Constraint on Lorentz invariance violation from Vela pulsar

The High Energy Stereoscopic System (H.E.S.S) Collaboration reported the discovery of a novel radiation component from the Vela pulsar by their Cherenkov telescopes. It is of great importance that gamma rays with energies of at least 20~TeV are recorded unexpectedly. The H.E.S.S Collaboration argued that such results may challenge the state-of-the-art models for the high-energy emission of pulsars. We point out in this work that these results also provide a unique opportunity to constrain certain Lorentz invariance violation parameters, leading to the realization of studying Lorentz invariance violation by using gamma-ray pulsars. The Lorentz invariance violation scale is constrained at the level of $E_{\mathrm{LV,}1}> 1.66\times 10^{17} \rm GeV$ for the linear scenario, and $E_{\mathrm{LV,}2}>3.53\times 10^{10} \rm GeV$ for the quadratic scenario. We anticipate that digging into the detailed features of the data of the Vela pulsar and analyzing potentially more very-high-energy photon data from pulsars in the future would improve the constraints on Lorentz invariance violation.