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 ($\ge 5 σ$ trial-corrected) evidence of extended secondary emission around Mkn~501, which is consistent with an IGMF with $B_\mathrm{rms}=1.5^{+2.0}_{-1.3}~\mathrm{fG}$ and a coherence length of $\ell_C=10^{+490}_{-5} ~\mathrm{kpc}$ (statistical uncertainties only). When including instrumental systematic uncertainties, the permissible IGMF strength is $B_\mathrm{rms}=1.5^{+8.5}_{-1.1}~\mathrm{fG}$, for fixed $\ell_C=10~\mathrm{kpc}$. 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.