Bayesian analysis of radio observations of the Be X-ray binary LS I +61°303

The binary star LS I + 61degrees 303 is remarkable for its periodic radio outbursts every 26.5 days. We recently discovered a similar to4.4 yr periodic modulation of the phase and amplitude of these outbursts using the Gregory-Loredo Bayesian algorithm for detecting periodic signals of unknown shape. In this paper we obtain improved estimates of both the orbital period P-1 and the modulation period P-2 based on a larger data set and examine the behavior of the spectral index between 2.2 and 8.3 GHz versus the modulation period. The new estimates are P-1 = 26.4960 +/- 0.0028 and P-2 = 1667 +/- 8 days, and our best estimate of the radio phase of periastron is similar to0.4. Analysis of the spectral index data indicates that the optical depth in the synchrotron emission region is always <<1 at 8.3 GHz and can reach values of similar to2.7 at 2.2 GHz. A test of the precessing Be star model of Lipunov & Nazin indicates that it is unlikely to be the correct mechanism to explain the 1667 day periodic modulation.