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 ${E}_{\mathrm{Q}\mathrm{G},1}=3.35\times {10}^{20}$ GeV for the linear
perturbation and ${E}_{\mathrm{Q}\mathrm{G},2}=9.19\times {10}^{13}$ GeV for the quadratic
perturbation. This value corresponds to a break energy ${E}_{\gamma ,\mathrm{b}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{k},1}\simeq 55.95\text{}\mathrm{T}\mathrm{e}\mathrm{V}$ for the linear and ${E}_{\gamma ,\mathrm{b}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{k},2}\simeq 73.66\text{}\mathrm{T}\mathrm{e}\mathrm{V}$ for the quadratic in the observed frame respectively.

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

## Preprint

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

Subject: Astrophysics - High Energy Astrophysical Phenomena