Upper limit on the axion-photon coupling from Markarian 421

Markarian 421 is a well-known nearby BL Lac blazar at the redshift z = 0.031 . Many previous works were investigated to constrain the axion-photon coupling from its TeV gamma-ray observations, showing the upper limit on the coupling constant g a γ ≲ 2.0 × 10 − 11 Ge V − 1 for the axion mass [ 5.0 × 10 − 10 eV ≲ m a ≲ 5.0 × 10 − 7 eV ] . While in this work, we obtain a more stringent upper limit on the axion-photon coupling from the 1038 days gamma-ray observations of the blazar Markarian 421. The long-term VHE gamma-ray spectra are measured by the collaborations Large Area Telescope on board NASA's Fermi Gamma-ray Space Telescope (Fermi-LAT) and High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory from 2015 June to 2018 July. We show the best-fit spectral energy distributions (SEDs) of Markarian 421 under the null and axion hypotheses. Then we set the axion-photon limit in the { m a , g a γ } plane. The 99% C . L . upper limit set by Markarian 421 is g a γ ≲ 4.0 × 10 − 12 Ge V − 1 for the axion mass [ 1.0 × 10 − 9 eV ≲ m a ≲ 1.0 × 10 − 8 eV ] . It is the most stringent upper limit in this axion mass region.