Cooling of Akmal-Pandharipande-Ravenhall neutron stars with a rotochemical heating source

Employing phenomenological density-dependent critical temperatures of strong singlet-state proton pairing and of moderate triplet-state neutron pairing, we investigate the effects of rotochemical heating on the thermal evolution of superfluid neutron stars whose cores consist of npe matter with the Akmal-Pandharipande-Ravenhall equation of state. Since the star is not quite in the weak interaction equilibrium state during spin-down, the departure from the chemical equilibrium leads to the rotochemical heating in a rotating NS which will increase the stellar＇s temperature. Our calculations show that the rotochemical heating delays the cooling of superfluid neutron stars considerably and makes the previous classification of NS cooling ambiguous. What＇s more, our model is currently consistent with all the observational data, and in particular some middle-aged and cold NSs （PRS J0205＋6449 in 3C 58, PRS J1357-6429, RX J007.0＋7303 in CTA 1, Vela） can be better explained when taking into account rotochemical heating.     

Phase transitions in nucleonic matter and neutron-star cooling

A new scenario for neutron-star cooling is suggested by the correspondence between pion condensation, induced by critical spin-isospin fluctuations, and the metal-insulator phase transition in a 2D electron gas. Above the threshold density for pion condensation, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino production. In the liquid phase just below the transition, the fluctuations play dual roles by (i) creating a multisheeted neutron Fermi surface that extends to low momenta and activates the normally forbidden direct Urca cooling mechanism, and (ii) amplifying the nodeless P-wave neutron superfluid gap while suppressing S-wave pairing. Lighter stars without a pion-condensed core undergo slow cooling, whereas enhanced cooling occurs in heavier stars via direct Urca emission from a thin shell of the interior.     

Hypernuclear physics for neutron stars

The role of hypernuclear physics for the physics of neutron stars is delineated. Hypernuclear potentials in dense matter control the hyperon composition of dense neutron star matter. The three-body interactions of nucleons and hyperons determine the stiffness of the neutron star equation of state and thereby the maximum neutron star mass. Two-body hyperon–nucleon and hyperon–hyperon interactions give rise to hyperon pairing which exponentially suppresses cooling of neutron stars via the direct hyperon URCA processes. Nonmesonic weak reactions with hyperons in dense neutron star matter govern the gravitational wave emissions due to the r-mode instability of rotating neutron stars.     

Rapid cooling of the neutron star in Cassiopeia A triggered by neutron superfluidity in dense matter

We propose that the observed cooling of the neutron star in Cassiopeia A is due to enhanced neutrino emission from the recent onset of the breaking and formation of neutron Cooper pairs in the (3)P(2) channel. We find that the critical temperature for this superfluid transition is ?0.5×10(9) K. The observed rapidity of the cooling implies that protons were already in a superconducting state with a larger critical temperature. This is the first direct evidence that superfluidity and superconductivity occur at supranuclear densities within neutron stars. Our prediction that this cooling will continue for several decades at the present rate can be tested by continuous monitoring of this neutron star.     

Effect of magnetic field decay on the chemical heating of cooling neutron stars

The effect of magnetic field decay on the chemical heating and thermal evolution of neutron stars is discussed in this paper. Our main goal is to study how the chemical heating mechanism and thermal evolution are changed by the field decay and how the magnetic field decay is modified by the thermal evolution. We compare stars cooling with chemical heating with one without chemical heating and find that the decay of the magnetic field is delayed significantly by the chemical heating. We find that the effect of chemical heating has been suppressed through the decaying magnetic field by the spin-down of the stars at a later stage. Compared with typical chemical heating, we find the decay of the magnetic field can even cause the surface temperature to turn down at an older age. When we discuss the cooling of neutron stars, we should consider the coupling effect of the magnetic field and the rotational evolution of neutron stars on the heating mechanisms.     

Neutron star equation of state in density dependent relativistic Hartree-Fock theory*

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M☉, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.     

Structure and cooling of compact stars

We study the structure and evolution of neutron stars (NSs), the interiors of which are modeled using microscopic approaches and constrained by the condition that the equation of state (EoS) of matter extrapolated to high densities should not contradict known observational data from compact stars and experimental data from heavy-ion collisions (HIC). We use modern cooling simulations to extract distributions of NS masses required to reproduce those of the yet sparse data in the Temperature-Age (TA) plane. By comparing the results with the mass distribution for young, nearby NSs used in population synthesis, we can sharpen the NS cooling constraints. The text was submitted by the author in English.     

Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

Are pulsar glitches triggered by a superfluid two-stream instability?

Mature neutron stars are expected to have several superfluid components. Strong evidence for this is provided by the glitches that have been observed in dozens of pulsars. We describe a superfluid analog of the two-stream instability that is well known in plasma physics and provide arguments that this instability is likely to be relevant for neutron stars. This is a new physical mechanism which may play a key role in explaining the glitch mechanism and which could also prove to be relevant in laboratory experiments on various superfluid systems.     

Prospects of detecting baryon and quark superfluidity from cooling neutron stars

Baryon and quark superfluidity in the cooling of neutron stars are investigated. Future observations will allow us to constrain combinations of the neutron or Lambda-hyperon pairing gaps and the star's mass. However, in a hybrid star with a mixed phase of hadrons and quarks, quark gaps larger than a few tenths of an MeV render quark matter virtually invisible for cooling. If the quark gap is smaller, quark superfluidity could be important, but its effects will be nearly impossible to distinguish from those of other baryonic constituents.     

Do Neutron Star Gravitational Waves Carry Superfluid Imprints?

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×10⁸ neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate.     

