New Tests of Milli-lensing in the Blazar PKS 1413 + 135

Symmetric achromatic variability (SAV) is a rare form of radio variability in blazars that has been attributed to gravitational milli-lensing by a ~10²-10⁵ M _⊙ mass condensate. Four SAVs have been identified between 1980 and 2020 in the long-term radio monitoring data of the blazar PKS 1413 + 135. We show that all four can be fitted with the same, unchanging, gravitational lens model. If SAV is due to gravitational milli-lensing, PKS 1413 + 135 provides a unique system for studying active galactic nuclei with unprecedented microarcsecond resolution, as well as for studying the nature of the milli-lens itself. We discuss two possible candidates for the putative milli-lens: a giant molecular cloud hosted in the intervening edge-on spiral galaxy, and an undetected dwarf galaxy with a massive black hole. We find a significant dependence of SAV crossing time on frequency, which could indicate a fast shock moving in a slower underlying flow. We also find tentative evidence for a 989 day periodicity in the SAVs, which, if real, makes possible the prediction of future SAVs: the next three windows for possible SAVs begin in 2022 August, 2025 May, and 2028 February.