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.
