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.     

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     

Formation of accreting millisecond X-ray pulsars

Accreting millisecond X-ray pulsars(AMXPs) are an important subclass of low-mass X-ray binaries(LMXBs), in which coherent millisecond X-ray pulsations can be observed during outburst states.They have dual characteristics of LMXBs and millisecond pulsars, providing a direct confirmation for the recycling scenario. However, their formation is not well understood. In this work, we simulate the evolution of LMXBs with the MESA code to explore the formation and evolution of AMXPs. Based on the binary evolutionary model of LMXBs and the model of accretion disk instability, we find that most of the observed AMXPs can be produced from LMXBs with orbital periods at the onset of Roche lobe overflow close to the bifurcation period and their observed properties can be explained by our models. The AMXPs with main sequence(MS) donors ultimately evolve into AMXPs with extremely low-mass He white dwarf donors.Moreover, our results indicate that these AMXPs with MS donors are likely to have donor stars near the terminal-age main sequence.     

低质量X射线双星的毫秒级准周期信号——最近的进展

最近对低质量X射线双星中的千赫兹准周期振动的研究表明 ,是辐射压力 ,而不是盘和磁球的相互作用以及处于盘内边界的广义相对论效应在短时标的盘切断机制上起作用。本文给出了一些研究结果及讨论。     

Pulsational instability of accretion disks around compact objects

Linear analysis shows that radial oscillations in accretion disks around compact object are overstable to axisymmetric perturbation under a variety of conditions. Furthermore, numerical simulations confirm that the radial oscillations induce quasi-periodic modulations of the disk luminosity. The disk oscillation model may be responsible for quasi-periodic oscillations (QPOs) observed in low mass X-ray binaries (LMXBs), cataclysmic variables (CVs), and other compact objects.     

Boundary layer emission in luminous LMXBs

We show that aperiodic and quasiperiodic variability of bright LMXBs – atoll and Z‐sources – on ∼ sec‐msec time scales is caused primarily by variations of the luminosity of the boundary layer. The emission of the accretion disk is less variable on these time scales and its power density spectrum follows P _disk(f ) ∝ f ^–1 law, contributing to observed flux variation at low frequencies and low energies only. The kHz QPOs have the same origin as variability at lower frequencies, i.e. independent of the nature of the “clock”, the actual luminosity modulation takes place on the neutron star surface. The boundary layer spectrum remains nearly constant in the course of the luminosity variations and is represented to certain accuracy by the Fourier frequency resolved spectrum. In the investigated range of ∼ (0.1 – 1) _Edd it depends weakly on the global mass accretion rate and in the limit ∼ _Edd is close toWien spectrum with kT ∼ 2.4 keV. Its independence on the global value of lends support to the theoretical suggestion by Inogamov & Sunyaev (1999) that the boundary layer is radiation pressure supported. Based on the knowledge of the boundary layer spectrum we attempt to relate the motion along the Z‐track to changes of physically meaningful parameters. Our results suggest that the contribution of the boundary layer to the observed emission decreases along the Z‐track from conventional ∼50% on the horizontal branch to a rather small number on the normal branch. This decrease can be caused, for example, by obscuration of the boundary layer by the geometrically thickened accretion disk at ∼ _Edd. Alternatively, this can indicate significant change of the structure of the accretion flow at ∼ _Edd and disappearance of the boundary layer as a distinct region of the significant energy release associated with the neutron star surface. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On The Low Frequency Quasi Periodic Oscillations Of X-Ray Sources

Based on the interpretation of the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) ascribed to the Keplerian and the periastron precession frequencies at the inner disk respectively, we ascribe the low frequency (0.1–10 Hz) Quasi Periodic Oscillations (LFQPO) and HBO (15–60 Hz QPO for Z sources or Atoll sources) to the periastron precession at some outer disk radius. It is assumed that both radii are correlated by a scaling factor of 0.4. The conclusions obtained include: All QPO frequencies increase with increasing accretion rate. The theoretical relations between HBO (LFQPO) frequency and the kHz QPO frequencies are similar to the measured empirical formula.     

