Fast Rotating Neutron Stars Research Articles

Consequence of head-on collision of ion acoustic waves in unmagnetized plasmas having generalized (r, q) distributed electrons and positrons

To explore the effect of the head-on collision (such as phase shifts, collisional processes, and production of solitons) of ion-acoustic waves (IAWs), a collisionless unmagnetized electron-positron-ion (e-p-i) plasma is considered. The electrons and positrons follow the generalized () distribution. To do this, using the extended Poincaré-Lighthill-Kuo (ePLK) approach, the two-sided Korteweg-de Vries (KdV) equations and phase shifts are derived. The main aim of this study is to investigate the consequence of spectral indices and on both the negative and positive phase changes following an IAW-to-IAW collision. It is found that for the effects of the spectral indices of electrons and positrons both positive and negative phase shifts after head-on collisions are modified. The compressive (only hump-shaped) as well as rarefactive (both hump and dip-shaped) solitons become produced for the effect of spectral indices. The results obtained in the study may be helpful to understand the collision processes as well as the consequence of the head-on collision of IAWs in electron-positron-ion plasmas in the ionosphere, auroral acceleration regions, solar wind, Saturn rings, active galactic nuclei, polar cup of fast rotating neutron stars, semiconductor plasmas, and intense laser fields as well as in laboratory experiment.

Influence of the Gravitational Darkening Effect on the Spectrum of a Hot, Rapidly Rotating Neutron Star

Abstract In this paper, we discuss the influence of the gravitational darkening effect on the emergent spectrum of a fast-rotating, flattened neutron star. Model atmosphere codes always calculate spectra of emergent intensities and fluxes emitted from the unit surface on the star in plane-parallel geometry. Here we took a step beyond that and calculated a small sample grid of theoretical spectra integrated over the distorted surface of a sample rotating neutron star seen by a distant observer at various inclination angles. We assumed parameters like two dimensionless angular velocities Ω ¯ 2 = 0.30 and 0.60, the effective temperature of a nonrotating star T eff = 2.20 × 107 K, the logarithm of the surface gravity of a spherical star log ( g ) = 14.40 (cgs), and inclination angles from i = 0° to i = 90° with step Δi = 10°. We assumed that the atmosphere consists of a mixture of hydrogen and helium with M H = 0.70 and M He = 0.30. At each point on the neutron star surface, we calculated true intensities for local values of parameters (T eff and log ( g ) ), and these monochromatic intensities are next integrated over the whole surface to obtain the emergent spectrum. In this paper, we compute for the first time theoretical spectra of the fast-rotating neutron star. Our work clearly shows that the gravitational darkening effect strongly influences the spectrum and should be included in realistic models of the atmospheres of rotating neutron stars.

Fast Rotating Neutron Stars: Oscillations and Instabilities

In this review article, we present the main results from our most recent research concerning the oscillations of fast rotating neutron stars. We derive a set of time evolution equations for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full general relativity, taking into account the contribution of a dynamic spacetime. Using our code, which features high accuracy at comparably low computational expense, we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit. We propose various universal relations combining bulk properties of isolated neutron stars as well as of binary systems before and after merger; these relations are independent of the true equation of state and may serve as a valuable tool for gravitational wave asteroseismology. We also present an introductory example using a Bayesian analysis.

Particle acceleration and radiation reaction in strong spherical electromagnetic waves

ABSTRACT Strongly magnetized and fast-rotating neutron stars are known to be efficient particle accelerators within their magnetosphere and wind. They are suspected to accelerate leptons, protons, and maybe ions to extreme relativistic regimes where the radiation reaction significantly feeds back to their motion. In the vicinity of neutron stars, magnetic field strengths are close to the critical value of Bc ∼ 4.4 · 109 T and particle Lorentz factors of the order γ ∼ 109 are expected. In this paper, we investigate the acceleration and radiation reaction feedback in the pulsar wind zone where a large-amplitude low-frequency electromagnetic wave is launched starting from the light cylinder. We design a semi-analytical code solving exactly the particle equation of motion including radiation reaction in the Landau–Lifshits approximation for a null-like electromagnetic wave of arbitrary strength parameter and elliptical polarization. Under conventional pulsar conditions, asymptotic Lorentz factor as high as 108−109 is reached at large distances from the neutron star. However, we demonstrate that in the wind zone, within the spherical wave approximation, radiation reaction feedback remains negligible.

