Identifying the physical periods in the radio emission from the $γ$-ray emitting binary LS I +61 303
The $γ$-ray emitting binary LS I +61 303 exhibits periodic emission across the electromagnetic spectrum, from radio up to the very-high-energy regime. The most prominent features are the three periods $P_1 = 26.5$ d, $P_2 = 26.9$ d, and $P_{\rm long} = 4.6$ 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. The detection of a fifth period, $P_3 = 26.3$ d, was recently claimed. Our aim is to determine which of these periods are intrinsic (likely related to physical processes) and which of these are secondary (resulting from interference). We avoided any assumption about the physical scenario and restricted our analysis to the phenomenology of the radio emission variability. We selected intervals from archival radio data and applied the generalized Lomb-Scargle periodogram. We fit the observational data to generate synthetic data that only contain specific signals. We analyzed these synthetic data to assess the impact of these signals and their interference on the light curves and the periodogram. The two-peaked profile, consisting of $P_1$ and $P_2$, was detected in the periodogram of the actual data for intervals that are significantly shorter than $P_{\rm long}$, provided that these intervals contain a 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 three periods $P_1$, $P_2$, and $P_{\rm long}$, the residuals being limited by noise. We have found that all three periods, i.e., $P_1$, $P_2$, and $P_{\rm long}$, could correspond to physically real processes occurring in LS I +61 303.