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.
We examine the time evolution of the frequencies of the gravitational wave after the bounce within the framework of relativistic linear perturbation theory using the results of one dimensional numerical simulations of core-collapse supernovae. Protoneutron star models are constructed in such a way that the mass and radius of protoneutron star become equivalent to the results obtained from the numerical simulations. Then, we find that the frequencies of gravitational waves radiating from protoneutron stars strongly depend on the mass and radius of protoneutron stars, but almost independently of…
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 $…
We describe the dynamical behavior of newborn pulsars modeled as homogeneous rotating spheroids. The dynamical evolution is triggered by the escape of trapped neutrinos, provided the initial equilibrium configuration. It is shown that for a given set of values of the initial angular momentum a shape transition to a triaxial ellipsoid configuration occurs. Gravitational waves are then generated by the breaking of the axial symmetry, and some aspects of their observation are discussed. We found a narrow window for the initial values of the angular frequency and the eccentricity able to enable a …
We examine the frequencies of the fundamental ($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 prob…
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 wit…
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 approxima…
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 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 phase transition from hadronic matter to quark matter at high density might be a strong first order phase transition in presence of a large surface tension between the two phases. While this implies a constant-pressure mixed phase for cold and catalyzed matter this is not the case for the hot and lepton rich matter formed in a protoneutron star. We show that it is possible to obtain a mixed phase with non-constant pressure by considering the global conservation of lepton number during the stage of neutrino trapping. In turn, it allows for the appearance of a new kind of mixed phase as long…
We study the hadron-quark mixed phase in protoneutron stars, where neutrinos are trapped and lepton number becomes a conserved quantity besides the baryon number and electric charge. Considering protoneutron-star matter as a ternary system, the Gibbs conditions are applied together with the Coulomb interaction. We find that there no crystalline ("pasta") structure appears in the regime of high lepton-number fraction; the size of pasta becomes very large and the geometrical structure becomes mechanically unstable due to the charge screening effect. Consequently the whole system is separated int…
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…
We have performed a set of 11 three-dimensional magnetohydrodynamical core collapse supernova simulations in order to investigate the dependencies of the gravitational wave signal on the progenitor's initial conditions. We study the effects of the initial central angular velocity and different variants of neutrino transport. Our models are started up from a 15 solar mass progenitor and incorporate an effective general relativistic gravitational potential and a finite temperature nuclear equation of state. Furthermore, the electron flavour neutrino transport is tracked by efficient algorithms f…
We study the gravitational wave signal from eight new 3D core-collapse supernova simulations. We show that the signal is dominated by $f$- and $g$-mode oscillations of the protoneutron star and its frequency evolution encodes the contraction rate of the latter, which, in turn, is known to depend on the star's mass, on the equation of state, and on transport properties in warm nuclear matter. A lower-frequency component of the signal, associated with the standing accretion shock instability, is found in only one of our models. Finally, we show that the energy radiated in gravitational waves is …
Extremely strong magnetic fields of the order of $10^{15}\,{\rm G}$ are required to explain the properties of magnetars, the most magnetic neutron stars. Such a strong magnetic field is expected to play an important role for the dynamics of core-collapse supernovae, and in the presence of rapid rotation may power superluminous supernovae and hypernovae associated to long gamma-ray bursts. The origin of these strong magnetic fields remains, however, obscure and most likely requires an amplification over many orders of magnitude in the protoneutron star. One of the most promising agents is the m…
The cooling process of a protoneutron star is investigated with focus on its sensitivity to properties of hot and dense matter. An equation of state, which includes the nucleon effective mass and nuclear symmetry energy at twice the saturation density as control parameters, is constructed for systematic studies. The numerical code utilized in this study follows a quasi-static evolution of a protoneutron star solving the general-relativistic stellar structure with neutrino diffusion. The cooling timescale evaluated from the neutrino light curve is found to be longer for the models with larger e…
