Axion effects on gamma-ray spectral irregularities. II: Implications of EBL absorption

The extragalactic background light (EBL) plays a crucial role in the propagation of high-energy particles throughout the Universe. In this work, we explore the impact of the EBL absorption effect on photon to axionlike particle (ALP) conversions from the very-high-energy gamma-ray spectral irregularities. For our purpose, we select four BL Lac blazars: Markarian 501, 1ES 0229+200, PKS 0301-243, and PKS 0447-439 for analysis. Their redshifts range from approximately 0.03 to 0.34. We first discuss the EBL absorption effect on the gamma-ray spectral energy distributions (SEDs) using three common EBL spectral models: Finke-10, Franceschini-17, and Saldana-Lopez-21. Then we consider the photon-ALP conversions in astrophysical magnetic fields. The best-fit chi-square distributions of these EBL models under the ALP assumption in the ALP parameter $\{m_a, g_{a\gamma}\}$ plane are provided, showing similar distributions. For comparison, we define a new delta chi-square, $\chi_d^2$, to quantify the difference in chi-square values. The distributions of $\chi_d^2$ and the gamma-ray SEDs corresponding to the maximum delta chi-square, $\chi^2_{d, \rm max}$, are also presented for comparison. Our results indicate that the influence of these different EBL models is non-dominant at the low-redshift gamma-ray axionscope. In these cases, choosing the latest model, Saldana-Lopez-21, is sufficient. However, as the redshift of the sources increases, this influence becomes more significant.