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 future. On the other hand the small deviations in some of the asteroseismology relations show that they are not only equation of state independent, but they are also quite insensitive to the gravitational theory. That is why solving the inverse problem can give us quite robust estimates of the neutron star parameters.
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…
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 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 multi…
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…
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 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 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…
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 study the conversion of neutron matter into strange matter as a detonation wave. The detonation is assumed to originate from a central region in a spherically symmetric background of neutrons with a varying radial density distribution. We present self-similar solutions for the propagation of detonation in static and collapsing backgrounds of neutron matter. The solutions are obtained in the framework of general relativistic hydrodynamics, and are relevant for the possible transition of neutron into strange stars. Conditions for the formation of either bare or crusted strange stars are discu…
We study the electromagnetic spectrum of accretion disks around neutron and strange stars in $\mathcal{R}^2$ gravity. Both static and rapidly rotating models are investigated. The results are compared with the General Relativistic results. We found difference between the results in both theories of about 50\% for the electromagnetic flux and about 20\% in the luminosity for models with equal mass and angular velocity in both theories. The observed differences are much lower for models rotating with Kelperian velocity and with equal masses.
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…
We study the structure of spherically symmetric and static objects in the presence of a nonminimally coupled scalar field having a potential of the form $V(ϕ)=-μ^2ϕ^2/2+λϕ^4/4$. We numerically solve equations of the system using two different realistic equations of state for neutron matter and give the mass-radius relations as well as the radial profiles of the scalar field, densities and the mass function for a sample configuration. We show that a specific solution type encountered in such systems causes characteristic neutron star mass-radius relations to turn into the ones belonging to stra…
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…
In the present paper we investigate self-consistently slowly rotating neutron and strange stars in R-squared gravity. For this purpose we first derive the equations describing the structure of the slowly rotating compact stars in $f(R)$-gravity and then simultaneously solve the exterior and the interior problem. The structure of the slowly rotating neutron stars is studied for two different hadronic equations of state and a strange matter equation of state. The moment of inertia and its dependence on the stellar mass and the $R$-squared gravity parameter $a$ is also examined in details. We fin…
Contrary to young neutron stars, young strange stars are not subject to the r-mode instability which slows rapidly rotating, hot neutron stars to rotation periods near 10 ms via gravitational wave emission. Young millisecond pulsars are therefore likely to be strange stars rather than neutron stars, or at least to contain significant quantities of quark matter in the interior.
Strangeness Transport in Binary Neutron Star Mergers
California Institute of Technology（加州理工学院）；KTH Royal Institute of Technology（皇家理工学院）；University of Southampton（南安普顿大学）；Walter Burke Institute for Theoretical Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所）；Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系宇宙高级研究伊利诺伊中心）；Kent State University（肯特州立大学）
We investigate the relevance of the gravitational-wave driven r-mode instability for strange stars. We find that the unstable r-modes affect strange stars in a way that is quite distinct from the neutron star case. For accreting strange stars we show that the onset of r-mode instability does not lead to the thermo-gravitational runaway that is likely to occur in neutron stars. Instead, the strange star evolves towards a quasi-equilibrium state on a timescale of about a year. This mechanism could thus explain the clustering of spin-frequencies inferred from kHz QPO data in Low-mass X-ray binari…
Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events, according to both numerical simulations and the multi-messenger observation of GW170817. The lifetime and evolution of such a differentially rotating star, is tightly related to the observations in the post-merger phase. Various studies on the maximum mass of differentially rotating neutron stars have been done in the past, most of which assume the so-called $j$-const law as the rotation profile inside the star and consider only neutron star equations of state. In this paper, we ex…
According to various models, the orbital and the epicyclic frequencies of particles moving on a circular orbit around compact objects are related to the quasi-periodic oscillations observed in the X-ray flux of some pulsars or black hole candidates. It is expected that they originate from the inner edge of the accretion discs, deep into the gravitational field of the compact objects. Considering the planned new generation X-ray timing observatories with large collective areas, the quasi-periodic oscillations might be an excellent tool for testing gravity in strong field regime and respectively…
Recycling strange stars to millisecond periods is studied within the framework of general relativity. We employ equations of state of strange quark matter based on the MIT Bag Model, with massive strange quarks and lowest order QCD interactions. The presence of the crust of normal matter is taken into account, with a bottom density assumed to be equal to the neutron-drip one. The calculations are performed by solving the exact 2-D equations for rigidly rotating stationary configurations in general relativity. Evolutionary tracks of accreting strange stars are computed, and their dependence on …
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 investigate the properties of anisotropic, spherically symmetric compact stars, especially neutron stars and strange quark stars, made of strongly magnetized matter. The neutron stars are described by SLy equation of state, the strange quark stars by an equation of state based on the MIT Bag model. The stellar models are based on an a priori assumed density dependence of the magnetic field and thus anisotropy. Our study shows that not only the presence of a strong magnetic field and anisotropy, but also the orientation of the magnetic field itself, have an important influence on the physica…
Oscillation modes of isolated compact stars can, in principle, be a fingerprint of the equation of state (EoS) of dense matter. We study the non-radial high-frequency l=2 spheroidal modes of neutron stars and strange quark stars, adopting a two-component model (core and crust) for these two types of stars. Using perturbed fluid equations in the relativistic Cowling approximation, we explore the effect of a strangelet or hadronic crust on the oscillation modes of strange stars. The results differ from the case of neutron stars with a crust. In comparison to fluid-only configurations, we find th…
We present the first relativistic calculations of the final phase of inspiral of a binary system consisting of two stars built predominantely of strange quark matter (strange quark stars). We study the precoalescing stage within the Isenberg-Wilson-Mathews approximation of general relativity using a multidomain spectral method. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational, taking into account the finite density at the stellar surface -- a distinctive feature with respect to the neutron star case. The gravitational-radiati…
The mergers of black hole-neutron star binaries are calcuated using a pseudo-general relativistic potential that incorporates ${\mathcal O}(v^2/c^2)^3$ post-Newtonian corrections. Both normal matter neutron stars and self-bound strange quark matter stars are considered as black hole partners. As long as the neutron stars are not too massive relative to the black hole mass, orbital decay terminates in stable mass transfer rather than an actual merger. For a normal neutron star, mass transfer results in a widening of the orbit but the stable transfer ends before the minimum neutron star mass is …
