In the presence of a strong magnetic field, accretion discs surrounding neutron stars, black holes, and white dwarfs have their inner edges at their Alfvén radii, i.e., at the distance where magnetic energy density becomes equal to the kinetic energy density. Young stars, X-ray binaries, active galactic nuclei possess discs which could generate jets. Jets arise at the inner boundary of the disc at the Alfvén radius when magnetic field is sufficiently strong. We emphasize here that not only accretion discs possess this feature. The inner edge of the heliospheric current sheet is located at the solar Alfvén radius. The inner edges of the Jovian magnetodisc and Saturnian ring current are also placed close to their Alfvén radii. Thus, in the presence of a strong magnetic field the inner edges of a lot of astrophysical discs are located at Alfvén radii regardless of the nature of their origin, material, and motion direction. This means that discs under such conditions are well described by MHD theory.
We consider a wide range of astrophysical objects surrounded by discs such as neutron stars, pulsars, white draws, black holes, X-ray binaries, active galaxy nuclei, young stars, Sun, giant planets in the solar system (Jupiter and Saturn), and note that many of them in the presence of magnetic field have the inner edges at the Alfvén radii independent of the nature of their origin, the motion direction inside the disc (towards the central body or out of it, or in the azimuthal direction), and the sort of material in the disc. Of course, other types of discs, for which the inner edges do not coincide with the Alfvén radii also exist. That is the case, for example, for the discs around stars, white dwarfs, or neutron stars with a weak magnetic field or without it, the cold non-magnetized matter undergoing free radial equatorial infall to a nonrotating black hole from the initial rest state, etc. However, we do not consider these objects in the present review.
Position of the inner edge of astrophysical discs plays a crucial role in different physical processes. It is one of the parameters which determine the total luminosity of an accretion disc, the position of powerful jets origin and maximum temperature in the discs, the location of the main emissions and the wave diapason of emissions, the location of strong field-aligned currents in the heliosphere and in the Jovian magnetosphere (in the last case these currents generate bright auroras in the main ovals). It also coincides with the last stable orbit near a black hole and determines the magnetospheric size for the outer planets in the solar system. Therefore, we pay the main attention to this subject. As we show in this paper, the inner edges of astrophysical discs in the presence of strong magnetic field are close to Alfvén radii.
Khodachenko et al. [
The real discs are very complicated and strongly stratified objects. However, here we would like to emphasize that in the presence of a strong magnetic field the location of the inner boundary of the disc at the Alfvén radius occurs in numerous forms in the universe. This relates not only to the accretion discs, but also to the heliospheric current sheet, the Jovian magnetodisc, and Kronian ring current. In the following sections this phenomenon is discussed in details.
Neutron stars arise as a result of gravitational collapse of cores of normal stars after exhaustion of all thermonuclear energy sources. At the end of a star evolution the envelope is thrown away during explosion and forms a planetary nebula, or a supernova remnant depending on the mass of the dying star. The neutron star masses range from 1.4 to 3 MSun, where MSun = 2×1030 kg is a solar mass, 1.4 MSun is a Chandrasekhar limit, and 3 MSun is an Oppenheimer-Volkoff limit. The neutron stars consist mainly of neutrons. Radius of a neutron star is ~10 - 20 km. The material density in neutron stars could be up to 1017 - 1018 kg·m–3. If a neutron star has a strong magnetic field, the external plasma flows to its auroral zones generating X-rays.
Pulsar is a rapidly rotating (the typical period 0.1 - 5 s) small, extremely dense neutron star that emits brief, sharp pulses of energy (not all neutron stars are pulsars). Pulsar has a very strong dipole-type magnetic field (1011 - 1015 G), and the beams of radiation are emitted along its magnetic dipole axis which does not coincide with the spin axis. Radio-pulsars are the mostly numerous class of pulsars. Most of radio pulsars are single neutron stars [
There is a group of pulsars called millisecond pulsars with the spin period 1 - 10 ms and magnetic field 108 - 109 G. About a half of millisecond pulsars are in binaries, i.e. in the stellar systems containing two stars orbiting around their common center of mass. Observations and theory of binary systems are summarized in [7-9]. If one star in a binary system is a neutron star, then the period of pulsar is the spin period of the accreting neutron star.
