Neutron Star Core Research Articles

First-order phase transitions in the cores of neutron stars

First-order phase transitions in the cores of neutron stars

Impact of the stiffness of equation of state on saturation properties of asymmetric nuclear matter and Urca cooling in neutron stars

Abstract We consider nuclear equation of state (EoS) based on the semi-realistic M3Y-Paris and M3Y-Reid effective nucleon-nucleon (NN) interactions to assess the influence of the stiffness of the isospin-asymmetric nuclear matter (ANM) on its isoscalar and isovector saturation properties, and on the β-stable proton fraction in neutron star (NS) matter. Two parameterizations schemes of the CDM3Y isovector density dependence of the NN interaction are adopted, one is scaled to the isoscalar density dependence and the other (IVF1) is developed independently of it. We found that the stiffer EoS yields larger binding saturation density that decreases with the isospin asymmetry (I), and slightly decreases the maximum asymmetry ( I max ) reached for bound ANM. The density-slope (L) of the symmetry energy is found to correlate directly with the stiffness of ANM, meanwhile the symmetry-energy curvature (K sym ) and the quadratic isovector incompressibility coefficient (K τ ) are found to correlate with it inversely. We found also that the stiffer EoS indicates larger neutron-rich npe μ NS matter under β-equilibrium. Only the CDM3Y-Paris EoSs of isoscalar incompressibility K 0 up to 270 MeV and that of CDM3Y-Reid with K 0 = 200 MeV indicate allowed direct Urca (DU) cooling process in β-stable NS matter, at densities greater than 3.5 ρ 0, based on the IVF1 density dependence. The stiffer EoS proposes a narrower density range for DU process in NS. According to the considered Paris (Reid) forces, muons can emerge in cold β-stable npe matter at ρ ≥ 0.85 ρ 0(0.79 ρ 0), which slightly decreases both the neutron richness at NS core and the DU threshold density.

Magnetic coupling through flux branching of adjacent type-I and -II superconductors in a neutron star

ABSTRACT The inner and outer cores of neutron stars are believed to contain type-I and -II proton superconductors, respectively. The type-I superconductor exists in an intermediate state, comprising macroscopic flux-free and flux-containing regions, while the type-II superconductor is flux-free, except for microscopic, quantized flux tubes. Here, we show that the inner and outer cores are coupled magnetically, when the macroscopic flux tubes subdivide dendritically into quantized flux tubes, a phenomenon called flux branching. An important implication is that up to ${\sim} 10^{12} (r_1/10^6 \, {\rm cm}) \, {\rm erg}$ of energy are required to separate a quantized flux tube from its progenitor macroscopic flux tube, where $r_1$ is the length of the macroscopic flux tube. Approximating the normal-superconducting boundary as sharp, we calculate the magnetic coupling energy between a quantized and macroscopic flux tube due to flux branching as a function of, $f_1$, the radius of the type-I inner core divided by the radius of the type-II outer core. Strong coupling delays magnetic field decay in the type-II superconductor. For an idealized inner core containing only a type-I proton superconductor and poloidal flux, and in the absence of ambipolar diffusion and diamagnetic screening, the low magnetic moments (${\lesssim} 10^{27} \, {\rm G \, cm^3}$) of recycled pulsars imply $f_1 \lesssim 10^{-1.5}$.

Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity

Within the framework of Einstein-Gauss-Bonnet theory in five-dimensional spacetime (5D EGB), we derive the hydrostatic equilibrium equations and solve them numerically to obtain neutron stars for both isotropic and anisotropic distribution of matter. The mass-radius relations are obtained for SLy equation of state, which describes both the solid crust and the liquid core of neutron stars, and for a wide range of the Gauss-Bonnet coupling parameter α. More specifically, we find that the contribution of the Gauss-Bonnet term leads to substantial deviations from Einstein gravity. We also discuss that after a certain value of α, the theory admits higher maximum masses compared with general relativity, however, the causality condition is violated in the high-mass region. Finally, our results are compared with the recent observations data on mass-radius diagram.

