Matching disc and curtain flows in magnetically disrupted accretion discs

An accretion curtain forms when a strongly magnetic star disrupts the inner region of its surrounding disc. It was previously shown that the disc expands vertically due to rapidly growing thermal pressure caused by magnetic heating over a narrow radial transition region inside the corotation radius. This allows material to flow from the disc into a magnetically channelled curtain through which it is transferred to the star. The curtain flow is trans-sonic and sub-Alfvénic, with small distortions of the stellar magnetic field. In the present paper, the disc and curtain flows are matched across the upper boundary of the disc transition region, and this is shown to determine the width of this region as a function of the stellar rotation rate. The sonic point position can adjust to allow steady mass transfer from the disc to the curtain flow. An upper limit can be defined for the rotation period of the star below which a strong magnetic channelling regime applies, with the outer edge of the disruption region lying inside a spherical Alfvén radius. The picture of a thin, magnetically channelled curtain flow fed from a thermally disrupted disc is self-consistent in this regime. A lower limit arises for the stellar angular velocity below which the sonic point merges with the curtain base, resulting in excessive mass loss from the disc which would be inconsistent with a steady solution. This corresponds to a lower limit on the disruption radius as a fraction of the corotation radius. It is noted that the spin-up timescale of the accreting star is significantly less than the lifetime of the system so that typical observed systems should lie in the strong magnetic regime.