A part of the ejected matter, after a supernova explosion, may remain bound to the remnant and fall back. This falling back material can form a disc surrounding the remnant star. Some of neutron stars possess accretion discs, while the others are accreting directly from the stellar wind. A disc can be formed of this material if its specific angular momentum l exceeds the Keplerian value at the surface of a newly born neutron
starlK = (GM*R*)1/2(1)
where M* is the mass of the star and R* is its radius, G is Newton’s gravitational constant (G = 6.673 × 10–11 m3·kg–1·s–2).
The character of material motion at the inner edge of the accretion disc depends on the magnetic field of the neutron star. In the case of a neutron star without magnetic field, the disc extends until its surface. Ghosh and Lamb [10,11] described the interaction of a dipolar stellar magnetic field with a surrounding disc. The authors found that the inner edge of the disc is located at the distance where the integrated magnetic stress acting on the disc becomes comparable to the integrated material stress associated with plasma inward radial drift and orbital motion (at Alfvén radius). Later Cheng et al. [
In the Ghosh and Lamb model [10,12] the corotation radius, defined as
where the angular velocities of the disc and the star (W*) are the same, also plays a key role. The magnetic field lines penetrating the disc inside the corotation radius spin up the star, whilst those penetrating the accretion disc outside the corotation radius brake the star down. The spin evolution of the star is therefore the result of a balance between the angular momentum carried by the accreting matter from the disc to the star, the magnetic spin-up torque from the accretion disc inside the corotation radius, and the magnetic spin-down torque from the accretion disc outside the corotation radius. The position of the inner edge of the accretion disc varies with the accretion rate so, that it becomes closer to the star when the accretion rate increases. Thus, it is expected that the star spins up, or at least spins down more slowly, when the accretion rate (or equivalently, the luminosity) is high [
A neutron star can interact with a surrounding disc in a variety of modes. In this interaction the inner part of an accretion disc plays a significant role leading to different observational properties of X-ray pulsars and low-mass X-ray binaries [
RL = c/W*(3)
where c is light velocity. There are three basic modes of interaction of a neutron star with a surrounding disc: accretor, propeller, and ejector [15-17]. If the inner radius of the disc is beyond the corotation radius, but smaller than the light cylinder radius, the system is expected to be in the propeller stage (a neutron star rotation is strong enough to prevent the accreting matter from the falling to the star). The ejector stage is assumed to take place when the inner radius is beyond the corotation radius and the light cylinder radius. For the accretor mode, the inner radius of the disc has to be smaller than the light cylinder radius, and accretion to the central object occurs when the corotation radius becomes larger than Alfvén radius.
Shvartsman [15,16] argued in the context of wind-fed, mass-exchange binaries, that a fast-rotating neutron star at first appears as an ejector (radio pulsar), in which the disc remains outside the light cylinder. After the star slows down, the inflowing matter can penetrate the light cylinder, allowing the propeller stage to commence. For a fallback disc, a fixed amount of mass is available in the disc, rather than a continuous supply as in the case of a mass-exchange binary. Finally, for a slowly rotating neutron star, the ejection changes to accretion.
The relativistic outflowing momentum flux in ejectors is always larger than the ram pressure of the surrounding material, therefore they never accrete. This is typical for either active or dead pulsars, which are still spun down by dipole losses. In propellers the incoming matter can penetrate down to the Alfvén radius, RA, but not further (because of the centrifugal barrier), and a stationary inflow cannot occur. For accretors the falling to the central object flow stops at the distance where the object’s magnetic pressure becomes equal to the kinetic flow pressure (e.g., at Alfvén radius) [15,16].
