Three Types of Cooling Superfluid Neutron Stars: Theory and Observations

Cooling of neutron stars (NSs) with the cores composed of neutrons, protons, and electrons is simulated assuming $^1$S$_0$ pairing of neutrons in the NS crust, and also $^1$S$_0$ pairing of protons and weak $^3$P$_2$ pairing of neutrons in the NS core, and using realistic density profiles of the superfluid critical temperatures $T_{\rm c}(\rho)$. The theoretical cooling models of isolated middle-aged NSs can be divided into three main types. (I) {\it Low-mass}, {\it slowly cooling} NSs where the direct Urca process of neutrino emission is either forbidden or almost fully suppressed by the proton superfluidity. (II) {\it Medium-mass} NSs which show {\it moderate} cooling via the direct Urca process suppressed by the proton superfluidity. (III) {\it Massive} NSs which show {\it fast} cooling via the direct Urca process weakly suppressed by superfluidity. Confronting the theory with observations we treat RX J0822--43, PSR 1055--52 and RX J1856--3754 as slowly cooling NSs. To explain these sufficiently warm sources we need a density profile $T_{\rm c}(\rho)$ in the crust with a rather high and flat maximum and sharp wings. We treat 1E 1207--52, RX J0002+62, PSR 0656+14, Vela, and Geminga as moderately cooling NSs. We can determine their masses for a given model of proton superfluidity, $T_{\rm cp}(\rho)$, and the equation of state in the NS core. No rapidly cooling NS has been observed so far.Comment: 12 pages, 10 figures, Astron. Astrophys., submitte

Cooling of Akmal-Pandharipande-Ravenhall neutron star models

We study the cooling of superfluid neutron stars whose cores consist of nucleon matter with the Akmal-Pandharipande-Ravenhall equation of state. This equation of state opens the powerful direct Urca process of neutrino emission in the interior of most massive neutron stars. Extending our previous studies (Gusakov et al. 2004a, Kaminker et al. 2005), we employ phenomenological density-dependent critical temperatures T_{cp}(\rho) of strong singlet-state proton pairing (with the maximum T_{cp}^{max} \sim 7e9 K in the outer stellar core) and T_{cnt}(\rho) of moderate triplet-state neutron pairing (with the maximum T_{cnt}^{max} \sim 6e8 K in the inner core). Choosing properly the position of T_{cnt}^{max} we can obtain a representative class of massive neutron stars whose cooling is intermediate between the cooling enhanced by the neutrino emission due to Cooper pairing of neutrons in the absence of the direct Urca process and the very fast cooling provided by the direct Urca process non-suppressed by superfluidity.Comment: 9 pages, 6 figures; accepted for publication in MNRA

Hyperons and massive neutron stars: vector repulsion and SU(3) symmetry

With the discovery of massive neutron stars such as PSR J1614-2230, the question has arisen whether exotic matter such as hyperons can exist in the neutron star core. We examine the conditions under which hyperons can exist in massive neutron stars. We consistently investigate the vector meson-hyperon coupling, going from SU(6) quark model to a broader SU(3) symmetry. We propose that the maximum neutron star mass decreases linearly with the strangeness content f_s of the neutron star core as M_max(f_s) = M_max(0) - 0.6 M_solar (f_s/0.1), which seems to be independent of the underlying nuclear equation of state and the vector baryon-meson coupling scheme. Thus, pulsar mass measurements can be used to constrain the hyperon fraction in neutron stars.Comment: 13 pages, 10 figure

The effects of r-process heating on fall-back accretion in compact object mergers

We explore the effects of r-process nucleosynthesis on fall-back accretion in neutron star(NS)-NS and black hole-NS mergers, and the resulting implications for short-duration gamma-ray bursts (GRBs). Though dynamically important, the energy released during the r-process is not yet taken into account in merger simulations. We use a nuclear reaction network to calculate the heating (due to beta-decays and nuclear fission) experienced by material on the marginally-bound orbits nominally responsible for late-time fall-back. Since matter with longer orbital periods t_orb experiences lower densities, for longer periods of time, the total r-process heating rises rapidly with t_orb, such that material with t_orb > 1 seconds can become completely unbound. Thus, r-process heating fundamentally changes the canonical prediction of an uninterrupted power-law decline in the fall-back rate dM/dt at late times. When the timescale for r-process to complete is > 1 second, the heating produces a complete cut-off in fall-back accretion after ~ 1 second; if robust, this would imply that fall-back accretion cannot explain the late-time X-ray flaring observed following some short GRBs. However, for a narrow, but physically plausible, range of parameters, fall-back accretion can resume after ~ 10 s, despite having been strongly suppressed for ~ 1-10 s after the merger. This suggests the intriguing possibility that the gap observed between the prompt and extended emission in short GRBs is a manifestation of r-process heating.Comment: 7 pages; 4 figures; submitted to MNRA

