Iron Kα line profiles and the inner boundary condition of accretion flows

Recent X-ray observations have shown evidence for exceptionally broad and skewed iron Kα emission lines from several accreting black hole systems. The lines are assumed to be due to fluorescence of the accretion disc illuminated by a surrounding corona and require a steep emissivity profile increasing into the innermost radius. This appears to question both standard accretion disc theory and the zero-torque assumption for the inner boundary condition, both of which predict a much less extreme profile. Instead it argues that a torque may be present due to magnetic coupling with matter in the plunging region or even to the spinning black hole itself. Discussion so far has centred on the torque acting on the disc. However, the crucial determinant of the iron line profile is the radial variation of the power radiated in the corona. Here we study the effects of different inner boundary conditions on the coronal emissivity and on the profiles of the observable Fe Kα lines. We argue that in the extreme case where a prominent highly redshifted component of the iron line is detected, requiring a steep emissivity profile in the innermost part and a flatter one outside, energy from the gas plunging into the black hole is being fed directly to the corona.     

A model of magnetically induced disc–corona for black hole binaries

We propose a model of magnetic connection (MC) of a black hole with its surrounding accretion disc based on large-scale magnetic field. The MC gives rise to transport of energy and angular momentum between the black hole and the disc, and the closed field lines pipe the hot matter evaporated from the disc, and shape it in the corona above the disc to form a magnetically induced disc–corona system, in which the corona has the same configuration as the large-scale magnetic field. We numerically solve the dynamic equations in the context of the Kerr metric, in which the large-scale magnetic field is determined by dynamo process and equipartition between magnetic pressure and gas pressure. Thus we can obtain a global solution rather than assuming the distribution of large-scale magnetic field beforehand. The main MC effects lie in three aspects. (1) The rotational energy of a fast-spinning black hole can be extracted, enhancing the dissipation in the accretion disc, (2) the closed field lines provide a natural channel for corona matter escaping from disc and finally falling into black hole and (3) the scope of the corona can be bounded by the conservation of magnetic flux. We simulate the high-energy spectra of this system by using Monte Carlo method, and find that the relative hardness of the spectra decreases as accretion rate or black hole spin a _* increases. We fit the typical X-ray spectra of three black hole binaries  (GRO J1655−40, XTE 1118+480 and GX 339−4)  in the low/hard or very high state.     

Towards incorporating a turbulent magnetic field in an accreting black hole model

A model proposed by Melia & Ruffert to evaluate the spectrum and radiation flux for accretion on to a black hole makes use of the 'equipartition assumption' in which the magnetic, turbulent and gravitational energy densities are assumed to be in approximate equilibrium for distances below the accretion radius, where Bondi–Hoyle infall begins. As a consequence, the mechanism for the dissipation of the magnetic field and the resulting effect on the flow of the accreting gas have not been treated quantitatively. Here we examine alternative approaches for modelling the dissipation of magnetic fields and turbulent flow to see how these may be incorporated into the model. The results of our study should be immediately applicable to the ever-improving measurements of the spectrum and size of the massive black hole at our Galactic Centre, in particular producing a more accurate estimate of its mass. Combined with greatly refined kinematic studies of this region, our work may constrain the dark matter concentration in the nucleus of our Galaxy.     

Optical and infrared signatures of ultra-luminous X-ray sources

We have constructed a model to describe the optical emission from ultra-luminous X-ray sources (ULXs). We assume a binary model with a black hole accreting matter from a Roche lobe filling companion star. We consider the effects of radiative transport and radiative equilibrium in the irradiated surfaces of both the star and a thin accretion disc. We have developed this model as a tool with which to positively identify the optical counterparts of ULXs, and subsequently derive parameters such as the black hole mass and the luminosity class and spectral type of the counterpart. We examine the dependence of the optical emission on these and other variables. We extend our model to examine the magnitude variation at infrared wavelengths, and we find that observations at these wavelengths may have more diagnostic power than in the optical. We apply our model to existing HST observations of the candidates for the optical counterpart of ULX X-7 in NGC 4559. All candidates could be consistent with an irradiated star alone, but we find that a number of them are too faint to fit with an irradiated star and disc together. Were one of these the optical counterpart to X-7, it would display a significant temporal variation.     

Solving linearized equations of the N-body problem using the Lie-integration method

Several integration schemes exist to solve the equations of motion of the N -body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s, this method was applied to solve the equations of motion of the N -body problem by giving the recurrence formulae for the calculation of the Lie-terms. The aim of this work is to present the recurrence formulae for the linearized equations of motion of N -body systems. We prove a lemma which greatly simplifies the derivation of the recurrence formulae for the linearized equations if the recurrence formulae for the equations of motions are known. The Lie-integrator is compared with other well-known methods. The optimal step-size and order of the Lie-integrator are calculated. It is shown that a fine-tuned Lie-integrator can be 30–40 per cent faster than other integration methods.