2013A&A...559A.129J

In the gamma-ray binary LS I +61°303, radio outbursts occur every 26.70 days and are modulated by a long-term periodicity of 1667 days. Until now the prediction of the periodical radio outbursts has been made using the orbital period P₁=26.4960±0.0028-days. This procedure implies timing residuals up to ∼7 days affected by a systematic error with a sawtooth pattern. On the other hand, the direct use of the known periodicity of the radio outbursts, that is of P_outburst= P_average=26.70±0.05d, is prevented because of a time variable phase term. Our aim is to analyze this phase term and determine its exact value at each given epoch. First, we modeled the systematic sawtooth pattern affecting the timing residuals between the observed outbursts and those predicted by P₁. Then, we removed this pattern from 6.7yr of 8.3GHz Green Bank Inferferometer radio data to generate noise-limited residuals. Finally, we determined a criterion to determine the phase term based on the number of elapsed cycles of the long-term modulation at a given epoch. The prediction of the outburst with P=P_average is now straightforward and produces noise-limited timing residuals.