The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula's domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars.
We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code and those computed by the full theory. Entire sequences of the low order counter-rotating f-modes are …
$f(R)$ theories of gravity are one of the most popular alternative explanations for dark energy and therefore studying the possible astrophysical implications of these theories is an important task. In the present paper we make a substantial advance in this direction by considering rapidly rotating neutron stars in $R^2$ gravity. The results are obtained numerically and the method we use is non-perturbative and self-consistent. The neutron star properties, such as mass, radius and moment of inertia, are studied in detail and the results show that rotation magnifies the deviations from general …
The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field in the black-hole spacetime. The analytically derived formula is shown to agree with direct numerical computations of the resonances. Our results provide an upper bound on the instability regime of rapidly-rotating Kerr black holes to massive scalar perturbations.
We construct rapidly rotating neutron star models in scalar-tensor theories with a massive scalar field. The fact that the scalar field has nonzero mass leads to very interesting results since the allowed range of values of the coupling parameters is significantly broadened. These deviations from pure general relativity can be very large for values of the parameters that are in agreement with the observations. The rapid rotation can magnify the differences several times compared to the static case. The universal relations between the normalized moment of inertia and quadrupole moment are also …
We present the field equations governing the equilibrium of rapidly rotating neutron stars in scalar-tensor theories of gravity, as well as representative numerical solutions. The conditions for the presence of a nontrivial scalar field and the deviations from the general relativistic solutions are studied. Two examples of scalar-tensor theories are examined - one case that is equivalent to the Brans-Dicke theory and a second case, that is perturbatively equivalent to Einstein's General Relativity in the weak field regime, but can differ significantly for strong fields. Our numerical results s…
We report on numerical calculations of orbital and epicyclic frequencies in nearly circular orbits around rotating neutron stars and strange quark stars. The FPS equation of state was used to describe the neutron star structure while the MIT bag model was used to model the equation of state of strange quark stars. The uniformly rotating stellar configurations were computed in full general relativity. We find that the vertical epicyclic frequency is very sensitive to the oblateness of the rotating star. For models of rotating neutron stars of moderate mass, as well as for strange quark star mod…
Viscosity driven bar mode secular instabilities of rapidly rotating neutron stars are studied using LORENE/Nrotstar code. These instabilities set a more rigorous limit to the rotation frequency of neutron star than the Kepler frequency/mass shedding limit. The procedure employed in the code comprises of perturbing an axisymmetric and stationary configuration of a neutron star and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. Symmetry breaking point was found out for Polytropic as well as 10 realistic Equations of states (EOS) from the CompOSE dat…
In this paper we investigate vacuum nonlinear electrodynamics corrections on rapidly rotating pulsar radiation and spin-down in the perturbative QED approach (post-Maxwellian approximation). An analytical expression for the pulsar's radiation intensity has been obtained and analyzed.
We study the orbital and epicyclic frequencies of particles orbiting around rapidly rotating neutron stars and strange stars in a particular scalar-tensor theory of gravity. We find very large deviations of these frequencies, when compared to their corresponding values in general relativity, for the maximum-mass rotating models. In contrast, for models rotating with spin frequency of 700Hz (approximately the largest known rotation rate of neutron stars), the deviations are generally small. Nevertheless, for a very stiff equation of state and a high mass the deviation of one of the epicyclic fr…
In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass-radius relations, moments of inertia and other results of interest are obtained and compared with the ones for non-rotating stars.
It is shown that rapidly-rotating Kerr black holes are characterized by the dimensionless ratio $τ_{\text{gap}}/τ_{\text{emission}}=O(1)$, where $τ_{\text{gap}}$ is the average time gap between the emission of successive Hawking quanta and $τ_{\text{emission}}$ is the characteristic timescale required for an individual Hawking quantum to be emitted from the black hole. This relation implies that the Hawking cascade from rapidly-rotating black holes has an almost continuous character. Our results correct some inaccurate claims that recently appeared in the literature regarding the nature of the…
We prove the existence of a unique family of non-oscillatory (purely-imaginary) polar quasinormal resonances of rapidly-rotating Kerr black holes. These purely imaginary resonances can be expressed in the compact form: w_n=-i2*pi*T_{BH}*(l+1+n), where T_{BH} is the black-hole temperature, l is the spheroidal harmonic index of the mode, and n=0,1,2,... is the resonance parameter. It is shown that our analytical results for the black-hole resonance spectrum agree with new numerical data that recently appeared in the literature.
