Testing planet formation from the ultraviolet to the millimeter

Gaps imaged in protoplanetary discs are suspected to be opened by planets. We compute the present-day mass accretion rates $\dot{M}_{\rm p}$ of seven hypothesized gap-embedded planets, plus the two confirmed planets in the PDS 70 disc. The accretion rates are based on disc gas surface densities $\Sigma_{\rm gas}$ from C$^{18}$O observations, and planet masses $M_{\rm p}$ from simulations fitted to observed gaps. Assuming accretion is Bondi-like, we find in eight out of nine cases that $\dot{M}_{\rm p}$ is consistent with the time-averaged value given by the current planet mass and system age, $M_{\rm p}/t_{\rm age}$. As system ages are comparable to circumstellar disc lifetimes, these gap-opening planets may be undergoing their last mass doublings, reaching final masses of $M_{\rm p} \sim 10-10^2 \, M_\oplus$ for the non-PDS 70 planets, and $M_{\rm p} \sim 1-10 \, M_{\rm J}$ for the PDS 70 planets. For another fifteen gaps without C$^{18}$O data, we predict $\Sigma_{\rm gas}$ by assuming their planets are accreting at their time-averaged $\dot{M}_{\rm p}$. Bondi accretion rates for PDS 70b and c are orders of magnitude higher than accretion rates implied by measured U-band and H$\alpha$ fluxes, suggesting most of the accretion shock luminosity emerges in as yet unobserved wavebands, or that the planets are surrounded by dusty, highly extincting, quasi-spherical circumplanetary envelopes. Thermal emission from such envelopes or from circumplanetary discs, on Hill sphere scales, peaks at wavelengths in the mid-to-far-infrared and can reproduce observed mm-wave excesses.