Models for jet power in elliptical galaxies: a case for rapidly spinning black holes

The power of jets from black holes is expected to depend on both the spin of the black hole and the structure of the accretion disc in the region of the last stable orbit. We investigate these dependencies using two different physical models for the jet power: the classical Blandford–Znajek (BZ) model and a hybrid model developed by Meier. In the BZ case, the jets are powered by magnetic fields directly threading the spinning black hole while in the hybrid model, the jet energy is extracted from both the accretion disc as well as the black hole via magnetic fields anchored to the accretion flow inside and outside the hole's ergosphere. The hybrid model takes advantage of the strengths of both the Blandford–Payne and BZ mechanisms, while avoiding the more controversial features of the latter. We develop these models more fully to account for general relativistic effects and to focus on advection-dominated accretion flows (ADAFs) for which the jet power is expected to be a significant fraction of the accreted rest mass energy.
We apply the models to elliptical galaxies, in order to see if these models can explain the observed correlation between the Bondi accretion rates and the total jet powers. For typical values of the disc viscosity parameter  α∼ 0.04 –0.3  and mass accretion rates consistent with ADAF model expectations, we find that the observed correlation requires   j ≳ 0.9  ; that is, it implies that the black holes are rapidly spinning. Our results suggest that the central black holes in the cores of clusters of galaxies must be rapidly rotating in order to drive jets powerful enough to heat the intracluster medium and quench cooling flows.     

On the spin paradigm and the radio dichotomy of quasars

We investigate whether models based on the assumption that jets in quasars are powered by rotating black holes can explain the observed radio dichotomy of quasars. We show that in terms of the 'spin paradigm' models, radio-loud quasars could be objects in which the rotation rate of the black hole corresponds to an equilibrium between spin-up by accretion and spin-down by the Blandford–Znajek mechanism. Radio-quiet quasars could be hosting black holes with an average spin much smaller than the equilibrium one. We discuss possible accretion scenarios which can lead to such a bimodal distribution of black hole spins.     

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.     

Iron line profiles and self-shadowing from relativistic thick accretion discs

We present Fe Kα line profiles from and images of relativistic discs with finite thickness around a rotating black hole using a novel code. The line is thought to be produced by iron fluorescence of a relatively cold X-ray-illuminated material in the innermost parts of the accretion disc and provides an excellent diagnostic of accretion flows in the vicinity of black holes. Previous studies have concentrated on the case of a thin, Keplerian accretion disc. This disc must become thicker and sub-Keplerian with increasing accretion rates. These can affect the line profiles and in turn can influence the estimation of the accretion disc and black hole parameters from the observed line profiles. We here embark on, for the first time, a fully relativistic computation which offers key insights into the effects of geometrical thickness and the sub-Keplerian orbital velocity on the line profiles. We include all relativistic effects such as frame-dragging, Doppler boost, time dilation, gravitational redshift and light bending. We find that the separation and the relative height between the blue and red peaks of the line profile diminish as the thickness of the disc increases. This code is also well suited to produce accretion disc images. We calculate the redshift and flux images of the accretion disc and find that the observed image of the disc strongly depends on the inclination angle. The self-shadowing effect appears remarkable for a high inclination angle, and leads to the black hole shadow being in this case, completely hidden by the disc itself.     

Relation between blue/ultraviolet continuum shape and the ratio of radio-to-optical emission for B3-VLA quasars

The low-frequency radio luminosity is believed to be an indicator of jet power, while the optical/ultraviolet (UV) emission is probably from accretion discs in the nuclei of steep-spectrum radio quasars. We present a correlation between the ratio of radio-to-optical luminosities and the continuum spectral index in blue/UV bands, which might indicate that the continuum shape in blue/UV bands is related to the ratio of jet to accretion power. The results may imply that the spectra and structure of accretion discs are probably affected by the interactions between jets and discs.     

