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

TL;DR

This work resolves the macrolensing properties of PKS 1830-211 in gamma rays by applying long-term Fermi-LAT data and sophisticated time-series analysis, revealing a recurring time delay of $\tau_{AB} = 20.26 \pm 0.62$ days between images A and B with global significance $\sim 2.5 \times 10^{-5}$. A novel DACF-based method places an upper bound on the gamma-ray magnification ratio, $\mu_\gamma \lesssim 1.8$, and shows no compelling evidence for microlensing. The gamma-ray delay is in mild tension with radio-based estimates, suggesting possible emission-region offsets or radio-opaque gamma-ray production zones, and highlighting the potential of time-delay cosmography for PKS 1830-211 when combined with improved lens models. Overall, the study demonstrates the power of well-sampled light curves and rigorous lag statistics to disentangle lensing delays from stochastic variability in blazars.

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 $μ_γ \lesssim$ 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.

Figures (15)

• Figure 1: Estimates of the time delay $\tau_{AB}$ between the A and B images of PKS 1830$-$211. The value measured in this work (green) is in mild tension with the radio-average estimate from the literature (black), and with predictions from lens modeling based on radio observations (yellow). The lower panel reports $\gamma$-ray estimates (gray, filled circles), and radio estimates (black, filled squares). The study of Agarwal:2025 reports an approximate delay estimate, while in our previous work, Paper I, and of Abhir:2021, no delay measurement was inferred. The corresponding observational time windows and references are reported in italics.
• Figure 1: Time lag estimates for the six LC segments analysed in Section \ref{['sec:time_series']}, along with their local significances. Time lag errors are based on simulations reflecting the statistical and sampling properties of the data, adopting the PSD index of the specific LC segment for the simulations (see Section \ref{['sec:method']})
• Figure 2: Strong variability is evident throughout the entire 28-day bin LAT LC of PKS 1830$-$211 shown in the main panel. The six active states utilized in the time-series analysis (green) are listed in Table \ref{['tab:segments']}. A close-up view of these segments is presented in the insets, using a 1-day binning. Dashed yellow lines indicate the time intervals when the Sun is within $8^\circ$ of the ROI center, which were censored in the time-series analysis. Down arrows represent 95% upper limits.
• Figure 3: DACF of the long-term 1-day bin LAT LC (MJD 54682-60178) of PKS 1830$-$211 is shown in cyan. The DACF obtained by the detrended LC is shown in blue, along with the local significance levels.
• Figure 4: DACF for the six time segments analyzed in this work, listed in Table \ref{['tab:segments']}. The respective LCs are shown in the panels of Figure \ref{['fig:LAT_LC']}. The blue, orange, green dashed lines represent the $2\sigma$, $3\sigma$, $4\sigma$ local significance (Section \ref{['subsec:local_sign_method']}).