A comparative analysis of standard accretion discs spectra: an application to ultraluminous X-ray sources

We compare standard models of accretion discs around black holes (BHs) that include the appropriate zero-torque inner boundary condition and relativistic effects on the emission and propagation of radiation. The comparison is performed adopting the multicolour disc blackbody model (MCD) as reference and looking for the parameter space in which it is in statistical agreement with 'more physical' accretion disc models. We find simple 'recipes' that can be used for adjusting the estimates of the physical inner radius of the disc, the BH mass and the accretion rate inferred using the parameters of the MCD fits. We applied these results to four ultraluminous X-ray sources for which MCD spectral fits of their X-ray soft spectral components have been published and find that, in three cases (NGC 1313 X-1, X-2 and M 81 X-9), the BH masses inferred for a standard disc around a Schwarzschild BH are in the interval  ∼100–200 M_⊙  . Only if the BH is maximally rotating are the masses comparable to the much larger values previously derived in the literature.     

A massive thick disc around a massive black hole and its runaway instability

We investigate the runaway instability of configurations consisting of a massive dense but non-self-gravitating thick disc/torus surrounding a massive black hole (MBH). We limit our model parameters to values that result in a self-consistent thick disc around an MBH. We identify, analytically, the index of the angular momentum distribution that will form a thick disc as an initial equilibrium state, and obtain the mass ratio of the disc to the central black hole for which the disc is dominated by the radiation pressure. In our theoretical framework we find that a self-consistent thick disc with constant angular momentum leads to a runaway instability on a dynamical time-scale. However, even a slight increase of the specific angular momentum outwards has a strong stabilizing effect on the accretion process. Finally, we discuss our results and present possible applications to high-energy emission.     

Magnetocentrifugal launching of jets from discs around Kerr black holes

Strong magnetic fields modify particle motion in the curved space–time of spinning black holes and change the stability conditions of circular orbits. We study conditions for magnetocentrifugal jet launching from accretion discs around black holes, whereby large-scale black hole lines anchored in the disc may fling tenuous coronal gas outwards. For a Schwarzschild black hole, magnetocentrifugal launching requires that the poloidal component of magnetic fields makes an angle less than  60°  to the outward direction at the disc surface, similar to the Newtonian case. For prograde rotating discs around Kerr black holes, this angle increases and becomes  90°  for footpoints anchored to the disc near the horizon of a critically spinning   a = M   black hole. Thus, a disc around a critically spinning black hole may centrifugally launch a jet even along the rotation axis.     

Episodic accretion in magnetically layered protoplanetary discs

We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 au such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion on to the protostar occurs in ∼10⁴-yr bursts with ̇ ∼10⁻⁵ M_⊙ yr⁻¹, separated by quiescent intervals lasting ∼10⁵ yr where ̇ ≈10⁻⁸ M_⊙ yr⁻¹. Such bursts could lead to repeated episodes of strong mass outflow in young stellar objects. The transition to this episodic mode of accretion occurs at an early epoch ( t ≪1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum-mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼1 au. The predicted rate of low-mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1–3 au.     

Determining the spin of two stellar-mass black holes from disc reflection signatures

We present measurements of the dimensionless spin parameters and inner-disc inclination of two stellar-mass black holes. The spin parameter of SWIFT J1753.5−0127 and GRO J1655−40 is estimated by modelling the strong reflection signatures present in their XMM–Newton observations. Using a newly developed, self-consistent reflection model which includes the blackbody radiation of the disc as well as the effect of Comptonization, blurred with a relativistic line function, we infer the spin parameter of SWIFT J1753.5−0127 to be  0.76^+0.11_−0.15  . The inclination of this system is estimated at  55°⁺²₋₇  . For GRO J1655−40, we find that the disc is significantly misaligned to the orbital plane, with an innermost inclination of  30°⁺⁵₋₁₀  . Allowing the inclination to be a free parameter, we find a lower limit for the spin of 0.90, this value increases to that of a maximal rotating black hole when the inclination is set to that of the orbital plane of J1655−40. Our technique is independent of the black hole mass and distance, uncertainties in which are among the main contributors to the spin uncertainty in previous works.     

High-frequency X-ray variability as a mass estimator of stellar and supermassive black holes

There is increasing evidence that supermassive black holes in active galactic nuclei (AGN) are scaled-up versions of Galactic black holes. We show that the amplitude of high-frequency X-ray variability in the hard spectral state is inversely proportional to the black hole mass over eight orders of magnitude. We have analysed all available hard-state data from RXTE of seven Galactic black holes. Their power density spectra change dramatically from observation to observation, except for the high-frequency (≳10 Hz) tail, which seems to have a universal shape, roughly represented by a power law of index −2. The amplitude of the tail,   C _M   (extrapolated to 1 Hz), remains approximately constant for a given source, regardless of the luminosity, unlike the break or quasi-periodic oscillation frequencies, which are usually strongly correlated with luminosity. Comparison with a moderate-luminosity sample of AGN shows that the amplitude of the tail is a simple function of black hole mass,   C _M = C / M   , where   C ≈ 1.25 M_⊙ Hz⁻¹  . This makes   C _M   a robust estimator of the black hole mass which is easy to apply to low- to moderate-luminosity supermassive black holes. The high-frequency tail with its universal shape is an invariant feature of a black hole and, possibly, an imprint of the last stable orbit.     

