Dmitry G. Yakovlev

Neutrino Emission from Neutron Stars

Abstract We review the main neutrino emission mechanisms in neutron star crusts and cores. Among them are the well-known reactions such as the electron–positron annihilation, plasmon decay, neutrino bremsstrahlung of electrons colliding with atomic nuclei in the crust, as well as the Urca processes and neutrino bremsstrahlung in nucleon–nucleon collisions in the core. We emphasize recent theoretical achievements, for instance, band structure effects in neutrino emission due to scattering of electrons in Coulomb crystals of atomic nuclei. We consider the standard composition of matter (neutrons, protons, electrons, muons, hyperons) in the core, and also the case of exotic constituents such as the pion or kaon condensates and quark matter. We discuss the reduction of the neutrino emissivities by nucleon superfluidity, as well as the specific neutrino emission produced by Cooper pairing of the superfluid particles. We also analyze the effects of strong magnetic fields on some reactions, such as the direct Urca process and the neutrino synchrotron emission of electrons. The results are presented in the form convenient for practical use. We illustrate the effects of various neutrino reactions on the cooling of neutron stars. In particular, the neutrino emission in the crust is critical in setting the initial thermal relaxation between the core and the crust. Finally, we discuss the prospects of exploring the properties of supernuclear matter by confronting cooling simulations with observations of the thermal radiation from isolated neutron stars.

Cooling neutron star in the Cassiopeia A supernova remnant: evidence for superfluidity in the core

According to recent results of Ho & Heinke, the Cassiopeia A supernova remnant contains a young (?330-yr-old) neutron star (NS) which has carbon atmosphere and shows notable decline of the effective surface temperature. We report a new (2010 November) Chandra observation which confirms the previously reported decline rate. The decline is naturally explained if neutrons have recently become superfluid (in triplet state) in the NS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) process that currently accelerates the cooling. This scenario puts stringent constraints on poorly known properties of NS cores: on density dependence of the temperature Tcn(?) for the onset of neutron superfluidity [Tcn(?) should have a wide peak with maximum ? (7–9) × 108 K]; on the reduction factor q of CPF process by collective effects in superfluid matter (q > 0.4) and on the intensity of neutrino emission before the onset of neutron superfluidity (30–100 times weaker than the standard modified Urca process). This is serious evidence for nucleon superfluidity in NS cores that comes from observations of cooling NSs

Thermal relaxation in young neutron stars

ABSTRA C T The internal properties of the neutron star crust can be probed by observing the epoch of thermal relaxation. After the supernova explosion, powerful neutrino emission quickly cools the stellar core, while the crust stays hot. The cooling wave then propagates through the crust, as a result of its finite thermal conductivity. When the cooling wave reaches the surface (age 10‐100 yrU, the effective temperature drops sharply from 250 eV to 30 or 100 eV, depending on the cooling model. The crust relaxation time is sensitive to the (poorly known) microscopic properties of matter of subnuclear density, such as the heat capacity, thermal conductivity, and superfluidity of free neutrons. We calculate the cooling models with the new values of the electron thermal conductivity in the inner crust, based on a realistic treatment of the shapes of atomic nuclei. Superfluid effects may shorten the relaxation time by a factor of 4. The comparison of theoretical cooling curves with observations provides a potentially powerful method of studying the properties of the neutron superfluid and highly unusual atomic nuclei in the inner crust.

Thermal Structure and Cooling of Superfluid Neutron Stars with Accreted Magnetized Envelopes

