Constraints on the extragalactic magnetic field strength from blazar spectra based on 145 months of Fermi-LAT observations

Properties of the extragalactic magnetic field (EGMF) outside of clusters and filaments of the large-scale structure are essentially unknown. The EGMF could be probed with $\gamma$-ray observations of distant (redshift $z > 0.1$) blazars. TeV $\gamma$ rays from these sources are strongly absorbed on extragalactic background light photons; secondary electrons and positrons produce cascade $\gamma$ rays with the observable flux dependent on EGMF parameters. We put constraints on the EGMF strength using 145 months of Fermi-LAT observations of the blazars 1ES 1218+304, 1ES 1101-232, and 1ES 0347-121, and imaging atmospheric Cherenkov telescope observations of the same sources. We perform a series of full direct Monte Carlo simulations of intergalactic electromagnetic cascades with the ELMAG 3.01 code and construct a model of the observable spectra inside the point spread functions of the observing instruments for a range of EGMF strengths. We compare the observed spectra with the models for various values of the EGMF strength $B$ and calculate the exclusion statistical significance for every value of $B$. We find that the values of the EGMF strength $B \le 10^{-17}$ G are excluded at a high level of the statistical significance $Z > 4 \sigma$ for all the four options of the intrinsic spectral shape considered (power-law, power-law with exponential cutoff, log-parabola, log-parabola with exponential cutoff). The value of $B = 10^{-16}$ G is not excluded; it is still a viable option of the EGMF strength. These results were obtained for the case of steady sources.