Neutron Star Core Research Articles

Hydrodynamical instabilities in the superfluid interior of neutron stars with background flows between the components

The interiors of mature neutron stars are expected to be superfluid. Superfluidity of matter on the microscopic scale can have a number of large scale, potentially observable consequences, as the superfluid component of the star can now flow relative to the `normal' component that is tracked by electromagnetic emission. The most spectacular of such phenomena are pulsar glitches, sudden spin-ups observed in many pulsars. A background flow of a normal-fluid component with respect to the superfluid is also known to lead to a number of instabilities in laboratory superfluids, possibly leading to turbulence and modifying the nature of the mutual friction coupling between the two fluids. In this paper we consider modes of oscillation in the crust and core of a superfluid neutron star, by conducting a plane-wave analysis. We explicitly account for a background flow between the two components (as would be expected in the presence of pinning) and the entrainment, and we consider both standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutual friction. We find that for standard mutual friction there are families of unstable inertial and sound waves both in the case of a counter-flow along the superfluid vortex axis and for counterflow perpendicular to the vortex axis and find that entrainment leads to a quantitative difference between instabilities in the crust and core of the star. For isotropic mutual friction we find no unstable modes, and speculate that instabilities in a straight vortex array may be linked to glitching behaviour, which then ceases until the turbulence has decayed.

Superfluid Phase Transitions and Effects of Thermal Pairing Fluctuations in Asymmetric Nuclear Matter

We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature (T) and density (ρ) with a low proton fraction (Yp ≤ 0.2), which is relevant to the inner crust and outer core of neutron stars. A strong-coupling theory developed for two-component atomic Fermi gases is generalized to the four-component case, and is applied to the system of spin-1/2 neutrons and protons. The phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to k = 2 fm−1 are described by multi-rank separable potentials. We show that the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}}= 1.68 MeV at {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.14}} with ρ0 = 0.17 fm−3. Also, the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} only above {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.70}}(0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{d}}} is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.

Dark matter and bubble nucleation in old neutron stars

We study the probability for nucleation of quark matter droplets in the dense cold cores of old neutron stars induced by the presence of a self-annihilating dark matter component, $\chi$. Using a parameterized form of the equation of state for hadronic and quark phases of ordinary matter, we explore the thermodynamic conditions under which droplet formation is facilitated by the energy injection from $\chi$ self-annihilations. We obtain the droplet nucleation time as a function of the dark matter candidate mass, $m_\chi$. We discuss further observational consequences.

Bulk viscosity in neutron stars with hyperon cores

It is well-known that r-mode oscillations of rotating neutron stars may be unstable with respect to the gravitational wave emission. It is highly unlikely to observe a neutron star with the parameters within the instability window, a domain where this instability is not suppressed. But if one adopts the `minimal' (nucleonic) composition of the stellar interior, a lot of observed stars appear to be within the r-mode instability window. One of the possible solutions to this problem is to account for hyperons in the neutron star core. The presence of hyperons allows for a set of powerful (lepton-free) non-equilibrium weak processes, which increase the bulk viscosity, and thus suppress the r-mode instability. Existing calculations of the instability windows for hyperon NSs generally use reaction rates calculated for the $\Sigma^-\Lambda$ hyperonic composition via the contact $W$ boson exchange interaction. In contrast, here we employ hyperonic equations of state where the $\Lambda$ and $\Xi^-$ are the first hyperons to appear (the $\Sigma^-$'s, if they are present, appear at much larger densities), and consider the meson exchange channel, which is more effective for the lepton-free weak processes. We calculate the bulk viscosity for the non-paired $npe\mu\Lambda\Xi^-$ matter using the meson exchange weak interaction. A number of viscosity-generating non-equilibrium processes is considered (some of them for the first time in the neutron-star context). The calculated reaction rates and bulk viscosity are approximated by simple analytic formulas, easy-to-use in applications. Applying our results to calculation of the instability window, we argue that accounting for hyperons may be a viable solution to the r-mode problem.

