Thermally driven outflows from pair-plasma pressure-mediated shock surfaces around Schwarzschild black holes

Introducing a spherical, steady, self-supported pair-plasma pressure-mediated shock surface around a Schwarzschild black hole as the effective physical atmosphere that may be responsible for the generation of astrophysical mass outflows from relativistic quasi-spherical accretion, we calculate the mass outflow rate R _̇ by simultaneously solving the set of equations governing transonic polytropic accretion and isothermal winds. R _̇ is computed in terms of only three inflow parameters, which, we believe, has been done for the first time in our work. We then study the dependence of R _̇ on various inflow as well as shock parameters, and establish the fact that the outflow rate is essentially controlled by the post-shock proton temperature.     

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.     

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.     

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.     

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.     

Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass M _BH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction     . We develop an iterative scheme based on the adiabatic approximation to study the BH–disc co-evolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen–Petterson effect) and interacts with the BH until the spin   J _BH  aligns with     . For a BH aligning with a corotating disc, the fractional increase in mass is typically less than a few per cent, while the spin modulus can increase up to a few tens of per cent. The alignment time-scale     is of  ∼10⁵–10⁶ yr  for a maximally rotating BH accreting at the Eddington rate. BH–disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular corotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.     

A textbook case of bow shock entrainment in a YSO outflow

Near-infrared images in H₂ line emission and submillimetre maps in CO J  = 3–2 emission illustrate the remarkable association between a molecular bow shock and the redshifted molecular outflow lobe in W75N. The flow lobe fits perfectly into the wake of the bow, as one would expect if the lobe represented swept-up gas. Indeed, these observations strongly support the 'bow shock' entrainment scenario for molecular outflows driven by young stars.   The characteristics of the bow shock and CO outflow lobe are compared with those of numerical simulations of jet-driven flows. These models successfully reproduce the bulge and limb-brightening in the CO outflow, although the model H₂ bow exhibits more structure extending back along the flow axis. We also find that the size of the flow, the high mass fraction in the flow at low outflow velocities (low γ values) and the high CO/H₂ luminosity ratio indicate that the system is evolved. We also predict a correlation, in evolved systems, between outflow age and the CO/H₂ luminosity ratio.     

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 runaway instability of thick discs around black holes I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time-scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M) and a large range of mass fluxes  ( m 10^-3 M s^-1)  . The implications of our results in the context of gamma-ray bursts are briefly discussed.     

Ultraluminous X-ray source populations in normal galaxies: a preliminary survey with Chandra

We present results of a Chandra survey of the ultraluminous X-ray sources (ULX) in 13 normal galaxies, in which we combine source detection with X-ray flux measurement. 22 ULX were detected, i.e. with   L _x > 1 × 10³⁹ erg s⁻¹ ( L ₁₀)  and 39 other sources were detected with   L _x > 5 × 10³⁸ erg s⁻¹ ( L ₅)  . We also use radial intensity profiles to remove extended sources from the sample. The majority of sources are not extended, which for a typical distance constrains the emission region size to less than 50 pc. X-ray colour–colour diagrams and spectral fitting results were examined for indicators of the ULX nature. In the case of the brighter sources, spectral fitting generally requires two-component models. In only a few cases do colour–colour diagrams or spectral fitting provide evidence of a black hole nature. We find no evidence of a correlation with stellar mass, however, there is a strong correlation with star formation as indicated by the 60-μm flux as found in previous studies.     

An external-shock origin of the relation for gamma-ray bursts

We investigate the possibility that the     relation between the peak energy E _p of the  ν F _ν  spectrum and energy output     for long-duration gamma-ray bursts (GRBs) arises from the external shock produced by the interaction of a relativistic outflow with the ambient medium. To that aim, we take into account the dependence of all parameters which determine E _p and     on the radial distribution of the ambient medium density and find that the     relation can be explained if the medium around GRBs has a universal radial stratification. For various combinations of GRB radiative process (synchrotron or inverse-Compton) and dissipation mechanism (reverse or forward shock), we find that the circumburst medium must have a particle density with a radial distribution different than the   R ⁻²  expected for the stellar wind corresponding to a constant mass-loss rate and terminal speed.     

Constraints on the mass and abundance of black holes in the Galactic halo: the high-mass limit

We establish constraints on the mass and abundance of black holes in the Galactic halo by determining their impact on globular clusters, which are conventionally considered to be little evolved. Using detailed Monte Carlo simulations and simple evolutionary models, we argue that black holes with masses M _bh≳(1–3)×10⁶ M_⊙ can comprise no more than a fraction f _bh≈0.17 of the total halo density at Galactocentric radius R ≈8 kpc. This bound arises from requiring stability of the cluster mass function. A more restrictive bound may be derived if we demand that the probability of destruction of any given, low-mass M _c≈(2.5–7.5)×10⁴ M_⊙] globular cluster not exceed 50 per cent; this bound is f _bh≲0.025–0.05 at R ≈8 kpc. This constraint improves those based on disc heating and dynamical friction arguments as well as current lensing results. At smaller radius the constraint on f _bh strengthens, while at larger radius an increased fraction of black holes is allowed.     

