Understanding the periodicities in radio and GeV emission from LS I +61

Context. One possible scenario to explain the emission from the stellar binary system LS I + 61°303 is that the observed flux is emitted by precessing jets powered by accretion. Accretion models predict two ejections along the eccentric orbit of LS I + 61°303: one major ejection at periastron and a second, lower ejection towards apastron. Our GeV gamma-ray observations show two peaks along the orbit (orbital period P1) but reveal that at apastron the emission is also affected by a second periodicity, P2. Strong radio outbursts also occur at apastron, which are affected by both periodicities (i.e. P1 and P2), and radio observations show that P2 is the precession of the radio jet. Consistently, a long-term modulation, equal to the beating of P1 and P2, affects both radio and gamma-ray emission at apastron but it does not affect gamma-ray emission at periastron. Aims. If there are two ejections, why does the one at periastron not produce a radio outburst there? Is the lack of a periastron radio outburst somehow related to the lack of P2 from the periastron gamma-ray emission? Methods. We develop a physical model in which relativistic electrons are ejected twice along the orbit. The ejecta form a conical jet that is precessing with P2. The jet radiates in the radio band by the synchrotron process and the jet radiates in the GeV energy band by the external inverse Compton and synchrotron self-Compton processes. We compare the output fluxes of our physical model with two available large archives: Owens Valley Radio Observatory (OVRO) radio and Fermi Large Area Telescope (LAT) GeV observations, the two databases overlapping for five years. Results. The larger ejection around periastron passage results in a slower jet, and severe inverse Compton losses result in the jet also being short. While large gamma-ray emission is produced, there is only negligible radio emission. Our results are that the periastron jet has a length of 3.0 × 106rs and a velocity β ~ 0.006, whereas the jet at apastron has a length of 6.3 × 107rs and β ~ 0.5. Conclusions. In the accretion scenario the observed periodicities can be explained if the observed flux is the intrinsic flux, which is a function of P1, times the Doppler factor, a function of βcos(f(P2)). At periastron, the Doppler factor is scarcely influenced by P2 because of the low β. At apastron the larger β gives rise to a significant Doppler factor with noticeable variations induced by jet precession