The accretion to a rotating neutron star with the magnetic dipole axis inclined relative the rotation axis, can lead to the phenomenon of an X-ray pulsar [
Bednarek [
Quite often X-ray pulsars reside in the binary systems built of a rotating magnetized neutron star (pulsar) and a normal star. Due to accretion from the normal star to the neutron star, plasma is accelerated up to very high velocities, which then brake dawn near the neutron star surface. That results in the increase of plasma temperature up to T ³ 107 - 108 K [
In the Keplerian rotating highly turbulent inner parts of the accretion disc (i.e., where Kepler’s laws of motion are valid due to the dominance of a massive body at the disc centre) the magnetic fields are strongly amplified and expelled from the disc. This leads to the formation of a magnetically structured accretion disc corona, sandwiching the disc, to which it is electrodynamically coupled. The interaction of inner parts of an accretion disc with a neutron star leads to a channeled accretion onto the magnetic pole zones, resulting in the phenomenon of an X-ray pulsar with the associated spin variations due to angular momentum transfer. Kuperus [
In models for disc accretion onto magnetized objects, the inner radius R0 of the Keplerian disc is conventionally expressed as R0 = xRA, where RA is the Alfvén radius for the spherical accretion and the parameter x, which depends on the fraction of the stellar magnetic flux threading the disc, is usually taken to be 0.5 (e.g., [
Eksi and Alpar [
Bednarek and Pabich [
While stars with normal mass after they have exhausted their nuclear fuel are transferred to neutron stars, less massive stars (like the Sun) become white dwarfs. The mass of a white dwarf is M* < 1.4 MSun. The radius R* of a typical white dwarf with a mass M* = MSun is of the order of ~10–2 RSun, where RSun = 7×105 km is the solar radius. If the mass of a celestial body is less than 0.08 MSun, the hydrogen burning fusion does not take place in its center. Such objects are called “brown dwarfs”, they represent an intermediate class of objects between stars and planets.
The stars in compact binary systems could be so close to each other that the gravity of a white dwarf distorts the secondary star, and the white dwarf accretes the matter from its companion. If after some time a sufficiently large amount of material from the companion star is accumulated on the white dwarf surface, so that the thermo-nuclear reactions suddenly begin, this would correspond to “a new star flash”. Such flash may be repeated again after tens-thousands years. In intermediate polar systems, the accretion disc is disrupted by the magnetic field of the white dwarf star. Due to the instabilities arising in the disc, the flashes inside the disc (with periodicity from a week up to a year) also could be seen. As the material in the accretion disc approaches the magnetic white dwarf, it is swept up by the magnetic field of the white dwarf forming accretion curtains along the magnetic field lines.
All active cataclysmic binary systems are semi-detached. In the semi-detached binary one component fills its Roche lobe, and mass transfer occurs from this star to the other. While in some systems the gas stream falls directly to the surface of the second star, in most cases it forms an accretion disc. Zhilkin and Bisikalo [
Depending on the strength of the surface magnetic field of a white dwarf, the accretion rate, and the angular momentum of matter, the accretion process can occur in different modes. Specific modes correspond to different types of accreting white dwarf systems, such as polars (direct accretion on a magnetic pole), intermediate polars (accretion on a magnetic pole from the accretion disc), and nonmagnetic white dwarfs (the accretion disc extends to the surface of the white dwarf). The physical processes in CVs are expected to be similar to those taking place in the X-ray binaries with the accreting neutron stars [
Alfvén radius coincides with the so-called magnetosphere radius for the magnetized neutron star or pulsar. Thus, as it was shown above, the inner edges of the discs around magnetized neutron stars, the X-ray pulsars, radio pulsars, and white dwarfs with intrinsic magnetic field are located near their Alfvén radii. If a neutron star has so week magnetic field, that its pressure cannot stop the falling plasma, the inner edge of accretion disc coincides with the neutron star surface.
