Magnetized accretion flows: effects of gas pressure

We study how axisymmetric magnetohydrodynamic (MHD) accretion flows depend on γ adiabatic index in the polytropic equation of state. This work is an extension of Mościbrodzka & Proga, where we investigated the γ dependence of two-dimensional Bondi-like accretion flows in the hydrodynamical (HD) limit. Our main goal is to study if simulations for various γ can give us insights into the problem of various modes of accretion observed in several types of accretion systems, such as black hole binaries (BHBs), active galactic nuclei (AGN) and gamma-ray bursts. We find that for  γ≳ 4/3  , the fast-rotating flow forms a thick torus that is supported by rotation and gas pressure. As shown before for  γ= 5/3  , such a torus produces a strong, persistent bipolar outflow that can significantly reduce the polar funnel accretion of a slowly rotating flow. For low γ, close to 1, the torus is thin and is supported by rotation. The thin torus produces an unsteady outflow which is too weak to propagate throughout the polar funnel inflow. Compared to their HD counterparts, the MHD simulations show that the magnetized torus can produce an outflow and does not exhibit regular oscillations. Generally, our simulations demonstrate how the torus thickness affects the outflow production. They also support the notion that the geometrical thickness of the torus correlates with the power of the torus outflow. Our results, applied to observations, suggest that the torus ability to radiatively cool and become thin can correspond to a suppression of a jet as observed in the BHBs during a transition from a hard/low to soft/high spectral state and a transition from a quiescent to hard/low state in AGN.     

Hot accretion discs with thermal Comptonization and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonization of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to ≲ 0.15 y^3/5 α^7/5 of the Eddington limit, where y and α are the Compton and viscosity parameters, respectively. The characteristic electron temperature and Thomson optical depth of the inner flow at accretion rates within an order of magnitude of that upper limit are ∼ 10⁹ K and ∼ 1, respectively. The resulting spectra are then in close agreement with the X-ray and soft γ-ray spectra from black hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

Instability of spherical accretion — I. Shock-free Bondi accretion

We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non-radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.     

Self-consistent computation of γ-ray spectra due to proton–proton interactions in black hole systems

In the inner regions of an accretion disc around a black hole, relativistic protons can interact with ambient matter to produce electrons, positrons and γ-rays. The resultant steady-state electron and positron particle distributions are self-consistently computed taking into account Coulomb and Compton cooling,  e⁻ e⁺  pair production (due to γ–γ annihilation) and pair annihilation. While earlier works used the diffusion approximation to obtain the particle distributions, here we solve a more general integro-differential equation that correctly takes into account the large change in particle energy that occurs when the leptons Compton scatter off hard X-rays. Thus this formalism can also be applied to the hard state of black hole systems, where the dominant ambient photons are hard X-rays. The corresponding photon energy spectrum is calculated and compared with broad-band data of black hole binaries in different spectral states. The results indicate that the γ-ray spectra  ( E > 0.8 MeV)  of both the soft and hard spectral states and the entire hard X-ray/γ-ray spectrum of the ultrasoft state could be due to p–p interactions. These results are consistent with the hypothesis that there always exists in these systems a γ-ray spectral component due to p–p interactions that can contribute between 0.5 and 10 per cent of the total bolometric luminosity. The model predicts that GLAST would be able to detect black hole binaries and provide evidence for the presence of non-thermal protons, which in turn would give insight into the energy dissipation process and jet formation in these systems.     

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.     

A possible energy mechanism for cosmological γ-ray bursts

We suggest that an extreme Kerr black hole with a mass ∼10⁶ M_⊙, a dimensionless angular momentum     and a marginally stable orbital radius     located in a normal galaxy may produce a γ -ray burst (GRB) by capturing and disrupting a star. During the capture period, a transient accretion disc is formed and a strong transient magnetic field ∼     lasting for     may be produced at the inner boundary of the accretion disc. A large amount of rotational energy of the black hole is extracted and released in an ultrarelativistic jet with a bulk Lorentz factor Γ larger than 10³ via the Blandford–Znajek process. The relativistic jet energy can be converted into γ -radiation via an internal shock mechanism. The GRB duration should be the same as the lifetime of the strong transient magnetic field. The maximum number of sub-bursts is estimated to be     because the disc material is likely to break into pieces with a size about the thickness of the disc h at the cusp     The shortest risetime of the burst estimated from this model is ∼     The model GRB density rate is also estimated.     

The excitation, propagation and dissipation of waves in accretion discs: the non-linear axisymmetric case

We analyse the non-linear propagation and dissipation of axisymmetric waves in accretion discs using the ZEUS-2D hydrodynamics code. The waves are numerically resolved in the vertical and radial directions. Both vertically isothermal and thermally stratified accretion discs are considered. The waves are generated by means of resonant forcing, and several forms of forcing are considered. Compressional motions are taken to be locally adiabatic  ( γ =5/3)  . Prior to non-linear dissipation, the numerical results are in excellent agreement with the linear theory of wave channelling in predicting the types of modes that are excited, the energy flux by carried by each mode, and the vertical wave energy distribution as a function of radius. In all cases, waves are excited that propagate on both sides of the resonance (inwards and outwards). For vertically isothermal discs, non-linear dissipation occurs primarily through shocks that result from the classical steepening of acoustic waves. For discs that are substantially thermally stratified, wave channelling is the primary mechanism for shock generation. Wave channelling boosts the Mach number of the wave by vertically confining the wave to a small cool region at the base of the disc atmosphere. In general, outwardly propagating waves with Mach numbers near resonance  ℳ_r≳0.01  undergo shocks within a distance of order the resonance radius.     

