  Hard X-ray observations with the Neil Gehrels Swift Observatory Burst Alert
Telescope (BAT) reveal superorbital modulation in the wind-accreting supergiant
high-mass X-ray binary (HMXB) 4U 1538-52 at a period of 14.9130 +/- 0.0026 days
that is consistent with four times the 3.73 day orbital period. These periods
agree with a previously suggested correlation between superorbital and orbital
periods in similar HMXBs. During the ~14 years of observations the superorbital
modulation changes amplitude, and since ~MJD 57,650 it was no longer detected
in the power spectrum, although a peak near the second harmonic of this was
present for some time. Measurements of the spin period of the neutron star in
the system with the Fermi Gamma-ray Burst Monitor show a long-term spin-down
trend which halted towards the end of the light curve, suggesting a connection
between dP(spin)/dt and superorbital modulation, as proposed for 2S 0114+650.
However, an earlier torque reversal from INTEGRAL observations was not
associated with superorbital modulation changes. B and V band photometry from
the Las Cumbres Observatory reveals orbital ellipsoidal photometric
variability, but no superorbital optical modulation. However the photometry was
obtained when the 14.9130 day period was no longer detected in the BAT power
spectrum. We revisit possible superorbital modulation in BAT observations of
IGR J16393-4643 but cannot conclusively determine whether this is present,
although is not persistent. We consider superorbital modulation mechanisms, and
suggest that the Corotating Interaction Region model, with small deviations
from orbital synchronization, appears promising.