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 consider generic axially symmetric rotating spacetimes and examine particle collisions in the ergoregion. The results are generic and agree with those obtained in the particular case of the rotating Teo wormhole in N. Tsukamoto and C. Bambi, Phys. Rev. D 91, 104040 (2015). It is shown that for sufficiently rapid rotation, the energy of a particle escaping to infinity can become arbitrary large (so-called super-Penrose process). Moreover, this energy is typically much larger than the center-of mass energy of colliding particles. In this sense the situation differs radically from that for col…
Context: Superluminous type Ia supernovae (SNe Ia) may be explained by super-Chandrasekhar-mass explosions of rapidly rotating white dwarfs (WDs). In a preceding paper, we showed that the deflagration scenario applied to rapidly rotating WDs generates explosions that cannot explain the majority of SNe Ia. Aims: Rotation of the progenitor star allows super-Chandrasekhar-mass WDs to form that have a shallower density stratification. We use simple estimates of the production of intermediate and iron group elements in pure detonations of rapidly rotating WDs to assess their viability in explaining…
Non-axisymmetric features are found in the core collapse of a rapidly rotating massive star, which might have important implications for magnetic field amplification and production of a bipolar outflow that can explode the star, as well as for r-process nucleosynthesis and natal kicks. The collapse of an evolved rapidly rotating massive star is followed in three-dimensional hydrodynamic simulations using the FLASH code with neutrino leakage. A rotating proto-neutron star (PNS) forms with a non-zero linear velocity. This can contribute to the natal kick of the remnant compact object. The PNS is…
We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force experienced by infalling observers exhibit transient growth near the horizon. The growth lasts arbitrarily long in the extremal limit, reproducing the horizon instability of extremal Kerr. We explain these results in terms of near-horizon geometry and discuss potential astrophysical implications.
We explore the formation process of a black hole (BH) through the pair-instability collapse of a rotating Population III very massive star in axisymmetric numerical relativity. As the initial condition, we employ a progenitor star which is obtained by evolving a rapidly rotating zero-age main sequence (ZAMS) star with mass $320M_\odot$ until it reaches a pair instability region. We find that for such rapidly rotating model, a fraction of the mass, $\sim 10M_\odot$, forms a torus surrounding the remnant BH of mass $\sim 130M_\odot$ and an outflow is driven by a hydrodynamical effect. We also pe…
This paper develops a novel numerical method for obtaining structures of rapidly rotating stars based on a self-consistent field scheme. The solution is obtained iteratively. Both rapidly rotating barotropic and baroclinic equilibrium states are calculated self-consistently using this method. Two types of rotating baroclinic stars are investigated by changing the isentropic surfaces inside the star. Solution sequences of these are calculated systematically and critical rotation models beyond which no rotating equilibrium state exists are also obtained. All of these rotating baroclinic stars sa…
We demonstrate that stability of r-modes in young rapidly rotating pulsars might be explained if one takes into account strong medium modifications of the nucleon-nucleon interaction because of the softening of pionic degrees of freedom in dense nucleon matter. Presence of the efficient direct Urca processes is not required. Within our model the most rapidly rotating observed young pulsar PSR J0537-6910 should have the mass $\geq 1.8M_{\odot}$.
Rapidly rotating black holes are a prime arena for understanding corrections to Einstein's theory of general relativity (GR). We construct solutions for rapidly rotating black holes in dynamical Chern-Simons (dCS) gravity, a useful and motivated example of a post-GR correction. We treat dCS as an effective theory and thus work in the decoupling limit, where we apply a perturbation scheme using the Kerr metric as the background solution. Using the solutions to the scalar field and the trace of the metric perturbation, we determine the regime of validity of our perturbative approach. We find tha…
Neutron stars are attractive places to look for dark matter because their high densities allow repeated interactions. Weakly interacting massive particles (WIMPs) may scatter efficiently in the core or in the crust of a neutron star. In this paper we focus on WIMP contributions to transport properties, such as shear viscosity or thermal conductivity, because these can be greatly enhanced by long mean free paths. We speculate that WIMPs increase the shear viscosity of neutron star matter and help stabilize r-mode oscillations. These are collective oscillations where the restoring force is the C…
Neutron stars are commonly considered as astronomical objects having highdensity interiors and an inner core region in which various hadronic matter phases are expected. Several studies show that the inner structures affect macroscopic phenomena of the star. However, we know that the inner structures of the star strongly depend on the equation of state (EOS). The EOS of high-density matter is still not clear and several recent observations indicate restrictions to EOSs. Theoretical studies should elucidate EOSs at high density and/or high temperature. For instance, many theoretical studies hav…