Are the magnetic fields of millisecond pulsars ∼108 G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are ～10⁸ G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The ～10⁸G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have <10¹¹ G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 10¹¹ G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict ～10⁸ G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted ～10⁸ G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields ?10⁸ G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields >10⁸ G with their magnetic dipole emission being balanced by low level accretion from their companions.     

CDM, Feedback and the Hubble Sequence

We have performed TreeSPH simulations of galaxy formation in a standard ΛCDM cosmology, including effects of star formation, energetic stellar feedback processes and a meta-galactic UV field, and obtain a mix of disk, lenticular and elliptical galaxies. The disk galaxies are deficient in angular momentum by only about a factor of two compared to observed disk galaxies. The stellar disks have approximately exponential surface density profiles, and those of the bulges range from exponential to r ^1/4, as observed. The bulge-to-disk ratios of the disk galaxies are consistent with observations and likewise are their integrated B-V colours, which have been calculated using stellar population synthesis techniques. Furthermore, we can match the observed I-band Tully-Fisher (TF) relation, provided that the mass-to-light ratio of disk galaxies is (M/L _I) ≃ 0.6–0.7. The ellipticals and lenticulars have approximately r ^1/4 stellar surface density profiles, are dominated by non-disklike kinematics and flattened due to non-isotropic stellar velocity distributions, again consistent with observations. This revised version was published online in September 2006 with corrections to the Cover Date.     

A theory of galactic mass and rotation curves

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr ₀ and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr ₀v²/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density (r) (in kg m^–2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.     

Vertical structure of the outer accretion disk in persistent low-mass X-ray binaries

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy E ≳ 10 keV exerts a significant influence on the vertical structure of the accretion disk at a distance R ≳ 10¹⁰ cm from the neutron star. At a distance R ∼ 10¹¹ cm, where the total surface density in the disk reaches Σ₀ ∼ 20 g cm⁻², X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature T _atm ≈ (2–3) × 10⁶ K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a ≲10% accuracy in the range of X-ray photon energies E < 20 keV.     

Programme of the Galactic meridian: Star counts and galactic models. 1. Distributions of stellar magnitudes and colours

A comparison of observed stellar distributions with a three-component model of the Galaxy is presented. The analysis is based on photometric and photoelectric data obtained along the main Galactic meridian and in two fields near the North Galactic pole (programme MEGA). The assumed model considers the Galaxy as composed of the disk (main sequence and disk red giants), the thick disk and spheroid populations. To model the observed colour distribution, we distinguish main sequence stars and disk red giants as the disk subsystem; white dwarfs, subdwarfs and intermediate giants as the thick disk subsystem; extreme subdwarfs, spheroid giants and horizontal branch stars as the spheroid subsystem. A statistical relation between the apparent and absolute magnitudes of stars which make the maximum contribution to the star counts for a given disk subsystem is derived. In order to achieve the best agreement between the model and observations, we fit the values of the ‘dip’ (aw) of the disk luminosity function, the correction to the absolute magnitude of disk red giants (ΔM_V^RG) and the expression for interstellar extinction. As the main result, we obtained aw = 0.6 (logarithmic scale) and ΔM_V^RG = 0.5 mag; the interstellar extinction has to be taken into account by the modified Sandage law.     

Gravitational instability of interstellar magnetic clouds

The gravitational instability of a nonrotating isothermal gaseous disk permeated by a uniform frozen-in magnetic field is investigated using a fourth-order perturbation technique. From the results it is found that the disk is stable whenn/B ₀ < (4/3³ G)^–1/2, wheren andB are the column density of the disk and unperturbed magnetic field, respectively, andG is the gravitational constant. The disk is gravitationally unstable only whenn/B ₀ > (4/3³ G)^–1/2.     

