Precessing accretion discs have long been suggested as explanations for the
long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ
Her. We show that an instability of the disc's response to the radiation
reaction force from the illumination by the central source can cause the disc
to tilt out of the orbital plane and precess in something like the required
manner. The rate of precession and disc tilt obtained for realistic values of
system parameters compare favourably with the known body of data on X-ray
binaries with long periods. We explore other possible types of behaviour than
steadily precessing discs that might be observable in systems with somewhat
different parameters. At high luminosities, the inner disc tilts through more
than 90 degrees, i.e. it rotates counter to the usual direction, which may
explain the torque reversals in systems such as 4U 1626-67.Comment: submitted to MNRAS, 17-Dec-97, revised submit 2-Nov-98. 15 pages
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