  The habitable zone (HZ) around a star is typically defined as the region
where a rocky planet can maintain liquid water on its surface. That definition
is appropriate, because this allows for the possibility that carbon-based,
photosynthetic life exists on the planet in sufficient abundance to modify the
planet's atmosphere in a way that might be remotely detected. Exactly what
conditions are needed, however, to maintain liquid water remains a topic for
debate. Historically, modelers have restricted themselves to water-rich planets
with CO2 and H2O as the only important greenhouse gases. More recently, some
researchers have suggested broadening the definition to include arid, 'Dune'
planets on the inner edge and planets with captured H2 atmospheres on the outer
edge, thereby greatly increasing the HZ width. Such planets could exist, but we
demonstrate that an inner edge limit of 0.59 AU or less is physically
unrealistic. We further argue that conservative HZ definitions should be used
for designing future space-based telescopes, but that optimistic definitions
may be useful in interpreting the data from such missions. In terms of
effective solar flux, Seff, the recently recalculated HZ boundaries are: recent
Venus-1.78, runaway greenhouse-1.04, moist greenhouse-1.01, maximum
greenhouse-0.35, early Mars-0.32. Based on a combination of different HZ
definitions, the frequency of potentially Earth-like planets around late-K and
M stars observed by Kepler is in the range of 0.4-0.5.
