  The present study aims to reinforce the evidence for the ~9 s pulsation in
the gamma-ray binary LS 5039, derived with a Suzaku observation in 2007 and
that with NuSTAR in 2016 (Yoneda et al 2000). Through a reanalysis of the
NuSTAR data incorporating the orbital Doppler correction, the 9.0538 s
pulsation was confirmed successfully even in the 3--10 keV range, where it was
undetectable previously. This was attained by perceiving an energy-dependent
drift in the pulse phase below 10 keV, and correcting the pulse timing of
individual photons for that effect. Similarly, an archival 0.7--12 keV data set
of LS 5039, taken with the ASCA GIS in 1999 October, was analyzed. The data
showed possible periodicity at about 8.882 s, but again the energy-dependent
phase drift was noticed below 10 keV. By correcting for this effect, and for
the orbital Doppler delays in the LS 5039 system, the 2.8--12 keV periodicity
became statistically significant at 8.891+- 0.001 s. The periods measured with
ASCA, Suzaku, and NuSTAR approximately follow an average period derivative of
dP/dt = 3.0 e-10 s/s. These results provide further evidence for the pulsation
in this object, and strengthen the scenario by (Yoneda et al 2000), that the
compact object in LS 5039 is a strongly magnetized neutron star.

High Energy Astrophysical Phenomena