Time‐series high‐resolution spectroscopy and photometry of ε Aurigae from 2006–2013: Another brick in the wall

We present continuous and time‐resolved R = 55 000 optical échelle spectroscopy of ε Aurigae from 2006–2013. Data were taken with the STELLA Echelle Spectrograph of the robotic STELLA facility at the Observatorio del Teide in Tenerife. Contemporaneous photometry with the Automatic Photoelectric Telescopes at Fairborn Observatory in Arizona is presented for the years 1996–2013. Spectroscopic observations started three years prior to the photometric eclipse and are still ongoing. A total of 474 high‐resolution échelle spectra are analyzed and made available in this paper. We identify 368 absorption lines of which 161 lines show the characteristic sharp disk lines during eclipse. Another 207 spectral lines appeared nearly unaffected by the eclipse. From spectrum synthesis, we obtained the supergiant atmospheric parameters T_eff = 7395 ± 70 K, log g ≈ 1, and [Fe/H] = +0.02 ± 0.2 with ξ_t = 9 km s^–1, ζ_RT = 13 km s^–1, and v sin i = 28 ± 3 km s^–1. The residual average line broadening expressed in km s^–1 varies with a period of 62.6 ± 0.7 d, in particular at egress and after the eclipse. Two‐dimensional line‐profile periodograms show several periods, the strongest with ≈110 d evident in optically thin lines as well as in the Balmer lines. Center‐of‐intensity weighted radial velocities of individual spectral lines also show the 110‐d period but, again, additional shorter and longer periods are evident and are different in the Balmer lines. The two main spectroscopic Hα periods, ≈ 116 d from the line core and ≈ 150 d from the center‐of‐intensity radial velocities, appear at 102 d and 139 d in the photometry. The Hβ and Johnson V I photometry on the other hand shows two well‐defined and phase‐coherent periods of 77 d and 132 d. We conclude that Hα is contaminated by changes in the circumstellar environment while the Hβ and V I photometry stems predominantly from the non radial pulsations of the F0 supergiant. We isolate the disk‐rotation profile from 61 absorption lines and found that low disk eccentricity generally relates to low disk rotational velocity (but not always) while high disk eccentricity always relates to high velocity. There is also the general trend that the disk‐absorption in spectral lines with higher excitation potential comes from disk regions with higher eccentricity and thus also with higher rotational velocity. The dependency on transition probability is more complex and shows a bi‐modal trend. The outskirts of the disk is distributed asymmetrically around the disk and appears to have been built up mostly in a tail along the orbit behind the secondary. Our data show that this tail continues to eclipse the F0 Iab primary star even two years after the end of the photometric eclipse. High‐resolution spectra were also taken of the other, bona‐fide, visual‐binary components of ε Aur (ADS 3605BCDE). Only the C‐component, a K3‐4‐giant, appears at the same distance than ε Aur but its radial velocity is in disagreement with a bound orbit. The other components are a nearby (≈ 7 pc) cool DA white dwarf, a G8 dwarf, and a B9 supergiant, and not related to ε Aur. The cool white dwarf shows strong DIB lines that suggest the existence of a debris disk around this star. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Early-Type Stars

Away from the young disk, several classes of early type stars are found. They include (i) the old, metal-poor blue horizontal branch stars of the halo and the metal-poor tail of the thick disk; (ii) metal-rich young A stars in a rapidly rotating subsystem but with a much higher velocity dispersion than the A stars of the young disk, and (iii) a newly discovered class of metal-poor young main sequence A stars in a subsystem of intermediate galactic rotation (V_rot ≈ 120 km s⁻¹). The existence and kinematics of these various classes of early type stars provide insight into the formation of the metal-poor stellar halo of the Galaxy and into the continuing accretion events suffered by our Galaxy. This revised version was published online in July 2006 with corrections to the Cover Date.     