Model dependence of transonic properties of accretion flows around black holes

We analytically study how the behaviour of accretion flows changes when the flow model is varied. We study the transonic properties of the conical flow, a flow of constant height and a flow in vertical equilibrium, and show that all these models are basically identical, provided that the polytropic constant is suitably changed from one model to another. We show that this behaviour is extendible even when standing shocks are produced in the flow. The parameter space where shocks are produced remains roughly identical in all these models when the same transformation among the polytropic indices is used. We present applications of these findings.     

Studies of accretion flows around rotating black holes – III. Shock oscillations and an estimation of the spin parameter from QPO frequencies

In the present communication of our series of papers dealing with the accretion flows in the pseudo-Kerr geometry, we discuss the effects of viscosity on the accretion flow around a rotating black hole. We find the solution topologies and give special attention to the solutions containing shocks. We draw the parameter space where standing shocks are possible and where the shocks could be oscillating and could produce quasi-periodic oscillations (QPOs) of X-rays observed from black hole candidates. In this model, the extreme locations of the shocks give the upper limits of the QPO frequencies  (ν_QPO)  which could be observed. We show that both the viscosity of the flow and the spin of the black hole a increase the QPO frequency while, as expected, the black hole mass reduces the QPO frequencies. Our major conclusion is that the highest observed frequency gives a strict lower limit of the spin. For instance, a black hole exhibiting  ν_QPO∼ 400  and  700 Hz  must have the spin parameters of   a > 0.25  and  >0.75  , respectively, provided viscosity of the flow is small. We discuss the implications of our results in the light of observations of QPOs from black hole candidates.     

Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry

The stationary, spherically symmetric, polytropic and inviscid accretion flow in the Schwarzschild metric has been set-up as an autonomous first-order dynamical system, and it has been studied completely analytically. Of the three possible critical points in the flow, the one that is physically realistic behaves like the saddle point of the standard Bondi accretion problem. One of the two remaining critical points exhibits the strange mathematical behaviour of being either a saddle point or a centre-type point, depending on the values of the flow parameters. The third critical point is always unphysical and behaves like a centre-type point. The treatment has been extended to pseudo-Schwarzschild flows for comparison with the general relativistic analysis.     

Radiation mechanisms and geometry of Cygnus X-1 in the soft state

We present X-ray/ γ -ray spectra of Cyg X-1 observed during the transition from the hard to the soft state and in the soft state by ASCA , RXTE and CGRO /OSSE in 1996 May and June. The spectra consist of a dominant soft component below ∼2 keV and a power-law-like continuum extending to at least ∼800 keV. We interpret them as emission from an optically thick, cold accretion disc and from an optically thin, non-thermal corona above the disc. A fraction f ≳0.5 of total available power is dissipated in the corona.
We model the soft component by multicolour blackbody disc emission taking into account the torque-free inner-boundary condition. If the disc extends down to the minimum stable orbit, the ASCA RXTE data yield the most probable black hole mass of M _X≈10 M_⊙ and an accretion rate,     , locating Cyg X-1 in the soft state in the upper part of the stable, gas-pressure-dominated, accretion-disc solution branch.
The spectrum of the corona is well modelled by repeated Compton scattering of seed photons from the disc off electrons with a hybrid, thermal/non-thermal distribution. The electron distribution can be characterized by a Maxwellian with an equilibrium temperature of kT _e∼30–50 keV, a Thomson optical depth of τ ∼0.3 and a quasi-power-law tail. The compactness of the corona is 2≲ℓ_h≲7, and a presence of a significant population of electron–positron pairs is ruled out.
We find strong signatures of Compton reflection from a cold and ionized medium, presumably an accretion disc, with an apparent reflector solid angle, Ω/2π∼0.5–0.7. The reflected continuum is accompanied by a broad iron K α line.     

Two- and three-dimensional numerical simulations of accretion discs in a close binary system

We perform 2D and 3D numerical simulations of an accretion disc in a close binary system using the simplified flux vector splitting (SFS) finite volume method. In our calculations, the gas is assumed to be ideal with γ =1.01, 1.05, 1.1 and 1.2 . The mass ratio of the mass-losing star to the mass-accreting star is unity. Our results show that spiral shocks are formed on the accretion disc in all cases. In 2D calculations we find that the smaller γ is, the more tightly the spiral winds. We observe this trend in 3D calculations as well in a somewhat weaker sense. Mach numbers in our discs are less than 10. These values are lower than the values in observed accretion discs in close binary systems.
Recently, Steeghs, Harlaftis & Horne found the first convincing evidence for spiral structure in the accretion disc of the eclipsing dwarf nova binary IP Pegasi, using the technique known as Doppler tomography. Although the Mach numbers in present calculations are rather low, we may claim that the spiral structure that we discovered in earlier numerical simulations is now found observationally.     

