The resulting limit cycle is a main ingredient for explaining the dwarf nova outbursts. However, other mutually related, effects also play a role. Particularly important are the varying mass-transfer rate from the secondary, self- illumination of the secondary and the disc, tidal instabilities. Other, non-standard, viscosity prescriptions in particular the one suggested by Merloni in which the total stress is proportional to a geometrical mean of total and gas pressure, are consistent with thermal stability see e.
Ciesielski et al. Observations argue against the existence of this instability. Stellar-mass black hole sources cross this limit both during their rise to peak luminosity and on their decline to quiescence, showing no symptoms of unstable behaviour. The issue is still not solved. The most recent numerical simulations by Yan-Fei Jiang et al. Timing measurements e. They were first noticed in dwarf novae, i. In general, oscillations are the result of restoring forces acting on perturbations. For instance, if one perturbs a fluid element radially inwards, it conserves its own angular momentum and will be rotating too slow for its new location.
Centripetal forces consequently push it outwards again.
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These kind of inertial oscillations are the so called epicyclic oscillations. Disc oscillations may be axisymmetric e. The field of studying the temporal behaviour of discs by means of oscillations is called discoseismology. It is assumed that the variation of oscillation modes in radial direction is much stronger than in vertical direction.
The radial boundary conditions depend on the type of mode and its capture zone see below. Geometrically thick discs , i. For constant angular momentum distribution this term vanishes. The positive square root of which gives the x-mode that is a surface gravity mode Figure 8. The negative square root gives a purely incompressible inertial c- mode whose poloidal velocity field represents a circulation around the pressure maximum. To non-axisymmetric oscillation modes, however, accretion tori are dynamically unstable.
Whether or not hydrodynamical oscillation modes may survive such global instabilities or the presence of a weak magnetic field MRI turbulence , is subject of current, numerical investigations. Theoretical models predict both line and continuous electromagnetic spectra of accretion discs. Comparison with observations shows a rather good general agreement. However, several details are not satisfactory fitted and others are fixed by empirical ad hoc assumptions.
Generally, the radiative transfer through the disc is not treated as accurately as in the case of stellar atmospheres. The two most acute difficulties that one faces in the accretion disc case are: a the disc geometry calls for a 3-D treatment of the problem, b the viscous energy generation rate is not known as a function of the position in the disc. Fundamental papers that discuss methods to deal with these difficulties; see e. Hubeny et al. In the black hole and neutron star accretion discs , the fact that radiation moves in a highly curved space spacetime further complicates the problem of calculating the spectra.
Several "ray-tracing" methods of calculating photon trajectories along their geodesics from the source to a distant observer's screen have been developed to deal with this issue; see e. Vincent et al. The protoplanetary discs appear in the spectra of young stellar objects as infra-red excess on top of a stellar blackbody signature.
General Relativity & Black Holes
Depending on the stage of the system, the excess hump can dominate class I the emission profile or is barely notable class III. Protoplanetary discs contain a large amount of dust, e. The Cataclysmic Variables CVs with accretion discs i. The bright dwarf novae discs are controlled by a temporary enhancement of the rate of mass transfer. The underluminous and cold dust or debris discs around WD are the result of tidally disrupted asteroids or planetoids. Generally, discs of CVs are divided into two states:. The thermal state is well described by the thin disc model and a multi-colour disc MCD blackbody model e.
These models provide excellent fits to the X-ray spectra of BHBs in the thermal and intermediate state. Figure credits: Davis et al. The data are taken from Puchnarewicz et al. Note that this is merely a comparison: the spectra do not represent best fits. Accretion discs often show all kinds of emission and absorption lines. The most prominent line is the fluorescent emission line of neutral or mildly ionised iron. It occurs in the X-ray band depending on the degree of ionisation between keV , i. The fluorescent Fe line is thus used to probe the vicinity of compact objects. The X-ray line photons are produced when X-rays from the hot inner flow corona irradiate the underlying cool, weakly ionised disc.
The iron in the disc absorbs the hard X-rays whereby an electron gets excited from the ground state K-shell to a higher energy level. After a while it assumes again the ground state by releasing the excess energy as a photon. Due to non-relativistic Doppler and special relativistic beaming and general relativistic effects gravitational red-shift the line is not a simple Gaussian spike but a skewed and asymmetric profile.
The reason why there are so far no direct observations of the immediate environment of black holes is that observed from Earth they have a very small apparent size in the sky. Such dimensions have long been out of reach for astronomical instruments. However, a new generation of interferometers will change that in the coming years first observations in Only those photons of an accretion disc which escape the black hole environment are observable. In an image, a black hole is thus silhouetted dark against the radiant accretion flow.
