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.     

An Upper Bound on Neutron Star Masses

We derive an upper bound on neutron star masses by using model equations of state in the nuclear matter density region and the causality limited equation of state in the ultradense region. Supposing that the model equations of state describe neutron star matter at nuclear matter density correctly we find as bound 3.75 M_⊙. For large fiducial densities one gets a maximum mass which is above a previous estimate.     

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.     

Evolution of massive close binaries and formation of neutron stars and black holes

Main results of computations of evolution for massive close binaries (10M +9.4M , 16M +15M , 32M +30M , 64M +60M ) up to oxygen exhaustion in the core are described. Mass exchange starting in core hydrogen, shell hydrogen and core helium burning stages was studied. Computations were performed assuming both the Ledoux and Schwarzschild stability criteria for semiconvection. The influence of UFI-neutrino emission on evolution of close binaries was investigated. The results obtained allow to outline the following evolutionary chain: two detached Main-Sequence stars — mass exchange — Wolf-Rayet star or blue supergiant plus main sequence star — explosion of the initially more massive star appearing as a supernova event — collapsed or neutron star plus Main-Sequence star, that may be observed as a runaway star — mass exchange leading to X-rays emission — collapsed or neutron star plus WR-star or blue supergiant — second explosion of supernova that preferentially disrupts the system and gives birth to two single high spatial velocity pulsars.Numerical estimates concerning the number and properties of WR-stars, pulsars and X-ray sources are presented. The results are in favour of the existence of UFI-neutrino and of the Ledoux criterion for describing semiconvection. Properties of several well-known X-ray sources and the binary pulsar are discussed on base of evolutionary chain of close binaries.     

On the relationship between pulsars and supernova remnants

We propose that single stars in the mass range 4–6·5M _⊙, that explode as Supernovae of Type I, are totally disrupted by the explosion and form shell-type remnants. More massive single stars which explode as Supernovae of Type II also give rise to shell-type remnants, but in this case a neutron star or a black hole is left behind. The first supernova explosion in a close binary also gives rise to a shell-type supernova remnant. The Crab-like filled-centre supernova remnants are formed by the second supernova explosion in a close binary. The hybrid supernova remnants, consisting of a filled centre surrounded by a shell, are formed if there is an active neutron star inside the shell.     

Evolution of massive binary stars in the LMC and its implications for radio pulsar population

The Hertzsprung-Russell diagram of the Large Magellanic Cloud compiled recently by Fitzpatrick & Garmany (1990) shows that there are a number of supergiant stars immediately redward of the main sequence although theoretical models of massive stars with normal hydrogen abundance predict that the region 4.5 ≤ logT _eff ≤ 4.3 should be un-populated (“gap”). Supergiants having surface enrichment of helium acquired for example from a previous phase of accretion from a binary companion, however, evolve in a way so that the evolved models and observed data are consistent — an observation first made by Tuchman & Wheeler (1990). We compare the available optical data on OB supergiants with computed evolutionary tracks of massive stars of metallicity relevant to the LMC with and without helium-enriched envelopes and conclude that a large fraction (≈ 60 per cent) of supergiant stars may occur in binaries. As these less evolved binaries will later evolve into massive X-ray binaries, the observed number and orbital period distribution of the latter can constrain the evolutionary scenarios of the supergiant binaries. The distributions of post main sequence binaries and closely related systems like WR + O stars are bimodal-consisting of close and wide binaries in which the latter type is numerically dominating. When the primary star explodes as a supernova leaving behind a neutron star, the system receives a kick and in some cases can lead to runaway O-stars. We calculate the expected space velocity distribution for these systems. After the second supernova explosion, the binaries in most cases, will be disrupted leading to two runaway neutron stars. In between the two explosions, the first born neutron star’s spin evolution will be affected by accretion of mass from the companion star. We determine the steady-state spin and radio luminosity distributions of single pulsars born from the massive stars under some simple assumptions. Due to their great distance, only the brightest radio pulsars may be detected in a flux-limited survey of the LMC. A small but significant number of observable single radio pulsars arising out of the disrupted massive binaries may appear in the short spin period range. Most pulsars will have a low velocity of ejection and therefore may cluster around the OB associations in the LMC.     

