Equation of state constraints from neutron stars

Recent measurements of thermal radiation from neutron stars have suggested a rather broad range of radiation radii ( ). Sources in M13 and Omega Cen imply R _∞∼12–14 km, but X7 in 47 Tuc implies R _∞∼16–20 km and RX J1856-3754 R _∞>17 km. If these measurements are all correct, only a limited selection of EOS’s could be consistent with them, but a broad range of neutron star masses (up to 2 M_⊙) would also be necessary. The surviving equations of state are incompatible with significant softening above nuclear saturation densities, such as would occur with Boson condensates, a low-density quark-hadron transition, or hyperons. Other potential constraints, such as from QPO’s, radio pulsar mass and moment of inertia measurements, and neutron star cooling, are compared. US DOE Grant DE-FG02-87ER-40317.     

Equation of state of neutron star cores and spin down of isolated pulsars

We study possible impact of a softening of the equation of state by a phase transition, or appearance of hyperons, on the spin evolution of isolated pulsars. Numerical simulations are performed using exact 2-D simulations in general relativity. The equation of state of dense matter at supranuclear densities is poorly known. Therefore, the accent is put on the general correlations between evolution and equation of state, and mathematical strictness. General conjectures referring to the structure of the one-parameter families of stationary configurations are formulated. The interplay of the back bending phenomenon and stability with respect to axisymmetric perturbations is described. Changes of pulsar parameters in a corequake following instability are discussed, for a broad choice of phase transitions predicted by different theories of dense matter. The energy release in a corequake, at a given initial pressure, is shown to be independent of the angular momentum of collapsing configuration. This result holds for various types of phases transition, with and without metastability. We critically review observations of pulsars that could be relevant for the detection of the signatures of the phase transition in neutron star cores. This work was partially supported by the Polish MNiI Grant no. 1P03D-008-27.     

强磁场下中子星外壳的组分和状态方程

本文计算和讨论了强磁场下由冷的催化物质组成的中子星外壳的组份和状态方程。文中考虑了晶格能和强磁场下均匀电子气体的交换能的贡献.得出结论:(1)强磁场使低密度区的状态方程变软;(2)强磁场对高密度区的状态方程几乎没有影响;(3)核质量公式对外壳的组份影响较明显.     

Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein–Maxwell equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass   M = 1.4 M_⊙  and surface magnetic fields of the order of 10¹⁵ G, a quadrupole ellipticity of the order of 10⁻⁶ to 10⁻⁵ should be expected. Low-mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10⁻³ in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.     

The drift model of “magnetars”

It is shown that the drift waves near the light cylinder can cause the modulation of emission with periods of order several seconds. These periods explain the intervals between successive pulses observed in AXPs, SGRs and radio pulsars with long periods. The model under consideration gives the possibility to calculate real rotation periods P of host neutron stars. It is shown that P≤1 s for the investigated objects. The magnetic fields at the surface of the neutron star are of order 10¹¹–10¹³ G and equal to the fields usual for the known radio pulsars.      

Heating and cooling of magnetars with accreted envelopes

We study the thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in an internal layer. We focus on the effect of magnetized (   B ≳ 10¹⁴  G) non-accreted and accreted outermost envelopes composed of different elements, from iron to hydrogen or helium. We discuss a combined effect of thermal conduction and neutrino emission in the outer neutron star crust and calculate the cooling of magnetars with a dipole magnetic field for various locations of the heat layer, heat rates and magnetic field strengths. Combined effects of strong magnetic fields and light-element composition simplify the interpretation of magnetars in our model: these effects allow one to interpret observations assuming less extreme (therefore, more realistic) heating. Massive magnetars, with fast neutrino cooling in their cores, can have higher thermal surface luminosity.     

Progenitors with enhanced rotation and the origin of magnetars

Among the dozen known magnetar candidates, there are no binary objects. Given that the fraction of binary neutron stars is estimated to be about 3–10 per cent, it is reasonable to address the question of solitarity of magnetars, to estimate theoretically the fraction of binary objects among them, and to identify the most probable companions. We present population synthesis calculations of massive binary systems. In this study, we adopt the hypothesis that magnetic field of a magnetar is generated at the protoneutron star stage due to a dynamo mechanism, so rapid rotation of the core of a progenitor star is essential. Our goal is to estimate the number of neutron stars originated from progenitors with enhanced rotation. In our calculations, the fraction of neutron stars originating from such progenitors is about 8–9 per cent. This should be considered as an upper limit to the fraction of magnetars, as some of the progenitors can lose momentum. Most of these objects are isolated due to coalescences of components prior to neutron star formation, or due to system disruption after the second supernova explosion. The fraction of such neutron stars in surviving binaries is about 1 per cent or lower. Their most numerous companions are black holes.     

A model of low-mass neutron stars with a quark core

We consider an equation of state that leads to a first-order phase transition from the nucleon state to the quark state with a transition parameter λ>3/2 (λ=ρ_Q/(ρ_N+P₀/c²)) in superdense nuclear matter. Our calculations of integrated parameters for superdense stars using this equation of state show that on the stable branch of the dependence of stellar mass on central pressure dM/dP_c>0) in the range of low masses, a new local maximum with M_max=0.082_⊙ and R=1251 km appears after the formation of a toothlike kink (M=0.08M_⊙, R=205 km) attributable to quark production. For such a star, the mass and radius of the quark core are M_core=0.005M_⊙ and R_core=1.73 km, respectively. In the model under consideration, mass accretion can result in two successive transitions to a quark-core neutron star with energy release similar to a supernova explosion: initially, a low-mass star with a quark core is formed; the subsequent accretion leads to configurations with a radius of ～1000 km; and, finally, the second catastrophic restructuring gives rise to a star with a radius of ～100 km.     

