Statistics and Evolution of Pulsars’ Parameters

The rotation periods, surface magnetic field strengths, as well as the spatial distribution of the several kinds of pulsars discovered sofar are analyzed statistically. It is revealed that the spatial distribution of the millisecond pulsars is more dispersive than that of the normal radio pulsars. And that the spatial distribution of the pulsars in low-mass X-ray binaries (LMXBs) is also more dispersive than that of the pulsars in high-mass X-ray binaries (HMXBs). The distribution of rotation periods of the isolated millisecond pulsars has a peak at 4.7ms, and the corresponding peak values for the normal radio pulsars and the millisecond pulsars in binaries are 0.6 s and 3.5ms, respectively. The surface magnetic field strengths of the FERMI pulsars (the gamma-ray pulsars observed by the Large Area Telescope/Fermi Gamma-ray Space Telescope) and normal pulsars are all concentrated around 1012 Gs. It is found also that some young high-energy pulsars are associated with supernova remnants. In combination with the formation and evolution models of pulsars, we have made some remarks on the characteristics of these distributions.     

Accretion, ablation and propeller evolution in close millisecond pulsar binary systems

A model for the formation and evolution of binary millisecond radio pulsars in systems with low mass companions (<0.1 M_⊙) is investigated using a binary population synthesis technique. Taking into account the non conservative evolution of the system due to mass loss from an accretion disk as a result of propeller action and from the companion via ablation by the pulsar, the transition from the accretion powered to rotation powered phase is investigated. It is shown that the operation of the propeller and ablation mechanisms can be responsible for the formation and evolution of black widow millisecond pulsar systems from the low mass X-ray binary phase at an orbital period of ～0.1 day. For a range of population synthesis input parameters, the results reveal that a population of black widow millisecond pulsars characterized by orbital periods as long as ～0.4 days and companion masses as low as ～0.005 M_⊙ can be produced. The orbital periods and minimum companion mass of this radio millisecond pulsar population critically depend on the thermal bloating of the semi-degenerate hydrogen mass losing component, with longer orbital periods for a greater degree of bloating. Provided that the radius of the companion is increased by about a factor of 2 relative to a fully degenerate, zero temperature configuration, an approximate agreement between observed long orbital periods and theoretical modeling of hydrogen rich donors can be achieved. We find no discrepancy between the estimated birth rates for LMXBs and black widow systems, which on average are ${\sim}1.3\times10^{-5}~{\rm yr}^{-1}$ and $1.3\times10^{-7}~{\rm yr}^{-1}$ respectively.     

Populating the Galaxy with low-mass X-ray binaries

We perform binary population-synthesis calculations to investigate the incidence of low-mass X-ray binaries (LMXBs) and their birth rate in the Galaxy. We use a binary-evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black hole (BH) LMXBs predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of BH LMXBs. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including LMXBs that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results.     

Effects of dynamo magnetic fields on observational properties of accreting millisecond X-ray pulsars

In this paper,we have investigated accreting millisecond X-ray pulsars,which are rapidly rotating neutron stars in low-mass X-ray binaries.These systems exhibit coherent X-ray pulsations that arise when the accretion flow is magnetically channeled to the stellar surface.Here,we have developed the fundamental equations for an accretion disk around accreting millisecond X-ray pulsars in the presence of a dynamo generated magnetic field in the inner part of the disk.We have also formulated the numerical method for the structure equations in the inner region of the disk and the highest accretion rate is enough to form the inner region of the disk,which is overpowered by radiation pressure and electron scattering.Finally,we have examined our results with the effects of dynamo magnetic fields on accreting millisecond X-ray pulsars.     

On pulsar-driven mass ejection in low-mass X-ray binaries

There is accumulating evidence for mass ejection in low-mass X-ray binaries(LMXBs)driven by radio pulsar activity during X-ray quiescence.We consider the condition for mass ejection by comparing the radiation pressure from a millisecond pulsar,and the gas pressure at the inner Lagrange point or at the surrounding accretion disk.We calculate the critical spin period of the pulsar below which mass ejection is allowed.Combining with the evolution of the mass transfer rate,we present constraints on the orbital ...     

