PREPRINT

# Expected Signature For the Lorentz Invariance Violation Effects on $\gamma -\gamma$ Absorption

Y. G. Zheng, S. J. Kang, K. R. Zhu, C. Y. Yang, J. M. Bai

Submitted on 3 November 2022, last revised on 9 November 2022

## Abstract

There are still some important unanswered questions about the unexpected very high energy $\gamma$-ray signatures. To help understand the mechanism, focusing on the linear and quadratic perturbation mode for subliminal case, the present paper revisited the expected signature for the Lorentz invariance violation effects on $\gamma -\gamma$ absorption in TeV spectra of Gamma-ray bursts (GRBs). We note that the existence of minimum photon energy threshold for the pair production process leads up to a break energy, which is sensitive to the quantum gravity energy scale. We suggest that energy spectral break in the few tens of TeV is a rough observational diagnostic for the LIV effects. The expected spectra characteristics are applied to a GRB 221009A. The results show that the cosmic opacity with Lorentz invariance violation effects considered here is able to roughly reproduce the observed $\gamma$-ray spectra for the source, which enabled us to constrain the lower limit of the linear values of energy scale at ${E}_{\mathrm{Q}\mathrm{G},1}=3.35×{10}^{20}$ GeV for the linear perturbation and ${E}_{\mathrm{Q}\mathrm{G},2}=9.19×{10}^{13}$ GeV for the quadratic perturbation. This value corresponds to a break energy for the linear and for the quadratic in the observed frame respectively.

## Preprint

Comment: Submitted, Comments welcome, 8 pages, 5 figures

Subject: Astrophysics - High Energy Astrophysical Phenomena