Probing Lorentz Invariance Violation with Absorption of Astrophysical γ-Rays by Solar Photons

We compute in detail the absorption optical depth for astrophysical γ -ray photons interacting with solar photons to produce electron–positron pairs. This effect is greatest for γ -ray sources at small angular distances from the Sun, reaching optical depths as high as τ _γ _γ ∼ 10 ^−2 . We also calculate this effect including modifications to the absorption cross-section threshold from subluminal Lorentz invariance violation (LIV). We show for the first time that subluminal LIV can lead to increases or decreases in τ _γ _γ compared to the non-LIV case. We show that, at least in principle, LIV can be probed with this effect with observations of γ -ray sources near the Sun at ≳20 TeV by HAWC or LHAASO, although a measurement will be extremely difficult due to the small size of the effect.