A lower bound on intergalactic magnetic fields from time variability of 1ES 0229+200 from MAGIC and Fermi/LAT observations

Context. Extended and delayed emission around distant TeV sources induced by the effects of propagation of gamma ray s through the intergalactic medium can be used for the measurement of the intergalactic magnetic field (IGMF).Aims. We search for delayed GeV emission from the hard-spectrum TeV gamma-ray emitting blazar 1ES 0229+200, with the goal of detecting or constraining the IGMF-dependent secondary flux generated during the propagation of TeV gamma rays through the intergalactic medium.Methods. We analysed the most recent MAGIC observations over a 5 year time span, and complemented them with historic data of the H.E.S.S. and VERITAS telescopes, along with a 12-year-long exposure of the Fermi/LAT telescope. We used them to trace source evolution in the GeV-TeV band over a decade and a half. We used Monte Carlo simulations to predict the delayed secondary gamma-ray flux, modulated by the source variability, as revealed by TeV-band observations. We then compared these predictions for various assumed IGMF strengths to all available measurements of the gamma-ray flux evolution.Results. We find that the source flux in the energy range above 200 GeV experiences variations around its average on the 14-year time span of observations. No evidence for the flux variability is found in the 1 - 100 GeV energy range accessible to Fermi/LAT. The non-detection of variability due to delayed emission from electromagnetic cascade developing in the intergalactic medium imposes a lower bound of B>1.8 x 10(-17) G for the long-correlation-length IGMF and B>10(-14) G for an IGMF of cosmological origin. Though weaker than the one previously derived from the analysis of Fermi/LAT data, this bound is more robust, being based on a conservative intrinsic source spectrum estimate and accounting for the details of source variability in the TeV energy band. We discuss implications of this bound for cosmological magnetic fields that might explain the baryon asymmetry of the Universe.