The black hole silhouette itself is confined by a ring of photons that originate from immediately outside the horizon second order image of the accretion flow and is calculated by integrating the photon trajectories through spacetime from the observer towards the black hole. This method is called ray-tracing. The image and silhouette that emerge from this calculation and that may be observed by EHT in the near future are rich in information about the properties of the accretion flow and in particular of the black hole.
Figure 12 shows images of a toroidal accretion flow ion torus around a supermassive Kerr black hole located at the galactic centre as seen by an observer on Earth. Abramowicz and Odele Straub , Scholarpedia, 9 8 Jump to: navigation , search. Post-publication activity Curator: Odele Straub Contributors:. Axel Brandenburg. Leo Trottier. Accretion discs are flattened astronomical objects made of rapidly rotating gas which slowly spirals onto a central gravitating body.
The gravitational energy of infalling matter extracted in accretion discs powers stellar binaries, active galactic nuclei , proto-planetary discs and some gamma-ray bursts.
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The black hole accretion in quasars is the most powerful and efficient stationary engine known in the universe. In accretion discs the high angular momentum of rotating matter is gradually transported outwards by stresses related to turbulence , viscosity, shear and magnetic fields. This gradual loss of angular momentum allows matter to progressively move inwards, towards the centre of gravity. The gravitational energy of the gaseous matter is thereby converted to heat.
A fraction of the heat is converted into radiation, which partially escapes and cools down the accretion disc. Accretion disc physics is thus governed by a non-linear combination of many processes, including gravity, hydrodynamics, viscosity, radiation and magnetic fields. The central part of a dense molecular cloud collapses to a proto-star surrounded by a proto-planetary accretion disc.
Self gravity and sedimentation trigger the formation of planets. Bipolar outflows slow jets often emerge from proto-planetary discs. U Gem is the prototype of a dwarf novae system, i. AGN are supermassive BH at centres of galaxies. Accretion produces radiative power that often outshines the host galaxy. The accretion disc is surrounded by moving gas clouds and encircled by a large torus of gas and dust.
Very fast almost speed of light jets emerge from many AGNs. GRBs are the most energetic explosions in the universe. The huge power of gamma-rays is possibly due to an extraction of the BH rotational energy the Blandford- Znajek mechanism. Mostly thin discs, thick discs early epochs , layered discs with a magnetically inactive 'dead zone' in the mid-plane region. Local: In the high state via MRI induced turbulent viscosity; Global: Direct dissipation by tidal spirals when the incoming supersonic flow shocks on the accretion disc.
Inner disc: Viscous friction MRI ; Outer disc: Possibly by global disturbances in the gravitational field gravito-turbulence. Thick discs corona : Bremsstrahlung, Compton scattering; Thin discs: Blackbody radiation. Inner disc: Neutrino emission; Outer disc: Advection. Wood, M. Wolff, J. Bjorkman, B.
Figure 2: A proto-star star in NGC Reconstruction of a possible look of a proto-planetary disc based on a Spitzer Space Telescope image. An evidence was found for water vapor in the surrounding area, which appears to be one of the key moments in the development of a planetary system around such a star: icy material is falling from the envelope that birthed the star onto a dense, surrounding disc.
Gutermuth Harvard-Smithsonian Center for Astrophysics. In reality, the image of the system is unresolved, and only the total flux from the secondary red and accretion disc blue is observed. The primary white dwarf is located at the centre of the accretion disc too small to be seen. The secondary and the accretion disc periodically eclipse each other, which results in periodic variations in the observed flux photometry and spectral features spectroscopy. From these variations Smak reconstructed size and shape of the accretion disc.
Figure 4: AGN unification scheme. Green arrows indicate the AGN type that is seen from a certain viewing angle. Image credit: NASA. Petrov, Figure 5: Microquasars found in several X-ray binaries in our Galaxy are scaled down versions of quasars, as pointed out by Felix Mirabel, who also coined the name "microquasar". This figure first appeared in several of Mirabel's articles. Figure 6: Black hole X-ray binaries in our Galaxy. The figure shows the companion star and the accretion disc drawn to scale. For a comparison, the Sun - Mercury distance is shown.
Figure by Jerome Arthur Orosz. Depending on the mass of the companion star, XRB are roughly divided into two categories: Low-mass X-ray binaries, LMXB in Figure 6, systems with coloured companion stars High-mass X-ray binaries, HMXB in Figure 6, systems with white companion stars The HMXB family has two sub-classes, i the soft X-ray transients that can contain a NS or a BH and exhibit quasi-periodic outbursts and ii the pulsars that contain a NS and emit a bean of radiation along the axis of the magnetic field not necessarily aligned with the NS rotational axis.
