A neutron star contains regions with particles which exhibit magnetic moments, which, in turn, generate respective magnetizations. By magnetoelastic interactions between the magnetization and the matter there arises a magnetostriction. The magnetostriction changes the mass density of the neutron star and hence its inertia tensor, and as a result it changes the rotation frequency of the star. We also sketch how the calculation of the magnetostriction in the different inner regions of the neutron star has to proceed, and which parameter inputs are needed.
In recent years, accreting neutron stars (NSs) in X-ray binary systems in supernova remnants have been discovered. They are a puzzle for the standard magneto-rotational evolution of NSs, as their age ($\lesssim 10^5$ years) is much less than expected duration of the preceding Ejector and Propeller stages. To explain such systems, we consider rotational evolution of NSs with fallback accretion and asymmetry in direct/backward transitions between Ejector and Propeller stages. It is shown that at certain values of the initial period and the magnetic field, a young neutron star may not enter the E…
After a brief review of population synthesis of close-by cooling neutron stars, I focus on the interpretation of dichotomy of spin periods of near-by coolers. The existence of two well separated groups -- short period ($\sim$0.1-0.3 s) radio pulsars and long period ($\sim$3-10 s) radio quiet sources, aka the Magnificent seven, -- can not be easily explained in unified models developed recently (Popov et al. 2010, Gull{ó}n et al. 2014). I speculate that the most natural solution of the problem can be in bimodal initial magnetic field distribution related to the existence of an additional mechan…
The maximum mass and rotational kinetic energy of rapidly rotating neutron stars
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学项目(iTHEMS)）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
The limiting rotational frequency of neutron stars may be determined by the strength of their crusts. As a star spins up from accretion, centrifugal forces will cause the crust to fail. If the crust breaks unevenly, a rotating mass quadrupole moment will radiate gravitational waves (GW). This radiation can prevent further spin up and may be a promising source for continuous GW searches. We calculate that for a breaking strain (strength) of neutron star crust that is consistent with molecular dynamics simulations, the crust may fail at rotational frequencies in agreement with observations.
We calculate the rotational broadening in the observed thermal spectra of neutron stars spinning at moderate rates in the Hartle-Thorne approximation. These calculations accurately account for the effects of the second-order Doppler boosts as well as for the oblate shapes and the quadrupole moments of the neutron stars. We find that fitting the spectra and inferring the bolometric fluxes under the assumption that a star is not rotating causes an underestimate of the inferred fluxes and, thus, radii. The correction depends on the stellar spin, radius, and observer's inclination. For a 10 km neu…
We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with $P_0\lesssim 0.5$ s can fit the data, and that if the a…
In continuation of our earlier work on the long-term evolution of the so-called high--B radio pulsars (HBRPs) with measured braking indices, we have investigated the long-term evolution of the remaining five HBRPs for which braking indices have not been measured yet. This completes our source-by-source analyses of HBRPs in the fallback disc model that was also applied earlier to anomalous X-ray pulsars (AXPs), soft gamma repeaters (SGRs), and dim isolated neutron stars (XDINs). Our results show that the X-ray luminosities and the rotational properties of these rather different neutron star pop…
We present the nucleosynthesis of magneto-rotational supernovae (MR-SNe) including neutrino-driven and magneto-rotational-driven ejecta based, for the first time, on 2D simulations with accurate neutrino transport. The models analysed here have different rotation and magnetic fields, allowing us to explore the impact of these two key ingredients. The accurate neutrino transport of the simulations is critical to analyse the slightly neutron-rich and proton-rich ejecta that are similar to the, also neutrino-driven, ejecta in standard supernovae. In the model with strong magnetic field, the r-pro…
The coupling between the angular momentum of a compact object and an external tidal field gives rise to the "rotational" tidal Love numbers, which affect the tidal deformability of a spinning self-gravitating body and enter the gravitational waveform of a binary inspiral at high post-Newtonian order. We provide numerical evidence for a surprising "hidden" symmetry among the rotational tidal Love numbers with opposite parities, which are associated to perturbations belonging to separate sectors. This symmetry, whose existence had been suggested on the basis of a Lagrangian description of the ti…
We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-star configurations (the so-called high-mass twins). We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family)…
Merging neutron stars are expected to produce hot, metastable remnants in rapid differential rotation, which subsequently cool and evolve into rigidly rotating neutron stars or collapse to black holes. Studying this metastable phase and its further evolution is essential for the prediction and interpretation of the electromagnetic, neutrino, and gravitational signals from such a merger. In this work, we model binary neutron star merger remnants and propose new rotation and thermal laws that describe post-merger remnants. Our framework is capable to reproduce quasi-equilibrium configurations fo…
Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include $X$-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, si…
Determining the differential-rotation law of compact stellar objects produced in binary neutron stars mergers or core-collapse supernovae is an old problem in relativistic astrophysics. Addressing this problem is important because it impacts directly on the maximum mass these objects can attain and hence on the threshold to black-hole formation under realistic conditions. Using the results from a large number of numerical simulations in full general relativity of binary neutron star mergers described with various equations of state and masses, we study the rotational properties of the resultin…
If a magnetar interior $B$-field exceeds $10^{15}$~G, it will unpair the proton superconductor in the stellar core by inducing diamagnetic currents that destroy the Cooper pair coherence. Then, the $P$-wave neutron superfluid in these non-superconducting regions will couple to the stellar plasma by scattering of protons off the quasiparticles that are confined in the cores of neutron vortices by the strong (nuclear) force. The dynamical timescales associated with this interaction span from several minutes at the crust-core interface to a few seconds in the deep core. We show that (a) the rapid…
Kochi University（高知大学）；Indian Institute of Science（印度科学学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；University of Tübingen（蒂宾根大学）
The effects of pinning between fluxoids and vortices in the core of a neutron star, on the dynamics of the core neutron superfluid are considered. The pinning impedes, but does not absolutely block, any radial as well as {\em azimuthal} motion of the neutron vortices with respect to the lattice of fluxoids. The time scale for the coupling of rotation of the core superfluid to the rest of the star is calculated, allowing for the effect of the finite frictional force on the neutron vortices due to their pinning with the fluxoids. This turns out to be the dominant mechanism for the coupling of th…
The strong magnetic field of neutron stars is intimately coupled to the observed temperature and spectral properties, as well as to the observed timing properties (distribution of spin periods and period derivatives). Thus, a proper theoretical and numerical study of the magnetic field evolution equations, supplemented with detailed calculations of microphysical properties (heat and electrical conductivity, neutrino emission rates) is crucial to understand how the strength and topology of the magnetic field vary as a function of age, which in turn is the key to decipher the physical processes …
Observations of gravitational waves from inspiralling neutron star binaries---such as GW170817---can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers." The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers $\mathfrak{f}^\text{o}$ and $\…
The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, $B_{\mathrm …
The optical excess in the spectra of dim isolated neutron stars (XDINs) is a significant fraction of their rotational energy loss-rate. This is strikingly different from the situation in isolated radio pulsars. We investigate this problem in the framework of the fallback disc model. The optical spectra can be powered by magnetic stresses on the innermost disc matter, as the energy dissipated is emitted as blackbody radiation mainly from the inner rim of the disc. In the fallback disc model, XDINs are the sources evolving in the propeller phase with similar torque mechanisms. In this this model…
We interpret recent observations of high-to-low frequency drifting features in the spectra of the repeating FRBs as evidence of sharply changing plasma properties in the emission region, presumably the neutron stars magnetospheres. The drifts are then FRBs' analogues of radius-to-frequency mapping in pulsars and Solar type-III radio burst (but not in a sense of a particular emission mechanism). The drifts rates of $\sim 100$ MHz ms$^{-1}$ at frequencies $\sim$ GHz translate to physical size of $\sim {c ω}/{\dotω} \sim$ few $\times 10^8$ cm, matching the hypothesis of the FRB origin in the magn…
The rotational properties and X-ray luminosity of PSR J0726-2612 are close to those of dim isolated neutron stars (XDINs). It was proposed that the source could be the first XDIN with observable pulsed radio emission. We have investigated the long-term evolution of the source to test this possibility in the fallback disc model. Reasonable model curves that can account for the evolution of PSR J0726-2612 consistently with its radio pulsar property are similar to those of high-B radio pulsars with dipole field strength $B_0 \sim$ a few $\times 10^{12}~$G at the pole of the star. In the same mode…
In this Letter we re-examine the idea that gravitational waves are required as a braking mechanism to explain the observed maximum spin-frequency of neutron stars. We show that for millisecond X-ray pulsars, the existence of spin equilibrium as set by the disk/magnetosphere interaction is sufficient to explain the observations. We show as well that no clear correlation exists between the neutron star magnetic field B and the X-ray outburst luminosity Lx when considering an enlarged sample size of millisecond X-ray pulsars.