Nucleosynthesis Constraints on the Energy Growth Timescale of a Core-collapse Supernova Explosion

Abstract Details of the explosion mechanism of core-collapse supernovae (CCSNe) are not yet fully understood. There are an increasing number of numerical examples by ab initio core-collapse simulations leading to an explosion. Most, if not all, of the ab initio core-collapse simulations represent a “slow” explosion in which the observed explosion energy (∼1051 erg) is reached in a timescale of ≳1 s. It is, however, unclear whether such a slow explosion is consistent with observations. In this work, by performing nuclear reaction network calculations for a range of the explosion timescale t grow, from the rapid to slow models, we aim at providing nucleosynthetic diagnostics on the explosion timescale. We employ one-dimensional hydrodynamic and nucleosynthesis simulations above the proto–neutron star core, by parameterizing the nature of the explosion mechanism by t grow. The results are then compared to various observational constraints: the masses of 56Ni derived for typical CCSNe, the masses of 57Ni and 44Ti observed for SN 1987A, and the abundance patterns observed in extremely metal-poor stars. We find that these observational constraints are consistent with the “rapid” explosion (t grow ≲ 250 ms), and especially the best match is found for a nearly instantaneous explosion (t grow ≲ 50 ms). Our finding places a strong constraint on the explosion mechanism; the slow mechanism (t grow ≳ 1000 ms) would not satisfy these constraints, and the ab initio simulations will need to realize a rapid explosion.

R-mode stabilization in neutron stars with hyperon cores

R-mode oscillations of neutron stars are known to be generally unstable with respect to the emission of gravitational waves. This instability can be suppressed by dissipative processes in the neutron star core. The standard minimal nucleonic model of the core cannot stabilize r-modes for many observed neutron stars, at the same time the probability to observe them unstable should be very low. One of the solutions to this problem is to account for possible presence of hyperons in the stellar core. Hyperons strongly enhance bulk viscosity in the core, which effectively suppresses the r-mode instability. We revisit the bulk viscosity calculations in the non-superfluid hyperon matter and briefly discuss the effect of baryon superfluidity. Our results suggest that the hyperon solution to the r-mode problem is more promising than it was thought before.

Glitches in neutron stars with magnetically decoupled core

The magnetically decoupled core model was proposed earlier as a way to solve the problem of inconsistency between the neutron star long-period precession and superfluid vortex pinning which is the base of most theories of pulsar glitches. It was assumed that the pinning takes place in the region of the neutron star core which, being magnetically decoupled, can rotate relative to the crust. In present work some aspects of the glitch spin-up stage in the framework of the proposed model are discussed. Estimated spin-up time-scales are compared with observational data. According to the estimations the Crab pulsar is likely posses a magnetically decoupling core region, while the results for the Vela pulsar is more controversial.

Searching for three-nucleon short-range correlations

Three nucleon short range correlations~(SRCs) are one of the most elusive structures in nuclei. Their observation and the subsequent study of their internal makeup will have a significant impact on our understanding of the dynamics of super-dense nuclear matter which exists at the cores of neutron stars. We discuss the kinematic conditions and observables that are most favorable for probing 3N-SRCs in inclusive electro-nuclear processes and make a prediction for a quadratic dependence of the probabilities of finding a nucleon in 2N- and 3N- SRCs. We demonstrate that this prediction is consistent with the limited high energy experimental data available, suggesting that we have observed, for the first time, 3N-SRCs in electro-nuclear processes. Our analysis enables us to extract $a_3(A,Z)$, the probability of finding 3N-SRCs in nuclei relative to the A=3 system.

Signatures for quark matter from multi-messenger observations

We review the prospects for detecting quark matter in neutron star cores. We survey the proposed signatures and emphasize the importance of data from neutron star mergers, which provide access to dynamical properties that operate on short timescales that are not probed by most other neutron star observables.

