Expected signature for the Lorentz invariance violation effects on γ−γ absorption

Abstract

There are still some significant and unanswered questions about the incredible very-high-energy $\ensuremath{\gamma}$-ray signatures. To help understand the mechanism, focusing on the linear and quadratic perturbation mode for the subluminal regime, we revisit the expected signature for the Lorentz invariance violation (LIV) effects on $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ absorption in the TeV spectra of gamma-ray bursts (GRBs). We note that there is a critical energy for the pair production process, which is sensitive to the assumed quantum gravity energy scale. We suggest that a reemergence of the energy spectrum of $\ensuremath{\gamma}$ rays at several tens of TeV is a rough observational diagnostic for the LIV effects. The expected spectra characteristics are applied to GRB 221009A. The results show that the cosmic opacity with LIV effects considered here can roughly reproduce the observed $\ensuremath{\gamma}$-ray spectra for the source, which enables us to constrain the upper limit of the values of the energy scale to ${E}_{\mathrm{QG},1}\ensuremath{\le}3.35\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{ }\mathrm{GeV}$ for the linear perturbation and ${E}_{\mathrm{QG},2}\ensuremath{\le}9.19\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }\mathrm{GeV}$ for the quadratic perturbation. These scenarios lead to updated bounds on the LIV coefficient, with ${\ensuremath{\xi}}_{1}^{\ensuremath{'}}\ensuremath{\ge}3.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ for the linear perturbation and ${\ensuremath{\xi}}_{2}^{\ensuremath{'}}\ensuremath{\ge}1.33\ifmmode\times\else\texttimes\fi{}{10}^{6}$ for the quadratic perturbation, in the standard model extension framework.