Superhumps in low-mass X-ray binaries

We propose a mechanism for the superhump modulations observed in optical photometry of at least two black-hole X-ray transients (SXTs). As in extreme mass-ratio cataclysmic variables (CVs), superhumps are assumed to result from the presence of the 3:1 orbital resonance in the accretion disc. This causes the disc to become non-axisymmetric and precess. However, the mechanism for superhump luminosity variations in low-mass X-ray binaries (LMXBs) must differ from that in CVs, where it is attributed to a tidally-driven modulation of the disc's viscous dissipation, varying on the beat between the orbital and disc precession period. By contrast in LMXBs, tidal dissipation in the outer accretion disc is negligible: the optical emission is overwhelmingly dominated by reprocessing of intercepted central X-rays. Thus a different origin for the superhump modulation is required. Recent observations and numerical simulations indicate that in an extreme mass-ratio system the disc area changes on the superhump period. We deduce that the superhumps observed in SXTs arise from a modulation of the reprocessed flux by the changing area. Therefore, unlike the situation in CVs, where the superhump amplitude is inclination-independent, superhumps should be best seen in low-inclination LMXBs, whereas an orbital modulation from the heated face of the secondary star should be more prominent at high inclinations. Modulation at the disc precession period (10 s of days) may indicate disc asymmetries such as warping. We comment on the orbital period determinations of LMXBs, and the possibility and significance of possible permanent superhump LMXBs.     

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.     

Decade time-scale modulation of low-mass X-ray binaries

Regular observations by the All-Sky Monitor aboard the Rossi X-ray Timing Explorer satellite have yielded well-sampled light curves with a time baseline of over 10 years. We find that up to eight of the 16 brightest persistent low-mass X-ray binaries (LMXBs) show significant, possible sinusoidal, variations with periods of the order of 10 years. We speculate on its possible origin and prevalence in the population of LMXBs, and we find the presence of a third object in the system, or long-period variability intrinsic to the donor star, as being attractive origins for the X-ray flux modulation we detect. For some of the objects in which we do not detect a signal, there is substantial short-term variation which may hide modest modulation on long time-scales. Decade time-scale modulations may thus be even more common.     

The X-ray hardness ratio variation in low-mass X-ray binaries

The behaviour of the hardness ratio in low-mass X-ray binaries (LMXRB) indicates that at some value of mass accretion rate , the X-ray intensity decreases with increasing . It is suggested here that, at some , wind from the accretion disk becomes appreciable and depletes the mass accretion on to the neutron star and thus reduces the X-ray intensity. This explains the behaviour of the hardness ratio in LMXRB. Possible implications of this on quasi-periodic oscillations are discussed.     

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 ...     

A fresh look at the low-mass X-ray binaries

The reported systemic velocities of the low-mass X-ray binaries (=LMXBs) are found to be unreliable, because of intrinsic Doppler shifts. We argue that the non-globular-cluster LMXBs form a disk population, whose typicalz-velocities are unlikely to exceed 30 km s^–1. They are moderately old and rare (among neutron-star sources) and have oscillated through the disk a number of times.     

Magnetic braking in cataclysmic and low-mass X-ray binaries

The chromosphreric-coronal emission of lower Main-Sequence single and binary stars can be correlated with an activity parameter of typeR=g(B-V)P ^–1, whereP is the rotation or orbital period andg(B-V) a function of the color resembling the convective turnover time. Observations indicate that the active region area coverage filling factor grows asR ², and the whole stellar surface becomes filled with closed loop structures atR3. A braking formula is proposed (Equation 4) to include all periods (0.^d1R30^d) and spectral types F-M. On the basis of this equation, the mass transfer rates in compact binaries (driven by the gradual loss of orbital angular momentum) are discussed. It is concluded that the magnetic braking has good chances of being that mechanism which drives the mass transfer in cataclysmic variables and galactic bulge X-ray sources.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Indonesia, 3–7 June, 1983.On leave from Observatory and Astrophysics Laboratory, University of Helsinki, Helsinki, Finland.     

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.     

The luminosity function of low-mass X-ray binaries in galaxies

The X-ray luminosity function of low-mass binaries constructed from the observations of point like X-ray sources in galactic bulges can be explained in terms of the main evolutionary relations for the rate of mass transfer onto a compact object. The observed scatter of luminosities for individual low-mass X-ray sources in our Galaxy is shown to be satisfactorily described by a symmetric quasi-Lorentz curve with a dispersion proportional to the mean luminosity. Such a form of the mean luminosity function for individual sources does not affect the power-law pattern of the luminosity function for the entire population of sources that is expected for a power-law dependence of the mass transfer rate in a close binary on the mass of the Roche lobe—filling optical component.     

