Thermal evolution of a rotating strange star in the colour superconductivity phase

Under the combination effect of recommencement heating due to the spin-down of strange stars (SSs) and heat preservation due to the weak conduction heat of the crust, Cooper pair breaking and formation (PBF) in colour superconducting quark matter arises. We investigate the cooling of SSs with a crust in the colour superconductivity phase including both deconfinement heating (DH) and the PBF process. We find that DH can delay the thermal evolution of SSs and the PBF process suppresses the early temperature rise of the stars. The cooling SSs behave within the brightness constraint of young compact objects when the colour superconductivity gap is small enough.     

Evolution of The Spin Periods of Neutron Stars in Low Mass X-ray Binaries

We present a numerical analysis of the spin evolution of neutron stars in low-mass X-ray binaries, trying to explain the discrepancy in the spin period distribution between observations of millisecond pulsars and theoretical results. In our calculations, we take account of possible effects of radiation pressure and irradiation-induced instability on the structure of the disk, and the evolution of the mass transfer rate, respectively. We report the following results: (1) The radiation pressure in the accretion disk leads to a slight increase of spin periods, and the variation of mass transfer rate caused by the neutron star irradiation can shorten the spin-down phase of evolution. (2) The calculated results of the model combining radiation pressure and irradiation show that the accretion is strongly limited by the radiation pressure in the high mass transfer phase. (3) The accreted mass and fastness parameter can affect the number of systems in the equilibrium state.     

Cooling of quark stars in the colour superconductive phase: effect of photons from glueball decay

The cooling history of a quark star in the colour superconductive phase is investigated. Here we specifically focus on the two-flavour colour (2SC) phase where the novel process of photon generation via glueball (GLB) decay has already been investigated. The picture we present here can, in principle, be generalized to quark stars entering a superconductive phase where similar photon generation mechanisms are at play. As much as 10⁴⁵–10⁴⁷ erg of energy is provided by the GLB decay in the 2SC phase. The generated photons slowly diffuse out of the quark star, keeping it hot and radiating as a blackbody (with possibly a Wien spectrum in gamma-rays) for millions of years. We discuss hot radio-quiet isolated neutron stars in our picture (such as RX J185635–3754 and RX J0720.4–3125) and argue that their nearly blackbody spectra (with a few broad features) and their remarkably tiny hydrogen atmosphere are indications that these might be quark stars in the colour superconductive phase where some sort of photon generation mechanism (reminiscent of the GLB decay) has taken place. Fits to observed data of cooling compact stars favour models with superconductive gaps of  Δ_2SC∼ 15–35 MeV  and densities  ρ_2SC= (2.5–3.0) ×ρ_N  (ρ_N being the nuclear matter saturation density) for quark matter in the 2SC phase. If correct, our model combined with more observations of isolated compact stars could provide vital information to studies of quark matter and its exotic phases.     

Signal of quark deconfinement in thermal evolution neutron stars with deconfinement heating

As neutron stars spin-down and contract, the deconfinement phase transition can continue to occur, resulting in energy release (so-called deconfinement heating) in case of the first-order phase transition. The thermal evolution of neutron stars is investigated to combine phase transition and the related energy release self-consistently. We find that the appearance of deconfinement heating during spin-down result in not only the cooling delay but also the increase of surface temperature of stars. For stars characterized by intermediate and weak magnetic field strength, a period of increasing surface temperature could exist. Especially, a sharp jump in surface temperature can be produced as soon as quark matter appears in the core of stars with a weak magnetic field. We think that this may serve as evidence for the existence of deconfinement quark matter. The results show that deconfinement heating facilitates the emergence of such characteristic signature during the thermal evolution process of neutron stars.     

Thermal evolution of rotating hybrid stars

As a neutron star spins down, the nuclear matter is continuously converted into quark matter due to the core density increase, and then latent heat is released. We have investigated the thermal evolution of neutron stars undergoing such deconfinement phase transition. We have taken into account the conversion in the frame of the general theory of relativity. The released energy has been estimated as a function of changed rate of deconfinement baryon number. The numerical solutions to the cooling equation are seen to be very different from those without the heating effect. The results show that neutron stars may be heated to higher temperatures which is well matched with pulsar's data despite the onset of fast cooling in neutron stars with quark matter cores. It is also found that the heating effect has a magnetic field strength dependence. This feature could be particularly interesting for high temperatures of low-field millisecond pulsars at a later stage. The high temperature could fit the observed temperature for PSR J0437−4715.     