We study the thermal structure of neutron stars with magnetized envelopes composed of accreted material, using updated thermal conductivities of plasmas in quantizing magnetic fields, as well as the equation of state and radiative opacities for partially ionized hydrogen in strong magnetic fields. The relation between the internal and local surface temperatures is calculated and fitted by an analytic function of the internal temperature, magnetic field strength, angle between the field lines and the normal to the surface, surface gravity, and the mass of the accreted material. The luminosity of a neutron star with a dipole magnetic field is calculated for various values of the accreted mass, internal temperature, and magnetic field strength. Using these results, we simulate cooling of superfluid neutron stars with magnetized accreted envelopes. We consider slow and fast cooling regimes, paying special attention to very slow cooling of low-mass, superfluid neutron stars. In the latter case, the cooling is strongly affected by the combined effect of magnetized accreted envelopes and neutron superfluidity in the stellar crust. Our results are important for the interpretation of observations of the isolated neutron stars hottest for their age, such as RX J0822� 43 and PSR B1055� 52. Subject headings: dense matter — magnetic fields — stars: individual (PSR B1055� 52, RX J0822� 4300) — stars: neutron

Cooling rates of neutron stars and the young neutron star in the Cassiopeia A supernova remnant

We explore the thermal state of the neutron star in the Cassio peia A supernova remnant using the recent result of Ho & Heinke (2009) that the thermal radiation of this star is well-described by a carbon atmosphere model and the emission comes from the entire stellar surface. Starting from neutron star cooling theory, we formulate a robust method to extract neutrino cooling rates of thermally relaxed stars at the neutrino cooling sta ge from observations of thermal surface radiation. We show how to compare these rates with the rates of standard candles ‐ stars with non-superfluid nucleon cores cooling slowly via t he modified Urca process. We find that the internal temperature of standard candles is a we ll-defined function of the stellar compactness parameter x = rg/R, irrespective of the equation of state of neutron star matte r (R and rg are circumferential and gravitational radii, respectivel y). We demonstrate that the data on the Cassiopeia A neutron star can be explained in terms of three parameters: fl, the neutrino cooling effi ciency with respect to the standard candle; the compactness x; and the amount of light elements in the heat blanketing envelope. For an ordin ary (iron) heat blanketing envelope or a low-mass (. 10 −13 M⊙) carbon envelope, we find the e ffi ciency fl∼ 1 (standard cooling) for x . 0.5 and fl ∼ 0.02 (slower cooling) for a maximum compactness x ≈ 0.7. A heat blanket containing the maximum mass (∼ 10 −8 M⊙) of light elements increases fl by a factor of 50. We also examine the (unlikely) possibility that the st ar is still thermally non-relaxed.

Measuring the cooling of the neutron star in Cassiopeia A with all Chandra X-ray Observatory detectors

The thermal evolution of young neutron stars (NSs) reflects the neutrino emission properties of their cores. Heinke & Ho (2010) measured a 3.6+/-0.6% decay in the surface temperature of the Cassiopeia A (Cas A) NS between 2000 and 2009, using archival data from the Chandra X-ray Observatory ACIS-S detector in Graded mode. Page et al. (2011) and Shternin et al. (2011) attributed this decay to enhanced neutrino emission from a superfluid neutron transition in the core. Here we test this decline, combining analysis of the Cas A NS using all Chandra X-ray detectors and modes (HRC-S, HRC-I, ACIS-I, ACIS-S in Faint mode, and ACIS-S in Graded mode) and adding a 2012 May ACIS-S Graded mode observation, using the most current calibrations (CALDB 4.5.5.1). We measure the temperature changes from each detector separately and test for systematic effects due to the nearby filaments of the supernova remnant. We find a 0.92%-2.0% decay over 10 years in the effective temperature, inferred from HRC-S data, depending on the choice of source and background extraction regions, with a best-fit decay of 1.0+/-0.7%. In comparison, the ACIS-S Graded data indicate a temperature decay of 3.1%–5.0% over 10 years, with a best-fit decay of 3.5+/-0.4%. Shallower observations using the other detectors yield temperature decays of 2.6+/-1.9% (ACIS-I), 2.1+/-1.0%(HRC-I), and 2.1+/-1.9% (ACIS-S Faint mode) over 10 years. Our best estimate indicates a decline of 2.9+/-0.5stat+/-1.0sys% over 10 years. The complexity of the bright and varying supernova remnant background makes a definitive interpretation of archival Cas A Chandra observations difficult. A temperature decline of 1–3.5% over 10 years would indicate extraordinarily fast cooling of the NS that can be regulated by superfluidity of nucleons in the stellar core.

