Episodic accretion on to strongly magnetic stars

Some accreting neutron stars and young stars show unexplained episodic flares in the form of quasi-periodic oscillations or recurrent outbursts. In a series of two papers, we present new work on an instability that can lead to episodic outbursts when the accretion disc is truncated by the star's strong magnetic field close to the corotation radius (where the Keplerian frequency matches the star's rotational frequency). In this paper we outline the physics of the instability and use a simple parametrization of the disc-field interaction to explore the instability numerically, which we show can lead to repeated bursts of accretion as well as steady-state solutions, as first suggested by Sunyaev and Shakura. The cycle time of these bursts increases with a decreasing accretion rate. These solutions show that the usually assumed 'propeller' state, in which mass is ejected from the system, need not occur even at very low accretion rates.