Fuelling quasars with hot gas

We consider a model for quasar formation in which massive black holes are formed and fuelled largely by the accretion of hot gas during the process of galaxy formation. In standard hierarchical collapse models, objects about the size of normal galaxies and larger form a dense hot atmosphere when they collapse. We show that if such an atmosphere forms a nearly 'maximal' cooling flow, then a central black hole can accrete at close to its Eddington limit. This leads to exponential growth of a seed black hole, resulting in a quasar in some cases. In this model, the first quasars form soon after the first collapses to produce hot gas. The hot gas is depleted as time progresses, mostly by cooling, so that the accretion rate eventually falls below the threshold for advection-dominated accretion, at which stage radiative efficiency plummets and any quasar turns off. A simple implementation of this model, incorporated into a semi-analytical model for galaxy formation, overproduces quasars when compared with observed luminosity functions, but is consistent with models of the X-ray background, which indicate that most accretion is obscured. It produces few quasars at high redshift owing to the lack of time needed to grow massive black holes. Quasar fuelling by hot gas provides a minimum level, sufficient to power most quasars at redshifts between one and two, to which other sources of fuel can be added. The results are sensitive to feedback effects, such as might result from radio jets and other outflows.     

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.     

Is the Bardeen–Petterson effect responsible for the warping and precession in NGC 4258?

Strong evidence for the presence of a warped Keplerian accretion disc in NGC 4258 (M 106) has been inferred from the kinematics of water masers detected at subparsec scales. Assuming a power-law accretion disc and using constraints on the disc parameters derived from observational data, we have analysed the relativistic Bardeen–Petterson effect driven by a Kerr black hole as the potential physical mechanism responsible for the disc warping. We found that the Bardeen–Petterson radius is comparable to or smaller than the inner radius of the maser disc (independent of the allowed value for the black hole spin parameter). Numerical simulations for a wide range of physical conditions have shown that the evolution of a misaligned disc due to the Bardeen–Petterson torques usually produces an inner flat disc and a warped transition region with a smooth gradient in the tilt and twist angles. Since this structure is similar to that seen in NGC 4258, we propose that the Bardeen–Petterson effect may be responsible for the disc warping in this galaxy. We estimated the time-scale necessary for the disc inside of the Bardeen–Petterson radius to align with the black hole's equator, as a function of the black hole spin. Our results show that the Bardeen–Petterson effect can align the disc within a few billion years in the case of NGC 4258. Finally, we show that if the observed curvature of the outer anomalous arms in the galactic disc of NGC 4258 is associated with the precession of its radio jet/counterjet, then the Bardeen–Petterson effect can provide the required precession period.     

On the influence of resonant absorption on the iron emission‐line profiles from accreting black holes

The fluorescent iron K α emission-line profile provides an excellent probe of the innermost regions of active galactic nuclei. Fe  xxv and Fe  xxvi in diffuse plasma above the accretion disc can affect the X-ray spectrum by iron K α resonant absorption. This in turn can influence the interpretation of the data and the estimation of the accretion disc and black hole parameters. We embark on a fully relativistic computation of this effect and calculate the iron line profile in the framework of a specific model in which rotating, highly ionized and resonantly absorbing plasma occurs close to the black hole. This can explain the features seen in the iron K α line profile recently obtained by Nandra et al. for the type 1 Seyfert galaxy NGC 3516. We show that the redshift of this feature can be mainly gravitational in origin and accounted for without the need to invoke fast accretion of matter on to the black hole. New X-ray satellites such as XMM , ASTRO-E and Chandra provide excellent opportunities to test the model against high-quality observational data.     

The growth history of supermassive black holes and the origin of the radio-loud–radio-quiet dichotomy

Monte Carlo simulations of the growth of supermassive black holes in semi-analytic models of galaxy formation are used to reconstruct characteristic merging and accretion histories. This paper shows that the growth pattern depends on the environment. In field galaxies black holes acquire most of their mass in a single accretion event. Refuellings and mergers with other black holes become important in groups and clusters. I also investigate whether the assumption that radio jets are powered by rotating black holes can explain the observed radio-loud–radio-quiet dichotomy. Wilson & Colbert speculated that rapidly rotating black holes are the natural product of major mergers, while normal accretion through a disc may not give rapidly spinning black holes if the conversion of rotational energy into electromagnetic energy is very efficient. Here I derive predictions for this model including the fraction of radio-loud quasars as a function of redshift and luminosity and compare these predictions with those of alternative proposals.     