Recently, several accreting neutron stars (NSs) in X-ray binary systems inside supernova remnants have been discovered. They represent a puzzle for the standard magneto-rotational evolution of NSs, as their ages ($\lesssim 10^5$ years) are much shorter than the expected duration of Ejector and Propeller stages preceding the onset of wind accretion. To explain appearance of such systems, we consider rotational evolution of NSs with early fallback accretion and asymmetry in forward/backward transitions between Ejector and Propeller stages (so-called hysteresis effect proposed by V. Shvartsman in…
We have investigated the critical conditions required for a steady propeller effect for magnetized neutron stars with optically thick, geometrically thin accretion disks. We have shown through simple analytical calculations that a steady-state propeller mechanism cannot be sustained at an inner disk radius where the viscous and magnetic stresses are balanced. The radius calculated by equating these stresses is usually found to be close to the conventional Alfven radius for spherical accretion, r_A. Our results show that: (1) a steady propeller phase can be established with a maximum inner disk…
The observational properties of Soft Gamma Repeaters and Ano\-malous X-ray Pulsars (SGR/AXP) indicate to necessity of the energy source different from a rotational energy of a neutron star. The model, where the source of the energy is connected with a magnetic field dissipation in a highly magnetized neutron star (magnetar) is analyzed. Some observational inconsistencies are indicated for this interpretation. The alternative energy source, connected with the nuclear energy of superheavy nuclei stored in the nonequilibrium layer of low mass neutron star is discussed.
The unknown equation of state (EoS) of neutron stars (NSs) is puzzling because of rich non-perturbative effects of strong interaction there. A method to constrain the EoS by using the detected X-ray plateaus of gamma-ray bursts (GRBs) is proposed in this paper. Observations show some GRB X-ray plateaus may be powered by strongly magnetized millisecond NSs. The properties of these NSs should then satisfy: (i) the spin-down luminosity of these NSs should be brighter than the observed luminosity of the X-ray plateaus; (ii) the total rotational energy of these NSs should be larger than the total e…
Pulsar glitches offer an insight into the dynamics of superfluids in the high density interior of a neutron star. To model these phenomena, however, one needs to have an understanding of the dynamics of a turbulent array of superfluid vortices moving through a pinning lattice. In this paper we develop a theoretical approach to describe vortex mediated mutual friction in a pinned, turbulent and rotating superfluid. Our model is then applied to the study of the post glitch rotational evolution in the Vela pulsar and in PSR J0537-6910. We show that in both cases a turbulent model fits the evoluti…
The superfluid and superconducting core of a cold rotating neutron star is expected to be threaded by a tremendous number of neutron quantised vortices and proton fluxoids. Their interactions are unavoidable and may have important astrophysical implications. In this paper, the various contributions to the force acting on a single vortex to which fluxoids are pinned are clarified. The general expression of the force is derived by applying the variational multifluid formalism developed by Carter and collaborators. Pinning to fluxoids leads to an additional Magnus type force due to proton circula…
In this work, we employ the dark matter equations of state (DMEOSs) obtained from the rotational curves of galaxies as well as the fermionic DMEOS with m = 1.0 GeV to study the structure of darkmatter admixed neutron stars (DMANSs). Applying the equation of state in the Skyrme framework for the neutron matter (NM), we calculate the mass-radius relation for different DMANSs with various DMEOSs and central pressure of dark matter (DM) to NM ratios. Our results show that for some DMEOSs, the mass-radius relations are in agreement with new observations, e.g. EXO 1745-248, 4U 1608-52, and 4U 1820-3…
Magnetic, thermal and rotational evolution of isolated neutron stars
Departament de Física Universitat d’Alacant（阿利坎特大学物理系）；Institut de Ciències de I’Espai (ICE-CSIC)（空间科学研究所（ICE-CSIC））；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所（IEEC））
Pulsars are rotating neutron stars that are seen to slow down, and the spin-down rate is thought to be due to magnetic dipole radiation. This leads to a prediction for the braking index n, which is a combination of spin period and its first and second time derivatives. However, all observed values of n are below the predicted value of 3. Here we provide a simple model that can explain the rotational evolution of young pulsars, including the n=2.51 of the 958-year-old pulsar in the Crab nebula. The model is based on a decrease in effective moment of inertia due to an increase in the fraction of…
The 2016 Vela glitch observed by the Mt Pleasant radio telescope provides the first opportunity to study pulse-to-pulse dynamics of a pulsar glitch, opening up new possibilities to study the neutron star's interior. We fit models of the star's rotation frequency to the pulsar data, and present three new results. First, we constrain the glitch rise time to less than 12.6s with 90% confidence, almost three times shorter than the previous best constraint. Second, we find definitive evidence for a rotational-frequency overshoot and fast relaxation following the glitch. Third, we find evidence for …