On the equation of state for the Λ field

The recently detected accelerated expansion of the Universe is related to the existence of a new type of matter called the Λ field or quintessence. Constraints were obtained on its equation of state from the absence of clustering of this matter on scales much smaller than the cosmological horizon. The question of how these constraints affect the possibility of fitting the accelerated expansion by such cosmological models as the Chaplygin gas model is discussed.     

Equation of state under nuclear statistical equilibrium conditions

We investigate a three-parameter equation of state for stellar matter under nuclear statistical equilibrium conditions in the ranges of temperatures 3×10⁹–10¹¹ K and densities 10⁴–10¹³ g cm^?3 and for various ratios of the total number of neutrons to the total number of protons within the range 1–1.5. These conditions correspond to the initial stages of the gravitational collapse of iron stellar cores that are accompanied by nonequilibrium matter neutronization. We analyze the effect of the excited levels of atomic nuclei on the thermodynamic properties of the matter. We show that this effect is insignificant at low densities, ρ?10¹⁰ g cm^?3, but it leads to an expansion of the instability region, γ<4/3, at higher densities. The incorporated effects of the Fermi degeneracy of free nucleons prove to be insignificant, because their concentrations are low at low temperatures. In the future, we plan to investigate the effects of Coulomb interactions and neutron-rich nuclei on the thermodynamic properties of the matter.     

The influence of turbulence pressure on the late stages of evolution of medium and small mass stars (I) Calculation of the turbulence pressure, equation of state and thermodynamic quantities

Using the mixing length theory we give expressions for turbulence pressure and the equation of state and various thermodynamic quantities when turbulence is included. On this basis we examined the size of turbulence in the evolution of two stars of masses 2.8 and 7.0M from the main sequence to the red giant and the AGB stages, Our results show that in the late stages the turbulence pressure near the surface of the star can be as much as 30% of the total pressure.     

The maximum mass of neutron stars

Summary. The maximum mass of neutron stars plays an important role in determining the end point of the evolution of massive stars. As the number of stellar mass black holes in binary x-ray sources grows, and as the mass spectrum of the black holes emerges, the value of the maximum mass of neutron stars has acquired great significance. Although it is now more than sixty years since the first attempt by Oppenheimer and Volkoff, no definitive answer can be given. This review will attempt to outline the main difficulties, both conceptual as well as technical, that stand in the way of a reliable estimate of the maximum mass. We shall also highlight how laboratory experiments, as well as astronomical observations, may help to clarify the true nature of the interior of neutron stars. Received 26 November 2001 / Published online 22 April 2002     

Stellar models with generalized polytropic equation of state

We find new classes of exact solutions to the Einstein field equations where the matter distribution satisfies a generalized polytropic equation of state. The matter distribution is uncharged with anisotropic pressures. Equations of state for polytropes and quark matter are contained as special cases. The matter variables and metric potentials can be obtained explicitly. Known solutions, for the choice of the gravitational potential made in this analysis, arise as special cases for particular choice of the equation of state parameters. A detailed physical analysis indicates that the model is well behaved.     

Early evolution of newly born magnetars with a strong toroidal field

We present a state-of-the-art scenario for newly born magnetars as strong sources of gravitational waves (GWs) in the early days after formation. We address several aspects of the astrophysics of rapidly rotating, ultra-magnetized neutron stars (NSs), including early cooling before transition to superfluidity, the effects of the magnetic field on the equilibrium shape of NSs, the internal dynamical state of a fully degenerate, oblique rotator and the strength of the electromagnetic torque on the newly born NS. We show that our scenario is consistent with recent studies of supernova remnant surrounding Anomalous X-ray Pulsars (AXPs) and Soft Gamma-Ray Repeaters (SGRs) in the Galaxy that constrains the electromagnetic energy input from the central NS to be  ≤ 10⁵¹  erg. We further show that if this condition is met, then the GW signal from such sources is potentially detectable with the forthcoming generation of GW detectors up to Virgo cluster distances where an event rate ∼1 yr⁻¹ can be estimated. Finally, we point out that the decay of an internal magnetic field in the 10¹⁶ G range couples strongly with the NS cooling at very early stages, thus significantly slowing down both processes: the field can remain this strong for at least 10³ yr, during which the core temperature stays higher than several times 10⁸ K.     

Feasibility and design of a solid state gamma-ray detector

For conventional radiation detectors fabricated from compound semi-conductors, the wide disparity between the transport properties of the electron and holes, means that detector performances are limited by the carrier with the poorest mobility-lifetime product (μτ). Finite drift lengths introduce an energy dependent depth term into the charge collection process, which effectively limit maximum detection volume to tens of mm³ – entirely unsuitable for the detection of gamma-rays. The recent introduction of the coplanar-grid charge-sensing techniques has overcome this problem by essentially discarding the carrier with the poorest transport properties, thus permitting high spectral resolution and high detection efficiency. For example, energy resolutions of 2% full-width half-maximum at 662 keV have been demonstrated with coplanar-grid CdZnTe detectors of volumes up to 2 cm³. Further improvements in detector performance and yield are being pursued through refinements in electrode design and material quality. Because coplanar-grid CdZnTe detectors can operate at room temperature, they are ideally suited for applications requiring portability, small size, or low power consumption such as planetary space missions. Other potential applications include well logging, medical diagnostics, and gamma-ray astronomy. We discuss the feasibility and design of a solid state gamma-ray detector based on CdZnTe and compare its performance to a large volume Ge detector. As will be shown, a significant improvement can be made if T1Br is used as the detection medium.