We have studied the long-term ( 1971–2005 ) behaviour of the 1.24 sec pulse period and the 35 day precession period of Her X-1 and show that both periods vary in a highly correlated way ( see also Staubert et al .
1997 and 2000 ) .
When the spin-up rate decreases , the 35 day turn-on period shortens .
This correlation is most evident on long time scales ( \sim 2000 days ) , e.g. , around four extended spin-down episodes , but also on shorter time scales ( a few 100 days ) on which quasi-periodic variations are apparent .
We argue that the likely common cause is variations of the mass accretion rate onto the neutron star .
The data since 1991 allow a continuous sampling and indicate a lag between the turn-on behaviour and the spin behaviour , in the sense that changes are first seen in the spin , about one cycle later in the turn-on .
Both the coronal wind model ( Schandl & Meyer 1994 ) as well as the stream-disk model ( Shakura et al .
1999 ) predict this kind of behaviour .