Stability of precessing superfluid neutron stars

We discuss a new superfluid instability occurring in the interior of mature neutron stars with implications for free precession. This instability is similar to the instability which is responsible for the formation of turbulence in superfluid helium. We demonstrate that the instability is unlikely to affect slowly precessing systems with weak superfluid coupling. In contrast, fast precession in systems with strong coupling appears to be generically unstable. This raises serious questions about our understanding of neutron star precession and complicates attempts to constrain neutron star interiors using such observations.     

Thermal properties and detectability of neutron stars - I cooling and heating of neutron stars

In this report, we first review earlier and recent developments in some of thermodynamic problems of neutron stars, especially those involving cooling mechanisms and theoretical predictions of surface temperatures of neutron stars. Emphasis is placed particularly on: the effect of equations of state and hence that of nuclear and strong interactions; the effect of better treatment of various neutrino cooling mechanisms, especially those involving pion condensates; and implication of these better and more detailed theoretical estimates on the prospect of directly observing thermal radiation from the surface of neutron stars. In connection with the last problem, we briefly review recent developments on the observational side — the HEAO-B and other programs already existing or expected to be planned for near future, which are directly related to the above problem. In connection with the possibilities of observing older neutron stars we briefly summarise various heating mechanisms.From these studies, we see that exciting possibilities exist through the HEAO-B and some other programs which may be realised in the 1980's, that we may observe radiation directly from neutron star surfaces if they are ? (3?5) × 10⁵°K. If such radiation is detected, the observed surface temperatures and further spectral studies may give invaluable insight into various important problems, such as magnetic properties of dense matter, equations of state, pion condensates, and other fundamental problems in nuclear, particle and high energy physics. If the surface temperatures of younger members of these stars (? 10⁴ years) are observationally found to be less than ≈ (5?10) × 10⁵°K (depending on the individual objects), we note that at the moment only pion coolings are consistent with observations, and the outcome may be equally far reaching. Among various observed neutron stars (pulsars) and neutron star candidates (e.g. supernova remnants), the Vela pulsar may prove to be the most rewarding one. If regular pulsar-like periodicities are discovered in radiations from any of supernova remnants, we can assume the presence of neutron stars in these objects. In that case, some supernova remnants, such as SN 1006, may also turn out to be promising. If we defect surface radiations from older pulsars (? 10⁵ years), that may support some of heating theories. At the end, we point out that there may be many point sources of very soft weak thermal X-rays across the sky (as old neutron stars accrete interstellar matter) and some of the closest ones may be detectable through the HEAO-B and similar devices.     

Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes

According to prevailing theory, relativistic degenerate stars with masses beyond the Chandrasekhar and Oppenheimer–Volkoff (OV) limits cannot achieve hydrostatic equilibrium through either electron or neutron degeneracy pressure and must collapse to form stellar black holes. In such end states, all matter and energy within the Schwarzschild horizon descend into a central singularity. Avoidance of this fate is a hoped-for outcome of the quantization of gravity, an as-yet incomplete undertaking. Recent studies, however, suggest the possibility that known quantum processes may intervene to arrest complete collapse, thereby leading to equilibrium states of macroscopic size and finite density. I describe here one such process which entails pairing (or other even-numbered association) of neutrons (or constituent quarks in the event of nucleon disruption) to form a condensate of composite bosons in equilibrium with a core of degenerate fermions. This process is analogous to, but not identical with, the formation of hadron Cooper pairs that give rise to neutron superfluidity and proton superconductivity in neutron stars. Fermion condensation to composite bosons in a star otherwise destined to collapse to a black hole facilitates hydrostatic equilibrium in at least two ways: (1) removal of fermions results in a decrease in the Fermi level which stiffens the dependence of degeneracy pressure on fermion density, and (2) phase separation into a fermionic core surrounded by a self-gravitating condensate diminishes the weight which must be balanced by fermion degeneracy pressure. The outcome is neither a black hole nor a neutron star, but a novel end state, a “fermicon star,” with unusual physical properties.     

Neutral color-spin-locking phase in neutron stars

We present results for the spin-1 color-spin-locking (CSL) phase using a NJL-type model in two-flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ≃ 1MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.     

The role of superfluidity in the structure of the neutron star inner crust

A self-consistent quantum approach to describe the inner crust structure of neutron stars is developed, within the Wigner–Seitz approximation. It is based on the generalized energy functional method involving explicitly neutron and proton pairing correlations. The energy functional is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the Wigner–Seitz cell with the one calculated microscopically for neutron matter. It is shown that the neutron and proton superfluidity influences significantly the ground state structure of the inner crust.     

Accreting neutron stars as probes of dense matter physics

There are over 100 accreting neutron stars in our galaxy, in which matter (typically H/He) is tidally transferred from a secondary companion to the neutron star. Accretion of this matter perturbs the thermal structure of the interior away from that of an isolated cooling neutron star. In this paper. we review how this accretion induces reactions in the crust of the neutron star that keep the interior hot. If the accretion is intermittent, then the heated surface layers are directly observable when accretion stops. This heating also affects the unstable ignition of light elements in the neutron star envelope. Observations of the neutron star cooling following an accretion outburst can in principle constrain the thermal properties of the crust and core.     

Revealing the physics of R modes in low-mass x-ray binaries

We consider the astrophysical constraints on the gravitational-wave-driven r-mode instability in accreting neutron stars in low-mass x-ray binaries. We use recent results on superfluid and superconducting properties to infer the core temperature in these neutron stars and show the diversity of the observed population. Simple theoretical models indicate that many of these systems reside inside the r-mode instability region. However, this is in clear disagreement with expectations, especially for the systems containing the most rapidly rotating neutron stars. The inconsistency highlights the need to reevaluate our understanding of the many areas of physics relevant to the r-mode instability. We summarize the current status of our understanding, and we discuss directions for future research which could resolve this dilemma.