The DECam Ecliptic Exploration Project (DEEP): V. The Absolute Magnitude Distribution of the Cold Classical Kuiper Belt

The DECam Ecliptic Exploration Project (DEEP) is a deep survey of the trans-Neptunian solar system being carried out on the 4-meter Blanco telescope at Cerro Tololo Inter-American Observatory in Chile using the Dark Energy Camera (DECam). By using a shift-and-stack technique to achieve a mean limiting magnitude of $r \sim 26.2$, DEEP achieves an unprecedented combination of survey area and depth, enabling quantitative leaps forward in our understanding of the Kuiper Belt populations. This work reports results from an analysis of twenty 3 sq.\ deg.\ DECam fields along the invariable plane. We characterize the efficiency and false-positive rates for our moving-object detection pipeline, and use this information to construct a Bayesian signal probability for each detected source. This procedure allows us to treat all of our Kuiper Belt Object (KBO) detections statistically, simultaneously accounting for efficiency and false positives. We detect approximately 2300 candidate sources with KBO-like motion at S/N $>6.5$. We use a subset of these objects to compute the luminosity function of the Kuiper Belt as a whole, as well as the Cold Classical (CC) population. We also investigate the absolute magnitude ($H$) distribution of the CCs, and find consistency with both an exponentially tapered power-law, which is predicted by streaming instability models of planetesimal formation, and a rolling power law. Finally, we provide an updated mass estimate for the Cold Classical Kuiper Belt of $M_{CC}(H_r < 12) = 0.0017^{+0.0010}_{-0.0004} M_{\oplus}$, assuming albedo $p = 0.15$ and density $\rho = 1$ g cm$^{-3}$.