However, the intrinsic effects caused by the unknown emission and acceleration mechanisms in the source could mitigate or enhance the LIV-induced time delay, which would impact the accuracy of the resulting constraints on LIV. A key challenge is then to distinguish an intrinsic time lag at the source from a delay induced by LIV. Long GRBs usually have significantly positive or negative intrinsic spectral lags and should not be used for LIV searches until reasonable progress is made on the modeling of the emission and acceleration mechanisms (Chen et al. 2005; Ukwatta et al. 2012; Bernardini et al. 2015), while short GRBs are consistent with null or negligible intrinsic spectral lag and are therefore an ideal tool to measure the LIV effect (Norris & Bonnell 2006; Bernardini et al. 2015, 2017; Xiao et al. 2022). Currently, in addition to short GRBs, active galactic nucleus (AGN) flares and gamma-ray pulsars are two other classes of astrophysical sources that have no significant intrinsic lag in general and are often used for LIV tests (Biller et al. 1999; Kaaret 1999; Aharonian et al. 2008; MAGIC Collaboration et al. 2017). It should be noted, however, that there is also evidence of intrinsic lags in some cases of AGN flares and pulsars. For example, MAGIC Collaboration during an observational campaign regarding Mkn 501 blazar found an indication of about 4 minutes time delay between the peaks at E  0.25 TeV and E > 1.2 TeV (MAGIC Collaboration et al. 2008), which may indicate a progressive acceleration of electrons in the emitting plasma blob. A robust method to study the correlations between arrival times and energy, based on a likelihood function built from the physical picture assumed for the emission, propagation, and detection of the photons was proposed by Martínez & Errando (2009). In the case of pulsars, there are some lags if the energy range is extended too much toward low energies (e.g., radio versus TeV). No real progress on the topic of intrinsic effects will be made without accurate models for production and acceleration mechanisms for each type of source. Perennes et al. (2020) first attempted to gain knowledge on source-intrinsic spectral lags of flaring AGNs at high and very high energies and on short timescales relevant for LIV searches, using leptonic AGN flare modeling. Concerning GRBs, some ways have been proposed to reduce the impact of intrinsic effects, e.g., fitting the observed spectral lags of statistical samples of GRBs at a range of different redshifts (Ellis et al. 2006; Bernardini et al. 2017; Xiao et al. 2022), or using only a limited observer-frame energy bands range corresponding to the fixed source-frame energy bands (Wei & Wu 2017). Anyway, there is no reason to think that the low and high-energy photons should be emitted simultaneously at the source, and while detecting distinct signals at different energy channels, we have no idea which one was sent first. Previous studies usually assumed that the intrinsic time delays are either an unknown constant for all GRBs considered or scale with the photon energy E according to some power-law function (Ellis et al. 2006; Biesiada & Piórkowska 2009a; Zhang & Ma 2015; Wei et al. 2017a; Acciari et al. 2020; Pan et al. 2020; Du et al. 2021).
Citation: Xiao et al. 2022
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