation are negligible. As the result, we find that the pulse profiles of highly compact neutron stars are qualitatively different from those for the standard neutron stars. In particular, the ratio of the maximum observed flux to the minimum one is significantly larger than that for the standard neutron stars. This study suggests that one would be able to constrain the equation of state for neutron stars through the observation of pulse profile with angles $i$ and $Θ$ determined by other methods.

astro-ph.HE↗

arXiv2018

Constraints on the nuclear equation of state and the neutron star structure from crustal torsional oscillations

We systematically examine torsional shear oscillations of neutron star crusts by newly taking into account the possible presence of the phase of cylindrical nuclei. In this study, we neglect an effect of magnetic fields, under which the shear oscillations can be damped by the magnetic interaction. First, by identifying the low frequency quasi-periodic oscillations (QPOs) observed in the soft-gamma repeaters (SGRs) as the fundamental torsional oscillations, we constrain the slope parameter of the nuclear symmetry energy, $L$, for reasonable values of the star's mass $M$ and radius $R$. Meanwhile, we find that the 1st overtone of torsional oscillations obtained for given $M$ and $R$ can be expressed well as a function of a new parameter $ς\equiv (K_0^4 L^5)^{1/9}$, where $K_0$ is the incompressibility of symmetric nuclear matter. Assuming that the lowest of the QPO frequencies above 500 Hz observed in SGR 1806-20 comes from the 1st overtone, we can constrain the value of $ς$. Then, for each neutron star model, such a value of $L$ as can be obtained from the observed low frequency QPOs translates to the optimal value of $K_0$ via the above constraint on $ς$. Finally, its consistency with allowed values of $K_0$ from empirical giant monopole resonances leads to neutron star models with relatively low mass and large radius, which are qualitatively similar to the prediction in earlier investigations. This result suggests that $L\simeq 58-73$ MeV, even when uncertainties in the neutron superfluid density inside the phase of cylindrical nuclei are allowed for.

astro-ph.HE↗

arXiv2018

Compactness of neutron stars and Tolman VII solutions in scalar-tensor gravity

We systematically examine the compactness of neutron stars as Tolman VII solutions in scalar-tensor theory of gravity. As a result, when the coupling constant is confined to values provided by astronomical observations we show that the maximum compactness of neutron stars in general relativity is higher than that in scalar-tensor gravity. In addition, we show that although ultra-compact stars, with radius smaller than the Regge-Wheeler potential peak, can exist in general relativity (e.g., Tolman VII solution), their scalarized counterparts cannot {be constructed} even in the limiting case of uniform density stars.

gr-qc↗

arXiv2017

Pulse profiles from a pulsar in scalar-tensor gravity

The pulse profile from a neutron star in scalar-tensor theory of gravity is examined for several stellar models, where we assume the existence of the antipodal hot spots on the neutron star based on the polar cap model. Then, we find that the pulse profile from the scalarized neutron star in scalar-tensor gravity is almost the same as that in general relativity, i.e., without a scalar field, if the stellar compactness of the both stars is very similar. That is, the existence of the scalar field does not directly change the pulse profile from the neutron star, while the stellar compactness is crucial for determining the pulse shape even in the scalar-tensor gravity. Additionally, we find that the pulse shape from the scalarized neutron star is more or less similar to that from the neutron star with the same mass in general relativity, while the ratio of the minimum amplitude to the maximum amplitude in the pulse profile depend strongly on the coupling constant in scalar-tensor gravity, depending on the angle between the rotational and magnetic axes and the angle between the rotational axis and the direction to the observer. So, the direct observation of the pulse profile together with the additional observation of the stellar mass, one may extract the imprint of the gravitational theory in strong field regime.

astro-ph.HE↗

arXiv2017

Sensitivity of pulsar light curves to spacetime geometry and efficacy of analytic approximations

In order to examine the pulse profile from a pulsar, we derive the formula for describing the flux from antipodal hot spots with any static, spherically symmetric spacetime. We find that the pulse profiles are almost independent of the gravitational geometry outside the star when the compactness of neutron stars is low enough, e.g., the stellar mass and radius are $1.4M_\odot$ and 14 km, respectively. On the other hand, the pulse profiles depend strongly on the gravitational geometry when the compactness of neutron stars is so high, e.g., the stellar mass and radius are $1.8M_\odot$ and 10 km, respectively. Thus, one may probe the spacetime geometry outside the star and even distinguish gravitational theories via the observation of pulse profile with the help of another observations for the stellar compactness, if the compactness of central object is high enough. We also derive the 1st and 2nd order approximation of the flux with respect to a parameter defined by the radio of the gravitational radius of considered spacetime to the stellar radius. Then, we find that the relative error from full order numerical results in the bending angle becomes $\sim 20-30\%$ with the 1st order and $\sim 5-10\%$ with the 2nd order approximations for a typical neutron star, whose mass and radius are $1.4M_\odot$ and 12 km, respectively. Our results with the 1st order approximation for the Schwarzschild spacetime are different from those obtained in the literature, which suggests that the 1st order approximation has been misunderstood to yield highly accurate prediction.

astro-ph.HE↗

arXiv2017

Probing mass-radius relation of protoneutron stars from gravitational-wave asteroseismology

The gravitational-wave (GW) asteroseismology is a powerful technique for extracting interior information of compact objects. In this work, we focus on spacetime modes, the so-called $w$-modes, of GWs emitted from a proto-neutron star (PNS) in the postbounce phase of core-collapse supernovae. Using results from recent three-dimensional supernova models, we study how to infer the properties of the PNS based on a quasi-normal mode analysis in the context of the GW asteroseismology. We find that the $w_1$-mode frequency multiplied by the PNS radius is expressed as a linear function with respect to the ratio of the PNS mass to the PNS radius. This relation is insensitive to the nuclear equation of state (EOS) employed in this work. Combining with another universal relation of the $f$-mode oscillations, we point out that the time dependent mass-radius relation of the PNS can be obtained by observing both the $f$- and $w_1$-mode GWs simultaneously. Our results suggest that the simultaneous detection of the two modes could provide a new probe into finite-temperature nuclear EOS that predominantly determines the PNS evolution.

astro-ph.HE↗