  (Abridged) Inspired by the Kepler planet discoveries, we consider the thermal
contraction of planets close to their parent star, under the influence of
evaporation. The mass-loss rates are based on hydrodynamic models of
evaporation that include both X-ray and EUV irradiation. We find that only
low-mass planets with hydrogen envelopes are significantly affected by
evaporation, with evaporation being able to remove massive hydrogen envelopes
inward of 0.1 AU for Neptune-mass objects.
  We construct a theoretical population of planets with varying core masses,
envelope masses, orbital separations, and stellar spectral types, and compare
these against the sizes and densities measured for low-mass planets, both in
the Kepler mission and from radial velocity surveys. This exercise leads us to
conclude that evaporation is the driving force of evolution for close-in Kepler
planets. In fact, some 50% of the Kepler planet candidates may have been
significantly eroded. Evaporation explains two striking correlations observed
in these objects: a lack of large radius/low density planets close to the
stars, and a bimodal distribution in planet sizes with a deficit of planets
around 2R_E. Planets that have experienced high X-ray exposures are generally
smaller than this size, and those with lower X-ray exposures are typically
larger. A bimodal distribution is naturally explained by the evaporation model,
where, depending on their X-ray exposure, close-in planets can either hold on
to hydrogen envelopes 1% in mass, or be stripped entirely.
  To quantitatively reproduce the observed features, we argue that not only do
low-mass Kepler planets need to be made of rocky cores overlaid with hydrogen
envelopes, but few of them should have initial masses above 20 M_E, and the
majority of them should have core masses of a few Earth masses.