We investigate protoneutron star matter using the state-of-the-art perturbative equation of state for cold and dense QCD in the presence of a fixed lepton fraction in which both electrons and neutrinos are included. Besides computing the modifications in the equation of state due to the presence of trapped neutrinos, we show that stable strange quark matter has a more restricted parameter space. We also study the possibility of nucleation of unpaired quark matter in the core of protoneutron stars by matching the lepton-rich QCD pressure onto a hadronic equation of state, namely TM1 with trappe…
Rotating and magnetized protoneutron stars (PNSs) may drive relativistic magneto-centrifugally accelerated winds as they cool immediately after core collapse. The wind fluid near the star is composed of neutrons and protons, and the neutrons become relativistic while collisionally coupled with the ions. Here, we argue that the neutrons in the flow eventually undergo inelastic collisions around the termination shock inside the stellar material, producing ~0.1-1 GeV neutrinos, without relying on cosmic-ray acceleration mechanisms. Even higher-energy neutrinos may be produced via particle acceler…
We summarize our current understanding of gravitational wave emission from core-collapse supernovae. We review the established results from multi-dimensional simulations and, wherever possible, provide back-of-the-envelope calculations to highlight the underlying physical principles. The gravitational waves are predominantly emitted by protoneutron star oscillations. In slowly rotating cases, which represent the most common type of the supernovae, the oscillations are excited by multi-dimensional hydrodynamic instabilities, while in rare rapidly rotating cases, the protoneutron star is born wi…
We study properties of gravitational waves based on the three-dimensional simulations, which demonstrate the neutrino-driven explosions aided by the standing accretion shock instability (SASI). Pushed by evidence supporting slow rotation prior to core-collapse, we focus on the asphericities in neutrino emissions and matter motions outside the protoneutron star. By performing a ray-tracing calculation in 3D, we estimate accurately the gravitational waveforms from anisotropic neutrino emissions. In contrast to the previous work assuming axisymmetry, we find that the gravitational waveforms vary …
The prediction of the equation of state of hot, dense nuclear matter is one of the most complicated and interesting problems in nuclear astrophysics. At the same time, knowledge of it is the basic ingredient for some of the most interesting studies. In the present work, we concentrate our study on the construction of the equation of state of hot, dense nuclear matter, related mainly to the interior of the neutron star. We employ a theoretical nuclear model, which includes momentum-dependent interaction among the nucleons, along with the \textit{state-of-the-art} microscopic calculations. Therm…
The gravitational collapse, bounce, the explosion of an iron core of an 11.2 $M_{\odot}$ star is simulated by two-dimensional neutrino-radiation hydrodynamic code. The explosion is driven by the neutrino heating aided by multi-dimensional hydrodynamic effects such as the convection. Following the explosion phase, we continue the simulation focusing on the thermal evolution of the protoneutron star up to $\sim$70 s when the crust of the neutron star is formed using one-dimensional simulation. We find that the crust forms at high-density region ($ρ\sim10^{14}$ g cm$^{-3}$) and it would proceed f…
The gravitational wave (GW) signal resulting from stellar core collapse encodes a wealth of information about the physical parameters of the progenitor star and the resulting core-collapse supernova (CCSN). We present a novel approach to constrain CCSN progenitor properties at collapse using two of the most detectable parts of the GW signal: the core-bounce signal and evolution of the dominant frequency mode from the protoneutron star. We focus on the period after core bounce but before explosion and investigate the predictive power of GWs from rotating CCSNe to constrain properties of the pro…
We present results from a new set of 3D general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parameterized electron capture in the collapse phase, and a multi-species neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino l…
During a failed core-collapse supernova, the protoneutron star eventually collapses under its own gravitational field and forms a black hole. This collapse happens quickly, on the dynamical time of the protoneutron star, $\lesssim$0.5 ms. During this collapse, barring any excessive rotation, the entire protoneutron star is accreted into the newly formed black hole. The main source of neutrinos is now removed and the signal abruptly shuts off over this formation timescale. However, while the source of neutrinos is turned off, the arrival times at an Earth-based detector will depend on the neutr…
