Bayesian evidence for spectral lag transition due to Lorentz Invariance Violation for 32 Fermi/GBM Gamma-ray Bursts

We use the spectral lag data of 32 long GRBs detected by Fermi/GBM, which has been recently collated in Liu et al (2022) to quantify the statistical significance of a transition in the spectral lag data based on Lorentz invariance violation (LIV) (for both sub-luminal and super-luminal propagation) using Bayesian model selection. We use two different parametric functions to model the null hypothesis of only intrinsic emission: a smooth broken power law model (SBPL) (proposed in Liu et al) as well as a simple power law model, which has been widely used before in literature. We find that for sub-luminal propagation, when we use the SBPL model as the null hypothesis, five GRBs show ``decisive evidence'' based on Jeffreys' scale for linear LIV and quadratic LIV. When we use the simple power-law model as the null hypothesis, we find that 10 and GRBs show Bayesian ``decisive evidence'' for linear and quadratic LIV, respectively. However these results should not be construed as evidence for LIV, as they would be in conflict with the most stringent upper limits. When we did a test for super-luminal LIV, we find that only four and two GRBs show Bayesian ``decisive evidence'' for linear and quadratic LIV, respectively, assuming a simple power law for the intrinsic emission. When we use the SBPL model, one GRB shows Bayesian ``decisive evidence'' for linear and quadratic LIV. This underscores the importance of adequately modelling the intrinsic emission while obtaining constraints on LIV using spectral lags, since inadequate modelling could masquerade as a signature of LIV.