McClintock and R. Remillard, , Black Hole Binaries. At peak, this GRB was visible with the naked eye. The accretion discs physics is governed by a non-linear combination of many processes, including gravity, hydrodynamics, viscosity, radiation and magnetic fields. According to a semi-analytic understanding of these processes developed over the past thirty years, the high angular momentum of matter is gradually removed by viscous stresses and transported outwards.
This allows matter in the accretion disc to gradually spiral down towards the gravity centre, with its gravitational energy degraded to heat. A fraction of the heat converts into radiation, which partially escapes and cools the accretion disc. Some authors take this difference as a defining condition: in an "accretion disc" there must be an extended region where the matter's angular momentum is not smaller than the Keplerian angular momentum in the same region.
This is illustrated in Figure 8. Figure 8: The "Bondi-like" and "disc-like" accretion flows. Most of the accretion disc types except proto-planetary and GRB ones have a negligible self-gravity: the external gravity of the central accreting object dominates. The external gravity is important in shaping several crucial aspects of the internal physics of accretion discs , including their characteristic frequencies that are connected to several important timescales and their size inner and outer radius.
Paczynski's model for the black hole gravity became a very popular tool in the accretion disc research. It is used by numerous authors in both analytic and numerical studies. Effects of special relativity have been added to Paczynski's model by Abramowicz et al. Karas and Semerak Newtonian models for rotating black holes are cumbersome and for this reason not widely used, see Abramowicz The rate of viscous dissipation of energy is.
Credit: J. There is a disagreement between experts on the viscosity prescription issue: some argue that only the hydromagnetic approach is physically legitimate and the alpha prescription is physically meaningless, while others stress that at present the magnetohydrodynamical simulations have not yet sufficiently maturated to be trusted, and that the models that use the alpha prescription capture more relevant physics.
All the detailed comparisons between theoretical predictions and observations performed to date were based on the alpha prescription. The energy budget may also include rotational energy that could be tapped from the central object. In the black hole case, this possibility was described in a seminal paper by Blandford and Znajek. The Blandford-Znajek process is an electromagnetic analogy of the well-known Penrose process.
Some of its aspects are not yet rigorously described in all relevant physical and mathematical details, and some remain controversial. It is believed that the Blandford-Znajek process may power the relativistic jets. Non-linear, coupled partial differential equations of radiative viscous hydrodynamics or magnetohydrodynamics that describe physics of accretion discs are too complex to be exactly solved analytically in the general case. Usually, analytic models assume that the accretion is stationary and axially symmetric.
For such discs, useful approximate solutions exist in extreme cases corresponding to the following three fundamental divisions as shown in Figure 1 :. Figure The main types of analytic accretion disc models in the parameter space of different geometries i. Credit: Aleksander Sadowski A thin discs has its "vertical" i. Detailed models of thin and thick discs are described in the sub-sections of this Scholarpedia article: Thin discs , Thick discs. Figure Radio maps of SS , a source containing a super-Eddington accretion disc. Newtonian hydrodynamic models of stationary and axially symmetric, thin accretion discs are described by equations similar to or equivalent to the 12 equations given in the table below.
In the case of the standard Shakura-Sunyaev discs further assumptions are made, which transform all the equations to the algebraic ones. The Kerr geometry version of 01 - 12 was written first by Lasota , and later elaborated by Abramowicz, Chen, Granath and Lasota ; see also Sadowski However, equations 01 - 12 in their form above are often used to model the black hole accretion discs. This is possible because of a brilliant discovery by Paczynski of the Newtonian model for the black hole gravity.
The best known and studied theoretical model.
Different analytic solutions are known for cases in which the total pressure is either dominated by gas or radiation pressure, and for the opacity described either by Kramers' law , or electron scattering. Notes: The flux formula in the box is probably the most often used one in the accretion disc research. The profiles of temperature, optical depth, ratio of scale height to radius, and the advection factor of a hot one-temperature accretion solution solid lines.
Figure credit: Yuan, Taam, Xue, Cui Nearly Eddington accretion. Large opacity. Cooled by radiation and advection, i. Radiatively much less efficient than the standard Shakura-Sunyaev discs. Rotation differs slightly but importantly from the Keplerian one. The pressure gradient along the disc plane direction is dynamically important. Slim discs models are described by a set of ordinary differential equations, and one must explicitly solve the eigenvalue problem connected with the regularity condition at the sonic radius which does not coincide with the ISCO.
Figure on the right shows the local flux of radiation for different mass accretion rates and the black hole spins. Each subplot contains six solid lines for the following mass accretion rates in the Eddington units : 0. Figure credit: Sadowski Branch IV pink : Polish doughnut thick disc, see next section. The different types of thin discs may coexist radially. Microquasars display distinct spectral states. In order of increasing luminosity these are the quiescent state, low state, intermediate state, high state, and very high state. Narayan with collaborators presented a model of accretion flows around black holes that unifies most of these states.
