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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.

The Cooling of compact stars

Abstract The cooling of a compact star depends very sensitively on the state of matter at supranuclear densities, which essentially controls the neutrino emission, as well as on the structure of the stellar outer layers which control the photon emission. Open issues concern the hyperon population, the presence of meson condensates, superfluidity and superconductivity, and the transition of confined hadronic matter to quark matter. This paper describes these issues and presents cooling calculations based on a broad collection of equations of state for neutron star matter and strange matter. These results are tested against the body of observed cooling data.

Surface temperature of a magnetized neutron star and interpretation of the ROSAT data. 1: Dipole fields

We model the temperature distribution at the surface of a magnetized neutron star and study the effects on the observed X-ray spectra and light curves. Generalrelativistic effects, i.e., redshift and lensing, are fully taken into account. Atmospheric effects on the emitted spectral flux are not included: we consider only blackbody emission at the local effective temperature. In this first paper we restrict ourselves to dipole fields. General features are studied and compared with the ROSAT data from the pulsars 0833 - 45 (Vela), 0656 + 14, 0630 + 178 (Geminga), and 1055 - 52, the four cases for which there is strong evidence that thermal radiation from the stellar surface is detected. The composite spectra we obtain are not very different from a blackbody spectrum at the stars effective temperature. We conclude that, as far as blackbody spectra are considered, temperature estimates using single-temperature models give results practically identical to our composite models. The change of the (composite blackbody) spectrum with the stars rotational phase is also not very large and may be unobservable inmost cases. Gravitational lensing strongly suppresses the light curve pulsations. If a dipole field is assumed, pulsed fractions comparable to the observed ones can be obtained only with stellar radii larger than those which are predicted by current models of neutron star struture, or with low stellar masses. Moreover, the shapes of the theoretical light curves with dipole fields do not correspond to the observations. The use of magnetic spectra may raise the pulsed fraction sufficiently but will certainly make the discrepancy with the light curve shapes worse: dipole fields are not sufficient to interpret the data. Many neutron star models with a meson condensate or hypersons predict very small radii, and hence very strong lensing, which will require highly nondipolar fields to be able to reproduce the observed pulsed fractions, if possible at all: this may be a new tool to constrain the size of neutron stars. The pulsed fractions obtained in all our models increase with photon energy: the strong decrease observed in Geminga at energies 0.3-0.5 keV is definitely a genuine effect of the magnetic field on the spectrum in contradistinction to the magnetic effects on the surface temperature considered her. Thus, a detailed analysis of thermal emission from the four pulsars we consider will require both complex surface field configurations and the inclusion of magnetic effects in the atmosphere (i.e., on the emitted spectrum).

NEUTRINO EMISSION FROM COOPER PAIRS AND MINIMAL COOLING OF NEUTRON STARS

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. Previous studies showed that the observed temperatures of young, cooling, isolated neutron stars with ages between 102 and 105 yr, with the possible exception of the pulsar in the supernova remnant CTA 1, are consistent with predictions of the minimal cooling paradigm as long as the neutron 3 P 2 pairing gap present in the stellar core is of moderate size. Recently, it has been found that Cooper-pair neutrino emission from the vector channel is suppressed by a large factor, of the order of 10–3, 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 3 P 2 gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature Tc for this gap covers a range of values between T min c 0.2 × 109 up to T max c 0.5 × 109 in the core of the star. This range of values guarantees that the Cooper-pair neutrino emission is operating efficiently in stars with ages between 103 to 105 yr, leading to the coldest predicted temperatures for young neutron stars. In addition, it is required that young neutron stars have heterogeneous 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.

Charting the Temperature of the Hot Neutron Star in a Soft X-Ray Transient

We explore the thermal evolution of a neutron star undergoing episodes of intense accretion, separated by long periods of quiescence. By using an exact cooling code, we follow in detail the flow of heat in the star due to the time-dependent accretion-induced heating from pycnonuclear reactions in the stellar crust, to the surface photon emission, and to the neutrino cooling. These models allow us to study the neutron stars of the soft X-ray transients. In agreement with recent work of Brown, Bildsten, & Rutledge, we conclude that the soft component of the quiescent luminosity of Aql X-1, of 4U 1608-522, and of the recently discovered SAX J1808.4 can be understood as thermal emission from a cooling neutron star with negligible neutrino emission. However, we show that, in the case of Cen X-4, despite its long recurrence time, strong neutrino emission from the neutron star inner core is necessary to understand the observed low ratio of quiescent to outburst luminosity. This result implies that the neutron star in Cen X-4 is heavier than the one in the other systems and the pairing critical temperature Tc in its center must be low enough (well below 109 K) to avoid a strong suppression of the neutrino emission.

Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints

▪ Abstract We review theoretical developments in studies of dense matter and its phase structure of relevance to compact stars. Observational data on compact stars, which can constrain the properties of dense matter, are presented critically and interpreted.

Period Clustering of the Anomalous X-Ray Pulsars and Magnetic Field Decay in Magnetars

We confront theoretical models for the rotational, magnetic, and thermal evolution of an ultramagnetized neutron star, or magnetar, with available data on the anomalous X-ray pulsars (AXPs). We argue that, if the AXPs are interpreted as magnetars, their clustering of spin periods between 6 and 12 s (observed at present in this class of objects), their period derivatives, their thermal X-ray luminosities, and the association of two of them with young supernova remnants can only be understood globally if the magnetic field in magnetars decays significantly on a timescale of the order of 104 yr.

The cooling of neutron stars by the direct Urca process

The first results are reported from a program to reanalyze the cooling of neutron stars by including the direct Urca process in calculations. It is found that the surface temperature of a young neutron star drops dramatically after about 100 yr if the direct Urca process is allowed and nucleons do not become superfluid. If nucleon superfluidity occurs throughout the direct Urca region, the surface temperature drops to a value determined by the superfluid transition temperature after about 100 yr and decreases slowly for the next 100,000 yr, at which time surface photon cooling takes over. By comparison with observational data, it is found that superfluid transition temperatures of the order of 10 exp 9 K are required in the whole direct Urca inner core.

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 stars 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.

Thermal Evolution and Light Curves of Young Bare Strange Stars

We study numerically the cooling of a young bare strange star and show that its thermal luminosity, mostly due to e(+)e(-) pair production from the quark surface, may be much higher than the Eddington limit. The mean energy of photons far from the strange star is approximately 10(2) keV or even more. This differs both qualitatively and quantitatively from the thermal emission from neutron stars and provides a definite observational signature for bare strange stars. It is shown that the energy gap of superconducting quark matter may be estimated from the light curves if it is in the range from approximately 0.5 MeV to a few MeV.