Modeling the luminosity function of galactic low-mass X-ray binaries

The evolution of the family of binaries with a low-mass star and a compact neutron star companion (low-mass X-ray binaries (LMXBs) with neutron stars) ismodeled by the method of population synthesis. Continuous Roche-lobe filling by the optical star in LMXBs is assumed to be maintained by the removal of orbital angular momentum from the binary by a magnetic stellar wind from the optical star and the radiation of gravitational waves by the binary. The developed model of LMXB evolution has the following significant distinctions: (1) allowance for the effect of the rotational evolution of a magnetized compact remnant on themass transfer scenario in the binary, (2) amore accurate allowance for the response of the donor star to mass loss at the Roche-lobe filling stage. The results of theoretical calculations are shown to be in good agreement with the observed orbital period-X-ray luminosity diagrams for persistent Galactic LMXBs and their X-ray luminosity function. This suggests that the main elements of binary evolution, on the whole, are correctly reflected in the developed code. It is shown that most of the Galactic bulge LMXBs at luminosities L _x > 10³⁷ erg s^?1 should have a post-main-sequence Roche-lobe-filling secondary component (low-mass giants). Almost all of the models considered predict a deficit of LMXBs at X-ray luminosities near ～10^36.5 erg s^?1 due to the transition of the binary from the regime of angular momentum removal by a magnetic stellar wind to the regime of gravitational waves (analogous to the widely known period gap in cataclysmic variables, accreting white dwarfs). At low luminosities, the shape of the model luminosity function for LMXBs is affected significantly by their transient behavior-the accretion rate onto the compact companion is not always equal to the mass transfer rate due to instabilities in the accretion disk around the compact object. The best agreement with observed binaries is achieved in the models suggesting that heavy neutron stars with masses 1.4–1.9M _⊙ can be born.     

脉冲星参数统计和演化

统计分析了目前发现的几种脉冲星的自转周期和表面磁场以及空间的分布情况,揭示出毫秒脉冲星比普通射电脉冲星、LMXB(低质量X射线双星)比HMXB(高质量X射线双星)的空间分布要更加弥散;孤立毫秒脉冲星自转周期分布的峰值为4.7 ms,而普通脉冲星的相应值为0.6 s,双星中毫秒脉冲星这一值为3.5 ms; FERMI脉冲...     

Where do the progenitors of millisecond pulsars come from?

Observations of a large population of millisecond pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, low‐mass X‐ray binaries (LMXBs) are considered as progenitors for some MSPs during the recycling process. We present a systematic study that combines different types of compact objects in binaries such as cataclysmic variables (CVs), LMXBs, and MSPs. We plot them together in the so called Corbet diagram. Larger and different samples are needed to better constrain the result as a function of the environment and formations. A scale diagram showing the distribution of MSPs for different orbital periods and the aspects for their progenitors relying on accretion induced collapse (AIC) of white dwarfs in binaries. Thus massive CVs (M ≥ 1.1 M_⊙) can play a vital role on binary evolution, as well as of the physical processes involved in the formation and evolution of neutron stars and their magnetic fields, and could turn into binary MSPs with different scales of orbital periods; this effect can be explained by the AIC process. This scenario also suggests that some fraction of isolated MSPs in the Galactic disk could be formed through the same channel, forming the contribution of some CVs to the single‐degenerate progenitors of Type Ia supernova. Furthermore, we have refined the statistical distribution and evolution by using updated data. This implies that the significant studies of compact objects in binary systems can benefit from the Corbet diagram.Observations of a large population of millisecond pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, low‐mass X‐ray binaries (LMXBs) are considered as progenitors for some MSPs during the recycling process. We present a systematic study that combines different types of compact objects in binaries such as cataclysmic variables (CVs), LMXBs, and MSPs. We plot them together in the so called Corbet diagram. Larger and different samples are needed to better constrain the result as a function of the environment and formations. A scale diagram showing the distribution of MSPs for different orbital periods and the aspects for their progenitors re     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

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.     

Crust–core coupling and r-mode damping in neutron stars: a toy model

r-modes in neutron stars with crusts are damped by viscous friction at the crust–core boundary. The magnitude of this damping, evaluated by Bildsten & Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for neutron stars spun up by accretion in low-mass X-ray binaries (LMXBs). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant-density neutron star having a crust with a constant shear modulus. We find that, at spin frequencies in excess of ≈50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared with the rigid-crust limit. We therefore revise down, by as much as a factor of 10²–10³ , the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron stars with solid crusts. The dependence of the crust–core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multivalued for some temperatures; this is related to avoided crossings between the r-mode and higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.     