Precessing warped accretion discs in X-ray binaries

We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing.
We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well-resolved solution.
We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable 'superorbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed recently by Wijers and Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.     

Modelling the behaviour of accretion flows in X-ray binaries

We review how the recent increase in X-ray and radio data from black hole and neutron star binaries can be merged together with theoretical advances to give a coherent picture of the physics of the accretion flow in strong gravity. Both long term X-ray light curves, X-ray spectra, the rapid X-ray variability and the radio jet behaviour are consistent with a model where a standard outer accretion disc is truncated at low luminosities, being replaced by a hot, inner flow which also acts as the launching site of the jet. Decreasing the disc truncation radius leads to softer spectra, as well as higher frequencies (including quasi periodic oscillations, QPOs) in the power spectra, and a faster jet. The collapse of the hot flow when the disc reaches the last stable orbit triggers the dramatic decrease in radio flux, as well as giving a qualitative (and often quantitative) explanation for the major hard–soft spectral transition seen in black holes. The neutron stars are also consistent with the same models, but with an additional component due to their surface, giving implicit evidence for the event horizon in black holes. We review claims of observational data which conflict with this picture, but show that these can also be consistent with the truncated disc model. We also review suggested alternative models for the accretion flow which do not involve a truncated disc. The most successful of these converge on a similar geometry, where there is a transition at some radius larger than the last stable orbit between a standard disc and an inner, jet dominated region, with the X-ray source associated with a mildly relativistic outflow, beamed away from the disc. However, the observed uniformity of properties between black holes at different inclinations suggests that even weak beaming of the X-ray emission may be constrained by the data. After collapse of the hot inner flow, the spectrum in black hole systems can be dominated by the disc emission. Its behaviour is consistent with the existence of a last stable orbit, and such data can be used to estimate the black hole spin. By contrast, these systems can also show very different spectra at these high luminosities, in which the disc spectrum (and probably structure) is strongly distorted by Comptonization. The structure of the accretion flow becomes increasingly uncertain as the luminosity approaches (and exceeds) the Eddington luminosity, though there is growing evidence that winds may play an important role. We stress that these high Eddington fraction flows are key to understanding many disparate and currently very active fields such as ULX, Narrow Line Seyfert 1’s, and the growth of the first black holes in the Early Universe.     

On the precession of accretion discs in X-ray binaries

In this Letter, recent results on the nodal precession of accretion discs in close binaries are applied to the discs in some X-ray binary systems. The ratio between the tidally forced precession period and the binary orbital period is given, as well as the condition required for the rigid precession of gaseous Keplerian discs. Hence the minimum precessional period that may be supported by a fluid Keplerian disc is determined. It is concluded that near-rigid body precession of tilted accretion discs can occur and generally reproduce observationally inferred precession periods, for reasonable system parameters. In particular, long periods in SS 433, Her X-1, LMC X-4 and SMC X-1 can be fitted by the tidal model. It is also found that the precession period that has been tentatively put forward for Cyg X-2 cannot be accommodated by a tidally precessing disc model for any realistic choice of system parameters.     

Simultaneous radio and X-ray observations of Galactic Centre low-mass X-ray binaries

We have performed simultaneous X-ray and radio observations of 13 Galactic Centre low-mass X-ray binaries in 1998 April using the Wide Field Cameras on board BeppoSAX and the Australia Telescope Compact Array, the latter simultaneously at 4.8 and 8.64 GHz. We detect two Z sources, GX 17+2 and GX 5−1, and the unusual 'hybrid' source GX 13+1. Upper limits, which are significantly deeper than previous non-detections, are placed on the radio emission from two more Z sources and seven atoll sources. Hardness–intensity diagrams constructed from the Wide Field Camera data reveal GX 17+2 and GX 5−1 to have been on the lower part of the horizontal branch and/or the upper part of the normal branch at the time of the observations, and the two non-detected Z sources, GX 340+0 and GX 349+2, to have been on the lower part of the normal branch. This is consistent with the previous empirically determined relation between radio and X-ray emission from Z sources, in which radio emission is strongest on the horizontal branch and weakest on the flaring branch. For the first time we have information on the X-ray state of atoll sources, which are clearly radio-quiet relative to the Z sources, during periods of observed radio upper limits. We place limits on the linear polarization from the three detected sources, and use accurate radio astrometry of GX 17+2 to confirm that it is probably not associated with the optical star NP Ser. Additionally we place strong upper limits on the radio emission from the X-ray binary 2S 0921−630, disagreeing with suggestions that it is a Z-source viewed edge-on.     