Dynamics of fast rotating neutron stars: An approach in the Hilbert gauge

We describe a set of time evolution equations and its numerical implementation for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full General Relativity, taking into account the contribution of a dynamic spacetime. We derive the perturbation equations for the spacetime in the Hilbert gauge, while the hydrodynamical evolution is based on perturbations of the energy-momentum tensor. In our numerical implementation, we use Kreiss-Oliger dissipation in order to achieve a stable time evolution. Our code features high accuracy at comparably low computational expense and we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit.

A relativistic particle pusher for ultra-strong electromagnetic fields

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above$\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to$10^{15}$or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

New quasi-universal relations for static and rapid rotating neutron stars

In the last few decades, lots of universal relations between different global physical quantities of neutron stars have been proposed to constrain the unobservable or hard to be observed properties of neutron stars. But few of them are related to the gravitational redshift or the gravitational binding energy, especially for the fast rotating neutron stars. Here we will focus on the universal relations related to these two quantities. Based on 11 equations of state (EOSs) from the predictions of microscopic nuclear many-body theories for normal or hybrid neutron stars, we proposed a set of new quasi-universal relations under three rotating cases: static, general rotating and Keplerian rotating. These new quasi-universal relations provide a potential way to constrain or estimate the unobservable or hard to be observed properties of neutron stars.

Universal relations for the Keplerian sequence of rotating neutron stars

We investigate the Keplerian (mass-shedding) sequence of rotating neutron stars. Twelve different equations of state are used to describe the nuclear structure. We find four fitting relations which connect the rotating frequency, mass and radius of stars in the mass-shedding limit to the mass and radius of stars in the static sequence. We show the breakdown of approximate relation for the Keplerian frequency derived by Lattimer and Prakash [Science, 304, 536, (2004)] and then we present a new, EOS-independent and more accurate relation. This relation fits the Keplerian frequency of rotating neutron stars to about $2\%$ for a large range of the compactness $M_{S}/R_{S}$ of the reference non-rotating neutron star, namely the static star with the same central density as the rotating one. The performance of the fitting formula is close to $4\%$ for $M_{S}/R_{S}\leq 0.05~M_{\odot}$/km ($f_{K}\leq 350$~Hz). We present additional EOS-independent relations for the Keplerian sequence including relations for $M_{K}f_{K}$ and $R_{K}f_{K}$ in terms of $M_{S}f_{S}$ and $R_{S}f_{S}$, respectively, one of $M_K/R_K$ as a function of $f_{K}/f_{S}$ and $M_S/R_S$, and a relation between the $M_K$, $R_K$ and $f_K$. These new fitting relations are approximately EOS-independent with an error in the worst case of $8\%$. The universality of the Keplerian sequence properties presented here add to the set of other neutron star universal relations in the literature such as the $I$-Love-$Q$ relation, the gravitational binding energy and the energy, angular momentum and radius of the last circular orbit of a test-particle around rotating neutron stars. This set of universal, analytic formulas, facilitate the inclusion of general relativistic effects in the description of relativistic astrophysical systems involving fast rotating neutron stars.

Accurate Ray-tracing of Realistic Neutron Star Atmospheres for Constraining Their Parameters

