Gamma-ray Time Delay and Magnification Ratio in the Gravitationally-Lensed Blazar PKS 1830-211

Abstract

We present the characterization of macrolensing properties of the gravitationally lensed system PKS 1830-211, utilizing data from the Fermi Large Area Telescope. While at gamma-rays we can not spatially resolve the lensed images, a macrolensing-induced time pattern is expected in the blazar's lightcurve, resulting from the delay between variable gamma-ray components originating from its two brightest lensed images. Compared to our previous study, here we employ high-quality lightcurves coupled with prolonged outburst activity, and improved time-series techniques. Analyzing six independent data segments, we identified a delay of 20.26 +/- 0.62 days (statistical and stochastic uncertainty), with a chance detection probability at the 2.5 x $10^{-5}$ level (post-trial). We also present a novel approach to the magnification ratio estimate based on a comparison with simulated data. Our work suggests that the gamma-ray flux ratio between the two main lens components is $\mu_{\gamma} \lesssim$ 1.8. We do not observe convincing evidence of microlensing effects, as previously claimed. The measured gamma-ray time delay is in 2-sigma tension with radio-based estimates, suggesting either distinct emission sites, underestimated radio uncertainties, or gamma-ray production in a region opaque to radio. Our study highlights the potential of well sampled lightcurves and advanced time-series techniques to distinguish true lensing-induced delays from stochastic variability. When combined with improved radio constraints and refined lens models, PKS 1830-211 and similar sources constitute promising systems for time-delay cosmography, offering new insights into both jet structure and cosmological parameters.