Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of thi
s theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.
It is now possible to model thermal relaxation of neutron stars after bouts of accretion during which the star is heated out of equilibrium by nuclear reactions in its crust. Major uncertainties in these models can be encapsulated in modest variation
s of a handful of fudge parameters that change the crustal thermal conductivity, specific heat, and heating rates. Observations of thermal relaxation constrain these fudge parameters and allow us to predict longer term variability in terms of the neutron star core temperature. We demonstrate this explicitly by modeling ongoing thermal relaxation in the neutron star XTE J1701-462. Its future cooling, over the next 5 to 30 years, is strongly constrained and depends mostly on its core temperature, uncertainties in crust physics having essentially been pinned down by fitting to the first three years of observations.
Neutron stars provide a fertile environment for exploring superfluidity under extreme conditions. It is not surprising that Cooper pairing occurs in dense matter since nucleon pairing is observed in nuclei as energy differences between even-even and
odd-even nuclei. Since superfluids and superconductors in neutron stars profoundly affect neutrino emissivities and specific heats, their presence can be observed in the thermal evolution of neutron stars. An ever-growing number of cooling neutron stars, now amounting to 13 thermal sources, and several additional objects from which upper limits to temperatures can be ascertained, can now be used to discriminate among theoretical scenarios and even to dramatically restrict properties of nucleon pairing at high densities. In addition, observations of pulsars, including their spin-downs and glitch histories, additionally support the conjecture that superfluidity and superconductivity are ubiquitous within, and important to our understanding of, neutron stars.
We present magnetohydrodynamic numerical simulations of the late post-supernova hypercritical accretion to understand its effect on the magnetic field of the new-born neutron star. We consider as an example the case of a magnetic field loop protrudin
g from the stars surface. The accreting matter is assumed to be non magnetized and, due to the high accretion rate, matter pressure dominates over magnetic pressure. We find that an accretion envelope develops very rapidly and once it becomes convectively stable the magnetic field is easily buried and pushed into the newly forming neutron star crust. However, for low enough accretion rates the accretion envelope remains convective for an extended period of time and only partial submergence of the magnetic field occurs due to a residual field that is maintained at the interface between the forming crust and the convective envelope. In this latter case, the outcome should be a weakly magnetized neutron star with a likely complicated field geometry. In our simulations we find the transition from total to partial submergence to occur around dotM ~ 10 M_sun/yr. Back-diffusion of the submerged magnetic field toward the surface, and the resulting growth of the dipolar component, may result in a delayed switch-on of a pulsar on time-scales of centuries to millenia.
It is assumed that accreting neutron stars (NSs) in LMXBs are heated due to the compression of the existing crust by the accreted matter which gives rise to nuclear reactions in the crust. It has been shown that most of the energy is released deep in
the crust by pycnonuclear reactions involving low-Z elements. We discuss if NSs in very-faint X-ray transients (VFXTs; those which have peak X-ray luminosities < 1E36 erg/s) can be used to test this model. Unfortunately we cannot conclusively answer this because of the large uncertainties in our estimates of the accretion rate history of those VFXTs, both the short-term (less than a few tens of thousands of years) and the one throughout their lifetime. The latter is important because it can be so low that the NSs might not have accreted enough matter to become massive enough that enhanced cooling processes become active. Therefore, they could be relatively warm compared to other systems for which such enhanced cooling processed have been inferred. However, the amount of matter can also not be too low because then the crust might not have been replaced significantly by accreted matter and thus a hybrid crust of partly accreted and partly original, albeit further compressed matter, might be present. This would inhibit the full range of pycnonuclear reactions to occur and thus very likely decreasing the amount of heat deposited in the crust. Furthermore, better understanding is needed how a hybrid crust affects other properties such as the thermal conductivity. We also show that some individual NS LMXBs might have hybrid crusts as well as the NSs in HMXBs. This has to be taken into account when studying the cooling properties of those systems when they are in quiescence. We show that the VFXTs are likely not the dominate transients that are associated with the brightest low-luminosity X-ray sources in globular clusters as was hypothesized.
In this review, I present a brief summary of the impact of nucleon pairing at supra-nuclear densities on the cooling of neutron stars. I also describe how the recent observation of the cooling of the neutron star in the supernova remnant Cassiopeia A
may provide us with the first direct evidence for the occurrence of such pairing. It also implies a size of the neutron 3P-F2 energy gap of the order of 0.1 MeV.
The supernova remnant Cassiopeia A contains the youngest known neutron star which is also the first one for which real time cooling has ever been observed. In order to explain the rapid cooling of this neutron star, we first present the fundamental p
roperties of neutron stars that control their thermal evolution with emphasis on the neutrino emission processes and neutron/proton superfluidity/superconductivity. Equipped with these results, we present a scenario in which the observed cooling of the neutron star in Cassiopeia A is interpreted as being due to the recent onset of neutron superfluidity in the core of the star. The manner in which the earlier occurrence of proton superconductivity determines the observed rapidity of this neutron stars cooling is highlighted. This is the first direct evidence that superfluidity and superconductivity occur at supranuclear densities within neutron stars.
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 3P2 channel. We find that the critical temperature for th
is superfluid transition is ~0.5x10^9 K. The observed rapidity of the cooling implies that protons were already in a superconducting state with a larger critical temperature. Our prediction that this cooling will continue for several decades at the present rate can be tested by continuous monitoring of this neutron star.
The minimal cooling paradigm for neutron star cooling assumes that enhanced cooling due to neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks, does not occur.
This scenario was developed to replace and extend the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation processes that occur near the critical temperature for superfluid/superconductor pairing. Recently, it has been found that Cooper-pair neutrino emission from the vector channel is suppressed by a large factor compared to the original estimates that violated vector current conservation. We show that Cooper-pair neutrino emission remains, nevertheless, an efficient cooling mechanism through the axial channel. As a result, the elimination of neutrino emission from Cooper-paired nucleons through the vector channel has only minor effects on the long-term cooling of neutron stars within the minimal cooling paradigm. We further quantify precisely the effect of the size of the neutron 3P2 gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature T_c for this gap covers a range of values between T_c^min < 0.2 x 10^9 K up to T_c^max > 0.5 times 10^9 K in the core of the star. In addition, it is required that young neutron stars have heterogenous envelope compositions: some must have light-element compositions and others must have heavy-element compositions. Unless these two conditions are fulfilled, about half of the observed young cooling neutron stars are inconsistent with the minimal cooling paradigm and provide evidence for the existence of enhanced cooling.