Nucleon Superfluidity vs Observations of Cooling Neutron Stars

Cooling simulations of neutron stars (NSs) are performed assuming that stellar cores consist of neutrons, protons and electrons and using realistic density profiles of superfluid critical temperatures $T_{cn}(\rho)$ and $T_{cp}(\rho)$ of neutrons and protons. Taking a suitable profile of $T_{cp}(\rho)$ with maximum $\sim 5 \times 10^9$ K one can obtain smooth transition from slow to rapid cooling with increasing stellar mass. Adopting the same profile one can explain the majority of observations of thermal emission from isolated middle--aged NSs by cooling of NSs with different masses either with no neutron superfluidity in the cores or with a weak superfluidity, $T_{cn} < 10^8$ K. The required masses range from $\sim 1.2 M_\odot$ for (young and hot) RX J0822-43 and (old and warm) PSR 1055-52 and RX J1856-3754 to $\approx 1.45 M_\odot$ for the (colder) Geminga and Vela pulsars. Observations constrain the $T_{cn}(\rho)$ and $T_{cp}(\rho)$ profiles with respect to the threshold density of direct Urca process and maximum central density of NSs.Comment: 4 pages, 2 figures, AA Letters, accepte

Equation of state and phase transitions in asymmetric nuclear matter

The structure of the 3-dimension pressure-temperature-asymmetry surface of equilibrium of the asymmetric nuclear matter is studied within the thermal Thomas-Fermi approximation. Special attention is paid to the difference of the asymmetry parameter between the boiling sheet and that of the condensation sheet of the surface of equilibrium. We derive the condition of existence of the regime of retrograde condensation at the boiling of the asymmetric nuclear matter. We have performed calculations of the caloric curves in the case of isobaric heating. We have shown the presence of the plateau region in caloric curves at the isobaric heating of the asymmetric nuclear matter. The shape of the caloric curve depends on the pressure and is sensitive to the value of the asymmetry parameter. We point out that the experimental value of the plateau temperature T \approx 7 MeV corresponds to the pressure P = 0.01 MeV/fm^3 at the isobaric boiling.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Nuclei beyond the drip line

In a Thomas-Fermi model, calculations are presented for nuclei beyond the nuclear drip line at zero temperature. These nuclei are in equilibrium by the presence of an external gas, as may be envisaged in the astrophysical scenario. We find that there is a limiting asymmetry beyond which these nuclei can no longer be made stable.Comment: Physical Review C (in press), 1 ReVteX file for text, 4 PS-files for figure

Shear-free radiating collapse and conformal flatness

Here we study some general properties of spherical shear-free collapse. Its general solution when imposing conformal flatness is reobtained [1,2] and matched to the outgoing Vaidya spacetime. We propose a simple model satisfying these conditions and study its physical consequences. Special attention deserve, the role played by relaxational processes and the conspicuous link betweeen dissipation and density inhomogeneity.Comment: 13 pages Latex. Some misprints in eqs.(17), (30) and (35) have been correcte

Magnetars as cooling neutron stars with internal heating

We study thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in a spherical internal layer. We explore the location of this layer as well as the heating rate that could explain high observable thermal luminosities of magnetars and would be consistent with the energy budget of neutron stars. We conclude that the heat source should be located in an outer magnetar's crust, at densities rho < 5e11 g/cm^3, and should have the heat intensity of the order of 1e20 erg/s/cm^3. Otherwise the heat energy is mainly emitted by neutrinos and cannot warm up the surface.Comment: 8 pages, 5 figures, submitted to MNRA

Bulk viscosity in superfluid neutron star cores. I. Direct Urca processes in npe\mu matter

The bulk viscosity of the neutron star matter due to the direct Urca processes involving nucleons, electrons and muons is studied taking into account possible superfluidity of nucleons in the neutron star cores. The cases of singlet-state pairing or triplet-state pairing (without and with nodes of the superfluid gap at the Fermi surface) of nucleons are considered. It is shown that the superfluidity may strongly reduce the bulk viscosity. The practical expressions for the superfluid reduction factors are obtained. For illustration, the bulk viscosity is calculated for two models of dense matter composed of neutrons, protons,electrons and muons. The presence of muons affects the bulk viscosity due to the direct Urca reactions involving electrons and produces additional comparable contribution due to the direct Urca reactions involving muons. The results can be useful for studying damping of vibrations of neutron stars with superfluid cores.Comment: 14 pages, 7 figures, latex, uses aa.cls, to be published in Astronomy and Astrophysic