Thermal Fluctuations of Matter Composition and Quark Nucleation in Compact Stars

At the extreme densities reached in the core of neutron stars, it is possible that deconfined quark matter is produced. The formation of this new phase of strongly interacting matter is likely to occur via a first-order phase transition for the typical temperatures reached in astrophysical processes. The first seeds of quark matter would then form through a process of nucleation within the metastable hadronic phase. Here, we address the role of the thermal fluctuations in the hadronic composition on the nucleation of two-flavor quark matter. At finite temperature, the thermodynamic quantities in a system fluctuate around average values. Nucleation being a local process, it is possible that it occurs in a subsystem whose composition makes the nucleation easier. We will consider the total probability of the nucleation as the product between the probability that a subsystem has a certain hadronic composition different from the average in the bulk, and the nucleation probability in that subsystem. We will show how those fluctuations of the hadronic composition can increase the efficiency of nucleation already for temperatures ∼(0.1−1) keV. However, for temperatures ≲(1−10) MeV, the needed overpressure exceeds the maximum pressure reached in compact stars. Finally, for even larger temperatures the process of nucleation can take place, even taking into account finite-size effects.

A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data

PSR J0740+6620 is the neutron star with the highest precisely determined mass, inferred from radio observations to be 2.08 ± 0.07 M ⊙. Measurements of its radius therefore hold promise to constrain the properties of the cold, catalyzed, high-density matter in neutron star cores. Previously, Miller et al. and Riley et al. reported measurements of the radius of PSR J0740+6620 based on Neutron Star Interior Composition Explorer (NICER) observations accumulated through 2020 April 17, and an exploratory analysis utilizing NICER background estimates and a data set accumulated through 2021 December 28 was presented in Salmi et al. Here we report an updated radius measurement, derived by fitting models of X-ray emission from the neutron star surface to NICER data accumulated through 2022 April 21, totaling ∼1.1 Ms additional exposure compared to the data set analyzed in Miller et al. and Riley et al., and to data from XMM-Newton observations. We find that the equatorial circumferential radius of PSR J0740+6620 is 12.92−1.13+2.09 km (68% credibility), a fractional uncertainty ∼83% the width of that reported in Miller et al., in line with statistical expectations given the additional data. If we were to require the radius to be less than 16 km, as was done in Salmi et al., then our 68% credible region would become R=12.76−1.02+1.49 km, which is close to the headline result of Salmi et al. Our updated measurements, along with other laboratory and astrophysical constraints, imply a slightly softer equation of state than that inferred from our previous measurements.

Estimate for the Neutrino Magnetic Moment from Pulsar Kick Velocities Induced at the Birth of Strange Quark Matter Neutron Stars

We estimate the magnetic moment of electron neutrinos by computing the neutrino chirality flip rate that can occur in the core of a strange quark matter neutron star at birth. We show that this process allows neutrinos to anisotropically escape, thus inducing the star kick velocity. Although the flip from left- to right-handed neutrinos is assumed to happen in equilibrium, the no-go theorem does not apply because right-handed neutrinos do not interact with matter and the reverse process does not happen, producing the loss of detailed balance. For simplicity, we model the star core as consisting of strange quark matter. We find that even when the energy released in right-handed neutrinos is a small fraction of the total energy released in left-handed neutrinos, the process describes kick velocities for natal conditions, which are consistent with the observed ones and span the correct range of radii, temperatures and chemical potentials for typical magnetic field intensities. The neutrino magnetic moment is estimated to be μν∼3.6×10−18μB, where μB is the Bohr magneton. This value is more stringent than the bound found for massive neutrinos in a minimal extension of the standard model.

X-ray emission spectrum for axion–photon conversion in magnetospheres of strongly magnetized neutron stars

Detecting axionic dark matter (DM) could be possible in an X-ray spectrum from strongly magnetized neutron stars (NSs). We examine the possibility of axion–photon conversion in the magnetospheres of strongly magnetized NSs. In the current work, we investigate how the modified Tolman–Oppenheimer–Volkoff (TOV) system of equations (in the presence of a magnetic field) affects the energy spectrum of axions and axions-converted-photon flux. We have considered the distance-dependent magnetic field in the modified TOV system of equations. We employ three different equations of states (EoSs), namely APR, FPS, and SLY, to solve these equations. We obtain the axions emission rate by including the Cooper-pair-breaking formation process and Bremsstrahlung process in the core of NSs using the NSCool code. We primarily focus on Magnificient seven (M7) star RXJ 1856.5-3754. We further investigate the impact of the magnetic field on the actual observables, such as axion energy spectrum and axion-converted-photon flux at an axion mass in meV range by assuming mass MNS∼1.4M⊙.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{NS} \\sim 1.4M_{\\odot }.$$\\end{document} We compare our calculated axion-converted-photon flux from all available archival data sets from PN+MOS+Chandra. We also study the variation of the energy spectrum at a fixed energy with varying central magnetic fields. Our predicted axion-converted-photon flux values as a function of axion energy closely follow the experimentally archival data, which allows us to put bounds on the axion mass for the three EoS.

