  Many exoplanets have been discovered with radii of 1-4 Earth radii, between
that of Earth and Neptune. A number of these are known to have densities
consistent with solid compositions, while others are "sub-Neptunes" likely to
have significant hydrogen-helium envelopes. Future surveys will no doubt
significantly expand these populations. In order to understand how the measured
masses and radii of such planets can inform their structures and compositions,
we construct models both for solid layered planets and for planets with solid
cores and gaseous envelopes, exploring a range of core masses, hydrogen-helium
envelope masses, and associated envelope entropies. For planets in the
super-Earth/sub-Neptune regime for which both radius and mass are measured, we
estimate how each is partitioned into a solid core and gaseous envelope,
associating a specific core mass and envelope mass with a given exoplanet. We
perform this decomposition for both "Earth-like" rock-iron cores and pure ice
cores, and find that the necessary gaseous envelope masses for this important
sub-class of exoplanets must range very widely from zero to many Earth masses,
even for a given core mass. This result bears importantly on exoplanet
formation and envelope evaporation processes.