A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. By using a Hamilton-Jacobi formalism, we show how the special relativistic rotational effects such as aberration of angles, Doppler boosting, and time dilatation naturally emerge from the general relativistic treatment of rotating compact objects. We use the Butterworth-Ipser metric expanded up to the second order in rotation and hence include effects of light bending, frame-dragging, and quadrupole deviations to our geodesic calculations. We also give detailed descriptions of …
We present analysis of neutrino and GW signals based on three-dimensional (3D) core-collapse supernova simulations of a rapidly rotating 27 $M_{\odot}$ star. We find a new neutrino signature that is produced by a lighthouse effect where the spinning of strong neutrino emission regions around the rotational axis leads to quasi-periodic modulation in the neutrino signal. Depending on the observer's viewing angle, the time modulation will be clearly detectable in IceCube and the future Hyper-Kamiokande. The GW emission is also anisotropic where the GW signal is emitted, as previously identified, …
We report results from a series of three-dimensional (3D) rotational core-collapse simulations for $11.2$ and 27 $M_{/odot}$ stars employing neutrino transport scheme by the isotropic diffusion source approximation. By changing the initial strength of rotation systematically, we find a rotation-assisted explosion for the 27$M_{/odot}$ progenitor, which fails in the absence of rotation. The unique feature was not captured in previous two-dimensional (2D) self-consistent rotating models because the growing non-axisymmetric instabilities play a key role. In the rapidly rotating case, strong spira…
We consider a neutrino-free hot neutron star that contains antikaon condensates in its core and is at finite entropy per baryon. We find the equation of state for a range of entropies and antikaon optical potentials and generate the mass profile of static as well as rotating stars. Rotation induces many changes in the stellar equilibrium, and hence its structural properties evolve. In this work, we report the effect of rotation on the mass and shape of a hot neutron star for different equations of state and thermodynamic conditions. Temperature profile of hot, static neutron star is also explo…
The authors try to probe the inner components of rapidly rotating compact stars such as the millisecond pulsar SAX J1808.4-3658 and the possible sub-millisecond pulsar XTE J1739-285 in their own way by comparing the genuine rotation frequencies under different theoretical models with the observational data, which may exert more stringent constraint on matter composition of compact stars. According to their treatment, the SAX J1808.4-3658 is a star with exotic matter and XTE J1739-285 a hybrid star.
In certain mass ranges, massive stars can undergo a violent pulsation triggered by the electron/positron pair instability that ejects matter, but does not totally disrupt the star. After one or more of these pulsations, such stars are expected to undergo core-collapse to trigger a supernova explosion. The mass range susceptible to this pulsational phenomena may be as low as 50-70 Msun if the progenitor is of very low metallicity and rotating sufficiently rapidly to undergo nearly homogeneous evolution. The mass, dynamics, and composition of the matter ejected in the pulsation are important asp…
We consider an instability of rapidly rotating neutron stars in low-mass X-ray binaries (LMXBs) with respect to excitation of r-modes (which are analogous to Earth's Rossby waves controlled by the Coriolis force). We argue that finite temperature effects in the superfluid core of a neutron star lead to a resonance coupling and enhanced damping (and hence stability) of oscillation modes at certain stellar temperatures. Using a simple phenomenological model we demonstrate that neutron stars with high spin frequency may spend a substantial amount of time at these `resonance' temperatures. This fi…
The gravitational-wave instability of r-modes in rapidly rotating compact stars is believed to spin them down to angular frequencies of about a tenth of the Kepler frequency soon after their birth in a Supernova. We point out that the r-mode perturbation also impacts the neutrino cooling and viscosity in hot compact stars via processes that restore weak equilibrium. We illustrate this fact with a simple model of spin-down due to gravitational wave emission in compact stars composed entirely of three-flavor degenerate quark matter (a strange quark star). Non-equilibrium neutrino cooling of this…
We report on the three-dimensional (3D) hydrodynamic evolution to iron core-collapse of a rapidly rotating 16 $M_{\odot}$ star. For the first time, we follow the 3D evolution of the angular momentum (AM) distribution in the iron core and convective shell burning regions for the final 10 minutes up to and including gravitational instability and core-collapse. In 3D, we find that convective regions show efficient AM transport that leads to an AM profile that differs in shape and magnitude from $\texttt{MESA}$ within a few shell convective turnover timescales. For different progenitor models, suc…
Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity ($ν_* \sim$ 200--600 Hz). We investigate the effects of rapid rotation on the observational appearance of a NS. We propose analytical formulae relating gravitational mass and equatorial radius of the rapidly rotating NS to the mass $M$ and radius $R$ of a non-rotating NS of the same baryonic mass using accurate fully relativistic computations. We compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild (MOS)…
