  We present a novel method for determining the surface density of
protoplanetary disks through consideration of disk 'dust lines' which indicate
the observed disk radial scale at different observational wavelengths. This
method relies on the assumption that the processes of particle growth and drift
control the radial scale of the disk at late stages of disk evolution such that
the lifetime of the disk is equal to both the drift timescale and growth
timescale of the maximum particle size at a given dust line. We provide an
initial proof of concept of our model through an application to the disk TW Hya
and are able to estimate the disk dust-to-gas ratio, CO abundance, and
accretion rate in addition to the total disk surface density. We find that our
derived surface density profile and dust-to-gas ratio are consistent with the
lower limits found through measurements of HD gas. The CO ice line also depends
on surface density through grain adsorption rates and drift and we find that
our theoretical CO ice line estimates have clear observational analogues. We
further apply our model to a large parameter space of theoretical disks and
find three observational diagnostics that may be used to test its validity.
First we predict that the dust lines of disks other than TW Hya will be
consistent with the normalized CO surface density profile shape for those
disks. Second, surface density profiles that we derive from disk ice lines
should match those derived from disk dust lines. Finally, we predict that disk
dust and ice lines will scale oppositely, as a function of surface density,
across a large sample of disks.