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of rapidly rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity is solved numerically without the slow rotation approximation. A critical curve of gravitational wave emission induced instability, which restricts the rotational frequencies of hot young neutron stars, is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the 'evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning down proceed. Rotational frequencies of 1.4-M_⊙ stars suffering from this instability decrease to around 100 Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors, who adopted the slow rotation approximation.     

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.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

The evolution of iron-core white dwarfs

Recent measurements by Hipparcos present observational evidence supporting the existence of some white dwarf (WD) stars with iron-rich core composition. In connection with this, the present paper is aimed at exploring the structure and evolution of iron-core WDs by means of a detailed and updated evolutionary code. In particular, we examined the evolution of the central conditions, neutrino luminosity, surface gravity, crystallization, internal luminosity profile and ages. We find that the evolution of iron-rich WDs is markedly different from that of their carbon–oxygen counterparts. In particular, cooling is strongly accelerated (up to a factor of 5 for models with pure iron composition) as compared with the standard case. Thus, if iron WDs were very numerous, some of them would have had time enough to evolve at lower luminosities than that corresponding to the fall-off in the observed WD luminosity function.     

Gravitational waves from r-modes

Detectability of gravitational waves emitted by newly born, hot, rapidly rotating neutron stars as they spin down due to the r-mode instability is discussed. It is shown that differential rotation induced by r-modes plays a fundamental role in the evolution of the mode’s instability, making it more difficult to detect these gravitational waves.     

An explosive end to intermediate-mass zero-metallicity stars and early Universe nucleosynthesis

We use the Cambridge stellar evolution code stars to model the evolution of 5 and  7 M_⊙  zero-metallicity stars. With enhanced resolution at the hydrogen- and helium-burning shell in the asymptotic giant branch (AGB) phases, we are able to model the entire thermally pulsing AGB (TP-AGB) phase. The helium luminosities of the thermal pulses are significantly lower than in higher metallicity stars so there is no third dredge-up. The envelope is enriched in nitrogen by hot-bottom burning of carbon that was previously mixed in during second dredge-up. There is no s -process enrichment owing to the lack of third dredge-up. The thermal pulses grow weaker as the core mass increases and they eventually cease. From then on the star enters a quiescent burning phase which lasts until carbon ignites at the centre of the star when the CO core mass is  1.36 M_⊙  . With such a high degeneracy and a core mass so close to the Chandrasekhar mass, we expect these stars to explode as type 1.5 supernovae, very similar to type Ia supernovae but inside a hydrogen-rich envelope.     

贫金属富碳天琴RR变星的形成

贫金属富碳恒星(Carbon-Enhanced Metal-Poor, CEMP)是研究宇宙早期恒星性质和化学演化的极佳样本,通常认为来自双星.目前发现的贫金属富碳星中有9颗天琴RR变星(RR Lyrae star, RRL),其中至少7颗未表现出任何双星特征.传统双星物质转移模型不足以充分解释贫金属富碳天琴RR变星(CEMP-RR Lyrae)单星的形成.之前研究表明氦白矮星和赫氏空隙星(HG)的并合模型可以解释部分富碳红巨星单星的碳增丰现象,因此贫金属富碳星单星也可能来自氦白矮星和赫氏空隙星的并合模型渠道.通过详细计算的氦白矮星和赫氏空隙星并合模型来检验这一演化渠道,结果表明:该并合模型在后续的演化过程中,其重力加速度、温度、表面碳丰度均能与观测符合较好.由此,氦白矮星和赫氏空隙星并合模型极有可能是贫金属富碳天琴RR变星的形成渠道之一.     

Magnetized relativistic jets and long-duration GRBs from magnetar spin-down during core-collapse supernovae

We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spin-down of a newly formed millisecond,   B ∼ 10¹⁵ G  , magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spin-down powers  (∼10⁵¹–10⁵² erg s⁻¹)  , the magnetar wind is superfast at almost all latitudes, while for lower spin-down powers  (∼10⁵⁰ erg s⁻¹)  , the wind is subfast but still super-Alfvénic. In all cases, the rates at which the neutron star loses mass, angular momentum and energy are very similar to the corresponding free wind values (≲30 per cent differences), in spite of the causal contact between the neutron star and the stellar envelope. In addition, in all cases that we consider, the magnetar drives a collimated  (∼5–10°)  relativistic jet out along the rotation axis of the star. Nearly all of the spin-down power of the neutron star escapes via this polar jet, rather than being transferred to the more spherical SN explosion. The properties of this relativistic jet and its expected late-time evolution in the magnetar model are broadly consistent with observations of long duration gamma-ray bursts (GRBs) and their associated broad-lined Type Ic SN.     