Abstract Thermal-dominated X-ray spectra of neutron stars in quiescent, transient X-ray binaries and neutron stars that undergo thermonuclear bursts are sensitive to mass and radius. The mass–radius relation of neutron stars depends on the equation of state (EoS) that governs their interior. Constraining this relation accurately is therefore of fundamental importance to understand the nature of dense matter. In this context, we introduce a pipeline to calculate realistic model spectra of rotating neutron stars with hydrogen and helium atmospheres. An arbitrarily fast-rotating neutron star with a given EoS generates the spacetime in which the atmosphere emits radiation. We use the Lorene/nrotstar code to compute the spacetime numerically and the Atm24 code to solve the radiative transfer equations self-consistently. Emerging specific intensity spectra are then ray-traced through the neutron star’s spacetime from the atmosphere to a distant observer with the Gyoto code. Here, we present and test our fully relativistic numerical pipeline. To discuss and illustrate the importance of realistic atmosphere models, we compare our model spectra to simpler models like the commonly used isotropic color-corrected blackbody emission. We highlight the importance of considering realistic model-atmosphere spectra together with relativistic ray-tracing to obtain accurate predictions. We also insist upon the crucial impact of the star’s rotation on the observables. Finally, we close a controversy that has been ongoing in the literature in the recent years, regarding the validity of the Atm24 code.

CENTRAL ENGINE OF LATE-TIME X-RAY FLARES WITH INTERNAL ORIGIN

ABSTRACT This work focuses on a sample of seven extremely late-time X-ray flares with peak time , among which two flares can be confirmed as the late-time activity of central engine. The main purpose is to investigate the mechanism of such late-time flares based on the internal origin assumption. In the hyper-accreting black hole (BH) scenario, we study the possibility of two well-known mechanisms acting as the central engine to power such X-ray flares, i.e., the neutrino–antineutrino annihilation and the Blandford–Znajek (BZ) process. Our results show that the annihilation luminosity is far below the observational data. Thus, the annihilation mechanism cannot account for such late-time flares. For the BZ process, if the role of outflows is taken into consideration, the inflow mass rate near the horizon will be quite low such that the magnetic field will probably be too weak to power the observed X-ray flares. We therefore argue that, for the late-time flares with internal origin, the central engine is unlikely to be associated with BHs. On the contrary, a fast rotating neutron star with strong bipolar magnetic fields may be responsible for such flares.

A propelling neutron star in the enigmatic Be-star γ Cassiopeia

Abstract The enigmatic X-ray emission from the bright optical star, γ Cassiopeia, is a long-standing problem. γ Cas is known to be a binary system consisting of a Be-type star and a low-mass (M ∼ 1 M⊙) companion of unknown nature orbiting in the Be-disk plane. Here we apply the quasi-spherical accretion theory onto a compact magnetized star and show that if the low-mass companion of γ Cas is a fast spinning neutron star, the key observational signatures of γ Cas are remarkably well reproduced. Direct accretion onto this fast rotating neutron star is impeded by the propeller mechanism. In this case, around the neutron star magnetosphere a hot shell is formed that emits thermal X-rays in qualitative and quantitative agreement with observed properties of the X-ray emission from γ Cas. We suggest that γ Cas and its analogs constitute a new subclass of Be-type X-ray binaries hosting rapidly rotating neutron stars formed in supernova explosions with small kicks. The subsequent evolutionary stage of γ Cas and its analogs should be the X Per-type binaries comprising low-luminosity slowly rotating X-ray pulsars. The model explains the enigmatic X-ray emission from γ Cas, and also establishes evolutionary connections between various types of rotating magnetized neutron stars in Be-binaries.

Effects of the quark-hadron phase transition on highly magnetized neutron stars

The presence of quark-hadron phase transitions in neutron stars can be related to several interesting phenomena. In particular, previous calculations have shown that fast rotating neutron stars, when subjected to a quark-hadron phase transition in their interiors, could give rise to the backbending phenomenon characterized by a spin-up era. In this work, we use an equation of state composed of two phases, containing nucleons (and leptons) and quarks. The hadronic phase is described in a relativistic mean field formalism that takes many-body forces into account, and the quark phase is described by the MIT bag model with a vector interaction. Stationary and axi-symmetric stellar models are obtained in a self-consistent way by solving numerically the Einstein-Maxwell equations by means of a pseudo-spectral method. As a result, we obtain the interesting backbending phenomenon for fast spinning neutron stars. More importantly, we show that a magnetic field, which is assumed to be axi-symmetric and poloidal, can also be enhanced due to the phase transition from normal hadronic matter to quark matter on highly magnetized neutron stars. Therefore, in parallel to the spin-up era, classes of neutron stars endowed with strong magnetic fields may go through a "magnetic-up era" in their lives.

