Mass transfer to feed accretion


Material can be transferred from the companion star to the companion star to the compact object, but by what process is matter transferred? To answer this we now consider the work of a French astronomer named Edouard Roche, who developed the concept of the Roche lobe. This is a region of space around a star, contained within a binary system, within which any orbiting material is gravitationally bound. The shape of this region is built up by plotting surfaces of equal potential (including terms for the centrifugal force as well as gravity). Close to each star (or object) these boundaries can be approximated to concentric spheres. Moving further from each object the shape of the surface is distorted due to its companion until a point is reached  where these surfaces intersect. This gives an approximate tear-drop shaped region around each object, joining at the Lagrange point, the position where the gravity of both objects effectively cancel out.


Wind-fed systems contain a high mass star. Such stars tend to have strong winds that can be captured by the gravity of the compact objects and drawn over to form an accretion disc. This can occur in one of three ways, depending on the type of star. The first of these was outlined above in the broad description of wind-based matter transfer. In this case the wind is considered to be homogenous. The wind particles are deflected by the gravitational field of the compact object and this causes the particles to lose kinetic energy, allowing them to begin to fall towards the compact object . 

These are observed more easily in X-rays when the out-flowing wind from the star is inhomogeneous in nature and appears ‘clumpy'. When a clump of material passes within the sphere of gravitational influence of the compact object it is attracted by the same process as outlined above. This is demonstrated in Figure below (left).

Wind fed accretion

The third main type occurs in systems known as Be X-ray binaries. In this case the stellar wind from the giant Be companion collapses to form a disc around the star. This disc is confined to a plane that is often different to that of the orbital plane of the compact object (see Figure above & right). As the compact object passes through the disc of wind material, this leads to a short period of mass transfer, and a burst of accretion. The majority of these systems have been identified as containing neutron stars, although it is predicted that a small number will contain black holes.

(Left) Mass transfer via in inhomogeneous `clumpy' wind. The schematic demonstrates this where d is the distance between the centre of the clump and the centre of the accreting compact object and R is the accretion radius (image from Ducci et al. 2009). (RightI) A disc of gas forms around the Be star  and orbits at the equator. as the compact object's orbit is inclined to the equator, mass will be able to transfer only when it encounters the disc, with outbursts occurring at regular intervals (image from {\tt\_1.htm}).

Accretion fed by Roche lobe overflow

If the companion star is more tightly bound to the compact object then it is possible for the star to fill its Roche lobe (as shown in Figure below). In this case material at the Lagrange point will feel an equal pull from both the star and the compact object. This allows material to flow across and feed the accretion process whilst slowly tearing away the stellar surface by a process called Roche lobe overflow. Material crossing the boundary carries with it considerable angular momentum,  which prevents free fall onto the compact object. Instead the matter begins to rotate in circular orbits, forming an accretion disc. This material is only able to accrete if it is able to find an effective means by which to transport the angular momentum outwards. To understand this we need to consider accretion.