“generic” 2MASS $J$-band detection completeness curve from @Skrutskie06[^6].

Several results emerge from the $J$-band magnitude distributions. First, the histogram of the simulated foreground population has two peaks (red curve). The fainter peak from M-type field dwarfs, constituting $\sim40$% of the simulated foreground population, lies below the 2MASS sensitivity limit of $J \sim 16.5-17$ mag. A bimodal shape is indeed seen in the deeper HAWK-I $J$-band magnitude histogram of the CCCP sources with $MedE < 1.1$ keV [@Preibisch11]. Second, for bright stars with $J \la 16$ mag, the $J$-band magnitude histogram of the simulated foreground population (red curve) agrees well both in number and shape with the magnitude distribution of CCCP sources with median energies $<1.1$ keV (black dashed curve). This indicates, in agreement with the low-$MedE$ distributions discussed in § \[me\_contamination\_subsection\], that most of the observed CCCP sources in this sub-sample can be attributed to foreground stars. Third, roughly 60% of the simulated stellar background population lies below the 2MASS sensitivity limit of $J \ga 16.5$ mag. Fourth, most of the simulated extragalactic objects lie below $J=21$ mag. The HAWK-I survey can detect some of these extragalactic objects near its detection limit [@Preibisch11].

Spatial Distributions Stratified by Median Energy and 