Planetary masses and radii

Since planet occurrence and primordial atmospheric retention probability increase with period, the occurrence-weighted median planets discovered by transit surveys may bear little resemblance to the low-occurrence, short-period planets sculpted by atmospheric escape ordinarily used to calibrate mass-radius relations and planet formation models. An occurrence-weighted mass-radius relation for the low-mass planets discovered so far by transit surveys orbiting solar-type stars requires both occurrence-weighted median Earth-mass and Neptune-mass planets to have a few percent of their masses in hydrogen/helium (H/He) atmospheres.

Unlike the Earth that finished forming long after the protosolar nebula was dissipated, these occurrence-weighted median Earth-mass planets must have formed early in their systems' histories. The existence of significant H/He atmospheres around Earth-mass planets confirms an important prediction of the core-accretion model of planet formation. It also implies core masses M_c_ in the range 2 M_{Earth}_<~M_c_<~8M_{Earth}_ that can retain their primordial atmospheres.