Alignment and precession of a black hole with a warped accretion disc

We consider the shape of an accretion disc whose outer regions are misaligned with the spin axis of a central black hole and calculate the steady state form of the warped disc in the case where the viscosity and surface densities are power laws in the distance from the central black hole. We discuss the shape of the resulting disc in both the frame of the black hole and that of the outer disc. We note that some parts of the disc and also any companion star maybe shadowed from the central regions by the warp. We compute the torque on the black hole caused by the Lense–Thirring precession, and hence compute the alignment and precession time-scales. We generalize the case with viscosity and hence surface density independent of radius to more realistic density distributions for which the surface density is a decreasing function of radius. We find that the alignment time-scale does not change greatly but the precession time-scale is more sensitive. We also determine the effect on this time-scale if we truncate the disc. For a given truncation radius, the time-scales are less affected for more sharply falling density distributions.     

The warped disc of NGC 4258

We consider the properties of the warped accretion disc in NGC 4258 which is delineated by maser emission. We use our analytical models to consider whether the disc could be warped by Lense–Thirring precession. We show that such models fit the shape of the disc well and we determine the goodness of fit for various combinations of the warp radius and the disc and black hole configurations. Though the fits are compelling evidence, we note that such a model has implications for the formation and longevity of the disc which might be problematic for the current understanding of Seyfert galaxies.     

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.     

XMM-EPIC observation of MCG–6-30-15: direct evidence for the extraction of energy from a spinning black hole?

We present XMM-Newton European Photon Imaging Camera (EPIC) observations of the bright Seyfert 1 galaxy MCG–6-30-15, focusing on the broad Fe K α line at ∼6 keV and the associated reflection continuum, which is believed to originate from the inner accretion disc. We find these reflection features to be extremely broad and redshifted, indicating an origin in the very central regions of the accretion disc. It seems likely that we have caught this source in the 'deep minimum' state first observed by Iwasawa et al. The implied central concentration of X-ray illumination is difficult to understand in any pure accretion disc model. We suggest that we are witnessing the extraction and dissipation of rotational energy from a spinning black hole by magnetic fields connecting the black hole or plunging region to the disc.     

Application of a relativistic accretion disc model to X-ray spectra of LMC X-1 and GRO J1655-40

We present a general relativistic accretion disc model and its application to the soft-state X-ray spectra of black hole binaries. The model assumes a flat, optically thick disc around a rotating Kerr black hole. The disc locally radiates away the dissipated energy as a blackbody. Special and general relativistic effects influencing photons emitted by the disc are taken into account. The emerging spectrum, as seen by a distant observer, is parametrized by the black hole mass and spin, the accretion rate, the disc inclination angle and the inner disc radius.
We fit the ASCA soft-state X-ray spectra of LMC X-1 and GRO J1655-40 by this model. We find that, having additional limits on the black hole mass and inclination angle from optical/UV observations, we can constrain the black hole spin from X-ray data. In LMC X-1 the constraint is weak, and we can only rule out the maximally rotating black hole. In GRO J1655-40 we can limit the spin much better, and we find 0.68 a 0.88 . Accretion discs in both sources are radiation-pressure dominated. We do not find Compton reflection features in the spectra of any of these objects.     

Black hole mergers: can gas discs solve the 'final parsec' problem?

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre-existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary's gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework.
The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high-photon-energy variability on the relatively long orbital time-scale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary.
We also find that the disc can drive the binary to merger on a reasonable time-scale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e.   a ₀≲ 0.05  pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is ≲0.001. Gas discs thus appear not to be an effective solution to the 'last parsec' problem for a significant class of mergers.     