Population statistics study of radio and gamma-ray pulsars in the Galactic plane

We present results of our pulsar population synthesis of normal and millisecond pulsars in the Galactic plane. Over the past several years, a program has been developed to simulate pulsar birth, evolution and emission using Monte Carlo techniques. We have added to the program the capability to simulate millisecond pulsars, which are old, recycled pulsars with extremely short periods. We model the spatial distribution of the simulated pulsars by assuming that they start with a random kick velocity and then evolve through the Galactic potential. We use a polar cap/slot gap model for γ-ray emission from both millisecond and normal pulsars. From our studies of radio pulsars that have clearly identifiable core and cone components, in which we fit the polarization sweep as well as the pulse profiles in order to constrain the viewing geometry, we develop a model describing the ratio of radio core-to-cone peak fluxes. In this model, short period pulsars are more cone-dominated than in our previous studies. We present the preliminary results of our recent study and the implications for observing these pulsars with GLAST and AGILE.      

Neutron stars in globular clusters: Formation and observational manifestations

Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M _⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M _⊙ or from binary components with masses >12 M _⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 10⁵ M _⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.     

On the Nature of the Compact Star in 4U 1728-34

The discovery of kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) with the Rossi X-Ray Timing Explorer has stimulated extensive studies of these sources. Recently, Osherovich & Titarchuk suggested a new model for kHz QPOs and the related correlations between kHz QPOs and low-frequency features in LMXBs. Here we use their results to study the mass-radius relation for the atoll source 4U 1728-34. We find that, if this model is correct, 4U 1728-34 is possibly a strange star rather than a neutron star.     

The physical nature of the short-period RS CVn system DV Psc

We re-examine the correlation between the frequencies of upper and lower kHz quasi-periodic oscillations (QPO) in bright neutron star low-mass X-ray binaries. By including the kHz QPO frequencies of the X-ray binary Cir X-1 and two accreting millisecond pulsars in our sample, we show that the full sample does not support the class of theoretical models based on a single resonance, while models based on relativistic precession or Alfvén waves describe the data better. Moreover, we show that the fact that all sources follow roughly the same correlation over a finite frequency range creates a correlation between the linear parameters of the fits to any subsample.     

Scenarios for the formation of binary and millisecond pulsars – A critical assessment

The evolution of high-and low-mass X-ray binaries (HMXB and LMXB) into different types of binary radio pulsars, the ‘high-mass binary pulsars’(HMBP) and ‘low-mass binary pulsars’ (LMBP) is discussed. The HMXB evolve either into Thorne-Zytkow objects or into short-period binaries consisting of a helium star plus a neutron star (or a black hole), resembling Cygnus X-3. The latter systems evolve (with or without a second common-envelope phase) into close binary pulsars, in which the companion of the pulsar may be a massive white dwarf, a neutron star or a black hole ( some final systems may also consist of two black holes). A considerable fraction of the systems may also be disrupted in the second supernova explosion. We discuss the possible reasons why the observed numbers of double neutron stars and of systems like Cyg X-3 are several orders of magnitude lower than theoretically predicted. It is argued that the observed systems form the tip of an iceberg of much larger populations of unobserved systems, some of which may become observable in the future. As to the LMBP, we consider in some detail the origins of systems with orbital periods in the range 1–20 days. We show that to explain their existence, losses of orbital angular momentum (e.g., by magnetic braking) and in a number of cases: also of mass, have to be taken into account. The masses of the low-mass white dwarf companions in these systems can be predicted accurately. We notice a clear correlation between spin period and orbital period for these systems, as well as a clear correlation between pulsar magnetic field strength and orbital period. These relations strongly suggest that increased amounts of mass accreted by the neutron stars lead to increased decay of their magnetic fields: we suggest a simple way to understand the observed value of the ‘bottom’ field strengths of a few times 10⁸ G. Furthermore, we find that the LMBP-systems in which the pulsar has a strong magnetic field (> 10¹¹ G) have an about two orders of magnitude larger birth rate (i.e., about 4 × 10^-4 yr^-1 in the Galaxy) than the systems with millisecond pulsars (which have B < 10⁹ G). Using the observational fact that neutron stars receive a velocity kick of ∼450 km/s at birth, we find that some 90% of the potential progenitor systems of the strong-field LMBP must have been disrupted in the Supernovae in which their neutron stars were formed. Hence, the formation rate of the progenitors of the strong-field LMBP is of the same order as the galactic supernova rate (4 × 10^-3 yr^-1). This implies that a large fraction of all Supernovae take place in binaries with a close low-mass (< 2.3 M⊙) companion.     