The fate of ultrahigh energy nuclei in the immediate environment of young fast-rotating pulsars

Young, fast-rotating neutron stars are promising candidate sources for the production of ultrahigh energy cosmic rays (UHECRs). The interest in this model has recently been boosted by the latest chemical composition measurements of cosmic rays, that seem to show the presence of a heavy nuclear component at the highest energies. Neutrons stars, with their metal-rich surfaces, are potentially interesting sources of such nuclei, but some open issues remain: 1) is it possible to extract these nuclei from the star's surface? 2) Do the nuclei survive the severe conditions present in the magnetosphere of the neutron star? 3) What happens to the surviving nuclei once they enter the wind that is launched outside the light cylinder? In this paper we address these issues in a quantitative way, proving that for the most reasonable range of neutron star surface temperatures (T<107 K), a large fraction of heavy nuclei survive photo-disintegration losses. These processes, together with curvature losses and acceleration in the star's electric potential, lead to injection of nuclei with a chemical composition that is mixed, even if only iron is extracted from the surface. We show that under certain conditions the chemical composition injected into the wind region is compatible with that required in previous work based on purely phenomenological arguments (typically ∼50% protons, ∼30% CNO and ∼20% Fe), and provides a reasonable explanation of the mass abundance inferred from ultra high energy data.

Fast rotating neutron stars with realistic nuclear matter equation of state

We construct equilibrium configurations of uniformly rotating neutron stars for selected relativistic mean-field nuclear matter equations of state (EOS). We compute in particular the gravitational mass ($M$), equatorial ($R_{\rm eq}$) and polar ($R_{\rm pol}$) radii, eccentricity, angular momentum ($J$), moment of inertia ($I$) and quadrupole moment ($M_2$) of neutron stars stable against mass-shedding and secular axisymmetric instability. By constructing the constant frequency sequence $f=716$ Hz of the fastest observed pulsar, PSR J1748-2446ad, and constraining it to be within the stability region, we obtain a lower mass bound for the pulsar, $M_{\rm min}=[1.2$-$1.4] M_\odot$, for the EOS employed. Moreover we give a fitting formula relating the baryonic mass ($M_b$) and gravitational mass of non-rotating neutron stars, $M_b/M_\odot=M/M_\odot+(13/200)(M/M_\odot)^2$ [or $M/M_\odot=M_b/M_\odot-(1/20)(M_b/M_\odot)^2$], which is independent on the EOS. We also obtain a fitting formula, although not EOS independent, relating the gravitational mass and the angular momentum of neutron stars along the secular axisymmetric instability line for each EOS. We compute the maximum value of the dimensionless angular momentum, $a/M\equiv c J/(G M^2)$ (or "Kerr parameter"), $(a/M)_{\rm max}\approx 0.7$, found to be also independent on the EOS. We compare and contrast then the quadrupole moment of rotating neutron stars with the one predicted by the Kerr exterior solution for the same values of mass and angular momentum. Finally we show that, although the mass quadrupole moment of realistic neutron stars never reaches the Kerr value, the latter is closely approached from above at the maximum mass value, as physically expected from the no-hair theorem. In particular the stiffer the EOS is, the closer the Kerr solution is approached.

I−QRelation for Rapidly Rotating Neutron Stars

We consider a universal relation between moment of inertia and quadrupole moment of arbitrarily fast rotating neutron stars. Recent studies suggest that this relation breaks down for fast rotation. We find that it is still universal among various suggested equations of state for constant values of certain dimensionless parameters characterizing the magnitude of rotation. One of these parameters includes the neutron star radius, leading to a new universal relation expressing the radius through the mass, frequency, and spin parameter. This can become a powerful tool for radius measurements.