By performing three-dimensional (3D) simulations that demonstrate the neutrino-driven core-collapse supernovae aided by the standing accretion shock instability (SASI), we study how the spiral modes of the SASI can have impacts on the properties of the gravitational-wave (GW) emission. To see the effects of rotation in the non-linear postbounce phase, we give a uniform rotation on the flow advecting from the outer boundary of the iron core, whose specific angular momentum is assumed to agree with recent stellar evolution models. We compute fifteen 3D models in which the initial angular momentu…
We explore the influence of progenitor mass and rotation on the gravitational-wave (GW) emission from core-collapse supernovae, during the postbounce, preexplosion, accretion-phase. We present the results from 15 two-dimensional (2D) neutrino radiation-hydrodynamic simulations from initial stellar collapse to $\sim$300 ms after core bounce. We examine the features of the GW signals for four zero-age main sequence (ZAMS) progenitor masses ranging from 12 $M_\odot$ to 60 $M_\odot$ and four core rotation rates from 0 to 3 rad s$^{-1}$. We find that GW strain immediately around core bounce is fair…
Gravitational-wave diagnostics are developed for discriminating between varieties of mixed poloidal-toroidal magnetic fields in neutron stars, with particular emphasis on differentially rotating protoneutron stars. It is shown that tilted torus magnetic fields, defined as the sum of an internal/external poloidal component, whose axis of symmetry is tilted with respect to the rotation axis, and an internal toroidal component, whose axis of symmetry is aligned with the rotation axis, deform the star triaxially, unlike twisted torus fields, which deform the star biaxially. Utilizing an analytic t…
We present results from full general relativistic three-dimensional hydrodynamics simulations of stellar core collapse of a 70 M$_\odot$ star with spectral neutrino transport. To investigate the impact of rotation on non-axisymmetric instabilities, we compute three models by parametrically changing the initial strength of rotation. The most rapidly rotating model exhibits a transient development of the low-$T/|W|$ instability with one-armed spiral flow at the early postbounce phase. Subsequently, the two-armed spiral flow appears, which persists during the simulation time. The moderately rotat…
A precise understanding of the equation of state (EOS) of dense and hot matter is key to modeling relativistic astrophysical environments, including core-collapse supernovae (CCSNe), protoneutron star (PNSs) evolution, and compact binary mergers. In this paper, we extend the microscopic zero-temperature BL (Bombaci and Logoteta) %nuclear equation of state nuclear EOS %derived by Bombaci and Logoteta to finite temperature and arbitrary nuclear composition. We employ this new EOS to describe hot $β$-stable nuclear matter and to compute various structural properties of nonrotating PNS. %protoneut…
We present neutrino-transport hydrodynamic simulations of electron-capture supernovae (ECSNe) in \texttt{FLASH} with new two-dimensional (2D) collapsing progenitor models. These progenitor models feature the 2D modelling of oxygen-flame propagation until the onset of core collapse. We perform axisymmetric simulations with 6 progenitor models that, at the time of collapse, span a range of propagating flame front radii. For comparison, we also perform a simulation with the same setup using the canonical, spherically-symmetrical progenitor model n8.8. We found that the variations in the progenito…
We propose a ray-tracing method to estimate gravitational waves (GWs) generated by anisotropic neutrino emission in supernova cores. To calculate the gravitational waveforms, we derive analytic formulae in a useful form, which are applicable also for three-dimensional computations. Pushed by evidence of slow rotation prior to core-collapse, we focus on asphericities in neutrino emission and matter motions outside the protoneutron star. Based on the two-dimensional (2D) models, which mimic SASI-aided neutrino heating explosions, we compute the neutrino anisotropies via the ray-tracing method in…
Massive stars generally end their lives as neutron stars (NSs) or black holes (BHs), with NS formation typically occurring at the low mass end and collapse to a BH more likely at the high mass end. In an intermediate regime, with a mass range that depends on the uncertain details of rotation and mass loss during the star's life, a NS is initially formed which then experiences fallback accretion and collapse to a BH. The electromagnetic consequence of such an event is not clear. Depending on the progenitor's structure, possibilities range from a long gamma-ray burst to a Type II supernova (that…