In a result of the core-collapse of a massive star at the end of its life after it has exhausted its nuclear fuel, a compact object with a mass > 3 MSun could be formed. It is called a “black hole” (for example, in the center of our Galaxy there is a supermassive black hole with mass ~ 3.5 × 106 MSun). It should be noted that the mass of a star is not a single parameter which determines its evolution. The stellar mass loss, in particular, is also important. Ginzburg [
The structure of magnetic fields near the discs around magnetized white dwarfs, neutron stars or magnetars is very different from the black hole case. The origin of a magnetic field in the central compact star determines the initial field topology. An interaction between the star and the surrounding disc makes the stellar magnetic field partially thread the accretion disc. The main difference in the interaction between a central object and the inner part of the disc in the cases of a neutron star and a black hole is caused by different magnetic field structures [
A black hole is an object, which has so strong gravitational field, that it does not radiate either electromagnetic or gravitational waves (all radiation and matter are confined inside the horizon of events—the effective boundary around the black hole, from which no information can escape to the entire world). The escape speed exceeds the speed of light within the event horizon, while outside it the escape speed is less than the speed of light.
Black holes are characterized by their mass, angular momentum, and electric charge. The radius of the event horizon for a non-rotating uncharged black hole (named as a Schwarzchild black hole) is equal to the gravitation or Schwarzchild radius
RG = 2GM*/c2(4)
which marks the point where the escape velocity equals the speed of light. The rotating uncharged black hall is called a Kerr black hole; a non-rotating charged black hall is known as a Reissner-Nordstrom black hall, whereas a charged and rotating black hall is called a KerrNewman black hall. For a rotating black hole the event horizon radius is less than RG. It follows from the quantum mechanics that all black halls may eventually evaporate.
Beyond RG the gravitational field of a black hole forces the surrounding gas to fall on it, with formation of a rapidly spinning disc. The gas in the disc has a very high temperature which leads to the generation of strong X-ray radiation. Moreover, under certain conditions the gas near a black hole may become turbulent, and as it flows to r ~ RG, magnetic field growths in it which leads to particle acceleration. As a result, the synchrotron emission (non-thermal radiation generated by relativistic charged particles in strong magnetic field) arises [
A black hole has no intrinsic magnetic field outside of its event horizon, but magnetic fields can be generated by plasma which surrounds the black hole and forms the accretion disc. Interaction of disc’s rotation with these electromagnetic fields may result in the appearance of sub-light narrow and very long jets. The magnetic flux between the black hole and the inner edge of disc is either outgoing towards the asymptotic jet or in-going towards the black hole.
As a confirmation of the existence of black holes, the high-energy phenomena, such as X-ray emissions and jets, and the observed character motions of nearby objects are considered. The identification of an invisible object like a black hole requires an estimation of its mass and size. Methods and results of a search for stellar mass black holes in binary systems and supermassive black holes in galactic nuclei of different types are described by Cherepashchuk [
The last stable circular orbit for the pseudo-Newtonian potential is located at 3RG. Shakura and Sunayev [
There is a space-time singularity in the center of a black hole, where the matter collapses inwards. Penrose and Floyd [
Although the Penrose process shows a possibility of energy extraction from the black hole, it is improbable as an engine for astrophysical jets, because of poor collimation of particles and poor event rate [
Quite often, black holes reside in the binary systems with low-mass star-donors. In a close binary system comprised of a visible star and a black hole, the outflow of matter from the surface of the visible star and its accretion on the black hole should be detectable in observations because the accreting gas releases large amount of energy [35,36]. In particular, black hole in accretion regime could emit X-rays. It should be mentioned that if the matter undergoes the free radial infall (in case if it was initially at rest and there was no magnetic field), it accretes to the black hole without any energy release or observational effects [