Computation of mass outflow rate from relativistic quasi-spherical accretion on to black holes

We compute the mass outflow rate R _m˙ from relativistic matter that is accreting quasi-spherically on to the Schwarzschild black holes. Taking the pair-plasma pressure-mediated shock surface as the effective boundary layer (of the black hole) from where the bulk of the outflow is assumed to be generated, computation of this rate is done using combinations of exact transonic inflow and outflow solutions. We find that R _m˙ depends on the initial parameters of the flow, the polytropic index of matter, the degree of compression of matter near the shock surface and the location of the shock surface itself. We thus not only study the variation of the mass outflow rate as a function of various physical parameters governing the problem, but also provide a sufficiently plausible estimation of this rate.     

Radiatively driven mass accretion on to galactic nuclei by circumnuclear starbursts

We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation–hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by M ˙ ( r )= η ( L _*/ c ²)( r / R )² (Δ R / R )(1 −  e ^−τ) at radius r , where the efficiency η ranges from 0.2 up to 1, L _* and R are respectively the bolometric luminosity and the radius of the starburst ring, Δ R is the extent of the emission regions, and τ is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to ∼ parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation–hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.     

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.     

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.     

Luminous hot accretion discs

We find a new two-temperature hot branch of equilibrium solutions for stationary accretion discs around black holes. In units of Eddington accretion rate defined as 10 L _Edd c ², the accretion rates to which these solutions correspond are within the range ̇ ₁≲ ̇ ≲1, where ̇ ₁ is the critical rate of advection-dominated accretion flow (ADAF). In these solutions, the energy loss rate of the ions by Coulomb energy transfer between the ions and electrons is larger than the viscously heating rate and it is the advective heating together with the viscous dissipation that balances the Coulomb cooling of ions. When ̇ ₁≲ ̇ ≲ ̇ ₂, where ̇ ₂∼5 ̇ ₁<1, the accretion flow remains hot throughout the disc. When ̇ ₂≲ ̇ ≲1, Coulomb interaction will cool the inner region of the disc within a certain radius ( r _tr∼several tens of Schwarzschild radii or larger depending on the accretion rate and the outer boundary condition) and the disc will collapse on to the equatorial plane and form an optically thick cold annulus. Compared with ADAF, these hot solutions are much more luminous because of the high accretion rate and efficiency; therefore, we call them luminous hot accretion discs.     

Ultraluminous X-ray source 1E 0953.8+6918 (M81 X-9): an intermediate-mass black hole candidate and its environs

We present a ROSAT and ASCA study of the Einstein source X-9 and its relation to a shock-heated shell-like optical nebula in a tidal arm of the M81 group of interacting galaxies. Our ASCA observation of the source shows a flat and featureless X-ray spectrum well described by a multicolour disc blackbody model. The source most likely represents an optically thick accretion disc around an intermediate-mass black hole  ( M ∼10² M_⊙)  in its high/soft state, similar to other variable ultraluminous X-ray sources observed in nearby disc galaxies. Using constraints derived from both the innermost stable orbit around a black hole and the Eddington luminosity, we find that the black hole is fast-rotating and that its mass is between ∼80 M_⊙–1.5×10² M_⊙. The inferred bolometric luminosity of the accretion disc is ∼(1.1×10⁴⁰ erg s⁻¹)/(cos  i ). Furthermore, we find that the optical nebula is very energetic and may contain large amounts of hot gas, accounting for a soft X-ray component as indicated by archival ROSAT PSPC data. The nebula is apparently associated with X-9; the latter may be powering the former and/or they could be formed in the same event (e.g. a hypernova). Such a connection, if confirmed, could have strong implications for understanding both the birth of intermediate-mass black holes and the formation of energetic interstellar structures.     

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.     

