Stellar-mass black hole binaries as ultraluminous X-ray sources

Ultraluminous X-ray sources (ULXs) with   L _x > 10³⁹ erg s⁻¹  have been discovered in great numbers in external galaxies with ROSAT , Chandra and XMM-Newton . The central question regarding this important class of sources is whether they represent an extension in the luminosity function of binary X-ray sources containing neutron stars and stellar-mass black holes (BHs), or a new class of objects, e.g. systems containing intermediate-mass BHs  (100–1000 M_⊙)  . We have carried out a theoretical study to test whether a large fraction of the ULXs, especially those in galaxies with recent star formation activity, can be explained with binary systems containing stellar-mass BHs. To this end, we have applied a unique set of binary evolution models for BH X-ray binaries, coupled to a binary population synthesis code, to model the ULXs observed in external galaxies. We find that for donor stars with initial masses  ≳10 M_⊙  the mass transfer driven by the normal nuclear evolution of the donor star is sufficient to potentially power most ULXs. This is the case during core hydrogen burning and, to an even more pronounced degree, while the donor star ascends the giant branch, although the latter phases last only ∼5 per cent of the main-sequence phase. We show that with only a modest violation of the Eddington limit, e.g. a factor of ∼10, both the numbers and properties of the majority of the ULXs can be reproduced. One of our conclusions is that if stellar-mass BH binaries account for a significant fraction of ULXs in star-forming galaxies, then the rate of formation of such systems is  ∼3 × 10⁻⁷ yr⁻¹  normalized to a core-collapse supernova rate of 0.01 yr⁻¹.     

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.     

Accretion disc variability in the hard state of black hole X-ray binaries

XMM–Newton X-ray spectra of the hard state black hole X-ray binaries (BHXRBs) SWIFT J1753.5−0127 and GX 339−4 show evidence for accretion disc blackbody emission, in addition to hard power laws. The soft and hard band power spectral densities (PSDs) of these sources demonstrate variability over a wide range of time-scales. However, on time-scales of tens of seconds, corresponding to the putative low-frequency Lorentzian in the PSD, there is additional power in the soft band. To interpret this behaviour, we introduce a new spectral analysis technique, the 'covariance spectrum', to disentangle the contribution of the X-ray spectral components to variations on different time-scales. We use this technique to show that the disc blackbody component varies on all time-scales, but varies more, relative to the power law, on longer time-scales. This behaviour explains the additional long-term variability seen in the soft band. Comparison of the blackbody and iron line normalizations seen in the covariance spectra in GX 339−4 implies that the short-term blackbody variations are driven by thermal reprocessing of the power-law continuum absorbed by the disc. However, since the amplitude of variable reflection is the same on long and short time-scales, we rule out reprocessing as the cause of the enhanced disc variability on long time-scales. Therefore, we conclude that the long time-scale blackbody variations are caused by instabilities in the disc itself, in contrast to the stable discs seen in BHXRB soft states. Our results provide the first observational evidence that the low-frequency Lorentzian feature present in the PSD is produced by the accretion disc.     

Parallel tracks in infrared versus X-ray emission in black hole X-ray transient outbursts: a hysteresis effect?

We report the discovery of a new hysteresis effect in black hole X-ray binary state transitions, that of the near-infrared (NIR) flux (which most likely originates in the jets) versus X-ray flux. We find, looking at existing data sets, that the IR emission of black hole X-ray transients appears to be weaker in the low/hard state rise of an outburst than the low/hard state decline of an outburst at a given X-ray luminosity. We discuss how this effect may be caused by a shift in the radiative efficiency of the inflowing or outflowing matter, or variations in the disc viscosity or the spectrum/power of the jet. In addition we show that there is a correlation (in slope but not in normalization) between IR and X-ray luminosities on the rise and decline, for all three low-mass black hole X-ray binaries with well-sampled IR and X-ray coverage:   L _NIR∝ L ^0.5–0.7_X  . In the high/soft state this slope is much shallower;   L _NIR∝ L ^0.1–0.2_X  , and we find that the NIR emission in this state is most likely dominated by the viscously heated (as opposed to X-ray heated) accretion disc in all three sources.     

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.     

Evolution of black hole intermediate-mass X-ray binaries: the influence of a circumbinary disc

We report the results of a systematic timing analysis of RXTE observations of GRS 1915+105 when the source was in its variability class θ, characterized by alternating soft and hard states on a time-scale of a few hundred seconds. The aim was to examine the high-frequency part of the power spectrum in order to confirm the hectohertz quasi-periodic oscillations (QPO) previously reported from observations from mixed variability behaviours. During the hard intervals (corresponding to state C in the classification of Belloni et al.), we find a significant QPO at a frequency of ∼170 Hz, although much broader (Q∼2) than previously reported. No other significant peak is observed at frequencies >30 Hz. A time-resolved spectral analysis of selected observations shows that the hard intervals from class θ show a stronger and steeper  (Γ= 2.8–3.0)  power-law component than hard intervals from other classes. We discuss these results in the framework of hectohertz QPOs reported from GRS 1915+105 and other black hole binaries.     

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.     

Impact of reverberation in flared accretion discs on temporal characteristics of X-ray binaries

Observations suggest that accretion discs in many X-ray binaries are likely flared. An outer edge of the disc intercepts radiation from the central X-ray source. Part of that radiation is absorbed and re-emitted in the optical/UV spectral ranges. However, a large fraction of that radiation is reflected and appears in the broad-band X-ray spectrum as a Compton reflection bump. This radiation is delayed and variability is somewhat smeared compared with the intrinsic X-ray radiation. We compute response functions for flat and flared accretion discs and for isotropic and anisotropic X-ray sources. A simple approximation for the response function which is valid in the broad range of the disc shapes and inclinations, inner and outer radii, and the plasma bulk velocity is proposed. We also study the impact of the X-ray reprocessing on temporal characteristics of X-ray binaries such as the power spectral density, auto- and cross-correlation functions, and time/phase lags. We propose a reprocessing model which explains the secondary peaks in the phase lag Fourier spectra observed in Cyg X-1 and other Galactic black hole sources. The position of the peaks could be used to determine the size of the accretion disc.     

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.     

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.     

Evolution of neutron stars in high-mass X-ray binaries

We consider the evolution of neutron stars during the X-ray phase of high-mass binaries. Calculations are performed assuming a crustal origin of the magnetic field. A strong wind from the companion can significantly influence the magnetic and spin behaviour of a neutron star even during the main-sequence life of the companion. In the course of evolution, the neutron star passes through four evolutionary phases ('isolated pulsar', propeller, wind accretion, and Roche lobe overflow). The model considered can naturally account for the observed magnetic fields and spin periods of neutron stars, as well as the existence of pulsating and non-pulsating X-ray sources in high-mass binaries. Calculations also predict the existence of a particular sort of high-mass binary with a secondary that fills its Roche lobe and a neutron star that does not accrete the overflowing matter because of fast spin.