Constraining the entropy of formation from young transiting planets

Recently K2 and TESS have discovered transiting planets with radii between $\sim$ 5-10 R$_\oplus$ around stars with ages $<100$ Myr. These young planets are likely to be the progenitors of the ubiquitous super-earths/sub-neptunes, that are well studied around stars with ages $\gtrsim 1$ Gyr. The formation and early evolution of super-earths/sub-neptunes are poorly understood. Various planetary origin scenarios predict a wide range of possible formation entropies. We show how the formation entropies of young ($\sim$20-60 Myr), highly irradiated planets can be constrained if their mass, radius and age are measured. This method works by determining how low-mass a H/He envelope a planet can retain against mass-loss. This lower bound on the H/He envelope mass can then be converted into an upper bound on the entropy. If planet mass measurements with errors $\lesssim 20$\% can be achieved for the discovered young planets around DS Tuc A and V1298 Tau, then insights into their origins can be obtained. For these planets, higher measured planet masses would be consistent with standard core-accretion theory. In contrast, lower planet masses ($\lesssim 6-7$ M$_\oplus$) would require a "boil-off" phase during protoplanetary disc dispersal to explain.