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Since planet occurrence and primordial atmospheric retention probabilityincrease with period, the occurrence-weighted median planets discovered bytransit surveys may bear little resemblance to the low-occurrence, short-periodplanets sculpted by atmospheric escape ordinarily used to calibratemass--radius relations and planet formation models. An occurrence-weightedmass--radius relation for the low-mass planets discovered so far by transitsurveys orbiting solar-type stars requires both occurrence-weighted medianEarth-mass and Neptune-mass planets to have a few percent of their masses inhydrogen/helium (H/He) atmospheres. Unlike the Earth that finished forming longafter the protosolar nebula was dissipated, these occurrence-weighted medianEarth-mass planets must have formed early in their systems' histories. Theexistence of significant H/He atmospheres around Earth-mass planets confirms animportant prediction of the core-accretion model of planet formation. It alsoimplies core masses $M_{\text{c}}$ in the range $2~M_{\oplus}\lesssimM_{\text{c}}\lesssim 8~M_{\oplus}$ that can retain their primordialatmospheres. If atmospheric escape is driven by photoevaporation due to extremeultraviolet (EUV) flux, then our observation requires a reduction in thefraction of incident EUV flux converted into work usually assumed inphotoevaporation models. If atmospheric escape is core driven, then theoccurrence-weighted median Earth-mass planets must have large Bond albedos. Incontrast to Uranus and Neptune that have at least 10% of their masses in H/Heatmospheres, these occurrence-weighted median Neptune-mass planets are H/Hepoor. The implication is that they experienced collisions or formed in muchshorter-lived and/or hotter parts of their parent protoplanetary disks thanUranus and Neptune's formation location in the protosolar nebula.

the astrophysical journal

The Occurrence-weighted Median Planets Discovered by Transit Surveys  Orbiting Solar-type Stars and Their Implications for Planet Formation and  Evolution