The estimations of neutron star mass and radius by the kHz QPOs

The kHz quasi‐periodic oscillations (QPOs) have been detected by the RXTE satellite in about thirty neutron stars (NSs) in low mass X‐ray binaries (LMXBs), which are usually interpreted to be related to the Keplerian motions in the orbit close to NS surface where the accreted matter is sucked onto the star. Based on the MHD Alfvén wave oscillation model and the relativistic precession model for the neutron star (NS) kHz QPOs, estimations of mass M and radius R of some NSs are given, which can give clues to evaluate the models. Furthermore, comparisons with theoretical M ‐R relations by stellar equations of state (EOSs) are presented (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Disk Planet Interactions And Early Evolution in Young Planetary Systems

We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration are investigated and found to depend on whether the single parameter M _p R ³/(M_* H ³), with M _p, M_*, R, and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness, respectively, exceeds a number of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without accreting significant mass. In that case, although there is sensitivity to computational parameters, in agreement with earlier work by Masset and Papaloizou [2003, ApJ, 588, 494] based on global simulations, the coorbital torques are proportional to the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway. This could lead to fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital periods.     

中子星X射线双星中kHz QPO现象的理论解释

罗西X射线时变探测器(RXTE)在中子星小质量X射线双星中发现了千赫兹准周期振荡现象(kHzQPO)。kHzQPO的频率一般在几百到上千赫兹,其动力学时标与吸积盘最内部区域物质的运动时标一致,因此普遍认为kHz QPO产生于中子星表面附近区域,携带了来自中心中子星及周围强引力场信息,如质量、自转周期、角动量、半径、磁场等。kHz QpO现象的理解为研究强引力场和致密物质状态开启了一扇新的窗口。着重介绍基于kHz QPO的基本现象和相应的理论模型。     

Tungsten isotopes in bulk meteorites and their inclusions—Implications for processing of presolar components in the solar protoplanetary disk

We present high precision, low‐ and high‐resolution tungsten isotope measurements of iron meteorites Cape York (IIIAB), Rhine Villa (IIIE), Bendego (IC), and the IVB iron meteorites Tlacotepec, Skookum, and Weaver Mountains, as well as CI chondrite Ivuna, a CV3 chondrite refractory inclusion (CAI BE), and terrestrial standards. Our high precision tungsten isotope data show that the distribution of the rare p‐process nuclide ¹⁸⁰W is homogeneous among chondrites, iron meteorites, and the refractory inclusion. One exception to this pattern is the IVB iron meteorite group, which displays variable excesses relative to the terrestrial standard, possibly related to decay of rare ¹⁸⁴Os. Such anomalies are not the result of analytical artifacts and cannot be caused by sampling of a protoplanetary disk characterized by p‐process isotope heterogeneity. In contrast, we find that ¹⁸³W is variable due to a nucleosynthetic s‐process deficit/r‐process excess among chondrites and iron meteorites. This variability supports the widespread nucleosynthetic s/r‐process heterogeneity in the protoplanetary disk inferred from other isotope systems and we show that W and Ni isotope variability is correlated. Correlated isotope heterogeneity for elements of distinct nucleosynthetic origin (¹⁸³W and ⁵⁸Ni) is best explained by thermal processing in the protoplanetary disk during which thermally labile carrier phases are unmixed by vaporization thereby imparting isotope anomalies on the residual processed reservoir.     

Distance law and formation of satellite systems

In the solar system satellite systems of Jupiter, Saturn and Uranus are typical ones. The distribution of the semi-major axis of satellite orbits in each system may be expressed by an empirical formula corresponding to the Titius-Bode law. We found that it can be written as a_n = B′ · Bⁿ, where B′ and B are constants. Values of B′ and B depend on formation conditions of each system. Satellites should be formed in the gas-satellitesimal disk around a planet and by aggregation of satellitesimals. The gas is the major component in the disk and its damping effect must play an important role in the process of aggregation of satellitesimals. It may be proved that radial small perturbation in the disk can cause the gravitational instability and the formation of gaseous rings with increased density, where satellitesimals can easy aggregat into satellites.