\[erg s$^{-1}$\] in the [*ROSAT*]{} PSPC energy band ($0.1-2.4$ keV): $<28.20> \pm 0.79$ for MS F-type stars; $<27.94> \pm 1.02$ for MS G-type stars; $<27.86> \pm 0.65$ for MS K-type stars; and $<27.44> \pm 0.76$ for MS M-type stars. For giant stars, we adopt $<28.91> \pm 0.86$ [@Pizzolato00]. X-ray spectral shapes were assumed to follow the stellar temperature-luminosity relations of @Gudel98 and @Pizzolato00 for MS and giant stars, respectively. The adopted temperature-luminosity relations in the [*ROSAT*]{} ($0.1-2.4$ keV) band are: $\log(T)$ \[MK\] $=-9.2 + 0.33\log(L_X)$ \[erg s$^{-1}$\] for MS stars and $\log(T)$ \[MK\] $=-5.1 + 0.2\log(L_X)$ \[erg s$^{-1}$\] for giants.

Third, given the X-ray luminosity in the [*ROSAT*]{} ($0.1-2.4$ keV) band, spectrum, distance, and line-of-sight absorption for each of the simulated stars, the count rate in the $Chandra$ ACIS detector in the ($0.5-8.0$ keV) band is obtained using the Portable Interactive Multi-Mission Simulator (PIMMS[^4])[^5]. The detectability of each simulated star is then evaluated by locally-defined thresholds of the source significance statistic, similar to our treatment of extragalactic contaminants (§ \[contaminants\_agn\_section\]). For the stars that satisfy the detection threshold, the XSPEC [*fakeit*]{} command was used to simulate the spectrum to derive X-ray median energies for individual stars.

A typical run of 