According to Fendt and Greiner [
For a binary system, in which accretion disc originates due to mass overflow from a primary star onto a compact star, Kuperus [
As it was shown by Tomsick et al. [
VA = B0 (μ0ρ0)–1/2(5)
(where B0 and ρ0 are magnetic field and plasma density, respectively) occurs at the distance where VA is smaller, which accordingly to Equation (5), means mainly that B0 is smaller, i.e. more far from the central object (as the gas flowing to r ~ RG becomes near the black hole turbulent and magnetic field in it growths). The fact found by Tomsick et al. [
Disc is the major element of spiral, lenticular (a lensshaped), and some irregular galaxies; it contains stars, gas, and dust orbiting the centre of a galaxy. The thickness of the disc is small in relation to its diameter. The formation of a star is often not an isolated process. Young stars occur in a star-forming region located mainly in the disc. A spiral galaxy, for example, has the disc (with the spiral arms), the halo, and the nucleus (sometime, the central bulge also). The halo and the nucleus are called the spherical component of the galaxy. Assembly of stars can be considered as a collisionless medium (similar to the collisionless gas). Angular velocity decreases in discs with increasing of the distance from the center of a galaxy.
Using the magnetic field model for the heliospheric current system, Alfvén extended it to the galactic scale. It has been proposed that a protogalaxy transfers away the angular momentum similarly to a protostar. As a result the galactic electric circuit is formed, in which the galaxy current should be 1017 - 1019 A. The currents flow in the plane of the galaxy, possibly waving up and down, along the spiral arms, and out along the axis of rotation (e.g., [
Most galaxies with active nuclei host supermassive black holes at their centers. The supermassive black holes with masses ~106 - 1010 solar masses (quasars) in active galactic nuclei (AGNs) are usually surrounded by rapidly rotating accretion discs [40,41]. Very active quasar could emit more energy than its galaxy. For explanation of this phenomenon the non-spherical accretion to the supermassive black hole was suggested [
The center of our Galaxy (Milky Way) is located in the direction of the constellation Sagittarius. As the dust becomes thicker to the center of the Galaxy, this region is invisible in optics. It is usually studied by observations in radio and/or in infrared wavelengths. The inner part of the Galaxy is a zone where young stars form. The brightest object in radio waves located in the Galaxy center is called Sgr A (Sagittarius A). Observations in X-rays, which also can penetrate the thick gas and dust, reveal that Sgr A can be further reduced to a few sources, including a mostly bright, small source called Sgr A*, which is identified with the supermassive black hole. The star S2 is currently closest to Sgr A*, it moves along an elliptical orbit with Sgr A* at one focus in accordance with Kepler’s law. It has an orbital period ~15 years, which was determined by the Earth-based IR observations at the European Southern Observatory in Chile.
Levine et al. [
Water maser emission at 22 GHz has been detected from more than hundred AGNs (see e.g., [
Seyfert galaxies (spiral or barred-spiral galaxies with bright compact nuclei) exhibit a strong continuum in the range from IR till X-rays. In some Seyfert galaxies a very asymmetric profile of the iron Ka line (e.g., its extended red wing) indicates that the emission arises in the innermost region of a relativistic accretion disc. The material velocity near the inner edge of accretion disc is close to the speed of light. Tomsick et al. [
The central engine in AGNs is surrounded by dusty optically thick clouds which form a clumpy torus. The torus size is of the order of a few parsecs (see e.g., [
Beskin [
Livio [
According to Camenzind [
The values of stellar masses occupy the range from ~0.08 till 100 MSun. The lower limit here is determined by the impossibility of thermo-nuclear reaction of the helium synthesis from hydrogen for low mass objects, while the upper limit is due to the instabilities arising for very high stellar masses.