Effects of inflationary bubbles on the polarization and temperature anisotropies of the cosmic microwave background

The broad X-ray iron line, detected in many active galactic nuclei, is likely to be produced by fluorescence from the X-ray-illuminated central parts of an accretion disc close to a supermassive black hole. The time-averaged shape of the line can be explained most naturally by a combination of special and general relativistic effects. Such line profiles contain information about the black hole spin and the accretion disc, as well as the geometry of the emitting region, and may help to test general relativity in the strong gravity regime. In this paper we embark on the computation of the temporal response of the line to the illuminating flux. Previous studies concentrated on the calculation of reverberation signatures from static sources illuminating the disc. In this paper we focus on the more physically justified case of flares located above the accretion disc and corotating with it. We compute the time-dependent iron line, taking into account all general relativistic effects, and show that its shape is of a very complex nature, and we also present light curves accompanying the iron line variability. We suggest that present and future X-ray satellites like XMM or Constellation-X may be capable of detecting features present in the computed reverberation maps.     

Small-scale inviscid accretion discs around black holes

Gas falling quasi-spherically on to a black hole forms an inner accretion disc if its specific angular momentum l exceeds l ∗∼ r _g c , where r _g is the Schwarzschild radius. The standard disc model assumes l ≫ l ∗. We argue that, in many black hole sources, accretion flows have angular momenta just above the threshold for disc formation, l ≳ l ∗, and assess the accretion mechanism in this regime. In a range l ∗< l < l _cr, a small-scale disc forms in which gas spirals fast into the black hole without any help from horizontal viscous stresses. Such an 'inviscid' disc, however, interacts inelastically with the feeding infall. The disc–infall interaction determines the dynamics and luminosity of the accretion flow. The inviscid disc radius can be as large as 14 r _g, and the energy release peaks at 2 r _g. The disc emits a Comptonized X-ray spectrum with a break at ∼100 keV. This accretion regime is likely to take place in wind-fed X-ray binaries and is also possible in active galactic nuclei.     

Radio and X-ray properties of relativistic beaming models for ultraluminous X-ray sources

We calculate the broad-band radio–X-ray spectra predicted by microblazar and microquasar models for ultraluminous X-ray sources (ULXs), exploring the possibility that their dominant power-law component is produced by a relativistic jet, even at near-Eddington mass accretion rates. We do this by first constructing a generalized disc–jet theoretical framework in which some fraction of the total accretion power, P _a, is efficiently removed from the accretion disc by a magnetic torque responsible for jet formation. Thus, for different black hole masses, mass accretion rates and magnetic coupling strength, we self-consistently calculate the relative importance of the modified disc spectrum, as well as the overall jet emission due to synchrotron and Compton processes. In general, transferring accretion power to a jet makes the disc fainter and cooler than a standard disc at the same mass accretion rate; this may explain why the soft spectral component appears less prominent than the dominant power-law component in most bright ULXs. We show that the apparent X-ray luminosity and spectrum predicted by the microquasar model are consistent with the observed properties of most ULXs. We predict that the radio synchrotron jet emission is too faint to be detected at the typical threshold of radio surveys to date. This is consistent with the high rate of non-detections over detections in radio counterpart searches. Conversely, we conclude that the observed radio emission found associated with a few ULXs cannot be due to beamed synchrotron emission from a relativistic jet.     

The evolution of misaligned accretion discs and spinning black holes

In this paper, we consider the process of alignment of a spinning black hole and a surrounding misaligned accretion disc. We use a simplified set of equations, that describe the evolution of the system in the case where the propagation of warping disturbances in the accretion disc occurs diffusively, a situation likely to be common in the thin discs in active galactic nuclei (AGN). We also allow the direction of the hole spin to move under the action of the disc torques. In such a way, the evolution of the hole–disc system is computed self-consistently. We consider a number of different situations and we explore the relevant parameter range, by varying the location of the warp radius R _w and the propagation speed of the warp. We find that the dissipation associated with the twisting of the disc results in a large increase in the accretion rate through the disc, so that AGN accreting from a misaligned disc are likely to be significantly more luminous than those accreting from a flat disc. We compute explicitly the time-scales for the warping of the disc and for the alignment process and compare our results with earlier estimates based on simplified steady-state solutions. We also confirm earlier predictions that, under appropriate circumstances, accretion can proceed in a counter-aligned fashion, so that the accreted material will spin-down the hole, rather than spinning it up. Our results have implication in a number of different observational features of AGN such as the orientation and shape of jets, the shape of X-ray iron lines and the possibility of obscuration and absorption of X-ray by the outer disc as well as the general issue of the spin history of black holes during their growth.