On the pre-supernova parameters of the Hercules X-1 system

On the assumption that, at the moment of the supernova explosion, the presently nondegenerate companion of Her X-1 was a Main-Sequence star with polytropic indexn=3, it is found that the effects of impact and ablation cannot have removed more than about 10% of its pre-supernova mass. A remnant mass for a neutron star of 1.4M was adopted. The effects of impact and ablation were calculated in the manner given by Wheeleret al. (1975). Depending on the ejection velocity of the SN shell, it is found that with a pre-SN mass of 2.2M (i.e., the maximum possible value) for the non-degenerate component, the initial binary period was in the range 2–4 days.     

A new representation of theH-functions of radiative transfer

The energetics involved in the formation of neutron stars in close binaries as a result of supernova explosions are considered. The gravitational binding energy of the neutron star must find proper outlets. The mass ejection and cosmic ray particles can carry away only a small fraction (up to a few per cent) of this energy. Most of the binding energy goes into rotational kinetic energy, gravitational radiation and neutrino emissions. A scenario is considered in which most of the gravitational binding energy goes into rotational kinetic energy and is, ultimately, radiated away as gravitational waves.     

Hyperfast pulsars as the remnants of massive stars ejected from young star clusters

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of  ∼1100 km s⁻¹  , which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis, we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole (IMBH) and (iii) a single stars and a hard binary IMBH. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of  10⁶– 10⁷ stars pc⁻³  . Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.     

The spin evolution of nascent neutron stars

The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ≤10¹³ G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.     

Gravitational collapse of magnetic neutron stars

Pulsars are presently believed to be rotating neutron stars with frozen-in magnetic fields. Because of the high density of neutron stars, general relativistic effects are important since they effect both the structure and stability of such stars. Besides this, the magnetic field outside the star is also affected. Instead of falling of asr ^(2+l) as in flat space, it is shown that each magnetic multipole varies as a hypergeometric function of radius. A closed form of these hypergeometric functions is given in terms of Legendre functions of the second kind. If the mass of a neutron star exceeds about 2.4m , the star becomes unstable and coliapses. For a quasistatically collapsing body, it is shown that the magnetic field seen by a distant observer vanishes as the radius approaches the gravitational radius.This work was supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research under AFOSR Grant 70-1866.     

Cosmic gamma-ray emission and comet collisions with compact stars

The probability that γ-ray bursts may be generated by the infall of comet-like objects on the neutron stars, as recently proposed by Harwit and Salpeter (1973), is reexamined. Although hypothetical cometary clouds around the parent star may survive the supernova outburst virtually untouched, the frequency of γ-outbursts due to the comet impact on the neutron star or white dwarf is only about 10^?3 of the observed occurrence. A considerably higher rate of comets passing per year at critical periastron distance must be assumed if the γ-ray outbursts are to be due to the collision of coments with compact stars.     

Slowly rotating relativistic stars

Equations are given which determine the moment of inertia of a rotating relativistic fluid star to second order in the angular velocity with no other approximation being made. The equations also determine the moment of inertia of matter located between surfaces of constant density in a rotationally distorted star; for example, the moments of inertia of the crust and core of a rotationally distorted neutron star can be calculated in this way. The method is applied ton=3/2 relativistic polytropes and to neutron star models constructed from the Baym-Bethe-Pethick-Sutherland-Pandharipande equation of state. Supported in part by the National Science Foundation. Alfred P. Sloan Research Fellow.     

Rotating black holes in neutron and quark stars: Phenomenon of pulsars

The phenomenon of pulsars is considered as the evidence for existence of black holes in neutron and quark stars. Within the framework of the degenerated star model with black-hole interior the existence of millisecond pulsars withP<0.5 ms and single pulsars with negative derivative of the period were predicted. The anisotropic accretion of neutron (or quark) star matter on to a rotating black hole leads to the formation of directed radiation (projector), which makes heat spots at surface (volcanos), that explains the nature of pulsating radiation and the complicated structure of impulses. This model gives both the mechanism of self-acceleration of degenerated star rotation (mass accretion on to the internal black hole) producing millisecond pulsars and also the mechanism of significant deceleration of rotation (ejection of neutral mass through a volcanic crater), leading to long-periodic X-ray pulsars. The black hole produces high densities and temperatures of the degenerated star mass that transforms gradually the neutron star into quark star (Cygnus X-3).     

