Super-orbital variability of LS I+61 degrees 303 at TeV energies

Context. The gamma-ray binary LS I +61 degrees 303 is a well-established source from centimeter radio up to very high energy (VHE; E > 100 GeV). The broadband emission shows a periodicity of similar to 26.5 days, coincident with the orbital period. A longer (super-orbital) period of 1667 +/- 8 days was proposed from radio variability and confirmed using optical and high-energy (HE; E > 100 MeV) gamma-ray observations. In this paper, we report on a four-year campaign performed by MAGIC together with archival data concentrating on a search for a long-timescale signature in the VHE emission from LS I +61 degrees 303. Aims. We focus on the search for super-orbital modulation of the VHE emission, similar to that observed at other energies, and on the search for correlations between TeV emission and an optical determination of the extension of the circumstellar disk. Methods. A four-year campaign has been carried out using the MAGIC telescopes. The source was observed during the orbital phases when the periodic VHE outbursts have occurred (phi = 0 : 55-0.75, one orbit = 26.496 days). Additionally, we included archival MAGIC observations and data published by the VERITAS collaboration in these studies. For the correlation studies, LS I +61 degrees 303 has also been observed during the orbital phases where sporadic VHE emission had been detected in the past (phi = 0 : 75-1.0). These MAGIC observations were simultaneous with optical spectroscopy from the LIVERPOOL telescope. Results. The TeV flux of the periodical outburst in orbital phases phi = 0 : 5-0.75 was found to show yearly variability consistent with the long-term modulation of similar to 4.5 years found in the radio band. This modulation of the TeV flux can be well described by a sine function with a best-fit period of 1610 +/- 58 days. The complete data, including archival observations, span two super-orbital periods. There is no evidence for a correlation between the TeV emission and the mass-loss rate of the Be star, but this may be affected by the strong, short-timescale (as short as intra-day) variation displayed by the H alpha fluxes.