Thorne–Żytkow objects with mirror neutron star cores?

A Thorne–Żytkow object can be formed when a neutron star is absorbed by the envelope of its giant companion star, spirals toward the center of the giant star due to the drag from the surrounding envelope, and merges with the star’s core. During in-spiral, dynamical friction is the main drag force acting on a neutron star inside the star envelope. However, dynamical friction is caused by the neutron star’s gravitational interaction with its own gravitationally induced wake. Therefore, exactly, the same gravitational drag force will act on a mirror neutron star, and if a significant part of the dark matter is in the form of mirror matter, then we expect the formation of Thorne–Żytkow objects with a mirror neutron star inside. We explore the plausibility of the existence of such exotic Thorne–Żytkow objects.

Analysis of Neutron Star f-mode Oscillations in General Relativity with Spectral Representation of Nuclear Equations of State

We study quasi-normal f-mode oscillations in neutron star (NS) interiors within a linearized general relativistic formalism. We utilize approximately 9000 nuclear equations of state (EOSs) using spectral representation techniques, incorporating constraints on nuclear saturation properties, chiral effective field theory for pure neutron matter, and perturbative quantum chromodynamics for densities pertinent to NS cores. The median values of the f-mode frequency, ν f (damping time, τ f ) for NSs with masses ranging from 1.4 to 2.0 M ⊙ lie between 1.80 and 2.20 kHz (0.13–0.22 s) for our entire EOS set. Our study reveals a weak correlation between f-mode frequencies and individual nuclear saturation properties, prompting the necessity for more intricate methodologies to unveil multiparameter relationships. We observe a robust linear relationship between the radii and f-mode frequencies for different NS masses. Leveraging this correlation alongside NICER observations of PSR J0740+6620 and PSR J0030+0451, we establish constraints that exhibit partial and minimal overlap for observational data from Riley et al. and Miller et al., respectively, with our nucleonic EOS data set. Moreover, NICER data align closely with the radius and frequency values for a few hadron–quark hybrid EOS models. This indicates the need to consider additional exotic particles such as deconfined quarks at suprasaturation densities. We conclude that future observations of the radius or f-mode frequency for more than one NS mass, particularly at the extremes of the viable NS mass scale, would either rule out nucleon-only EOSs or provide definitive evidence in its favor.

Chaos in inhomogeneous neutrino fast flavor instability

In dense neutrino gases, the neutrino-neutrino coherent forward scattering gives rise to a complex flavor oscillation phenomenon not fully incorporated in simulations of neutron star mergers (NSM) and core collapse supernovae (CCSNe). Moreover, it has been proposed to be chaotic, potentially limiting our ability to predict neutrino flavor transformations in simulations. To address this issue, we explore how small flavor perturbations evolve in the nonlinear regime of the neutrino quantum kinetic equation within a narrow centimeter-scale region inside a NSM and a toy neutrino distribution. Our findings reveal that paths in the flavor state space of solutions with similar initial conditions diverge exponentially, exhibiting chaos. This inherent chaos makes the microscopic scales of neutrino flavor transformations unpredictable. However, the domain-averaged neutrino density matrix remains relatively stable, with chaos minimally affecting it. This particular property suggests that domain-averaged quantities remain reliable despite the exponential amplification of errors. Published by the American Physical Society 2024

Pulsar as a Weber detector of gravitational waves and a probe to its internal phase transitions

