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Abstract

PDS 70c is a source of Ha emission and variable sub-mm signal. Understanding its emission mechanisms may enable observations of accretion rates and physical conditions in the circum-planetary environment. We report ALMA observations of PDS 70 at 145 GHz (Band 4), 343.5 GHz (Band 7) and 671 GHz (Band 9) and compare with data at 97.5 GHz (Band 3), taken within two months. The radio spectrum (SED) is analyzed with an analytical circumplanetary disk (CPD) model. In a novel approach including the free-free continuum from H I, metals (e.g. K I) and H-. New detections in Bands 3 (tentative at 2.6sigma), 4 (5sigma), and 7 (re-detected at 9sigma) are consistent with optically thick thermal emission from PDS 70c (spectral index 2+-0.2). However, a Band 9 non-detection lies 2.6sigma below an optically thick extrapolation. A viscous dusty disk 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 SED (within 3sigma of Band 9). By contrast, uniform-slab models suggest much lower emission measures to account for the Band 9 drop, with ionisation fractions ~1e-7, and an outer radius ~0.1 au. Such conditions are recovered if the CPD interacts with a planetary magnetic field, leading to a radially variable viscosity alpha(R)<~1 and midplane temperatures ~1e3 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 ~600 GHz is only recovered if a thin shocked layer is present at the CPD surface, as suggested by simulations. A photospheric shock or accretion funnels are ruled out as radio emission sources because their small solid angles would require T~1e6 K, which is unrealistic for planetary accretion.