The gravitational wave signal from a binary neutron star merger carries the imprint of the deformability properties of the coalescing bodies, and then of the equation of state of neutron stars. In current models of the waveforms emitted in these events, the contribution of tidal deformation is encoded in a set of parameters, the tidal Love numbers. More refined models include tidal-rotation couplings, described by an additional set of parameters, the rotational tidal Love numbers, which appear in the waveform at $6.5$ post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, we…
The kHz QPOs observed in a neutron star low mass X-ray binary are likely to be produced in the innermost regions of accretion disk around the neutron star. The rotational dynamics of the inner disk can be characterized by the presence of either sub-Keplerian or super-Keplerian accretion flow depending on the relative fastness of the neutron spin as compared to the Keplerian frequency at the inner disk radius. Within the magnetosphere-disk interaction model, the frequency difference between the two kHz QPOs observed in a given source can be estimated to be slightly higher than or nearly around …
By extending our recent framework to describe the tidal deformations of a spinning compact object, we compute for the first time the tidal Love numbers of a spinning neutron star to linear order in the angular momentum. The spin of the object introduces couplings between electric and magnetic distortions and new classes of spin-induced ("rotational") tidal Love numbers emerge. We focus on stationary tidal fields, which induce axisymmetric perturbations. We present the perturbation equations for both electric-led and magnetic-led rotational Love numbers for generic multipoles and explicitly sol…
The location of the cutoff in the gravitational-wave spectrum of black hole-neutron star mergers is correlated strongly with the neutron-star radius for the case that the neutron star is disrupted by the black hole during the merger. However, the modulation which appears in the spectrum due to the mode mixing makes it difficult to measure the cutoff frequency if gravitational waves are observed from inclined direction or the binary is precessing. In this letter, we show that the cutoff frequency can be measured even in such situations with a method we have recently proposed to reconstruct the …
A $Z_1^2$ framework for rotational-parameter estimation and uncertainty quantification in high-energy pulsars
Homi Bhabha Center for Science Education, Tata Institute of Fundamental Research（塔塔基础研究所霍米·巴巴科学教育中心）；St. Xavier’s College（圣泽维尔学院）；Department of Physics, University of Mumbai（孟买大学物理系）；Center for Basic Sciences at Pt. Ravishankar Shukla University（Pt. Ravishankar Shukla大学基础科学中心）；Indian Institute of Science Education and Research Bhopal（印度科学教育与研究学院博帕尔分校）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；USRA STI（美国大学空间研究协会STI）
We study electroweakly interacting particles in rotating matter. The existence of the electric current along the axis of the matter rotation is predicted in this system. This new galvano-rotational effect is caused by the parity violating interaction between massless charged particles in the rotating matter. We start with the exact solution of the Dirac equation for a fermion involved in the electroweak interaction in the rotating frame. This equation includes the noninertial effects. Then, using the obtained solution, we derive the induced electric current which turns out to flow along the ro…
Neutron stars spinning at moderate rates (~300-600Hz) become oblate in shape and acquire a nonzero quadrupole moment. In this paper, we calculate profiles of atomic features from such neutron stars using a ray-tracing algorithm in the Hartle-Thorne approximation. We show that line profiles acquire cores that are much narrower than the widths expected from pure Doppler effects for a large range of observer inclinations. As a result, the effects of both the oblateness and the quadrupole moments of neutron stars need to be taken into account when aiming to measure neutron star radii from rotation…
Superluminous supernovae (SLSNe) have been suggested to be powered by strongly magnetized, rapidly rotating neutron stars which are often called magnetars. In this process, rotational energy of the magnetar is radiated via magnetic dipole radiation and heats the supernova ejecta. However, if magnetars are highly distorted in their geometric shape, rotational energy is mainly lost as gravitational wave radiation and thus such magnetars cannot power SLSNe. By simply comparing electromagnetic and gravitational wave emission timescales, we constrain upper limits to the ellipticity of magnetars by …
Using the energy variational method of magneto-solid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro's form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfvén mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux durin…
The condensation of neutrons into a 3P2 superfluid phase occurs at densities relevant for the interior of neutron stars. The triplet pairing breaks rotational symmetry spontaneously and leads to the existence of gapless modes (angulons) that are relevant for many transport coefficients and to the star's cooling properties. We derive the leading terms of the low energy effective field theory, including the leading coupling to electroweak currents, valid for a variety of possible 3P2 phases.
Within a minimum model for neutron stars consisting of nucleons, electrons and muons at $β$-equilibrium using about a dozen Equation of States (EOSs) from microscopic nuclear many-body theories and 40,000 EOSs randomly generated using an explicitly isospin-dependent parametric EOS model for high-density neutron-rich nucleonic matter within its currently known uncertainty range, we study correlations among the f-mode frequency, its damping time and the tidal deformability as well as the compactness of neutron stars. Except for quark stars, both the f-mode frequency and damping time of canonical…