The structure of blue supergiant winds and the accretion in supergiant high-mass X-ray binaries

We have developed a stellar wind model for OB supergiants to investigate the effects of accretion from a clumpy wind on the luminosity and variability properties of high-mass X-ray binaries. Assuming that the clumps are confined by ram pressure of the ambient gas and exploring different distributions for their mass and radii, we computed the expected X-ray light curves in the framework of the Bondi–Hoyle accretion theory, modified to take into account the presence of clumps. The resulting variability properties are found to depend not only on the assumed orbital parameters but also on the wind characteristics. We have then applied this model to reproduce the X-ray light curves of three representative high-mass X-ray binaries: two persistent supergiant systems (Vela X−1 and 4U 1700−377) and the supergiant fast X-ray transient IGR J11215−5952. The model can reproduce the observed light curves well, but requiring in all cases an overall mass loss from the supergiant about a factor of 3–10 smaller than the values inferred from ultraviolet lines studies that assume a homogeneous wind.     

The secondary stars in cataclysmic variables and low-mass X-ray binaries

We critically re-examine the available data on the spectral types, masses and radii of the secondary stars in cataclysmic variables (CVs) and low-mass X-ray binaries (LMXBs), using the new catalogue of Ritter &38; Kolb as a starting point. We find there are 55 reliable spectral type determinations and only 14 reliable mass determinations of CV secondary stars (10 and 5, respectively, in the case of LMXBs). We derive new spectral type–period, mass–radius, mass–period and radius–period relations, and compare them with theoretical predictions. We find that CV secondary stars with orbital periods shorter than 7–8 h are, as a group, indistinguishable from main-sequence stars in detached binaries. We find that it is not valid, however, to estimate the mass from the spectral type of the secondary star in CVs or LMXBs. We find that LMXB secondary stars show some evidence for evolution, with secondary stars which are slightly too large for their mass. We show how the masses and radii of the secondary stars in CVs can be used to test the validity of the disrupted magnetic braking model of CV evolution, but we find that the currently available data are not sufficiently accurate or numerous to allow such an analysis. As well as considering secondary star masses, we also discuss the masses of the white dwarfs in CVs, and find mean values of ⁻ M  = 0.69 ± 0.13 M_⊙ below the period gap, and ⁻ M  = 0.80 ± 0.22 M_⊙ above the period gap.     

Warped accretion discs and the long periods in X-ray binaries

Precessing accretion discs have long been suggested as explanations for the long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ Her. We show that an instability of the response of the disc to the radiation reaction force from the illumination by the central source can cause the disc to tilt out of the orbital plane and precess in something like the required manner. The rate of precession and disc tilt obtained for realistic values of system parameters compare favourably with the known body of data on X-ray binaries with long periods. We explore other possible types of behaviour than steadily precessing discs that might be observable in systems with somewhat different parameters. At high luminosities, the inner disc tilts through more than 90°, i.e., it rotates counter to the usual direction, which may explain the torque reversals in systems such as 4U 1626−67.     

A comment on the colour–colour diagrams of low-mass X-ray binaries

Disc-accreting neutron stars come in two distinct varieties, atolls and Z sources, named after their differently shaped tracks on a colour–colour diagram as the source luminosity changes. Here we present analysis of three transient atoll sources showing that there is an additional branch in the colour–colour diagram of atoll sources which appears at very low luminosities. This new branch connects to the top of previously known C-shaped (atoll) path, forming a horizontal track where the average source flux decrease from right to left. This turns the C-shape into a Z. Thus both atolls and Z sources share the same topology on the colour–colour diagram and evolve in similar way, as a function of increasing averaged mass accretion rate. This strongly favours models in which the underlying geometry of these sources changes in similar ways. A possible scenario is one where the truncated disc approaches the neutron star when the accretion rate increases, but in the atolls the disc is truncated by evaporation (similarly to black holes), and in the Z sources it is truncated by the magnetic field.