It is believed that cores of neutron stars provide a natural laboratory where exotic high baryon density phases of quantum chromo dynamics (QCD) may exist. In fact, the theoretically well-established neutron superfluid phase is also believed to be found only inside neutron stars. Focus on neutrons stars has tremendously intensified in recent years with the direct detection of gravitational waves (GWs) by LIGO/Virgo from binary neutron star (BNS) merger events which has allowed the possibility of directly probing the properties of the interior of a neutron star. A truly remarkable phenomenon manifested by rapidly rotating neutron stars is in their avatar as Pulsars. The accuracy of pulsar timing can reach the level of one part in 10[Formula: see text], comparable to that of atomic clocks. Indeed, it was such a great accuracy which had allowed the first indirect detection of GWs from a BNS system. Such an incredible accuracy of pulse timings points to a very interesting possibility. Any deformation of the pulsar, even if it is extremely tiny, has the potential of leaving its imprints on the pulses through introduction of tiny perturbations in the entire moment of inertia (MI) tensor. While, the diagonal components of perturbed MI tensor affect the pulse timings, the off-diagonal components lead to wobbling of pulsar, directly affecting the pulse profile. This opens up a new window of opportunity for exploring various phase transitions occurring inside a pulsar core, through induced density fluctuations, which may be observable as perturbations in the pulse timing as well as its profile. Such perturbations also naturally induce a rapidly changing quadrupole moment of the star, thereby providing a new source of GW emission. Another remarkable possibility arises when we consider the effect of an external GW on neutron star. With the possibility of detecting any minute changes in its configuration through pulse observations, the neutron star has the potential of performing as a Weber detector of GW. This brief review will focus on these specific aspects of a pulsar. Specifically, the focus will be on the type of physics which can be probed by utilizing the effect of changes in the MI tensor of the pulsar on pulse properties.

Pulsar glitches from quantum vortex networks

Neutron stars or pulsars are very rapidly rotating compact stars with extremely high density. One of the unsolved long-standing problems of these enigmatic celestial bodies is the origin of pulsars’ glitches, i.e., the sudden rapid deceleration in the rotation speed of neutron stars. Although many glitch events have been reported, there is no consensus on the microscopic mechanism responsible for them. One of the important characterizations of the glitches is the scaling law P(E)∼E-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P(E) \\sim E^{-\\alpha }$$\\end{document} of the probability distribution for a glitch with energy E. Here, we reanalyse the accumulated up-to-date observation data to obtain the exponent α≈0.88\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\approx 0.88$$\\end{document} for the scaling law, and propose a simple microscopic model that naturally deduces this scaling law without any free parameters. Our model explains the appearance of these glitches in terms of the presence of quantum vortex networks arising at the interface of two different kinds of superfluids in the core of neutron stars; a p-wave neutron superfluid in the inner core which interfaces with the s-wave neutron superfluid in the outer core, where each integer vortex in the s-wave superfluid connects to two half-quantized vortices in the p-wave superfluid through structures called “boojums”.

Thermal evolution and axion emission properties of strongly magnetized neutron stars

Emission properties of compact astrophysical objects such as Neutron stars (NSs) are associated with crucial astronomical observables. In the current work, we obtain the mass, pressure profiles of the non-rotating NSs using the modified Tolman Oppenheimer Volkoff (TOV) system of equations in the presence of intense magnetic field. We obtain the profiles by using a specific distance-dependent magnetic field in the modified TOV equations. We employ three different equations of states (EoS) to solve the TOV equations by assuming the core of NSs comprises a hadronic matter. Employing the above profiles, we determine the cooling rates of spherically symmetric NSs as a function of time with and without including the magnetic field using the NSCool code. We have also determined the cooling rates as a function of radius for three different NSs. Furthermore, we determine the luminosity of neutrinos, axions, and photons emitting from the NSs in the presence and absence of a magnetic field for an axion mass 16 meV and three different EoS. Our comparative study indicates that the cooling rate and luminosities of neutrinos, axions, and photons change significantly due to the impact of the strong magnetic field. We also find that due to the magnetic field, the axion mass bound increases slightly compared to without a magnetic field.

Prospects for direct detection of black hole formation in neutron star mergers with next-generation gravitational-wave detectors

A direct detection of black hole formation in neutron star mergers would provide invaluable information about matter in neutron star cores and finite temperature effects on the nuclear equation of state. We study black hole formation in neutron star mergers using a set of 190 numerical relativity simulations consisting of long-lived and black-hole-forming remnants. The postmerger gravitational-wave spectrum of a long-lived remnant has greatly reduced power at a frequency f greater than fpeak, for f≳4 kHz, with fpeak∈[2.5,4] kHz. On the other hand, black-hole-forming remnants exhibit excess power in the same large f region and manifest exponential damping in the time domain characteristic of a quasinormal mode. We demonstrate that the gravitational-wave signal from a collapsed remnant is indeed a quasinormal ringing. We report on the opportunity for direct detections of black hole formation with next-generation gravitational-wave detectors such as Cosmic Explorer and Einstein Telescope and set forth the tantalizing prospect of such observations up to a distance of 100 Mpc for an optimally oriented and located source with an SNR of 4. Published by the American Physical Society 2024

