What determines the $\gamma$-ray luminosities of classical novae?

Classical novae in the Milky Way have now been well-established as high-energy GeV $\gamma$-ray sources. In novae with main-sequence companions, this emission is believed to result from shocks internal to the nova ejecta, as a later fast wind collides with an earlier slow outflow. To test this model and constrain the $\gamma$-ray production mechanism, we present a systematic study of a sample of recent Galactic novae, comparing their $\gamma$-ray properties ($\gamma$-ray luminosity and duration) with their outflow velocities, peak $V$-band magnitudes, and the decline times of their optical light curves ($t_2$). We uniformly estimate distances in a luminosity-independent manner, using spectroscopic reddening estimates combined with three-dimensional Galactic dust maps. Across our sample, $\gamma$-ray luminosities ($>$100 MeV) vary by three orders of magnitude, spanning $10^{34}-10^{37}$ erg s$^{-1}$. Novae with larger velocity of the fast outflow (or larger differential between the fast and slow outflow) have larger $\gamma$-ray luminosities, but are detectable for a shorter duration. The optical and $\gamma$-ray fluxes are correlated, consistent with substantial thermal emission in the optical from shock-heated gas. Across six novae with $\gamma$-ray and infrared light curves, evidence for dust formation appears soon after the end of the detected $\gamma$-ray emission. Dusty and non-dusty novae appear to have similar $\gamma$-ray luminosities, though novae that have more material processed by the shocks may be more likely to form dust. We find that the properties of the $\gamma$-ray emission in novae depend heavily on the ejecta properties, and are consistent with expectations for internal shocks.