CHANDRA PHASE-RESOLVED X-RAY SPECTROSCOPY OF THE CRAB PULSAR

We present the first phase-resolved study of the X-ray spectral properties of the Crab pulsar that covers all pulse phases. The superb angular resolution of the Chandra X-Ray Observatory enables distinguishing the pulsar from the surrounding nebulosity, even at pulse minimum. Analysis of the pulse-averaged spectrum measures interstellar X-ray extinction due primarily to photoelectric absorption and secondarily to scattering by dust grains in the direction of the Crab Nebula. We confirm previous findings that the line of sight to the Crab is underabundant in oxygen, although more so than recently measured. Using recent abundances and cross sections from Wilms, Allen, and McCray, we find ½O=H �¼ð 3:33 � 0:25 Þ� 10 � 4 . Analysis of the spectrum as a function of pulse phase measures the low-energy X-ray spectral index even at pulse minimum—albeit with large statistical uncertainty—and we find marginal evidence for variations of the spectral index. The data are also used to set a new (3 � ) upper limit to the temperature of the neutron star of logT1 < 6:30. Subject headings: atomic processes — ISM: general — pulsars: individual (Crab Pulsar) — stars: neutron — techniques: spectroscopic — X-rays: stars

Cooling Neutron Stars with Accreted Envelopes

The relationships between the effective surface temperature Teff and the internal temperature Tb of nonmagnetized neutron stars with and without accreted envelopes are calculated for Teff > 5 × 104 K. We use updated equations of state and radiative opacities, and we improve considerably the electron conductive opacity. We examine various models of accreted layers (H, He, C, and O subshells produced by nuclear burning of accreted matter). The resulting Teff-Tb relationship is remarkably insensitive to the details of the models and depends mainly on the accreted mass ΔM. For Teff > 105 K, the accreted matter is generally more heat transparent. Even a small accreted mass (ΔM 10-13 M☉) affects appreciably the cooling of a neutron star, leading to higher Teff at the neutrino cooling stage and to lower Teff at the subsequent photon stage. We illustrate this by simulating the standard cooling of neutron stars. The presence of accreted matter yields better agreement of our model cooling curves with the blackbody fits to the ROSAT spectral observations of cooling neutron stars, without invoking quark matter or superfluidity in the neutron star cores.

Heat blanketing envelopes and thermal radiation of strongly magnetized neutron stars

AbstractnStrong (B≫109 G) and superstrong (B≳1014xa0G) magnetic fields profoundly affect many thermodynamic and kinetic characteristics of dense plasmas in neutron star envelopes. In particular, they produce strongly anisotropic thermal conductivity in the neutron star crust and modify the equation of state and radiative opacities in the atmosphere, which are major ingredients of the cooling theory and spectral atmosphere models. As a result, both the radiation spectrum and the thermal luminosity of a neutron star can be affected by the magnetic field. We briefly review these effects and demonstrate the influence of magnetic field strength on the thermal structure of an isolated neutron star, putting emphasis on the differences brought about by the superstrong fields and high temperatures of magnetars. For the latter objects, it is important to take proper account of a combined effect of the magnetic field on thermal conduction and neutrino emission at densities ρ≳1010 gu2009cm−3. We show that the neutrino emission puts a B-dependent upper limit on the effective surface temperature of a cooling neutron star.n

Cooling of isolated neutron stars as a probe of superdense matter physics

We review a current state of cooling theory of isolated neutron stars. The main regulators of neutron star cooling are discussed. We outline the sensitivity of cooling models to equation of state of matter in the neutron star core; the presence or absence of enhanced neutrino emission; superfluidity of baryonic component of matter. A comparison of the cooling theory with observations of thermal emission of isolated neutron stars gives a potentially powerful method to study fundamental properties of superdense matter in neutron star interiors. The prospects of studying neutron star parameters and internal structure are outlined.