XMM-Newton Detection and Spectrum of the Second Fastest Spinning Pulsar PSR J0952−0607

Abstract With a spin frequency of 707 Hz, PSR J0952−0607 is the second fastest spinning pulsar known. It was discovered in radio by LOFAR in 2017 at an estimated distance of either 0.97 or 1.74 kpc and has a low-mass companion with a 6.42 hr orbital period. We report the discovery of the X-ray counterpart of PSR J0952−0607 using XMM-Newton. The X-ray spectra can be well-fit by a single power law (PL) model (Γ ≈ 2.5) or by a thermal plus PL model ( and Γ ≈ 1.4). We do not detect evidence of variability, such as that due to orbital modulation from pulsar wind and companion star interaction. Because of its fast spin rate, PSR J0952−0607 is a crucial source for understanding the r-mode instability, which can be an effective mechanism for producing gravitational waves. Using the high end of our measured surface temperature, we infer a neutron star core temperature of ∼107 K, which places PSR J0952−0607 within the window for the r-mode to be unstable unless an effect such as superfluid mutual friction damps the fluid oscillation. The measured luminosity limits the dimensionless r-mode amplitude to be less than ∼1 × 10−9.

Simulating Binary Neutron Stars with Hybrid Equation of States: Gravitational Waves, Electromagnetic Signatures and Challenges for Numerical Relativity

The gravitational wave and electromagnetic signatures connected to the merger of two neutron stars allow us to test the nature of matter at supranuclear densities. Since the Equation of State governing the interior of neutron stars is only loosely constrained, there is even the possibility that strange quark matter exists inside the core of neutron stars. We investigate how strange quark matter cores affect the binary neutron star coalescence by performing numerical relativity simulations. Interestingly, the strong phase transition can cause a reduction of the convergence order of the numerical schemes to first order if the numerical resolution is not high enough. Therefore, an additional challenge is added in producing high-quality gravitational wave templates for Equation of States with a strong phase transition. Focusing on one particular configuration of an equal mass configuration consistent with GW170817, we compute and discuss the associated gravitational wave signal and some of the electromagnetic counterparts connected to the merger of the two stars. We find that existing waveform approximants employed for the analysis of GW170817 allow describing this kind of systems within the numerical uncertainties, which, however, are several times larger than for pure hadronic Equation of States, which means that even higher resolutions have been employed for an accurate gravitational wave model comparison. We also show that for the chosen Equation of State, quasi-universal relations describing the gravitational wave emission after the moment of merger seem to hold and that the electromagnetic signatures connected to our chosen setup would not be bright enough to explain the kilonova associated to GW170817.

Thermodynamics conditions of matter in neutron star mergers

Matter in neutron star collisions can reach densities up to few times the nuclear saturation threshold and temperatures up to one hundred MeV. Understanding the structure and composition of such matter requires many-body nonperturbative calculations that are currently highly uncertain.Unique constraints on the neutron star matter are provided by gravitational-wave observations aided by numerical relativity simulations. In this work, we explore the thermodynamical conditions of matter and radiation along the merger dynamics. We consider 3 microphysical equation of state models and numerical relativity simulations including an approximate neutrino transport scheme. The neutron star cores collision and their multiple centrifugal bounces heat the initially cold matter to several tens of MeV. Streams of hot matter with initial densities $\sim1-2\rho_0$ move outwards and cool due to decompression and neutrino emission. The merger can result in a neutron star remnant with densities up to $3-5\rho_0$ and temperatures $\sim 50$~MeV. The highest temperatures are confined in an approximately spherical annulus at densities $\sim\rho_0$. Such temperatures favour positron-neutron capture at densities $\sim\rho_0$, thus leading to a neutrino emission dominated by electron antineutrinos. We study the impact of trapped neutrinos on the remnant matter's pressure, electron fraction and temperature and find that it has a negligible effect. Disks around neutron star or black hole remnant are neutron rich and not isentropic, but they differ in size, entropy and lepton fraction depending on the nature of the central object. In presence of a black hole, disks are smaller and mostly transparent to neutrinos; in presence of a massive neutron star, they are more massive, geometrically and optically thick.