Gravitational wave asteroseismology of fast rotating neutron stars with realistic equations of state

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 significantly even if the Cowling approximation is dropped and the full general relativistic case is considered, although the normalization used here(frequencies and damping times in the nonrotating limit) could differ considerably. We also address the inverse problem, i.e. we investigate in detail what kind of observational data is required in order to determine characteristical neutron star parameters. It is shown that masses, radii and rotation rates can be estimated quite accurately using the derived asteroseismology relations. We also compute the instability window for certain models, i.e. the limiting curve in a T-\Omega-plane where the secular Chandrasekhar-Friedman-Schutz(CFS) instability overcomes dissipative effects, and show that some of the modern realistic EoS will lead to a larger instability window compared to all of the polytropic ones presented so far in the literature. Additionally, we calculate the r-mode instability window and compare it with the f-mode-case. The overall results for the instability window suggest that it is vital to take into account oscillations with l=3,4 when considering gravitational wave asteroseismology using the f-mode in rapidly rotating neutron stars, as these modes can become CFS unstable for a much larger range of parameters than pure quadrupolar oscillations.

High-frequency cutoff and change of radio emission mechanism in pulsars

Pulsars are fast rotating neutron stars with a strong magnetic field, that emit over a wide frequency range. In spite of all efforts during the 40 years after the discovery of pulsars, the mechanism of their radio emission so far remains unknown. We propose a new approach to solving this problem for a subset of pulsars with a high-frequency cutoff of the spectrum from the Pushchino catalogue (the “Pushchino” sample). We provide a theoretical explanation of the observed dependence of the high-frequency cutoff on the pulsar period, and we predict the dependence of the cutoff position from the magnetic field. This explanation is based on a new mechanism for electron radio emission in pulsars. Namely, radiation occurs in the inner (polar) gap, when electrons are accelerated in the electric field that is increasing from zero level at the star surface. In this case the acceleration of electrons passes through a maximum and goes to zero when the electron velocity approaches the speed of light. All the radiated power is located within the radio frequency band. The averaging of radiation intensity over the polar cap, with some natural assumptions of the coherence of the radiation, leads to the observed spectra. It also leads to an acceptable estimate of the power of radio emission.

Gravitational wave asteroseismology with fast rotating neutron stars

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 can be used for gravitational wave asteroseismology. The estimation of the damping/growth time is based on the quadrupole formula and our results agree very well with Newtonian ones in the appropriate limit.

Large amplitude behavior of the bulk viscosity of dense matter

We study the bulk viscosity of dense matter, taking into account nonlinear effects that arise in the large amplitude ‘supra-thermal’ region where the deviation of the chemical potentials from chemical equilibrium fulfills . This regime is relevant to unstable modes, such as r-modes, which grow in amplitude until saturated by nonlinear effects. We study the damping due to direct and modified Urca processes in hadronic matter, and due to non-leptonic weak interactions in strange quark matter. We give general results valid for an arbitrary equation of state of dense matter and find that the viscosity can be strongly enhanced by supra-thermal effects. Our study confirms previous results on quark matter and shows that the nonlinear enhancement is even stronger in the case of hadronic matter. Our results can be applied to calculations of the r-mode-induced spin-down of fast-rotating neutron stars, where the spin-down time will depend on the saturation amplitude of the r-mode.

Measurement results from an avalanche amplifying pnCCD for single photon imaging

The company PNSensor and the MPI Semiconductor Laboratory are developing and have produced first prototypes of pnCCDs with an avalanche readout which aim at single photon sensitivity in the visible wavelength range. This resolution is provided by an avalanche diode integrated in the readout chain of every CCD column. The diode features a new topology and can collect signal electrons from the CCDs’ depleted buried channel. The pixel-structure has been derived from pnCCDs and was optimized for lowest leakage current and for compatibility with the avalanche structures. All advantages of the pnCCDs are maintained, including high quantum efficiency (between 80% and 100%), high frame rate (up to 1000 frames/s) and low leakage current. Possible applications are in the field of High Time Resolution Astrophysics (HTRA). There, fast imaging of faint objects in the visible, such as, e.g. close binary stars or fast rotating neutron stars, requires single photon sensitivity and high frame rates. We present results from proof-of-principle tests carried out on first laboratory prototypes of such devices.