tokens: from this distribution to infer a simulated distribution for the X-ray non-detected sources (see Figure 8 ). This result provides additional support for the need for a large population of CT AGNs to explain the black hole mass density while adhering to constraints imposed by the cosmic X-ray background (Comastri et al. 2015 ). It should be noted the distributions presented here are derived from modeled X-ray data with certain assumptions (e.g., source redshift, photon index, lack of intervening dust on larger scales), and that a more thorough treatment is required to understand the underlying distributions. A detailed analysis of such modeling is left for future work. 4.4. X-Ray Stacking Analysis As an additional test of our ability to select heavily obscured AGNs with no X-ray counterparts, we performed an X-ray stacking analysis using stackfast . 10 10 http://www.dartmouth.edu/stackfast/ For this analysis we chose to focus strictly on sources within the Chandra footprint, as Chandra yields the highest S/N of our three X-ray observatories. The stackfast software uses pre-reduced Chandra ACIS data products based on individual observations to match against a set of input sources. The pre-reduction stage allows stackfast to work much more efficiently than other stacking methods, as the data are only sorted and screened once, at initialization; the result is a set of stackable X-ray events containing position, energy, grade, and exposure times for each source within the master set of Chandra observations. For each of the sources in our sample, we extracted photon counts and exposure times in both soft (0.5–2 keV) and hard (2–7 keV) energies, and estimated X-ray fluxes and luminosities (see Table 6 ). Fluxes are computed using count-rate-to-flux ratios characteristic of Chandra ACIS-I responses in Cycle 12 (in approximately the middle time frame of the observations in our stacking analyses), and assuming a power-law spectrum with typical Galactic absorption ( = cm) and photon index Γ = 1.4. This spectral shape is broadly consistent with the observed ratios of hard and soft source counts in our stacking analyses as shown in Table 6 . The count-rate-to-flux ratios adopted are 1.11 × 10 erg cm count (0.5–2 keV count rate to 0.5–2 keV flux) and 3.04 × 10 erg cm count (2–7 keV count rate to 2–10 keV flux). We obtained uncertainties in the stacked flux by bootstrap resampling of the input sources. This yields uncertainties on the average flux for the sample, which reflect the distribution in input fluxes and are typically larger than Poisson photon counting uncertainties. Additional details regarding stackfast can be found in earlier implementations of the code (e.g., Hickox et al. 2007 ; Chen et al. 2013 ; Goulding et al. 2017 ). Table 6 X-Ray Stacking Data and Results Note. X-ray stacking results for energy ranges of 0.5–2 and 2–7 keV. For each energy range, we present exposure time, photon counts, and flux and luminosity estimates. The flux and
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