  We provide estimates of volcanism versus time for planets with Earth-like
composition and masses from 0.25 to 25 times Earth, as a step toward predicting
atmospheric mass on extrasolar rocky planets. Volcanism requires melting of the
silicate mantle. We use a thermal evolution model, calibrated against Earth, in
combination with standard melting models, to explore the dependence of
convection-driven decompression mantle melting on planet mass. Here we show
that (1) volcanism is likely to proceed on massive planets with plate tectonics
over the main-sequence lifetime of the parent star; (2) crustal thickness (and
melting rate normalized to planet mass) is weakly dependent on planet mass; (3)
stagnant lid planets live fast (they have higher rates of melting than their
plate tectonic counterparts early in their thermal evolution) but die young
(melting shuts down after a few Gyr); (4) plate tectonics may not operate on
high mass planets because of the production of buoyant crust which is difficult
to subduct; and (5) melting is necessary but insufficient for efficient
volcanic degassing - volatiles partition into the earliest, deepest melts,
which may be denser than the residue and sink to the base of the mantle on
young, massive planets. Magma must also crystallize at or near the surface, and
the pressure of overlying volatiles must be fairly low, if volatiles are to
reach the surface. If volcanism is detected in the Tau Ceti system, and tidal
forcing can be shown to be weak, this would be evidence for plate tectonics.
