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

We present the detection of a time delay between variable $\gamma$-ray components originating from the two brighter gravitationally lensed images of the blazar PKS 1830-211, utilizing data from the Large Area Telescope (LAT) on board the \textit{Fermi} Gamma-ray Space Telescope. The accurate $\gamma$-ray measurement was possible thanks to high-quality light curves enabled by the long, continuous observations by the LAT, coupled with strong outburst activity in 2019-2020. We analyzed six flaring episodes independently using an auto-correlation function analysis. We employed a new, improved methodology for the detrending of the $\gamma$-ray light curve, i.e. the removal of the underlying low-frequency trend. We identified a delay of $20.26 \pm 0.62$ days (statistical and stochastic uncertainty) with a chance detection probability of $2.5 \times 10^{-5}$. This is $\sim 5$ days shorter than previous radio measurements. Additional delay patterns emerged from the time series analysis of the light curves, none of which could be convincingly attributed to the putative third lensed image of the blazar.