Australia Telescope National Facility

Accretion Processes in Magnetic Binaries
Lilia Ferrario , Jianke Li , Curtis Saxton , Kinwah Wu, PASA, 16 (3), 234.

Next Section: Radiation properties of magnetically
Title/Abstract Page: Accretion Processes in Magnetic
Previous Section: Introduction
Contents Page: Volume 16, Number 3

The magneto-hydrodynamics of accretion: magnetic levitation

A stellar magnetic field tends to be a closed configuration which, from a theoretical viewpoint, seems to prevent accretion. On the other hand, it is observationally indisputable that magnetic stars do accrete matter from their surroundings, either from a protoplanetary accretion disc, as in the Classic T Tauri stars, or from a companion star losing mass via Roche overflow, as in low mass x-ray binaries, where the primary star is a neutron star, or in the mCVs, where the accreting object is a magnetic white dwarf. The mechanisms which lead to field chanelled accretion flow remain substantially unresolved due to the complicated non-linear effects arising from the interaction between the magnetic field and matter.

The current picture on field-matter interaction may be that the accreting matter entering the magnetosphere consists of diamagnetic blobs which are continuosly stripped, as their surface layers become magnetised, by reconnection processes. Therefore, during their penetration into the magnetosphere, they feed the curtains, or funnels, of material until they are slowly depleted of all their matter and finally disappear.

Once threading has occurred, the accreting material behaves like a magnetised fluid, and the conditions for ideal MHD are thus satisfied.

In magnetically confined accretion flows the toroidal dynamics is only weakly coupled to the poloidal dynamics, and thus the velocity and magnetic field can be separated into toroidal and poloidal components. In a steady-state, axisymmetrical magnetically-channelled flow, the Bernoulli integral along a poloidal magnetic field line can then be written as (Li & Wilson 1999 and references therein):

$\begin{displaymath} \mu = \frac{1}{2} v_p^2 + \int \frac{d P}{\rho} - \frac{GM}{r} + \frac{1}{2} \Omega^2 \varpi^2 - \alpha \Omega \varpi^2, \end{displaymath}$

(1)

where v_p is the poloidal flow velocity, $\rho$ is the plasma density, $\varpi$ is the cylindrical radius, $\Omega$ is the angular velocity, M is the stellar mass, r is the radius, G is the gravitational constant, P is the pressure and $\mu$ is the total energy per unit mass in the rotating frame which has angular velocity $\alpha$ . The quantities $\mu$ and $\alpha$ are constant along a given poloidal field line.

Li & Wilson (1999) have shown that it is possible to find solutions to the above Bernoulli integral of the funnel flow, but only under certain conditions. Their conclusion is that while solutions do not exist if v_p << V_A, where V_A is the Alfvén velocity (defined by the poloidal magnetic field), solutions can be found if v_p is initially Near Alfvénic, that is when

D = v_p²/V_A² is in the range 0.22 - 0.7, for an initial Mach number M_d=0.1 (see Figure 1). Solutions still exist for higher initial values of D, but they are not as well behaved.If M_d is increased above this range, then a simultaneous increase of D improves the solution while a decrease of M_d worsens it. More generally, Li & Wilson (1999) find that solutions depend on a range of flow parameters which cannot be strictly constrained. However, they argue that the true solution is likely to be close to the lower limit D=0.22, being the one to yield the smoothest behaviour.

**Figure 1:** Solution of the Bernoulli integral. The horizontal axis denotes the dimensionless arc distance s, and the vertical distance is the Mach number u = v_p/c_s. Here, the initial Mach number M_d is set equal to 0.1. The lower initial limit of
D = v_p²/V_A²= 0.22 and the upper limit D = 0.7.
$\begin{figure} \epsfxsize=0.7\textwidth \epsfbox[15 8 570 777]{ferrario1.eps}\end{figure}$

Since the strength of the toroidal magnetic field $B_\Phi$ at the base of the funnel increases with D, and since

$D \propto 1/\rho$ , this term will decrease along the funnel, thus reducing the strength of the toroidal field as the matter leaves the orbital plane and starts flowing towards the stellar surface. The existence of large toroidal fields at the coupling region was not envisaged in early models (eg Ghosh & Lamb 1979a, 1979b) in which the material in funnel flows is stress free at the inner edge of the accretion disc. On the contrary, the large toroidal fields found by Li & Wilson (1999) and implied by Li, Wickramasinghe & Rüdiger (1996) spin up the disc by the magnetic stress

$B_\Phi B_z/4\pi$ , in order to transfer the angular momentum of the accreting material back to the disc.

The most important result from the work of Li & Wilson (1999) may be that these strong toroidal fields are also responsible for magnetic accretion by causing what has been called ``magnetic levitation''. This phenomenon is due to the gradient of $B_\Phi^2/8\pi$ which exerts a significant magnetic pressure force which pushes the gas in the vertical direction off the orbital plane. This initial push allows the gas to overcome the potential barrier caused by the dipolar field being ``pinched'' towards the star, due to the radial balance of gravity and Lorentz forces.

Next Section: Radiation properties of magnetically
Title/Abstract Page: Accretion Processes in Magnetic
Previous Section: Introduction
Contents Page: Volume 16, Number 3

ASKAP

Public