Multi-Frequency Observations of pds70c Radio Emission Mechanisms in the Circumplanetary Environment

Aims. PDS 70c is a source of H alpha emission and variable sub-millimetre signal. Knowledge of the emission mechanisms may enable observations of accretion rates and physical conditions in the circumplanetary environment. Methods. We report ALMA observations of PDS 70 at 145 GHz (Band 4), 343.5 GHz (Band 7), and 671 GHz (Band 9) and compare them with archival data at 97.5 GHz (Band 3). The derived radio spectral energy distribution (SED) of PDS 70c is coeval within two months, and is interpreted in terms of analytic models of dusty and viscous discs (i.e. circumplanetary discs, CPDs). In a novel approach, we include the free-free continuum from H I, metals (e.g. K I) and H-. Results. New detections in Bands 3 (tentative at 2.6 sigma), 4 (5 sigma), and 7 (re-detected at 9 sigma) are consistent with optically thick thermal emission from PDS 70c (spectral index alpha = 2 +/- 0.2). However, a non-detection in Band 9 breaks this trend, with a flux density falling below an optically thick extrapolation at 2.6 sigma. A viscous dusty disc is inconsistent with the data, even with the inclusion of ionised jets. Interestingly, the central temperatures in such CPD models are high enough to ionise H I, with huge emission measures and an optically thick spectrum that marginally accounts for the radio SED (within 3 sigma of Band 9). Since there is no room for steeper components (with alpha > 2), the dust-to-gas ratio is lower than 10(-5). By contrast, uniform-slab models suggest much lower emission measures to account for the Band 9 drop, with ionisation fractions of similar to 10(-7) and an outer radius of similar to 0.1 au. Such conditions are recovered if the CPD interacts with a planetary magnetic field, leading to a radially variable viscosity, alpha(R) less than or similar to 1, and central temperatures of similar to 10(3) K that regulate metal ionisation. However, the H- opacity still results in an optically thick SED, overshooting Band 9. We find that the optically thin turnover at greater than or similar to 600 GHz is only recovered if a thin shocked layer is present at the CPD surface, as is suggested by simulations. A photospheric shock or accretion funnels are ruled out as radio emission sources because their small solid angles require T similar to 10(6) K, which are unrealistic temperatures in planetary shock accretion. Conclusions. The SED of PDS 70c collected here is optically thick up to Band 7 but probably (2.6 sigma) turns over towards Band 9. An optically thick spectrum can be explained by atomic plasma radiation from a magnetised disc, where the radio opacity stems from metal and H- free-free. If so, PDS 70c is depleted of sub-millimetre-emitting dust by a factor of at least 1000. However, the turnover can only be accounted for by H I free-free from an accretion shock at the surface of a CPD.