Origin of the long-term modulation of radio emission of LS I +61 303

Context. One of the most unusual aspects of the X-ray binary LS I + 61 degrees 303 is that at each orbit (P-1 = 26 : 4960 +/- 0 : 0028 d) one radio outburst occurs whose amplitude is modulated with Plong, a long-term period of more than 4 yr. It is still not clear whether the compact object of the system or the companion Be star is responsible for the long-term modulation. Aims. We study here the stability of Plong. Such a stability is expected if P-long is due to periodic (P-2) Doppler boosting of periodic (P-1) ejections from the accreting compact object of the system. On the contrary it is not expected if P-long is related to variations in the mass loss of the companion Be star. Methods. We built a database of 36.8 yr of radio observations of LS I + 61 degrees 303 covering more than 8 long-term cycles. We performed timing and correlation analysis. We also compared the results of the analyses with the theoretical predictions for a synchrotron emitting precessing (P-2) jet periodically (P-1) refilled with relativistic electrons. Results. In addition to the two dominant features at P-1 and P-2, the timing analysis gives a feature at P-long = 1628 +/- 48 days. The determined value of P-long agrees with the beat of the two dominant features, i.e. Pbeat = 1/(nu(1) - nu(2)) = 1626 +/- 68 d. Lomb-Scargle results of radio data and model data compare very well. The correlation coefficient of the radio data oscillates at multiples of Pbeat, as does the correlation coe ffi cient of the model data. Conclusions. Cycles in varying Be stars change in length and disappear after 2-3 cycles following the well-studied case of the binary system zeta Tau. On the contrary, in LS I + 61 degrees 303 the long-term period is quite stable and repeats itself over the available 8 cycles. The long-term modulation in LS I + 61 degrees 303 accurately reflects the beat of periodical Doppler boosting (induced by precession) with the periodicity of the ejecta. The peak of the long-term modulation occurs at the coincidence of the maximum number of ejected particles with the maximum Doppler boosting of their emission; this coincidence occurs every 1/nu(1)-nu(2) and creates the long-term modulation observed in LS I + 61 degrees 303.