Neutron star observations: Prognosis for equation of state constraints

A new classification of neutron star cooling scenarios, involving either "minimal" cooling or "enhanced" cooling, is proposed. The minimal cooling scenario replaces and extends the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation process. This emission dominates that due to the modified Urca process for temperatures close to the critical temperature for superfluid pairing. Minimal cooling is distinguished from enhanced cooling by the absence of neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks. Within the minimal cooling scenario, theoretical cooling models can be considered to be a four parameter family involving the equation of state (including various compositional possibilities) of dense matter, superfluid properties of dense matter, the composition of the neutron star envelope, and the mass of the neutron star. The consequences of minimal cooling are explored through extensive variations of these parameters. The results are compared with the inferred properties of thermally emitting neutron stars in order to ascertain if enhanced cooling occurs in any of them. All stars for which thermal emissions have been clearly detected are at least marginally consistent with the lack of enhanced cooling, given the combined uncertainties in ages and temperatures or luminosities. The two pulsars PSR 0833-45 (Vela) and PSR 1706-44 would require enhanced cooling in case their ages and/or temperatures are on the lower side of their estimated values, whereas the four stars PSR 0656+14, PSR 1055-52, Geminga, and RX J0720.4-3125 may require some source of internal heating in case their age and/or luminosity are on the upper side of their estimated values. The new upper limits on the thermal luminosity of PSR J0205+6449 (in the supernova remnant 3C 58) and RX J0007.0+7302 (in CTA 1) are indicative of the occurrence of some enhanced neutrino emission beyond the minimal scenario.

https://iopscience.iop.org/article/10.1086/424844/pdf

Minimal Cooling of Neutron Stars: A New Paradigm

One of the major uncertainties in the dense matter equation of state has been the nuclear symmetry energy. The density dependence of the symmetry energy is important in nuclear astrophysics, as it controls the neutronization of matter in core-collapse supernovae, the radii of neutron stars and the thicknesses of their crusts, the rate of cooling of neutron stars, and the properties of nuclei involved in r-process nucleosynthesis. We show that fits of nuclear masses to experimental masses, combined with other experimental information from neutron skins, heavy ion collisions, giant dipole resonances and dipole polarizabilities, lead to stringent constraints on parameters that describe the symmetry energy near the nuclear saturation density. These constraints are remarkably consistent with inferences from theoretical calculations of pure neutron matter, and, furthermore, with astrophysical observations of neutron stars. The concordance of experimental, theoretical and observational analyses suggests that the symmetry parameters S v and L are in the range 29.0‐32.7 MeV and 40.5‐61.9 MeV, respectively, and that the neutron star radius, for a 1.4 M star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence). We can also set tight limits to the size of neutron star crusts and the fractional moment of inertia they contain, as well as the overall moment of inertia and quadrupole polarizability of 1.4 M stars. Our results also have implications for the disk mass and ejected mass of compact mergers involving neutron stars.

https://iopscience.iop.org/article/10.1088/0004-637X/771/1/51/pdf

Constraining the Symmetry Parameters of the Nuclear Interaction

https://arxiv.org/pdf/astro-ph/0508056.pdf

The cooling of compact stars

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 this theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.

/pdf/neutron-stars-cooling-and-transport-1equgwjsa8.pdf

Neutron Stars—Cooling and Transport

With the successful launch of Chandra and XMM/Newton X-ray space missions combined with the lower energy band observations, we are now in the position where careful comparison of neutron star cooling theories with observations will make it possible to distinguish among various competing theories. For instance, the latest theoretical and observational developments appear to exclude both nucleon and kaon direct Urca cooling. In this way we can now have realistic hopes for determining various important properties, such as the composition, degree of superfluidity, equation of state, and stellar radius. These developments should help us obtain better insight into the properties of dense matter.

Confronting Neutron Star Cooling Theories with New Observations

With the successful launch of Chandra and XMM/Newton X-ray space missions combined with the lower-energy band observations, we are in the position where careful comparison of neutron star cooling theories with observations will make it possible to distinguish among various competing theories. For instance, the latest theoretical and observational developments already exclude both nucleon and kaon direct URCA cooling. In this way we can now have realistic hope for determining various important properties, such as the composition, degree of superfluidity, the equation of state and steller radius. These developments should help us obtain better insight into the properties of dense matter.

The structure and evolution of neutron stars

proach. Numerical results for the equation of state (EOS) with the mixing ratios of the respective components and the hyperon energy gaps including the temperature dependence are presented. These are meant to serve as physical inputs for Y -cooling calculations of NSs. By paying attention to the uncertainties of the EOS and the YY interactions, it is shown that both Λ and Σ − are superfluid as soon as they appear although the magnitude of the critical temperature and the density region where superfluidity exists depend considerably on the YY pairing potential. Considering momentum triangle condition and the occurrence of superfluidity, it is found that a so-called “hyperon cooling”(neutrino-emission from direct Urca process including Y ) combined with Y -superfluidity may be able to account for observations of the colder class of NSs. It is remarked that Λ-hyperons play a decisive role in the hyperon cooling scenario. Some comments are given regarding the consequences of the less attractive ΛΛ interaction recently suggested by the “NAGARA event” 6He.

Occurrence of Hyperon Superfluidity in Neutron Star Cores

For neutron stars with hyperon-mixed cores, neutrino emissivity is studied using the properties of neutron star matter determined under the equation of state, which is obtained by introducing a repulsive three-body force universal for all the baryons so as to assure the maximum mass of neutron stars compatible with observations. The case without a meson condensate is treated. We choose the inputs provided by nuclear physics, with a reliable allowance. Paying attention to the density dependence of the critical temperatures of the baryon superfluids, which reflect the nature of the baryon-baryon interaction and control neutron star cooling, we show what neutrino emission processes are efficient in regions both with and without hyperon mixing. By comparing the calculated emissivities with respect to densities, we can conclude that at densities lower than about 4 times the nuclear density, the Cooper-pair process arising from the neutron 3 P2 superfluid dominates, while at higher densities the hyperon direct Urca process dominates. For the hyperon direct Urca process to be a candidate responsible for rapid cooling compatible with observations, a moderately large energy gap of the Λ-particle 1 S0 superfliud is required to suppress its large emissivity. The implications of these results are discussed in the relation to thermal evolution of neutron stars.

/pdf/baryon-superfluidity-and-neutrino-emissivity-of-neutron-3h7bhqwc10.pdf

Ryozo Tamagaki

Papers

Confronting Neutron Star Cooling Theories with New Observations

Confronting Neutron Star Cooling Theories with New Observations

The structure and evolution of neutron stars

Occurrence of Hyperon Superfluidity in Neutron Star Cores

Baryon Superfluidity and Neutrino Emissivity of Neutron Stars