On the formation and evolution of black hole binaries

We present the results of a systematic study of the formation and evolution of binaries containing black holes and normal-star companions with a wide range of masses. We first reexamine the standard formation scenario for close black hole binaries, where the progenitor system, a binary with at least one massive component, experienced a common-envelope phase and where the spiral-in of the companion in the envelope of the massive star caused the ejection of the envelope. We estimate the formation rates for different companion masses and different assumptions about the common-envelope structure and other model parameters. We find that black hole binaries with intermediate- and high-mass secondaries can form for a wide range of assumptions, while black hole binaries with low-mass secondaries can only form with apparently unrealistic assumptions (in agreement with previous studies).
We then present detailed binary evolution sequences for black hole binaries with secondaries of 2 to 17 M_⊙ and demonstrate that in these systems the black hole can accrete appreciably even if accretion is Eddington-limited (up to 7 M_⊙ for an initial black hole mass of 10 M_⊙) and that the black holes can be spun up significantly in the process. We discuss the implications of these calculations for well-studied black hole binaries (in particular GRS 1915+105) and ultraluminous X-ray sources of which GRS 1915+105 appears to represent a typical Galactic counterpart. We also present a detailed evolutionary model for Cygnus X-1, a massive black hole binary, which suggests that at present the system is most likely in a wind mass-transfer phase following an earlier Roche-lobe overflow phase. Finally, we discuss how some of the assumptions in the standard model could be relaxed to allow the formation of low-mass, short-period black hole binaries, which appear to be very abundant in nature.     

Weighing the black holes in ultraluminous X-ray sources through timing

We describe a new method to estimate the mass of black holes in Ultraluminous X-ray Sources (ULXs). The method is based on the recently discovered 'variability plane', populated by Galactic stellar-mass black-hole candidates (BHCs) and supermassive active galactic nuclei (AGNs), in the parameter space defined by the black-hole mass, accretion rate and characteristic frequency. We apply this method to the two ULXs from which low-frequency quasi-periodic oscillations have been discovered, M82 X-1 and NGC 5408 X-1. For both sources we obtain a black-hole mass in the range  100–1300 M_⊙  , thus providing evidence for these two sources to host an intermediate-mass black hole.     

Variability of black hole accretion discs: the cool, thermal disc component

We extend the model of King et al. for variability in black hole accretion discs by taking proper account of the thermal properties of the disc. Because the degree of variability in the King et al. model depends sensitively on the ratio of disc thickness to radius, H / R , it is important to follow the time dependence of the local disc structure as the variability proceeds. In common with previous authors, we develop a one-zone model for the local disc structure. We agree that radial heat advection plays an important role in determining the inner disc structure, and also find limit-cycle behaviour. When the stochastic magnetic dynamo model of King et al. is added to these models, we find similar variability behaviour to before.
We are now better placed to put physical constraints on model parameters. In particular, we find that in order to be consistent with the low degree of variability seen in the thermal disc component of black hole binaries, we need to limit the energy density of the poloidal field that can be produced by local dynamo cells in the disc to less than a few per cent of the energy density of the dynamo field within the disc itself.     

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a ‘mini-’ state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.     

Measuring the accretion rate and kinetic luminosity functions of supermassive black holes

We derive accretion rate functions (ARFs) and kinetic luminosity functions (KLFs) for jet-launching supermassive black holes. The accretion rate as well as the kinetic power of an active galaxy is estimated from the radio emission of the jet. For compact low-power jets, we use the core radio emission while the jet power of high-power radio-loud quasars is estimated using the extended low-frequency emission to avoid beaming effects. We find that at low luminosities the ARF derived from the radio emission is in agreement with the measured bolometric luminosity function (BLF) of active galactic nucleus (AGN), i.e. all low-luminosity AGN launch strong jets. We present a simple model, inspired by the analogy between X-ray binaries (XRBs) and AGN, that can reproduce both the measured ARF of jet-emitting sources as well as the BLF. The model suggests that the break in power-law slope of the BLF is due to the inefficient accretion of strongly sub-Eddington sources. As our accretion measure is based on the jet power it also allows us to calculate the KLF and therefore the total kinetic power injected by jets into the ambient medium. We compare this with the kinetic power output from supernova remnants (SNRs) and XRBs, and determine its cosmological evolution.     

Quasi-stars: accreting black holes inside massive envelopes

We study the structure and evolution of 'quasi-stars', accreting black holes embedded within massive hydrostatic gaseous envelopes. These configurations may model the early growth of supermassive black hole seeds. The accretion rate on to the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass,   M _*+ M _BH≈ M _*  . This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. We use analytic models and numerical stellar structure calculations to study the structure and evolution of quasi-stars. We show that the photospheric temperature of the envelope scales as   T _ph∝ M ^−2/5_BH M ^7/20_*  , and decreases with time while the black hole mass increases. Once   T _ph < 10⁴ K  , the photospheric opacity drops precipitously and T _ph hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population III) opacities, this limiting temperature is approximately 4000 K. After a quasi-star reaches this limiting temperature, it is rapidly dispersed by radiation pressure. We find that black hole seeds with masses between 10³ and  10⁴ M_⊙  could form via this mechanism in less than a few Myr.     

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.     

A variable Quasi-Periodic Oscillation in M82 X-1. Timing and spectral analysis of XMM–Newton and RossiXTE observations

We report results from a spectral and timing analysis of M82 X-1, one of the brightest known ultraluminous X-ray sources. Data from a new 105-ks XMM–Newton observation of M82 X-1, performed in 2004 April, and of archival RossiXTE observations are presented. A very soft thermal component is present in the XMM spectrum. Although it is not possible to rule out a residual contamination from the host galaxy, modelling it with a standard accretion disc would imply a black hole (BH) mass of  ≈10³ M_⊙  . An emission line was also detected at an energy typical for fluorescent Fe emission. The power density spectrum of the XMM observation shows a variable Quasi-Periodic Oscillation (QPO) at frequency of 113 mHz with properties similar to those discovered by Strohmayer and Mushotzky. The QPO was also found in seven archival RXTE observations, that include those analysed by Strohmayer and Mushotzky, and Fiorito and Titarchuk. A comparison of the properties of this QPO with those of the various types of QPOs observed in Galactic black hole candidates strongly suggests an association with the type-C, low-frequency QPOs. Scaling the frequency inversely to the BH mass, the observed QPO frequency range (from 50 to 166 mHz) would yield a BH mass anywhere in the interval few tens to  1000  M_⊙  .