The runaway instability of self-gravitating tori with non-constant specific angular momentum around black holes

We discuss the runaway instability of axisymmetric tori with non-constant specific angular momentum around black holes, taking into account self-gravity of the tori. The distribution of specific angular momentum of the tori is assumed to be a positive power law with respect to the distance from the rotational axis. By employing the pseudo-Newtonian potential for the gravity of the spherical black hole, we have found that self-gravity of the tori causes a runaway instability if the amount of the mass which is transferred from the torus to the black hole exceeds a critical value, i.e. 3 per cent of the mass of the torus. This has been shown by two different approaches: (1) by using equilibrium models and (2) by dynamical simulations. In particular, dynamical simulations using an SPH code have been carried out for both self-gravitating and non-self-gravitating tori. For non-self-gravitating models, all tori are runaway stable. Therefore we come to the conclusion that self-gravity of the tori has a stronger destabilizing effect than the stabilizing effect of the positive power-law distribution of the angular momentum.     

Gravitational wave emission from a companion black hole in the presence of an accretion disc around a super-massive Kerr black hole

Gravitational wave signal characteristics from a binary black hole system in which the companion moves through the accretion disc of the primary are studied. We chose the primary to be a super-massive  ( M = 10⁸ M_⊙)  Kerr black hole and the companion to be a massive black hole  ( M = 10⁵ M_⊙)  to clearly demonstrate the effects. We show that the drag exerted on the companion by the disc is sufficient to reduce the coalescence time of the binary. The drag is primarily due to the fact that the accretion disc on a black hole deviates from a Keplerian disc and becomes sub-Keplerian due to inner boundary condition on the black hole horizon. We consider two types of accretion rates on to the companion. The companion is deeply immersed inside the disc and it can accrete at the Bondi rate which depends on the instantaneous density of the disc. However, an accretion disc can also form around the smaller black hole and it can accrete at its Eddington rate. Thus, this case is also studied and the results are compared. We find that the effect of the disc will be significant in reducing the coalescence time and one needs to incorporate this while interpreting gravitational wave signals emitted from such a binary system.     

A spectroscopic study of V603 Aquilae: stellar parameters and continuumline variations

A time-resolved spectroscopic study of V603 Aql (Nova Aquilae 1918) is presented. An orbital period of P _orb=01385±00002, consistent with previous results, and a radial velocity semi-amplitude of K =20±3 km s¹ are obtained from the radial velocity variations of the H emission line. Similar K values are also found in H , H , and He  i emission lines. Using the measured FWHM of the H line and assuming that the derived semi-amplitude is that of the white dwarf, we deduce a most likely mass ratio of q =0.24±0.05 and stellar masses of M ₂=0.29±0.04 M and M ₁=1.2±0.2 M for the secondary and primary (the white dwarf) star, respectively. The dynamical solution also indicates a very low orbital inclination, i =13°±2°. We find that the continuum and line variations are modulated with both the positive and the negative superhump periods, indicating that they arise from similar regions of the accretion disc. Moreover, we find, for the first time from spectroscopy, evidence of negative superhumps in addition to the positive superhumps. Positive superhumps are explained within the disc instability model as caused by an eccentric disc surrounding the white dwarf, which is precessing (apsidal advance) because of tidal instabilities, causing the observed positive superhumps. A nodal precession in the accretion disc is currently believed to be the cause of the observed negative superhumps. The low value of q is consistent with the expected value for systems that show superhumps, in accordance with the eccentric disc model. We find no evidence of periodicity associated with the spin period.     

Testing models of X-ray reflection from irradiated discs

We model the reflected spectrum expected from localized magnetic flares above an ionized accretion disc. We concentrate on the case of very luminous magnetic flares above a standard accretion disc extending down to the last stable orbit, and use a simple parametrization to allow for an X-ray-driven wind. Full disc spectra including relativistic smearing are calculated. When fitted with the constant-density reflection models, these spectra give both a low reflected fraction and a small linewidth as seen in the hard spectra from galactic black hole binaries and active galactic nuclei. We fit our calculated spectra to real data from the low/hard state of Nova Muscae and Cyg X-1 and show that these models give comparable χ ² to those obtained from the constant-density reflection models, which implied a truncated disc. This explicitly demonstrates that the data are consistent either with magnetic flares above an ionized disc extending down to the last stable orbit around a black hole, or with non-ionized, truncated discs.     

Circumplanetary disc properties obtained from radiation hydrodynamical simulations of gas accretion by protoplanets

We investigate the properties of circumplanetary discs formed in three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities.
We find that the analytical prediction of circumplanetary disc radii in an evacuated gap  ( R _Hill/3)  from Quillen & Trilling yields a good estimate for discs formed by high-mass protoplanets. The radial density profiles of the circumplanetary discs may be described by power laws between   r ⁻²  and   r ^−3/2  . We find no evidence for the ring-like density enhancements that have been found in some previous models of circumplanetary discs. Temperature profiles follow a  ∼ r ^−7/10  power law regardless of protoplanet mass or nebula grain opacity. The discs invariably have large scaleheights  ( H / r > 0.2)  , making them thick in comparison with their encompassing circumstellar discs, and they show no flaring.