Identifying the physical periods in the radio emission from the \u03b3-ray emitting binary LS I +61 303

Context. The γ-ray emitting binary system LS I +61 303 exhibits periodic emission across the electromagnetic spectrum, extending from radio frequencies up to the very-high-energy regime. The most prominent features are three periods with values P1 = 26.5 d, P2 = 26.9 d, and Plong = 4.6 years. Occasionally, a fourth period of 26.7 d is also detected. Mathematically, these four periods are interrelated via the interference pattern of a beating. Competing scenarios that seek to determine which of these periods are physical and which are secondary are under debate. In addition, the detection of a fifth period, P3 = 26.3 d, was recently claimed. Aims. Our aim is to determine which of these periods are intrinsic (i.e., whether they are likely to be related to physical processes) and which of these are secondary (i.e., resulting from interference). We chose to avoid any assumption concerning the physical scenario and restricted our analysis to the phenomenology of the radio emission variability. Methods. We selected intervals from archival radio data and applied the generalized Lomb-Scargle periodogram. We fit the observational data to generate synthetic datasets that only contain specific signals in the form of pure sine waves. We analyzed these synthetic data to assess the impact of these signals and their interference on the light curves and the periodogram. Results. The two-peaked profile, consisting of P1 and P2, was detected in the periodogram of the actual data for intervals that are significantly shorter than Plong, provided that these intervals contain the minimum of the long-term modulation. The characteristics of the observational data and their periodogram could only be reproduced with synthetic data if these explicitly included all of the three periods, P1, P2, and Plong, with the residuals being limited by noise. Conclusions. We have found, for the first time, that all three periods, P1, P2, and Plong, could, in fact, correspond to physically real processes occurring in LS I +61 303. This should be considered when modeling the physical processes in this binary system.