An accretion disc that provides material for planet formation is referred to as a protoplanetary disc. The size of protoplanetary discs could be up to 1000 AU. Usually young stars are surrounded by protoplanetary discs. The interaction between a magnetic star and a surrounding accretion is important for understanding the spin evolution of objects as diverse as T Tauri stars and X-ray pulsars. T Tauri stars are very young (<10 million years old), lightweight (from 0.5 to 2 MSun), variable stars with spectral type ranging from F to M, and radius of less than 3 - 4 RSun named after their prototype—T Tauri. They are found near gas and dust clouds and are identified by their optical variability, strong emission lines, and broad absorption lines. T Tauri stars are still in the process of gravitational contraction. They may be subdivided on two types: classical T Tauri stars, which are slow rotators and have accretion discs (observed excess ultraviolet and infrared emissions are associated with accretion flows), and weak-lined T Tauri stars, which are fast rotators with no signatures of an accretion disc. The weak-lined T Tauri stars are believed to represent a later evolutionary stage, when the star has got rid of its accretion disc [
In the T Tauri classical star stage, when most of the original core has been accreted and the young stellar object is being fed by lower accretion rates through the surrounding Keplerian accretion disc, the high-speed jet becomes optically visible. When the disc disappears in the weak-lined T Tauri star phase, the jet disappears also with it [
Above we considered only the accretion discs, however, discs (or some part of disc) formed by the out-flowing gas/plasma could also exist. For example, Bespalov and Zheleznyakov [
Bednarek [
The heliosphere is a region around the Sun through which the solar wind (i.e., the plasma ejected from the Sun) with its magnetic field extends and where the influence of the solar wind is significant. The mass loss rate for the Sun is 2×10–14 MSun/year [
Alfvén considered the heliospheric current sheet (with the electric current 3 × 109 A) to be a part of the heliospheric electric current system, in which the Sun acts as a unipolar inductor producing the current. The current transfers angular momentum from the central body to the surrounding plasma [
Zhao and Hoeksema [
Jupiter is located at ~5.2 AU from the Sun and possesses the largest magnetic field among the planets in the solar system. Its dipole magnetic moment is 4.28 G× RJ3, where RJ = 7.14 × 107 m is the jovian radius. Magnetodisc of Jupiter is formed due to the fast rotation of the planet (the rotation period is about 10 hours) and the presence of inter-magnetospheric sources of plasma. In particular, the volcanic activity on the jovian satellite Io provides about 1 T of ions per second. The total azimuthal current in the magnetodisc is estimated as ~108 A and the effective magnetic moment of the magnetodisc field exceeds Jovian dipole magnetic moment by a factor ~2.6 (see e.g., [
Hill et al. [
From figure 6 from Delamere and Bagenal [
The dominating motion of plasma in the inner part of the disc around Jupiter takes place in the azimuthal direction, thus the azimuthal velocity determines the Alfvén radius. Using the Alfvén radius (which is one of the input parameters in the paraboloid magnetospheric magnetic field model for Jupiter) for determination of the inner boundary of the disc enables to interpret observations with a good accuracy [3,59]. The distance to the inner edge of magnetodisc in this study was chosen to be 18.4 RJ.
At the inner edge of the Jovian magnetodisc the geometry of magnetic field lines changes from the dipoletype to the disc-type. This is also connected with the appearance of a visible radial outflow of plasma (~10 km·s–1) [
Saturn is the second largest planet in the solar system. It is a rapidly rotating planet (rotation period is ~10.6 hours) located at 9.5 AU from the Sun. It possesses a strong magnetic field, the dipole magnetic moment of Saturn equals 0.21, where RS = 60330 km is Saturn’s radius. A small analog of the Jovian magnetodisc (named a ring current) exists in the Saturn’s magnetosphere. It is also formed due to the fast planetary rotation and the existence of plasma sources inside the magnetosphere (mainly, the kronian satellite Enceladus). The magnetosphere of Saturn may be considered as an intermediate between the terrestrial and the Jovian magnetospheres.
