Discovery of a periodical apoastron GeV peak in LS I+61°303

Aims. The aim of this paper is to analyse the previously discovered discontinuity of the periodicity of the GeV gamma-ray emission of the radio-loud X-ray binary LS I +61 degrees 303 and to determine its physical origin. Methods. We used a wavelet analysis to explore the temporal development of periodic signals. The wavelet analysis was first applied to the whole data set of available Fermi-LAT data and then to the two subsets of orbital phase intervals Phi = 0.0-0.5 and Phi = 0.5-1.0. We also performed a Lomb-Scargle timing analysis. We investigated the similarities between GeV gamma-ray emission and radio emission by comparing the folded curves of the Fermi-LAT data and the Green Bank Interferometer radio data. Results. During the epochs when the timing analysis fails to determine the orbital periodicity, the periodicity is present in the two orbital phase intervals Phi = 0.0-0.5 and Phi = 0.5-1.0. That is, there are two periodical signals, one towards periastron (i.e., Phi = 0.0-0.5) and another one towards apoastron (Phi = 0.5-1.0). The apoastron peak seems to be affected by the same orbital shift as the radio outbursts and, in addition, reveals the same two periods P-1 and P-2 that are present in the radio data. Conclusions. The gamma -ray emission of the apoastron peak normally just broadens the emission of the peak around periastron. Only when it appears at Phi approximate to 0.8-1.0 because of the orbital shift, it is enough detached from the first peak to become recognisable as a second orbital peak, which is the reason why the timing analysis fails. Two gamma -ray peaks along the orbit are predicted by the two-peak accretion model for an eccentric orbit that was proposed by several authors for LS I +61 degrees 303.