Directly Detecting the Envelopes of Low-mass Planets Embedded In Protoplanetary Discs and The Case For TW Hydrae

Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1-D models and 3-D simulations to calculate the envelopes around low-mass cores (several to tens of $M_{\oplus}$) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is optically thin at radio wavelengths, radio observations can see through the disc and probe the denser envelope within the planet's Hill sphere. When the optically thin disc is observed with the resolution reaching one disc scale height, the radio thermal flux from the planetary envelope around a 10 M$_{\oplus}$ core is more than 10 % higher than the flux from the background disc. The emitting region can be extended and elongated. Finally, our model suggests that the au-scale clump at 52 au in the TW Hydrae disc revealed by ALMA is consistent with the envelope of an embedded 10-20 $M_{\oplus}$ planet, which can explain the detected flux, the spectral index dip, and the tentative spirals. The observation is also consistent with the planet undergoing pebble accretion. Future ALMA and ngVLA observations may directly reveal more such low-mass planets, enabling us to study core growth and even reconstruct the planet formation history using the embedded "protoplanet" population.