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The High Mass X-ray Binary (HMXB) SMC X-1 demonstrates an orbital variationof 3.89 days and a super-orbital variation with an average length of 55 days.As we show here, however, the length of the super-orbital cycle varies byalmost a factor of two, even across adjacent cycles. To study both the orbitaland super-orbital variation we utilize lightcurves from the Rossi X-ray TimingExplorer All Sky Monitor (RXTE-ASM). We employ the orbital ephemeris fromWojdowski et al. (1998) to obtain the average orbital profile, and we show thatthis profile exhibits complex modulation during non-eclipse phases.Additionally, a very interesting ``bounceback'' in X-ray count rate is seenduring mid-orbital eclipse phases, with a softening of the emission duringthese periods. This bounceback has not been previously identified in pointedobservations. We then define a super-orbital ephemeris (the phase of thesuper-orbital cycle as a function of date) based on the ASM lightcurve andanalyze the trend and distribution of super-orbital cycle lengths. SMC X-1exhibits a bimodal distribution of these lengths, similar to what has beenobserved in other systems (e.g., Her X-1), but with more dramatic changes incycle length. There is some hint, but not conclusive evidence, for a dependenceof the super-orbital cycle length upon the underlying orbital period, as hasbeen observed previously for Her X-1 and Cyg X-2. Using our super-orbitalephemeris we are also able to create an average super-orbital profile over the71 observed cycles, for which we witness overall hardening of the spectrumduring low count rate times. We combine the orbital and super-orbitalephemerides to study the correlation between the orbital and super-orbitalvariations in the system.

Tracking the Orbital and Super-orbital Periods of SMC X-1