Long-term periodicity in LS I+61°303 as beat frequency between orbital and precessional rate

Context. In the binary system LS I + 61 degrees 303 the peak flux density of the radio outburst, which is related to the orbital period of 26.4960 +/- 0.0028 d, exibits a modulation of 1667 +/- 8 d. The radio emission at high spatial resolution appears structured in a precessing jet with a precessional period of 27-28 d. Aims. How close is the precessional period of the radio jet to the orbital period? Any periodicity in the radio emission should be revealed by timing analysis. The aim of this work is to establish the accurate value of the precessional period. Methods. We analyzed 6.7 years of the Green Bank Interferometer database at 2.2 GHz and 8.3 GHz with the Lomb-Scargle and phase dispersion minimization methods and performed simulations. Results. The periodograms show two periodicities, P-1 = 26.49 +/- 0.07 d (v(1) = 0.03775 d(-1)) and P-2 = 26.92 +/- 0.07 d (v(2) = 0.03715 d(-1)). Whereas radio outbursts have been known to have nearly orbital occurrence P-1 with timing residuals exhibiting a puzzling sawtooth pattern, we probe in this paper that they are actually periodical outbursts and that their period is P-average = 2/v(1)+v(2) = 26.70 +/- 0.05 d. The period P-average as well as the long-term modulation P-beat = 1/v(1)+v(2) = 1667 +/- 393 d result from the beat of the two close periods, the orbital P-1 and the precessional P-2 periods. Conclusions. The precessional period, indicated by the astrometry to be of 27-28 d, is P-2 = 26.92 d. The system LS I + 61 degrees 303 seems to be one more case in astronomy of beat, i.e., a phenomenon occurring when two physical processes create stable variations of nearly equal frequencies. The very small difference in frequency creates a long-term variation of period 1/(v(1)+v(2)). The long-term modulation of 1667 d results from the beat of the two close orbital and precessional rates.