Detection of nearly periodic spin period reversals in Vela X-1 on long time-scales: inkling of solar-like cycle in the donor star?

We explore the long-term evolution of the spin period of the high-mass X-ray binary pulsar Vela X-1 over a period of 46 yr. Our analysis indicates nearly periodic variations in the spin period of the pulsar on time-scales of about 5.9 yr. There is suggestion of an overall spin-down behaviour of the pulsar though it is noticed that the source appears to stay near its equilibrium period 283.4 s since MJD 51000, with rather erratic spin-up/spin-down episodes around this value. Our study suggests nearly cyclic turnover in the spin behaviour of the pulsar from spin-up to spin-down regimes on time-scales of about 17-19 yr. To our knowledge, this is the first report of periodic variation in the spin behaviour of a wind-fed accreting pulsar. We also observe erratic episodes of spin-up and spin-down behaviour on relatively shorter time-scales that is a well-known archetype of this wind-fed X-ray pulsar. We investigate whether nearly periodic long-term spin period changes in the pulsar can be explained by using known mechanisms of torque reversals in the accretion powered neutron stars. It appears that changes in the accretion environment of the pulsar using current ideas can probably lead to long-term spin period changes in this X-ray pulsar.