Multi-frequency observations of PDS 70c: Radio emission mechanisms in the circum-planetary environment

TL;DR

This study presents near-coeval ALMA observations of PDS 70c across Bands 3–9 and interprets the radio SED with analytic circumplanetary disc models that include HI free-free, metal/free-free, and H− opacity. Dust-only CPD models fail to reproduce the Band 9 turnover, while free-free emission from ionised CPD gas—potentially enhanced by magnetic disc processes—provides a viable explanation, though Band 9 constraints require careful treatment of H− opacity and surface-layer physics. A uniform slab approach and CPD surface-shock simulations offer a plausible pathway to the observed turnover, with the surface-shock scenario emerging as the most natural match to the data. The results imply a strongly dust-depleted CPD and place meaningful limits on the planetary accretion rate and magnetic field, highlighting the diagnostic power of multi-frequency radio observations for characterising circumplanetary environments and accretion physics.

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.

Figures (16)

• Figure 1: Multi-frequency imaging of PDS 70. The black insets at the top left of each image zoom on the central region (with tick-marks separated by $0\overset{\prime\prime}{.}1$), while the orange insets at the bottom right zoom on the expected position of PDS 70c for circular Keplerian rotation around a $0.97\,M_{\odot}$ star (with tick-marks at $0\overset{\prime\prime}{.}05$). The red plus symbol in the central inset marks the nominal position of the star. In all insets the linear grey scale stretches over the range of intensities in each region, and the contour levels start at $3\,\sigma$ and are incremented in units of $\sigma$. Intensities within each contour level are colour-coded differently. The two circles are centred on the positions of PDS 70b and PDS 70d (no radio counterparts are detected). Images in $a)$ to $d)$, along the top row, correspond to restorations of the corresponding non-parametric model images (that fit the visibility data), in $e)$ to $h)$, along the bottom row. A beam ellipse in $a)$ to $d)$ is shown in blue, on the top right. The pixel size in the model images is fixed at $4\times4\,$mas$^2$. For each band the Briggs parameter used for the restoration, the clean bean and the noise can be found in Table \ref{['tab:summary']}.
• Figure 2: Point-source injections tests in Band 9. a) Same as Fig. \ref{['fig:summary']}, with additional insets. b) Same as a) but with four point sources, injected at the centre of each inset, and with a flux density corresponding to an optically thick extrapolation of the Band 7 flux density for PDS 70c.
• Figure 3: Dirty maps in natural weights of the residual Band 7 visibilities, after subtraction of the disc. The grey scale stretches over the full intensity scale, and for each of seven epochs. The inset zooms into PDS 70c, with contours at 90 and 120 $\mu$Jy beam$^{-1}$, fixed for ease of comparison across epochs. As in Fig. \ref{['fig:summary']}, the circles are centred on PDS 70b and d, and are drawn here to ease the search for any variable counterparts.
• Figure 4: Flux density of PDS 70c at 343.5 GHz (Band 7), as a function of Julian day. The scatter is consistent with the uncertainties.
• Figure 5: Corner plot for synthetic data. The orange posteriors show the synthetic optically thin case, calculated with $\dot{M}_{\rm p}=10^{-9} \, M_{\rm Jup}\, {\rm yr}^{-1}$ and $\alpha=10^{-3}$. The outcome illustrates the degeneracy between $\dot{M}_{\rm p}$ and $\alpha$ inherent to the parametric CPD model of Zhu2018MNRAS.479.1850Z. The grey posteriors show the synthetic optically thick case, calculated with $\dot{M}_{\rm p}=10^{-5} \, M_{\rm Jup}\, {\rm yr}^{-1}$ (and the same $\alpha=10^{-3}$). Both synthetic SEDs were obtained using only the dust component of the CPD model following Zhu2018MNRAS.479.1850Z, with errors set to 10% of the flux.