Hourly radio variability of PDS70c from time-differential photometry

The radio emission mechanisms from accreting protoplanets, and their variability, link observations and physical properties. We revisit the variability of the ~343GHz (ALMA Band7) flux density from PDS70c (F_B7). The subtraction of the extended time-averaged signal may enable the measurement of the flux density from variable and embedded point sources. Visibility alignment and self-calibration yields close to thermal residuals in each execution block (EB) of ALMA observations, allowing the time-differential photometry of point-source in the visibility domain. The variability of PDS70c is checked against synthetic control point sources. In images of the 2017 ALMA dataset, with three ~1h EBs, PDS70c was detected only on 6 Dec. 2017, where F_B7 rose by 228%+-69% (3.3sigma). Time-differential photometry confirms a rise by 170%+-46% (3.7sigma). An application to ~2h EBs from the 2023 dataset resulted in constant flux densities, within a scatter of ~15%. However, F_B7(t) shows some scatter when splitting the deep 2023 EBs in 20min intervals, with a chi2 test significant at 2.6sigma, and an intrinsic dispersion of 49%21%. The radio variability of PDS70c, observed over hours but averaged out on longer timescales, is indeed expected if the signal is due to HI free-free from an accretion shock on a circum-planetary disk surface. A planet-to-environment mass ratio <1E-4 is required to avoid smoothing by radiative diffusion if the signal is due to thermal emission from the environment.