Effects of Lorentz invariance violation on charged particles and photon production in astrophysical sources

TL;DR

This work investigates how Lorentz invariance violation (LIV) reshapes high-energy radiation in astrophysical sources by implementing a kinematic LIV framework, where the dispersion relation is $E^2 = m^2 + p^2 + \sum_n \delta_n p^{n+2}$, and the Lorentz factor becomes $\gamma^2_{\text{LIV}} = \frac{E^2}{m^2 - (n+1)\delta_n E^{n+2}}$. It derives LIV-modified synchrotron power and photon energy and extends these ideas to inverse Compton scattering, revealing how LIV can enhance cross sections and shift emission toward new high-energy regions, with constraints arising from thresholds $E^{n+2} = \frac{m^2}{(n+1)\delta_n}$. The authors further couple these LIV effects to first-order Fermi acceleration, demonstrating altered maximum energies, particle spectra, and SSC emission, including distinct LIV-induced high-energy components. They find that perturbative LIV predictions can lead to non-physical divergences at extreme energies, underscoring the need for a dynamical LIV–QED treatment, and suggest that forthcoming multi-messenger observations, alongside precise trajectory analyses, may constrain LIV parameters despite current upper limits from the Pierre Auger Observatory.

Abstract

We investigate the impact of Lorentz invariance violation (LIV) on radiation processes in astrophysical sources, focusing on synchrotron and inverse Compton interactions. We derive modified expressions for radiated power and photon energy under LIV assumptions and incorporate them into first-order Fermi acceleration models. Our analysis reveals energy thresholds beyond which LIV, within a kinematic framework, significantly alters particle dynamics and photon spectra, introducing non-physical divergences that highlight limitations in perturbative approaches. We model synchrotron self-Compton (SSC) emission in the presence of LIV and assess its consequences for photon fluxes from blazars, including Markarian 501 and the BL Lac population. LIV introduces distinct high-energy emission regions that deviate from standard expectations. Comparisons with observational data, particularly upper limits from the Pierre Auger Observatory, suggest that future multi-messenger observations, together with the full analysis of particle's trajectories, could constrain LIV parameters through the non-detection of such excesses.

Figures (25)

• Figure 1: Final photon energy in the reference frame of the electron as a function of its initial energy. A scattering angle of $\pi/2$ was adopted. Different values of $\delta_n^{(\gamma)}$ are shown for the first two orders of violation. The electron LIV parameter was set to $0$. The result for the first violation order was previously obtained in Abdalla_2018.
• Figure 2: Klein-Nishina cross section for a photon-electron interaction. Different values of $\delta_n^{(\gamma)}$ are shown for the first two orders of violation. The electron LIV parameter was set to $0$. The result for the first violation order was previously obtained in Abdalla_2018.
• Figure 3: Average of the cosine of the scattering angle of photons as a function of the initial photon energy. Different values of $\delta_n^{(\gamma)}$ are shown for the first two orders of violation. The electron LIV parameter was set to $0$.
• Figure 4: Maximum electron energy as a function of breaking parameter $\delta_n^{(e)}$. Electrons are accelerated via the first-order Fermi mechanism and are susceptible to synchrotron losses. A magnetic field of $B = 10^{-10} \ T$ was adopted. Both cases of $n=1$ and $n=2$ are shown.
• Figure 5: Maximum proton energy as a function of the breaking parameter $\delta_n^{(p)}$. Protons are accelerated via the first-order Fermi mechanism and are susceptible to synchrotron losses. A magnetic field of $B = 10^{-10} \ T$ was adopted. Both cases of $n=1$ and $n=2$ are shown.