Millisecond radio pulsars with known masses: Parameter values and equation of state models

The recent fast growth of a population of millisecond pulsars with precisely measured mass provides an excellent opportunity to characterize these compact stars at an unprecedented level. This is because the stellar parameter values can be accurately computed for known mass and spin rate and an assumed equation of state (EoS) model. For each of the 16 such pulsars and for a set of EoS models from nucleonic, hyperonic, strange quark matter and hybrid classes, we numerically compute fast spinning stable stellar parameter values considering the full effect of general relativity. This first detailed catalogue of the computed parameter values of observed millisecond pulsars provides a testbed to probe the physics of compact stars, including their formation, evolution and EoS. We estimate uncertainties on these computed values from the uncertainty of the measured mass, which could be useful to quantitatively constrain EoS models. We note that the largest value of the central density ρ_c in our catalogue is ∼5.8 times the nuclear saturation density ρ_sat, which is much less than the expected maximum value 13ρ_sat. We argue that the ρ_c-values of at most a small fraction of compact stars could be much larger than 5.8ρ_sat. Besides, we find that the constraints on EoS models from accurate radius measurements could be significantly biased for some of our pulsars, if stellar spinning configurations are not used to compute the theoretical radius values.     

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.     

The population of faint transients in the Galactic Centre

BeppoSAX has detected a population of faint transient X-ray sources in the Galactic Centre. I show that a simple irradiated disc picture gives a consistent fit to the properties of this population, and that it probably consists of low-mass X-ray binaries (LMXBs) that have evolved beyond their minimum orbital periods of ∼80 min. Since all post-minimum systems are transient, and neutron star LMXBs are more common than black hole LMXBs in the Galaxy, the majority of these systems should contain neutron stars, as observed. This picture predicts that the Galactic Centre transients should have orbital periods in the range ∼80–120 min, and that most of them should repeat in the next few years. In this case, the total number of post-minimum transients in the Galaxy would be considerably smaller than the usual estimates of its total LMXB population. I discuss possible reasons for this.     

The Parkes Southern Pulsar Survey — II. Final results and population analysis

A survey of the entire southern sky for millisecond and low-luminosity pulsars using the ATNF Parkes radio telescope has now been completed. The survey detected 298 pulsars, of which 101 were previously unknown. The new pulsars include 17 millisecond pulsars. This is the largest sample of both normal and millisecond pulsars detected in any survey. Combining our sample with other recent surveys in the Northern Hemisphere, we present a statistical study of the populations of both normal and millisecond pulsars. We find that the improved statistics allow us to estimate the number and birth-rate of both types of pulsar down to a 400-MHz luminosity limit of 1 mJy kpc². The local surface densities of potentially observable normal pulsars and millisecond pulsars are both about 30 kpc⁻², corresponding to ∼ 30000 potentially observable pulsars of each type in the Galaxy. Once beaming effects are taken into consideration we estimate that the active population of normal pulsars is ∼ 160000. Although there is evidence for flattening of the luminosity function of normal pulsars, this is not evident for millisecond pulsars which probably have a substantial population with luminosities below 1 mJy kpc². After correcting for beaming effects, we estimate that a normal pulsar is born with a luminosity greater than 1 mJy kpc² between once every 60 and 330 yr in the Galaxy. The birth-rate of millisecond pulsars is at least 3 × 10⁻⁶ yr⁻¹ above the same luminosity limit. Modelling the observed transverse speeds of millisecond pulsars using a dynamical simulation, we find their mean birth velocity to be 130 ± 30 km s⁻¹, significantly lower than that of the normal pulsars.