International Journal of Astronomy and Astrophysics, 2012, 2, 81-96 http://dx.doi.org/10.4236/ijaa.2012.22012 Published Online June 2012 (http://www.SciRP.org/journal/ijaa) Accretion and Current Discs Controlled by Strong Magnetic Field Elena Belenkaya1, Maxim Khodachenko2 1Institute of Nuclear Physics, Moscow State University, Moscow, Russia 2Space Research Institute, Austrian Academy of Sciences, Graz, Austria Email: [email protected] Received March 30, 2012; revised April 17, 2012; accepted May 1, 2012 ABSTRACT 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. Keywords: Disc; Alfvén Radius; Star; Planet; Compact Object 1. Introduction these currents generate bright auroras in the main ovals). It also coincides with the last stable orbit near a black We consider a wide range of astrophysical objects sur- hole and determines the magnetospheric size for the outer rounded by discs such as neutron stars, pulsars, white planets in the solar system. Therefore, we pay the main draws, black holes, X-ray binaries, active galaxy nuclei, attention to this subject. As we show in this paper, the young stars, Sun, giant planets in the solar system (Jupi- inner edges of astrophysical discs in the presence of strong ter and Saturn), and note that many of them in the pre- sence of magnetic field have the inner edges at the magnetic field are close to Alfvén radii. Alfvén radii independent of the nature of their origin, the Khodachenko et al. [1] constructed the magnetosphe- motion direction inside the disc (towards the central body ric model for a magnetized giant exoplanet at a close or out of it, or in the azimuthal direction), and the sort of orbit around its host star (“Hot Jupiter”). Weak intrinsic material in the disc. Of course, other types of discs, for magnetic dipole moments of tidally locked close-in giant which the inner edges do not coincide with the Alfvén exoplanets have been shown in previous studies to be radii also exist. That is the case, for example, for the discs unable to provide an efficient magnetospheric protection around stars, white dwarfs, or neutron stars with a weak for their expanding upper atmospheres against the stellar magnetic field or without it, the cold non-magnetized plasma flow, which should lead to significant non-ther- matter undergoing free radial equatorial infall to a non- mal atmosphere mass loss. In [1] besides the intrinsic rotating black hole from the initial rest state, etc. How- planetary magnetic dipole, in the paraboloid magneto- ever, we do not consider these objects in the present re- spheric model (PMM) [2-4] for an exoplanet, the current view. systems of the magnetotail, magnetopause currents, and Position of the inner edge of astrophysical discs plays the ring current of a magnetodisc are included. In the a crucial role in different physical processes. It is one of PMM, the magnetopause is represented by a paraboloid the parameters which determine the total luminosity of surface co-axial with the direction of the ambient stellar an accretion disc, the position of powerful jets origin and wind plasma. It is supposed in the PMM that the inner maximum temperature in the discs, the location of the edge of the magnetodisc is located at the place where main emissions and the wave diapason of emissions, the rigid corotation of plasma is braked down. This happens location of strong field-aligned currents in the helio- in the magnetospheric equatorial plane at the Alfvén ra- sphere and in the Jovian magnetosphere (in the last case dius, determined from the equality of energy densities of Copyright © 2012 SciRes. IJAA 82 E. BELENKAYA, M. KHODACHENKO the plasma rotational motion and the dipole magnetic of pulsar is the spin period of the accreting neutron star. field. Beyond the Alfvén radius an outflow of the sub- A part of the ejected matter, after a supernova explo- corotating plasma begins. The escaping along the mag- sion, may remain bound to the remnant and fall back. netic field lines, plasma deforms the original planetary This falling back material can form a disc surrounding magnetic dipole field by stretching the field lines and the remnant star. Some of neutron stars possess accretion creating the magnetodisc. discs, while the others are accreting directly from the The real discs are very complicated and strongly stra- stellar wind. A disc can be formed of this material if its tified objects. However, here we would like to emphasize specific angular momentum l exceeds the Keplerian that in the presence of a strong magnetic field the loca- value at the surface of a newly born neutron star, 1/2 tion of the inner boundary of the disc at the Alfvén radius lK = (GM*R*) (1) occurs in numerous forms in the universe. This relates where M* is the mass of the star and R* is its radius, G is not only to the accretion discs, but also to the heliosphe- Newton’s gravitational constant (G = 6.673 × 10–11 ric current sheet, the Jovian magnetodisc, and Kronian m3·kg–1·s–2). ring current. In the following sections this phenomenon The character of material motion at the inner edge of is discussed in details. the accretion disc depends on the magnetic field of the neutron star. In the case of a neutron star without mag- 2. Accretion Discs netic field, the disc extends until its surface. Ghosh and 2.1. Discs around Neutron Stars, Pulsars and Lamb [10,11] described the interaction of a dipolar stel- White Dwarfs lar magnetic field with a surrounding disc. The authors found that the inner edge of the disc is located at the dis- Neutron stars arise as a result of gravitational collapse of tance where the integrated magnetic stress acting on the cores of normal stars after exhaustion of all thermo- disc becomes comparable to the integrated material stress nuclear energy sources. At the end of a star evolution the associated with plasma inward radial drift and orbital envelope is thrown away during explosion and forms a motion (at Alfvén radius). Later Cheng et al. [11] con- planetary nebula, or a supernova remnant depending on sidering the neutron star—accretion disc system also the mass of the dying star. The neutron star masses range stated that the position of the inner edge of the accretion 30 from 1.4 to 3 MSun, where MSun = 2×10 kg is a solar disc is of the order of Alfvén radius. mass, 1.4 MSun is a Chandrasekhar limit, and 3 MSun is an In the Ghosh and Lamb model [10,12] the corotation Oppenheimer-Volkoff limit. The neutron stars consist radius, defined as mainly of neutrons. Radius of a neutron star is ~10 - 20 13 R 2 (2) km. The material density in neutron stars could be up to c GM** 1017 - 1018 kg·m–3. If a neutron star has a strong magnetic where the angular velocities of the disc and the star (*) field, the external plasma flows to its auroral zones gene- are the same, also plays a key role. The magnetic field rating X-rays. lines penetrating the disc inside the corotation radius spin Pulsar is a rapidly rotating (the typical period 0.1 - 5 s) up the star, whilst those penetrating the accretion disc small, extremely dense neutron star that emits brief, outside the corotation radius brake the star down. The sharp pulses of energy (not all neutron stars are pulsars). spin evolution of the star is therefore the result of a bal- 11 Pulsar has a very strong dipole-type magnetic field (10 ance between the angular momentum carried by the ac- 15 - 10 G), and the beams of radiation are emitted along its creting matter from the disc to the star, the magnetic magnetic dipole axis which does not coincide with the spin-up torque from the accretion disc inside the corota- spin axis. Radio-pulsars are the mostly numerous class of tion radius, and the magnetic spin-down torque from the pulsars. Most of radio pulsars are single neutron stars [5]. accretion disc outside the corotation radius. The position Istomin [6] stated that the source of pulsar’s radio emis- of the inner edge of the accretion disc varies with the sion could be, for example, the stream of the relativistic accretion rate so, that it becomes closer to the star when electron-positron plasma generated in the magnetosphere the accretion rate increases. Thus, it is expected that the of a neutron star. star spins up, or at least spins down more slowly, when There is a group of pulsars called millisecond pulsars the accretion rate (or equivalently, the luminosity) is high with the spin period 1 - 10 ms and magnetic field 108 - [13].