Effective collision strengths for fine-structure forbidden transitions among the 3s23p3 levels of K v

In wind-fed X-ray binaries the accreting matter is Compton-cooled and falls freely on to the compact object. The matter has a modest angular momentum l and accretion is quasi-spherical at large distances from the compact object. Initially small non-radial velocities grow in the converging supersonic flow and become substantial in the vicinity of the accretor. The streamlines with l >( GMR ∗)^1/2 (where M and R ∗ are the mass and radius of the compact object) intersect outside R ∗ and form a two-dimensional caustic which emits X-rays. The streamlines with low angular momentum, l <( GMR ∗)^1/2, run into the accretor. If the accretor is a neutron star, a large X-ray luminosity results. We show that the distribution of accretion rate/luminosity over the star surface is sensitive to the angular momentum distribution of the accreting matter. The apparent luminosity depends on the side from which the star is observed and can change periodically with the orbital phase of the binary. The accretor then appears as a 'Moon-like' X-ray source.     

Dynamics of the boxy elliptical galaxy NGC 1600

We use three-integral models to infer the distribution function (DF) of the boxy E3–E4 galaxy NGC 1600 from surface brightness and line-profile data on the minor and major axes. We assume axisymmetry and that the mass-to-light ratio is constant in the central ∼1 R _e. Stars in the resulting gravitational potential move mainly on regular orbits. We use an approximate third integral K from perturbation theory and write the DF as a sum of basis functions in the three integrals E , L _z and K . We then fit the projected moments of these basis functions to the kinematic observables and deprojected density, using a non-parametric algorithm. The deduced dynamical structure is radially anisotropic, with σ _θ σ _r ≈ σ _φ σ _r ≈0.7 on the major axis. Both on the minor axis and near the centre the velocity distribution is more isotropic; thus the model is flattened by equatorial radial orbits. The kinematic data are fitted without the need for a central black hole; the central mass determined previously from ground-based data therefore overestimates the actual black-hole mass. The mass-to-light ratio of the stars is M L _V =6  h ₅₀. The anisotropy structure of NGC 1600 with a radially anisotropic main body and more nearly isotropic centre is similar to that found recently in NGC 1399, 2434, 3379 and 6703, suggesting that this pattern may be common amongst massive elliptical galaxies. We discuss a possible merger origin of NGC 1600 in the light of these results.     

Evidence of a high-velocity ionized outflow in a second narrow-line quasar PG 0844+349

Following the discovery of X-ray absorption in a high-velocity outflow from the bright quasar PG 1211 + 143 we have searched for similar features in XMM–Newton archival data of a second (high accretion rate) quasar PG 0844+349. Evidence is found for several faint absorption lines in both the EPIC and RGS spectra, whose most likely identification with resonance transitions in H-like Fe, S and Ne implies an origin in highly ionized matter with an outflow velocity of order ∼0.2c. The line equivalent widths require a line-of-sight column density of   N _H∼ 4 × 10²³ cm⁻²  , at an ionization parameter of log  ξ∼ 3.7  . Assuming a radial outflow being driven by radiation pressure from the inner accretion disc, as suggested previously for PG 1211 + 143, the flow in PG 0844+349 is also likely to be optically thick, in this case within ∼25 Schwarzschild radii. Our analysis suggests that a high-velocity, highly ionized outflow is likely to be a significant component in the mass and energy budgets of active galactic nuclei accreting at or above the Eddington rate.     

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

Active galactic nuclei jet mass loading and truncation by stellar winds

Active galactic nuclei can produce extremely powerful jets. While tightly collimated, the scale of these jets and the stellar density at galactic centres implies that there will be many jet/star interactions, which can mass load the jet through stellar winds. Previous work employed modest wind mass outflow rates, but this does not apply when mass loading is provided by a small number of high mass-loss stars. We construct a framework for jet mass loading by stellar winds for a broader spectrum of wind mass-loss rates than has previously been considered. Given the observed stellar mass distributions in galactic centres, we find that even highly efficient (0.1 Eddington luminosity) jets from supermassive black holes of masses M _BH≲ 10⁴ M_⊙ are rapidly mass loaded and quenched by stellar winds. For  10⁴ M_⊙ < M _BH < 10⁸ M_⊙  , the quenching length of highly efficient jets is independent of the jet's mechanical luminosity. Stellar wind mass loading is unable to quench efficient jets from more massive engines, but can account for the observed truncation of the inefficient M87 jet, and implies a baryon-dominated composition on scales ≳2 kpc therein even if the jet is initially pair plasma dominated.     

Variability associated with α accretion disc theory for standard and advection-dominated discs

The α turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory, modelling a steady state only on spatial or time-scales greater than those of the turbulence. The extent of the scale separation determines the relative precision error (RPE) of the predicted luminosity L _ν. Turbulence and the use of α implies that (1) field line stretching gives a magnetic pressure  α²/6 of the total pressure generally, and a one-to-one relation between α and the pressure ratio for thin discs, and (2) large turbulent scales in advection-dominated accretion flows (ADAFs) predict a lower L _ν precision than thin discs for a given observation duration and central mass. The allowed variability (or RPE) at frequency ν increases with the size of the contributing region. For X-ray binary ADAFs, the RPE ∼ 5 per cent at R  ≤ 1000 Schwarzchild radii ( R _s) for averages over  1000 s. However, current data for galaxies like NGC 4258 and M87 give RPEs in L _ν of 50–100 per cent even at R  ≤ 100  R _S. More data are required, but systematic deviations from ADAF predictions are more significant than random deviations, and may constrain properties of the turbulence, the accretion mode, the assumption of a steady state or the accretion rate.     

The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

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.