The Nearby Evolved Stars Survey II: Constructing a volume-limited sample and first results from the James Clerk Maxwell Telescope

The Nearby Evolved Stars Survey (NESS) is a volume-complete sample of $\sim$850 Galactic evolved stars within 3\,kpc at (sub-)mm wavelengths, observed in the CO $J = $ (2$-$1) and (3$-$2) rotational lines, and the sub-mm continuum, using the James Clark Maxwell Telescope and Atacama Pathfinder Experiment. NESS consists of five tiers, based on distances and dust-production rate (DPR). We define a new metric for estimating the distances to evolved stars and compare its results to \emph{Gaia} EDR3. Replicating other studies, the most-evolved, highly enshrouded objects in the Galactic Plane dominate the dust returned by our sources, and we initially estimate a total DPR of $4.7\times 10^{-5}$ M$_\odot$ yr$^{-1}$ from our sample. Our sub-mm fluxes are systematically higher and spectral indices are typically shallower than dust models typically predict. The 450/850 $\mu$m spectral indices are consistent with the blackbody Rayleigh--Jeans regime, suggesting a large fraction of evolved stars have unexpectedly large envelopes of cold dust.