  Smaller terrestrial planets (< 0.3 Earth masses) are less likely to retain
the substantial atmospheres and ongoing tectonic activity probably required to
support life. A key element in determining if sufficiently massive "sustainably
habitable" planets can form is the availability of solid planet-forming
material. We use dynamical simulations of terrestrial planet formation from
planetary embryos and simple scaling arguments to explore the implications of
correlations between terrestrial planet mass, disk mass, and the mass of the
parent star. We assume that the protoplanetary disk mass scales with stellar
mass as Mdisk ~ f Mstar^h, where f measures the relative disk mass, and 1/2 < h
< 2, so that disk mass decreases with decreasing stellar mass. We consider
systems without Jovian planets, based on current models and observations for M
stars. We assume the mass of a planet formed in some annulus of a disk with
given parameters is proportional to the disk mass in that annulus, and show
with a suite of simulations of late-stage accretion that the adopted
prescription is surprisingly accurate. Our results suggest that the fraction of
systems with sufficient disk mass to form > 0.3 Earth mass habitable planets
decreases for low-mass stars for every realistic combination of parameters.
This "habitable fraction" is small for stellar masses below a mass in the
interval 0.5 to 0.8 Solar masses, depending on disk parameters, an interval
that excludes most M stars. Radial mixing and therefore water delivery are
inefficient in lower-mass disks commonly found around low-mass stars, such that
terrestrial planets in the habitable zones of most low-mass stars are likely to
be small and dry.
