  We analyzed images of comet 49P/Arend-Rigaux on 33 nights between 2012
January and May and obtained R-band lightcurves of the nucleus. Through usual
phasing of the data we found a double-peaked lightcurve having a synodic
rotation period of 13.450 +/- 0.005 hr. Similarly, phase dispersion
minimization and the Lomb-Scargle method both revealed rotation periods of
13.452 hr. Throughout the 2011/12 apparition, the rotation period was found to
increase by a small amount, consistent with a retrograde rotation of the
nucleus. We also reanalyzed the publicly available data from the 1984/85
apparition by applying the same techniques, finding a rotation period of 13.45
+/- 0.01 hr. Based on these findings we show that the change in rotation period
is less than 14 seconds per apparition. Furthermore, the amplitudes of the
light curves from the two apparitions are comparable, to within reasonable
errors, even though the viewing geometries differ, implying that we are seeing
the comet at a similar sub-Earth latitude. We detected the presence of a short
term jet-like feature in 2012 March which appears to have been created by a
short duration burst of activity on March 15. Production rates obtained in
2004/05, along with reanalysis of previous results from 1984/85 imply a strong
seasonal effect and a very steep fall-off after perihelion. This, in turn,
implies that a single source region dominates activity, rather than leakage
from the entire nucleus.
