Bayesian Analysis of Radio Observations of the Be X‐Ray Binary LS I +61o303

The binary star LS I +61°303 is remarkable for its periodic radio outbursts every 26.5 days. We recently discovered a ~4.4 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 ~0.4. 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 ~2.7 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.