Evolution of massive close binaries

The further evolution of a massive X-ray binary consisting of a compact object and an OB supergiant is outlined. The supergiant exceeds its critical Roche lobe and a second stage of mass transfer starts. The remnant of the mass losing star — a pure helium star — develops a collapsing iron core and finally undergoes a supernova explosion. If the compact companion is a black hole the system remains bound; if the compact companion is a neutron star the system is disrupted unless an extra kick allowing an asymmetric explosion is given. Computations were performed for the massive binary 22.5M _⊙+2M _⊙. The possible final evolutionary products are: (1) a black hole and a compact object, in a binary system, (2) two run-away pulsars, (3) a binary pulsar. As final parameters for the described system the eccentricity and period for the recently discovered binary pulsar 1913+16 may be found. An orbital inclination ofi=40° may be derived. The probability for the generation of binary pulsars is very low; in most cases the system is disrupted during the supernova explosion.     

The physics of strong magnetic fields in neutron stars

In this paper we present a new result, namely that the primal magnetic field of the collapsed core during a supernova explosion will, as a result of the conservation of magnetic flux, receive a massive boost to more than 90 times its original value by the Pauli paramagnetization of the highly degenerate relativistic electron gas just after the formation of the neutron star. Thus, the observed super-strong magnetic field of neutron stars may originate from the induced Pauli paramagnetization of the highly degenerate relativistic electron gas in the interior of the neutron star. We therefore have an apparently natural explanation for the surface magnetic field of a neutron star.     

Synchrotron neutrino-pair radiation in neutron stars

The neutrino-pair radiation by electrons in a non-quantizing magnetic field B is investigated. For a relativistic degenerate electron gas the emissivity of this process is mainly given by \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _r = 5 \times 10^{15} (pF/mc)^{4/3} \,B_{13}^{2/3} T_y^{12/8} \,{\rm erg} \times {\rm cm}^{ - 3} \times {\rm sec}^{- 1} $\end{document} where pF is the electron Fermi momentum. Under typical neutron star conditions at B ∼ 10¹³G neutrino synchrotron radiation appears to be one of the most effective mechanisms of neutrino energy loss in the envelopes of neutron stars; this mechanism may also compete with other known neutrino production mechanisms in the neutron star cores if pion condensate or quark matter is absent.     

Analytic formulas for the mass-transfer rate and the evolution of a close binary system of neutron (degenerate) stars

We derive approximate analytic relations between the mass-transfer rate in a close binary system described in terms of the Roche potential and its basic parameters, such as the total mass of the binary, the radius of its circular orbit, the mass of the mass-losing component, and the degree of its Roche lobe overfilling. Using simplifying assumptions (conservative mass transfer, a short relaxation time of matter on the mass-gaining component compared to the mass-transfer time scale, adiabaticity and quasi-stationarity of the mass flow through the Lagrangian point L ₁) allows the evolution of a binary system of neutron (degenerate) stars to be described in terms of two ordinary differential equations. This makes it possible to qualitatively analyze the evolution process, which is useful in those cases where the evolution of a close binary system must be investigated in general terms, for example, in terms of the scenario for the transformation of the collapse of a rotating presupernova core into a supernova explosion proposed by Imshennik and Nadyozhin (1992) and Imshennik (1992).     

Low-Mass Quark Stars or Quark White Dwarfs

An equation of state is considered that, in superdense nuclear matter, results in a phase transition of the first kind from the nucleon state to the quark state with a transition parameter > 3/2 ( = _Q /( _N + P ₀/c ²)). A calculation of the integrated parameters of superdense stars on the basis of this equation of state shows that on the stable branch of the dependence of stellar mass on central pressure (dM/dP _c > 0), in the low-mass range, following the formation of a tooth-shaped break (M = 0.08 M , R = 200 km) due to quark formation, a new local maximum with M _max = 0.082 M and R = 1251 km is also formed. The mass and radius of the quark core of such a star turn out to be M _core = 0.005 M and R _core = 1.7 km, respectively. Mass accretion in this model can result in two successive transitions to a neutron star with a quark core, with energy release like supernova outbursts.     

On the progenitors of core-collapse supernovae

Theory holds that a star born with an initial mass between about 8 and 140 times the mass of the Sun will end its life through the catastrophic gravitational collapse of its iron core to a neutron star or black hole. This core collapse process is thought to usually be accompanied by the ejection of the star’s envelope as a supernova. This established theory is now being tested observationally, with over three dozen core-collapse supernovae having had the properties of their progenitor stars directly measured through the examination of high-resolution images taken prior to the explosion. Here I review what has been learned from these studies and briefly examine the potential impact on stellar evolution theory, the existence of “failed supernovae”, and our understanding of the core-collapse explosion mechanism.