Measurement of femtogauss intergalactic magnetic fields towards Mkn 501

The intergalactic magnetic field (IGMF) is expected either to be generated via astrophysical processes or to be a relic of phase transitions in the early universe. Upper bounds are set via observations of Faraday rotation measure. Lower bounds have been derived from the non-detection of secondary gamma-rays possibly produced in electromagnetic cascades. We investigate the presence of IGMFs by studying the GeV gamma-ray emission from the nearby blazar Mkn 501 (z=0.034), searching for evidence of the extended halo from electromagnetic cascades. We analyse 14 years of data from Fermi-LAT and Swift-XRT/BAT to construct a time-average synchrotron-self Compton model for the TeV spectrum of Mkn 501. This injection spectrum is used to simulate the resulting cascade emission with the ELMAG code for different magnetic field and coherence length configurations. These templates are fit to the Fermi-LAT data to find a best-fitting model for the cascade emission. We find significant (5 σ trial-corrected) evidence of extended secondary emission around Mkn 501, which is consistent with an IGMF with B rms=1.5+2.0-1.3 fG and a coherence length of C=10+490-5 kpc (statistical uncertainties only). When including instrumental systematic uncertainties, the permissible IGMF strength is B rms=1.5+8.5-1.1 fG, for fixed C=10 kpc. The source needs to actively inject TeV gamma-rays for at least 45000 years to match the level of secondary emission. Our results indicate that the secondary gamma-rays are significantly present in the Fermi-LAT data and furthermore, that the effect of plasma-heating by pairs in the cascade appears to be negligible for Mkn 501. The energy spectrum of Mkn 501 favours pair conversion in the intervening low-density inter-galactic medium.