Analysing the atolls: X-ray spectral transitions of accreting neutron stars

We systematically analyse all the available X-ray spectra of disc accreting neutron stars (atolls and millisecond pulsars) from the RXTE data base. We show that while all these have similar spectral evolution as a function of mass accretion rate, there are also subtle differences. There are two different types of hard/soft transition, those where the spectrum softens at all energies, leading to a diagonal track on a colour–colour diagram, and those where only the higher energy spectrum softens, giving a vertical track. The luminosity at which the transition occurs is correlated with this spectral behaviour, with the vertical transition at   L / L _Edd∼ 0.02  while the diagonal one is at ∼0.1. Superimposed on this is the well-known hysteresis effect, but we show that classic, large-scale hysteresis occurs only in the outbursting sources, indicating that its origin is in the dramatic rate of change of mass accretion rate during the disc instability. We show that the long-term mass accretion rate correlates with the transition behaviour, and speculate that this is due to the magnetic field being able to emerge from the neutron star surface for low average mass accretion rates. While this is not strong enough to collimate the flow except in the millisecond pulsars, its presence may affect the inner accretion flow by changing the properties of the jet.     

Smoothed particle hydrodynamic simulations of viscous accretion discs around black holes

Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one- and two-dimensional flows) using smoothed particle hydrodynamics. We discover that for a large region of the parameter space spanned by energy, angular momentum and polytropic index, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock wave disappears. In the intermediate viscosity, the disc oscillates very significantly in the viscous time-scale. Our simulations indicate that these centrifugally supported high density regions close to a black hole play an active role in the flow dynamics, and consequently, the radiation dynamics.     

Inflow and outflow from the accretion disc of the microquasar SS 433: UKIRT spectroscopy

A succession of near-infrared (near-IR) spectroscopic observations, taken nightly throughout an entire cycle of SS 433's orbit, reveal (i) the persistent signature of SS 433's accretion disc, having a rotation speed of  ∼500 km s⁻¹  , (ii) the presence of circumbinary disc recently discovered at optical wavelengths by Blundell, Bowler & Schmidtobreick (2008) and (iii) a much faster outflow than has previously been measured for the disc wind, with a terminal velocity of  ∼1500 km s⁻¹  . The increased wind terminal velocity results in a mass-loss rate of  ∼10⁻⁴ M_⊙ yr⁻¹  . These, together with the newly (upwardly) determined masses for the components of the SS 433 system, result in an accurate diagnosis of the extent to which SS 433 has super-Eddington flows. Our observations imply that the size of the companion star is comparable with the semiminor axis of the orbit which is given by     , where e is the eccentricity. Our relatively spectral resolution at these near-IR wavelengths has enabled us to deconstruct the different components that comprise the Brackett-γ (Brγ) line in this binary system, and their physical origins. With this line being dominated throughout our series of observations by the disc wind, and the accretion disc itself being only a minority (∼15 per cent) contribution, we caution against use of the unresolved Brγ line intensity as an 'accretion signature' in X-ray binaries or microquasars in any quantitative way.     

Shock oscillation model for quasi-periodic oscillations in stellar mass and supermassive black holes

We numerically examine centrifugally supported shock waves in 2D rotating accretion flows around a stellar mass  (10 M_⊙)  and a supermassive  (10⁶ M_⊙)  black holes over a wide range of input accretion rates of     . The resultant 2D shocks are unstable with time and the luminosities show quasi-periodic oscillations (QPOs) with modulations of a factor of 2–3 and with periods of a tenth of a second to several hours, depending on the black hole masses. The shock oscillation model may explain the intermediate frequency QPOs with 1–10 Hz observed in the stellar mass black hole candidates and also suggest the existence of QPOs with the period of hours in active galactic nuclei. When the accretion rate     is low, the luminosity increases in proportion to the accretion rate. However, when     greatly exceeds the Eddington critical rate     , the luminosity is insensitive to the accretion rate and is kept constantly around  ∼3 L _E  . On the other hand, the mass-outflow rate     increases in proportion to     and it amounts to about a few per cent of the input mass-flow rate.     

Super-Eddington accretion discs around Kerr black holes

We calculate the structure of the accretion disc around a rapidly rotating black hole with a super-Eddington accretion rate. The luminosity and height of the disc are reduced by the advection effect. In the case of large viscosity parameter, α>0.03, the accretion flow deviates strongly from thermodynamic equilibrium and overheats in the central region. With increasing accretion rate, the flow temperature steeply increases, reaches maximum, and then falls off. The maximum is achieved in the advection-dominated regime of accretion. The maximum temperature in the disc around a massive black hole of M =10⁸ M⊙ with α=0.3 is of order 3×10⁸ K. The discs with large accretion rates can emit X-rays in quasars as well as in galactic black hole candidates.