The K2 Galactic Archaeology Program Data Release 2: Asteroseismic results from campaigns 4, 6, & 7

Studies of Galactic structure and evolution have benefitted enormously from Gaia kinematic information, though additional, intrinsic stellar parameters like age are required to best constrain Galactic models. Asteroseismology is the most precise method of providing such information for field star populations $\textit{en masse}$, but existing samples for the most part have been limited to a few narrow fields of view by the CoRoT and Kepler missions. In an effort to provide well-characterized stellar parameters across a wide range in Galactic position, we present the second data release of red giant asteroseismic parameters for the K2 Galactic Archaeology Program (GAP). We provide $\nu_{\mathrm{max}}$ and $\Delta \nu$ based on six independent pipeline analyses; first-ascent red giant branch (RGB) and red clump (RC) evolutionary state classifications from machine learning; and ready-to-use radius & mass coefficients, $\kappa_R$ & $\kappa_M$, which, when appropriately multiplied by a solar-scaled effective temperature factor, yield physical stellar radii and masses. In total, we report 4395 radius and mass coefficients, with typical uncertainties of $3.3\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $\kappa_R$ and $7.7\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $\kappa_M$ among RGB stars, and $5.0\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $\kappa_R$ and $10.5\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $\kappa_M$ among RC stars. We verify that the sample is nearly complete -- except for a dearth of stars with $\nu_{\mathrm{max}} \lesssim 10-20\mu$Hz -- by comparing to Galactic models and visual inspection. Our asteroseismic radii agree with radii derived from Gaia Data Release 2 parallaxes to within $2.2 \pm 0.3\%$ for RGB stars and $2.0 \pm 0.6\%$ for RC stars.