Evolution of a 3-M⊙ star from the main sequence to the ZZ Ceti stage: the role played by element diffusion

The purpose of this paper is to present new full evolutionary calculations for DA white dwarf stars with the major aim of providing a physically sound reference frame for exploring the pulsation properties of the resulting models in future communications. Here, white dwarf evolution is followed in a self-consistent way with the predictions of time-dependent element diffusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to white dwarf formation. In particular, we follow the evolution of a 3-M_⊙ model from the zero-age main sequence (the adopted metallicity is   Z =0.02)  , all the way from the stages of hydrogen and helium burning in the core up to the thermally pulsing phase. After experiencing 11 thermal pulses, the model is forced to evolve towards its white dwarf configuration by invoking strong mass loss episodes. Further evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch.
Emphasis is placed on the evolution of the chemical abundance distribution caused by diffusion processes and the role played by hydrogen burning during the white dwarf evolution. We find that discontinuities in the abundance distribution at the start of the cooling branch are considerably smoothed out by diffusion processes by the time the ZZ Ceti domain is reached. Nuclear burning during the white dwarf stage does not represent a major source of energy, as expected for a progenitor star of initially high metallicity. We also find that thermal diffusion lessens even further the importance of nuclear burning.
Furthermore, the implications of our evolutionary models for the main quantities relevant for adiabatic pulsation analysis are discussed. Interestingly, the shape of the Ledoux term is markedly smoother compared with previous detailed studies of white dwarfs. This is translated into a different behaviour of the Brunt–Väisälä frequency.     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

Magnetic field evolution of accreting neutron stars – III

The evolutionary scenario of a neutron star magnetic field is examined assuming a spin-down induced expulsion of magnetic flux originally confined to the core, in a case in which the expelled flux undergoes ohmic decay. The nature of field evolution, for accreting neutron stars, is investigated incorporating the crustal microphysics and material movement resulting from accretion. This scenario may explain the observed field strengths of neutron stars but only if the crustal lattice contains a large amount of impurity, which is in direct contrast to the models that assume an original crustal field.     

The population of pulsars with interpulses and the implications for beam evolution

The observed fraction of pulsars with interpulses, their period distribution and the observed pulse width versus pulse period correlation are shown to be inconsistent with a model in which the angle α between the magnetic axis and the rotation axis is random. This conclusion appears to be unavoidable, even when non-circular beams are considered. Allowing the magnetic axis to align from a random distribution at birth with a time-scale of  ∼7 × 10⁷ yr  can, however, explain those observations well. The time-scale derived is consistent with that obtained via independent methods. The probability that a pulsar beam intersects the line of sight is a function of the angle α and therefore beam evolution has important consequences for evolutionary models and for estimations of the total number of neutron stars. The validity of the standard formula for the spin-down rate, which is independent of α, appears to be questionable.     

Fallback Disk-Involved Spin-Down of Young Radio Pulsars

Disks originating from supernova fallback have been suggested to surround young neutron stars. Interaction between the disk and the magnetic field of the neutron star may considerably influence the evolution of the star through the so called propeller effect. There are many controversies about the efficiency of the propeller mechanism proposed in the literature. We investigate the fallback disk-involved spin-down of young pulsars. By comparing the simulated and measured results of pulsar evolution, we present some possible constraints on the propeller torques exerted by the disks on neutron stars.     

Magnetic fields of Ap stars as a result of the Tayler instability

Ap star magnetism is often attributed to fossil magnetic fields which have not changed much since the pre‐main‐sequence epoch of the stars. Stable magnetic field configurations are known which could persist probably for the entire mainsequence life of the star, but they may not show the complexity and diversity exhibited by the Ap stars observed. We suggest that the Ap star magnetism is not a result of stable configurations, but is the result of an instability based on strong toroidal magnetic fields buried in the stars. The highly nonaxisymmetric remainders of the instability are reminiscent of the diversity of fields seen on Ap stars. The strengths of these remnant magnetic fields are actually between a few per cent up to considerable fractions of the internal toroidal field; this means field strengths of the order of kGauss being compatible with what is observed. The magnetic fields emerge at the surface rather quickly; rough estimates deliver time‐scales of the order of a few years. Since rotation stabilizes the instability, normal A stars may still host considerable, invisible toroidal magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Accretion disc–stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned, and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc–magnetosphere interaction is large , and consider different outer boundary conditions. In general the field line twisting produces field line inflation (e.g. Bardou & Heyvaerts), and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc, and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be caused by the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in the light of the significant effect that field line twisting has on the magnetic torque resulting from star–disc interactions.