Galactic core-collapse supernovae are among the possible sources of gravitational waves. We investigate the ability of gravitational-wave observatories to extract the properties of the collapsing progenitor from the gravitational waves radiated. We use simulations of supernovae that explore a variety of progenitor core rotation rates and nuclear equations of state and examine the ability of current and future observatories to determine these properties using gravitational-wave parameter estimation. We use principal component analysis of the simulation catalog to determine the dominant features…
From the basic concepts of general relativity, we investigate the rotation of the polarization angle by a moving gravitational lens. Particularly, we clarify the existing confusion in the literature by showing and explaining why such rotation must explicitly depend on the relative motion between the observer and the lens. We update the prediction of such effect on the double pulsar PSR J0737-3039 and estimate a rotation angle of $\sim 10^{-7}rad$. Despite its tiny signal, this is $10$ orders of magnitude larger than the previous prediction by Ruggiero and Tartaglia, which apparently was misgui…
Neutron stars are the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. Theoretical studies in connection with recent observational data of isolated neutron stars, as well as binary neutron stars systems, offer an excellent opportunity to provide robust solutions on the dense nuclear problem. In the present work, we review recent studies concerning the applications of various theoretical nuclear models on a few recent observations of binary neutron stars or neutron-star--black-hole systems. In particular, using a simple and well-es…
We present numerical-relativity simulations of spherically symmetric core collapse and compact-object formation in scalar-tensor theories of gravity. The additional scalar degree of freedom introduces a propagating monopole gravitational-wave mode. Detection of monopole scalar waves with current and future gravitational-wave experiments may constitute smoking gun evidence for strong-field modifications of General Relativity. We collapse both polytropic and more realistic pre-supernova profiles using a high-resolution shock-capturing scheme and an approximate prescription for the nuclear equati…
The metallicity dependence and evolutionary times of merging binary black holes: Combined constraints from individual gravitational-wave detections and the stochastic background
We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), …
Gravitational waves (GWs) provide unobscured insight into the birthplace of neutron stars (NSs) and black holes in core-collapse supernovae (CCSNe). The nuclear equation of state (EOS) describing these dense environments is yet uncertain, and variations in its prescription affect the proto-neutron star (PNS) and the post-bounce dynamics in CCSNe simulations, subsequently impacting the GW emission. We perform axisymmetric simulations of CCSNe with Skyrme-type EOSs to study how the GW signal and PNS convection zone are impacted by two experimentally accessible EOS parameters, (1) the effective m…
We investigate the effects of observatory locations on the probability of discovering optical/infrared counterparts of gravitational wave sources. We show that for the LIGO--Virgo network, the odds of discovering optical/infrared (OIR) counterparts show some latitude dependence, but weak or no longitudinal dependence. A stronger effect is seen to arise from the timing of LIGO/Virgo observing runs, with northern OIR observatories having better chances of finding the counterparts in northern winters. Assuming identical technical capabilities, the tentative mid-2017 three-detector network observi…
We compare the impacts of uncertainties in both binary population synthesis models and the cosmic star formation history on the predicted rates of Gravitational Wave compact binary merger (GW) events. These uncertainties cause the predicted rates of GW events to vary by up to an order of magnitude. Varying the volume-averaged star formation rate density history of the Universe causes the weakest change to our predictions, while varying the metallicity evolution has the strongest effect. Double neutron-star merger rates are more sensitive to assumed neutron-star kick velocity than the cosmic st…
Asymmetric mass ejection in the early phase of supernova (SN) explosions can impart a kick velocity to the new-born neutron star (NS). For neutrino-driven explosions the NS acceleration was shown to be mainly caused by the gravitational attraction of the anisotropically expelled inner ejecta, while hydrodynamic forces contribute on a subdominant level, and asymmetric neutrino emission plays only a secondary role. Two- and three-dimensional hydrodynamic simulations demonstrated that this gravitational tug-boat mechanism can explain the observed space velocities of young NSs up to more than 1000…