The Impact of Asymmetric Dark Matter on the Thermal Evolution of Nucleonic and Hyperonic Compact Stars

We investigate the impact of asymmetric fermionic dark matter (DM) on the thermal evolution of neutron stars (NSs), considering a scenario where DM interacts with baryonic matter (BM) through gravity. Employing the two-fluid formalism, our analysis reveals that DM accrued within the NS core exerts an inward gravitational pull on the outer layers composed of BM. This gravitational interaction results in a noticeable increase in baryonic density within the core of the NS. Consequently, it strongly affects the star’s thermal evolution by triggering the early onsets of the direct Urca (DU) processes, causing enhanced neutrino emission and rapid star cooling. Moreover, the photon emission from the star’s surface is modified due to a reduction in radius. We demonstrate the effect of DM gravitational pull on nucleonic and hyperonic DU processes that become kinematically allowed even for NSs of low mass. We then discuss the significance of observing NSs at various distances from the Galactic center. Given that the DM distribution peaks toward the Galactic center, NSs within this central region are expected to harbor higher fractions of DM, potentially leading to distinct cooling behaviors.

Rapid neutron star cooling triggered by dark matter

ABSTRACT We study the effect of asymmetric fermionic dark matter (DM) on the thermal evolution of neutron stars (NSs). No interaction between DM and baryonic matter is assumed, except the gravitational one. Using the two-fluid formalism, we show that DM accumulated in the core of a star pulls inwards the outer baryonic layers of the star, increasing the baryonic density in the NS core. As a result, it significantly affects the star’s thermal evolution by triggering an early onset of the direct Urca (DU) process and modifying the photon emission from the surface caused by the decrease of the radius. Thus, due to the gravitational pull of DM, the DU process becomes kinematically allowed for stars with lower masses. Based on these results, we discuss the importance of NS observations at different distances from the Galactic Centre. Since the DM distribution peaks towards the Galactic Centre, NSs in this region are expected to contain higher DM fractions that could lead to a different cooling behavior.

Constraints onBose–Einsteincondensate stars as neutron stars models from new observational data

AbstractWe evaluate the feasibility of Bose–Einstein condensate stars (BECS) as models for the interior of neutron stars (NSs). BECS are compact objects composed of bosons, formed through the spin‐parallel pairing of neutrons. Here, we utilize the astronomical data from GW170817, XMMU J173203.3‐344518 (the lightest NS known), and a novel lower limit on NS core heat capacity to scrutinize the compatibility of BECS with these recent observations of NSs. Our specific focus is to constrain the values of the scattering length , parameter determining the strength of particle interactions in the model. Our analysis suggests that if the stars involved in GW170817 were BECSs, the scattering length of their constituent bosons should fall within the to fm range. Additionally, at a scattering length of fm, stars with mass and radius characteristics akin to XMMU J173203.3‐344518 are identified. Moreover, we find that the heat capacity depends on the mass and temperature of BECS, and surpasses the established lower bound for NS cores when fm. In summary, our results endorse BECS models with fm, providing NS observables in agreement with diverse observations and contributing to the understanding of NS interiors.

Constraints on Phase Transitions in Neutron Star Matter

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities cs2>0.1 in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range Δρ/ρ<0.2 (at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined.

Combined magnetic field evolution in neutron star cores and crusts: ambipolar diffusion, Hall effect, and Ohmic dissipation

ABSTRACT Neutron star magnetic field evolution is mediated through the Hall effect and Ohmic dissipation in the crust while ambipolar diffusion is taking place in the core. These effects have been studied in detail in either part of the star, however, their combined, simultaneous evolution and interplay has not been explored in detail yet. Here, we present simulation results of the simultaneous evolution of the magnetic field in the core due to ambipolar diffusion and the crust due to Hall effect and Ohmic decay, under the assumption of axial symmetry. We find that a purely poloidal field generates a toroidal field in the crust, due to the Hall effect, that sinks into the core. A purely toroidal field remains toroidal and spreads into the core and the crust. Finally, for a mixed poloidal–toroidal field, the north–south symmetry is broken due to the Hall effect in the crust, however, ambipolar diffusion, tends to restore it. We examine the role of ambipolar diffusion to the magnetic field decay and we compare the rate of the conversion of magnetic field energy into heat, finding that it enhances the magnetic field decay in neutron stars.