Analyzing the Pioneer 11 plasma data in Saturn’s magnetosphere, Frank et al. [
For the Voyager encounters, Connerney et al. [
Belenkaya et al. [
At the present time hundreds of extrasolar exoplanets have been detected. Many of them are located at distances less than 0.5 AU and have masses of the order of the Jovian mass. The upper atmospheres of such planets, located close to their parent stars, are strongly heated by the stellar XUV radiation therefore these planets are called “Hot Jupiters”. Cohen et al. [
The paraboloid model of a planetary magnetosphere, originally constructed by Alexeev [
Khodachenko et al. [
where rp is the planetary radius, δθ is the angular thickness of the disc, Bd0 is the value of the planetary dipole magnetic field in the equatorial plane at the surface of the planet, μ0 is a permeability of the vacuum, Wp is the planetary angular rotation rate, and dMp(th)/dt is the planetary thermal mass loss. At the inner edge of the disc the azimuthal velocity shift arises due to change of the magnetic field lines form. This results in an electric field along the strongly conducting magnetic field lines, generated in the rest frame of the rotating planet. As a consequence, the field-aligned currents flow there.
Location of the inner edge of magnetodisc around a magnetized exoplanet is a very important parameter. In particular, it determines the substellar magnetopause distance from the exoplanet center which characterizes a scale of the whole magnetosphere. Besides that, it influences the value of the magnetodisc’s magnetic field, which may give a significant contribution to the total magnetospheric field [
One of the main tasks of the theory of astronomical discs is to study their structure and location. In the present review we considered different types of astrophysical discs: discs around stars, planets, exoplanets, and compact objects. We also shortly discussed the discs around supermassive black holes in AGNs (quasars) and discs in binary systems (twin sources of X-ray, twin and millisecond radio pulsars) existing due to the mass exchange between two stars-companions realized through the disc.
Beskin and Tchekhovskoy [
Lery and Frank [
As stated by Lery and Frank [
Abubekerov and Lipunov [
Ferreira and Petrucci [
In the other systems, the matter can be rotationally ejected at the Alfvén radius. The ejected matter carries away angular momentum and brakes the central rotation magnetized object. This scenario could be realized for a strong magnetic field. As it has been considered in this paper, the Sun, Jupiter, Saturn, and close-in giant exoplanets are surrounded by discs with the outflowing plasmas, and the inner edges of these discs coincide with the corresponding Alfvén radii.
The angular momentum of gas/plasma flowing in or out from the central body prevents the matter from direct fall on the object. Instead, the gas/plasma settles into a disc-like structure whose orientation is defined by its angular momentum. This is a reason for the prevalence of discs in astrophysics [
Discs occur in a wide range of astrophysical contexts, differing in size, in origin, in material and direction of motion inside them. One specific feature common for a large group of astrophysical discs in the presence of a sufficiently strong magnetic field is considered in this paper. It consists in the fact that a lot of discs have their inner edges near Alfvén radii. The reason is that in the presence of magnetic field, the MHD theory describes the plasma motion, and in particular, determines the location where plasma begins to form disc (for outflow) or leave it (for in-fall), thus creating its inner edge. The inner edge of a disc arises in a place, where the external influence becomes significant. The magnetic field may play a role of such an external agent. It could be either a strong magnetic field of the central body, or the magnetic field carried by the disc material and surrounding magnetized plasma.
Work at the Institute of Nuclear Physics, Moscow State University was supported by the RFBR Grants No 11-05-00894 and 12-05-00219. The authors are thankful to the Ministry of Education and Science of the Russian Federation Grant No 07.514.11.4020 and to EU FP7 projects EUROPLANET/JRA3 and IMPEX for support of their collaboration and to Igor Alexeev and Vladimir Kalegaev for construction of the planetary magnetospheric models. MLK also acknowledges the support from the Austrian Science Foundation (FWF) via the projects P21197-N16 and S11606-N16.