At low mass accretion rates, the inner ADAF zone in the model radiates extremely inefficiently, and the outer thin disc is restricted to large radii. The luminosity therefore is low, and this configuration is identified with the quiescent state. For larger accretion rates the radiative efficiency of the ADAF increases rapidly and the system becomes fairly luminous. The spectrum is very hard and peaks around keV. This is the low state.
For still greater rates, the ADAF progressively shrinks in size, the transition radius decreases, and the X-ray spectrum changes continuously from hard to soft. This is the intermediate state. Finally, the inner ADAF zone disappears altogether and the thin accretion disc extends down to the marginally stable orbit. The spectrum is dominated by an ultrasoft component with a weak hard tail.
This is the high state. Mineshige, Kusnose, Matsumoto Ap. For "thick discs" models of accretion discs one assumes that: Matter distribution is stationary and axially symmetric, i. From equation 3. Abramowicz et al. When they are known, the analytic solution is given by,. The mass loss 3. In the case of neutron stars, this leads to a modulation of the luminosity of the boundary layer at the neutron star surface. Although oscillations originate in the disc, the are observed in radiation that comes from the boundary layer. This is relevant for the observed neutron star quasi periodic oscillation QPO Horak et al.
Daigne and Font, or Montero et al. It may determine the life-time of a massive torus around a black hole, which is relevant to some models of gamma ray bursts. The analytic formula 3. In particular, there is obviously a cusp there. Sikora noticed unpublished that the upper limit for the radiative power of an object in which gravity and radiation pressure are in equilibrium is given by the Planck power and the object gravitational and radiative cross sections,. A "Polish doughnut" is a radiation pressure supported thick accretion discs around a central black hole.
It prevents astrophysically realistic doughnuts i. Figure 1: Schematic S-curve showing the local limit-cycle behaviour in accretion discs. A glaring example is the satellite RXTE that revolutionized their study by revealing the richness of their timing and spectral properties. A rough picture of their evolution has then begun to emerge see Corbel at al. X-ray binaries spend most of their time in quiescence at very low mass accretion rates. They occasionally produce outbursts that last from a few months to a year, during which their flux rises by several orders of magnitude across the whole electromagnetic spectrum.
An example of light curve is shown in the right panel of Fig. The origin of these outbursts is commonly explained by the release of gravitational power of the accreting material coming from the secondary star and forming an accretion disc around the central compact object.
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The gas drifts slowly in the accretion disc and, as it approaches the black hole, it is heated up to very high temperatures. Through relatively complex mechanisms, X-ray binaries are also able to eject similarly to Active Galactic Nuclei a fraction of the accreting material at relativistic speed in the form of collimated jets , usually observed in the radio band but that can, at least in extreme cases, contribute significantly to the X-ray emission Corbel et al.
Jetted X-ray binaries are also called microquasars due to their global similarities, but on a much smaller scale, to quasars Mirabel et al. The letters A, B, C, D indicate different time of the outburst and are also reported on the right plot. During the outburst, a BHB shows very different spectral and temporal states than can be easily distinguished in the so-called hardness-Intensity Diagram HID where the X-ray luminosity is plotted versus the hardness ratio HR of the X-ray spectrum, producing an hysteresis with a typical Q-shaped track.
At the beginning of the outburst A-B segment in the HID , the system is in the so-called hard state during which the X-ray spectrum has a hard power law shape up to a few tens of keV, signature of non-thermal processes in a very hot, optically thin , plasma usually called the ' corona '. Then, when the system reaches high luminosities B-C segment in the HID , it transits in a few days, through the bright intermediate state, into the so-called soft state.
Discrete optically thin super-luminal ejections occur at the transition. It is still not clear yet whether these discrete ejections differ fundamentally from the flat-spectrum steady jets observed in the hard states or if they are different manifestations of the same phenomenon. Coriat et al, and even undetectable in most cases. This suggests the disappearance or strong fading of the jet component.
Examples of typical X-ray spectra in the soft and hard states are plotted in the left panel of Fig. Dunn et al. Above a luminosity of the order of 0. The mass accretion rate is therefore not the unique parameter governing the transition. BHB also exhibit noticeably different X-ray timing properties between the hard and soft states. A good fit requires however the addition of a series of generally broad peaked noise components Lorentzians.
One can also find thin features, especially in the bright hard states and intermediate states, referred to as Quasi- Periodic Oscillations QPO with frequencies in the range 0. During the transition to the soft state, and close to the super-luminal ejection events, most of the variability suddenly disappears. In the soft state, the power density spectrum is featureless and its integrated amplitude also called the rms has a much lower level than in the hard state. Fast variability is also observed in Optical and IR with very complex interconnections with the X-rays e.
Kanbach et al.