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.
State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of proto-neutron star modes during post-bounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e. g-modes, p-modes and the f-mode, with fundamental properties of the system, such as the surface gravity of the proto-neutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progen…
We study radial oscillations of non-rotating neutron stars (NSs) in four-dimensional General Relativity. The interior of the NS was modelled within a recently proposed multicomponent realistic equation of state (EoS) with the induced surface tension (IST). In particular, we considered the IST EoS with two sets of model parameters, that both reproduce all the known properties of normal nuclear matter, give a high quality description of the proton flow constraint, hadron multiplicities created in nuclear-nuclear collisions, consistent with astrophysical observations and the observational data fr…
We investigate the equilibrium and radial stability of spherically symmetric relativistic stars, considering a polytropic equation of state (EoS), within the framework of $f(R,T)$ gravity with a conservative energy-momentum tensor. Both modified stellar structure equations and Chandrasekhar's pulsation equations are derived for the $f(R,T)= R+ h(T)$ gravity model, where the function $h(T)$ assumes a specific form in order to safeguard the conservation equation for the energy-momentum tensor. The neutron star properties, such as radius, mass, binding energy and oscillation spectrum are studied …
We study the oscillations of neutron and strange stars in $R^2$ gravity. More precisely the nonradial $f$-modes are examined and the differences with pure general relativity are investigated. Using these results we build several gravitational wave asteroseismology relations. Our goal is to determine up to what extend these relations are equation of state independent and whether they deviate enough from general relativity in order to produce an observable effect. The results show that the differences coming from $R^2$ gravity are up to 10\% and that will be difficult to be observed in the near …
In the present paper we examine gravitational wave asteroseismology relations for f-modes of rapidly rotating neutron stars. An approach different to the previous studies is employed - first, the moment of inertia is used instead of the stellar radius, and second, the normalization of the oscillation frequencies and damping times is different. It was shown that in the non-rotating case this can lead to a much stronger equation of state independence and our goal is to generalize the static relations to the rapidly rotating case and values of the spherical mode number $l\ge2$. We employ realisti…
We construct new, multivariate empirical relations for measuring neutron star radii and tidal deformabilities from the dominant gravitational wave frequency in the post-merger phase of binary neutron star mergers. The relations determine neutron star radii and tidal deformabilities for specific neutron star masses with consistent accuracy and depend only on two observables: the post-merger peak frequency $f_{\rm peak}$ and the chirp mass $M_{\rm chirp}$. The former could be measured with good accuracy from gravitational waves emitted in the post-merger phase using next-generation detectors, wh…
Gravitational-wave signals from coalescing binary neutron stars can yield important information about the properties of nuclear-matter equation of state from the early part of the signal through tidal effects to the properties and oscillation frequencies of the merger product. We investigate a direct link between the properties of isolated neutron stars and their merger, by comparing the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars with the gravitational-wave frequency associated with the merger of two neutron stars. We calculate the quadrupolar ($l=2$) $f$-mode os…
We investigate damping and growth times of the f-mode for rapidly rotating stars and a variety of different polytropic equations of state in the Cowling approximation. We discuss the differences in the eigenfunctions of co- and counterrotating modes and compute the damping times of the f-mode for several EoS and all rotation rates up to the Kepler-limit. This is the first study of the damping/growth time of this type of oscillations for fast rotating neutron stars in a general relativistic framework. We use these frequencies and damping/growth times to create robust empirical formulae which ca…
Magnetic flares and induced oscillations of magnetars (super-magnetized neutron stars) are promising sources of gravitational waves (GWs). We suggest that the GW emission, if any, would last longer than the observed X-ray quasi-periodic oscillations (X-QPOs), calling for the longer-term GW analyses from a day to months than the current searches. Like the pulsar timing, the oscillation frequency would also evolve with time because of the decay or reconfiguration of magnetic field, which is crucial for the GW detection. With the observed GW frequency and its time-derivatives, we can probe the in…
In the present paper we study the oscillations of fast rotating neutron stars with realistic equations of state (EoS) within the Cowling approximation. We derive improved empirical relations for gravitational wave asteroseismology with f-modes and for the first time we consider not only quadrupolar oscillations but also modes with higher spherical order (l=|m|=3,4). After performing a systematic comparison with polytropic EoS, it is shown that the empirical relations found in this case approximately also hold for realistic EoS. Even more, we show that these relations will not change significan…
We present an alternative way of tracing the existence of a scalar field based on the analysis of the gravitational wave spectrum of a vibrating neutron star. Scalar-tensor theories in strong-field gravity can potentially introduce much greater differences in the parameters of a neutron star than the uncertainties introduced by the various equations of state. The detection of gravitational waves from neutron stars can set constraints on the existence and the strength of scalar fields. We show that the oscillation spectrum is dramatically affected by the presence of a scalar field, and can prov…
In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime ($w$ modes), are independent from the perturbations of scalar field and the effects of scalar field can be mounted only via the background properties. Using two diff…
We incorporate realistic, tabulated equations of state into fully relativistic simulations of magnetized neutron stars along with a neutrino leakage scheme which accounts for cooling via neutrino emission. Both these improvements utilize open-source code (GR1D) and tables from http://stellarcollapse.org. Our implementation makes use of a novel method for the calculation of the optical depth which simplifies its use with distributed adaptive mesh refinement. We present various tests with and without magnetization and preliminary results both from single stars and from the merger of a binary sys…
The inspiral and merger of a binary neutron star (NSNS) can lead to the formation of a hypermassive neutron star (HMNS). As the HMNS loses thermal pressure due to neutrino cooling and/or centrifugal support due to gravitational wave (GW) emission, and/or magnetic breaking of differential rotation it will collapse to a black hole. To assess the importance of shock-induced thermal pressure and cooling, we adopt an idealized equation of state and perform NSNS simulations in full GR through late inspiral, merger, and HMNS formation, accounting for cooling. We show that thermal pressure contributes…
Fudan University（复旦大学）；INFN Sezione di Catania, Dipartimento di Fisica, Universitá di Catania（意大利国家核物理研究所卡塔尼亚分部、物理学系、卡塔尼亚大学）；University of Geosciences, Wuhan（武汉地球科学学院）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC, Fudan University（国家自然科学基金委上海理论核物理研究中心，复旦大学）
We study thermal evolution of isolated neutron stars in scalar-tensor theories for the first time. Whether the rapid cooling due to the direct Urca process occurs or not is an interesting question in the viewpoint of the temperature observation of isolated neutron stars. Moreover, investigation of the cooling effect of nucleon superfluidity also has the large uncertainties though it is important in modern cooling theory. The cooling effect is typically influenced by the proton fraction and the central density. If a fifth force is mediated due to modification of gravity, the relation between th…
We present new results for pulsating neutron stars. We have calculated the eigenfrequencies of the modes that one would expect to be the most important gravitational-wave sources: the fundamental fluid f-mode, the first pressure p-mode and the first gravitational-wave w-mode, for twelve realistic equations of state. From this numerical data we have inferred a set of ``empirical relations'' between the mode-frequencies and the parameters of the star (the radius R and the mass M). Some of these relation prove to be surprisingly robust, and we show how they can be used to extract the details of t…