Hybrid neutron stars in the Thomas-Fermi theory

The baryon-quark phase transition is studied for the equation of state (EOS) of neutron star (NS) matter. The Thomas-Fermi (TF) approximation is employed in a semiclassical mean-field (MF) model for the EOS of baryonic matter including hyperons. The EOS of quark matter is also extracted from the Nambu--Jona-Lasinio (NJL) model. The phase transition from baryons to quarks is considered in the NS structure under the Maxwell and Gibbs constructions. Our findings for the maximum mass of NSs, as compared with the almost $2{M}_{\ensuremath{\bigodot}}$ pulsars $\mathrm{J}1614\ensuremath{-}2230$ and $\mathrm{J}0348+0432$, indicate that a region of baryon-quark mixed phase can exist in the inner core of NSs, while the existence of a pure phase is not allowed.

Phases of Hadron-Quark Matter in (Proto) Neutron Stars

In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size of this phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu–Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov–Nambu–Jona-Lasinio model which includes the ’t Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter.

Dark matter heating vs. rotochemical heating in old neutron stars

Dark matter (DM) particles in the Universe accumulate in neutron stars (NSs) through their interactions with ordinary matter. It has been known that their annihilation inside the NS core causes late-time heating, with which the surface temperature becomes a constant value of Ts≃(2−3)×103 K for the NS age t≳106−7 years. This conclusion is, however, drawn based on the assumption that the beta equilibrium is maintained in NSs throughout their life, which turns out to be invalid for rotating pulsars. The slowdown in the pulsar rotation drives the NS matter out of beta equilibrium, and the resultant imbalance in chemical potentials induces late-time heating, dubbed as rotochemical heating. This effect can heat a NS up to Ts≃106 K for t≃106−7 years. In fact, recent observations found several old NSs whose surface temperature is much higher than the prediction of the standard cooling scenario and is consistent with the rotochemical heating. Motivated by these observations, in this letter, we reevaluate the significance of the DM heating in NSs, including the effect of the rotochemical heating. We then show that the signature of DM heating can still be detected in old ordinary pulsars, while it is concealed by the rotochemical heating for old millisecond pulsars. To confirm the evidence for the DM heating, however, it is necessary to improve our knowledge on nucleon pairing gaps as well as to evaluate the initial period of the pulsars accurately. In any cases, a discovery of a very cold NS can give a robust constraint on the DM heating, and thus on DM models. To demonstrate this, as an example, we also discuss the case that the DM is the neutral component of an electroweak multiplet, and show that an observation of a NS with Ts≲103 K imposes a stringent constraint on such a DM candidate.

Role of Δs in determining the properties of neutron stars in parameterized hydrostatic equilibrium

The possible existence of [Formula: see text] resonances is inspected in the cold dense matter of neutron star (NS) core in the presence of hyperons. The diverse effects of variation in [Formula: see text] mass on their formation and the equation of state (EoS) are studied in this work with an effective chiral model and the resultant NS properties are calculated with the help of parameterized Tolman–Oppenheimer–Volkoff (PTOV) equations to bring out the two important features of pressure in the context of massive NSs. The [Formula: see text] puzzle is re-explored and resolved taking into account the concept of modified/parametrized inertial pressure and self-gravity in case of massive pulsars like PSR J1614−2230 and PSR J0348-0432. It is seen that although the presence of exotic matter like the hyperons and [Formula: see text] softens the EoS considerably, their presence in massive NSs can be successfully explained with the theory of parametrized hydrostatic equilibrium conditions. The results of this work also satisfy the constraints on [Formula: see text] and [Formula: see text] from the gravitational wave (GW170817) detection of binary NS merger. The constraint on baryonic mass from PSR J0737-3039 is also satisfied with the solutions of the PTOV equations for all the [Formula: see text] masses considered.

