2023ApJS..269....8W

The Chandra Cygnus OB2 Legacy Survey is a wide and deep X-ray survey of the nearby and massive Cygnus OB2 association. The survey has detected ∼8000 X-ray sources, the majority of which are pre-main-sequence X-ray-emitting young stars in the association itself. To facilitate quantitative scientific studies of these sources, as well as the underlying OB association, it is important to understand the sensitivity of the observations and the level of completeness the observations have obtained. Here we describe the use of a hierarchical Monte Carlo simulation to achieve this goal by combining the empirical properties of the observations, analytic estimates of the source verification process, and an extensive set of source detection simulations. We find that our survey reaches a 90% completeness level for a pre-main-sequence population at the distance of Cyg OB2 at an X-ray luminosity of 4 × 10³⁰ erg s^–1 and a stellar mass of 1.3 M_⊙ for a randomly distributed population. For a spatially clustered population such as Cyg OB2 the 90% completeness level is reached at 1.1 M_⊙ instead, as the sources are more concentrated in areas of our survey with a high exposure. These simulations can easily be adapted for use with other X-ray observations and surveys, and we provide X-ray detection efficiency curves for a very wide array of source and background properties to allow these simulations to be easily exploited by other users.