Separating source-intrinsic and Lorentz invariance violation induced delays in the very high-energy emission of blazar flares

Aims. The aim of the present study is to explore how to disentangle energy-dependent time delays due to a possible Lorentz invariance violation (LIV) at Planck scale from intrinsic delays expected in standard blazar flares. Methods. We first characterised the intrinsic time delays in BL Lacs and flat-spectrum radio quasars in standard one-zone time-dependent synchrotron self-Compton or external Compton models, during flares produced by particle acceleration and cooling processes. We simulated families of flares with both intrinsic and external LIV-induced energy-dependent delays. Discrimination between intrinsic and LIV delays is then investigated in two different ways. A technique based on Euclidean distance calculation between delays obtained in the synchrotron and in the inverse-Compton spectral bumps is used to assess their degree of correlation. A complementary study is performed using spectral hardness versus intensity diagrams in both energy ranges. Results. We show that the presence of non-negligible LIV effects, which essentially act only at very high energy (VHE), can drastically reduce the strong correlation expected between the X-ray and the VHE gamma-ray emission in leptonic scenarios. The LIV phenomenon can then be hinted at measuring the Euclidean distance dE from simultaneous X-ray and gamma-ray flare monitoring. Large values of minimum distance dE, min would directly indicate the influence of non-intrinsic time delays possibly due to LIV in SSC flares. LIV effects can also significantly modify the VHE hysteresis patterns in hardness-intensity diagrams and even change their direction of rotation compared to the X-ray behaviour. Both observables could be used to discriminate between LIV and intrinsic delays, provided high-quality flare observations are available.