Confronting gravitational-wave observations with modern nuclear physics constraints

Multi-messenger observations of neutron star (NS) mergers have the potential to revolutionize nuclear astrophysics. They will improve our understanding of nucleosynthesis, provide insights about the equation of state (EOS) of strongly-interacting matter at high densities, and enable tests of the theory of gravity and of dark matter. Here, we focus on the EOS, where both gravitational waves (GWs) from neutron-star mergers and X-ray observations from space-based detectors such as NICER will provide more stringent constraints on the structure of neutron stars. Furthermore, recent advances in nuclear theory have enabled reliable calculations of the EOS at low densities using effective field theory based Hamiltonians and advanced techniques to solve the quantum many-body problem. In this paper, we address how the first observation of GWs from GW170817 can be combined with modern calculations of the EOS to extract useful insights about the EOS of matter encountered inside neutron stars. We analyze the impact of various uncertainties, the role of phase transitions in the NS core, and discuss how future observations will improve our understanding of dense matter.

Permanent mean spin source of the chiral magnetic effect in neutron stars

We suggest the generalization of the Anomalous Magneto-Hydro-Dynamics (AMHD) in the chiral plasma of a neutron star (NS) accounting for the mean spin in the ultrarelativistic degenerate electron gas within the magnetized NS core as a continuing source of the chiral magnetic effect. Using the mean field dynamo model generalized in AMHD, one can obtain the growth of a seed magnetic field up to 1018 G for an old non-superfluid NS at its neutrino cooling era t < 106 yr, while neglecting any matter turbulence within its core and assuming the rigid NS rotation. The application of the suggested approach to the evolution of magnetic fields observed in magnetars, B∼ 1015 G, should be self-consistent with all approximations used in the suggested laminar dynamo, at least, up to the jumps of growing fields.

Analytical derivation of expressions for the specific heat of superfluid Fermi liquids with anisotropic spin-triplet p-wave pairing at finite temperatures

Analytical expressions for the specific heat of superfluid Fermi liquids (SFLs) with anisotropic spin-triplet p-wave pairing of the 3He-A type have been obtained based on a generalised Fermi-liquid approach both at the low temperatures of 0 &amp;lt; T ≪Tc0 (n) and near the temperature of the phase transition [Tc0 (n)] from a normal to a superfluid phase in the absence of a magnetic field. Apart from liquid 3He-A, we also study dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing (similar to 3He-A) at subnuclear (n &amp;lt; n0, where n0 = 0.17 fm–3 is the nuclear density) and supernuclear densities (n &amp;gt; n0) in view of generalised Skyrme forces (with additional terms depending on the density n). At 0 &amp;lt; T ≪Tc0 (n), we have obtained an asymptotic expansion for the specific heat CSNM(SFL)(T,n), in which, apart from the main term ∼ T 3 (known for 3He-A in the limit of T → 0) there is an additional correction term (∼ T5), which may reach several percent of the contribution from the main term to the decomposition of the specific heat of SNM (or SFLs). An analytical formula has also been derived for calculating the specific heat CSNM(SFL)(T,n) at temperatures near Tc0(n). The expressions obtained for the CSNM(T,n) functions (valid for an arbitrary parametrisation of the effective Skyrme interaction in neutron matter) have been defined for SNM with the generalised BSk21 parametrisation of Skyrme forces. In addition, dependency graphs were plotted for the specific heat CBSk21(t, y) in the reduced temperature range of 0 &amp;lt; t ≡ T/Tc0(n) ≪ 1 and at t ≲ 1 for dense SNM (at 0.1 ≤ y ≡ n/n0 ≤ 1.7). These results may be of interest for neutron star physics in connection with neutron star cooling (in the presence of neutron superfluidity with anisotropic spin-triplet p-wave Cooper pairing in the outer part of dense liquid neutron star cores).

Influence of the interactions of scalar mesons on the behavior of the symmetry energy

Symmetry energy behavior of scalar mesons interactions is analyzed within the framework of the standard relativistic mean field model. Whereas the presence of the $\delta$ meson itself makes the symmetry energy stiffer, the crossing term $\delta\textrm{-}\sigma$ allows its slope to decrease to the suggested experimental value. Moreover, such controlling of the symmetry energy does not significantly affect the stiffness of the equation of state and acceptable neutron star masses result. Interestingly, for the most plausible value of the symmetry energy slope, the phase transition occurs in the neutron star core.