Recovering the O VII Absorption Distributions from X-Ray Data

The absorption by gas toward background continuum sources informs us about the cosmic density of gas components as well as the hosts responsible for the absorption (galaxies, clusters, cosmic filaments). Cosmic absorption line distributions are distorted near the detection threshold (S/N $\approx 3$) due to true lines being scattered to lower S/N and false detections occurring at the same S/N. We simulate absorption line distributions in the presence of noise and consider two models for recovery: a parametric fitting of the noise plus a cut-off power law absorption line distribution; a non-parametric fit where the negative absorption line distribution (emission lines) is subtracted from the positive S/N absorption line distribution (flip and subtract). We show that both approaches work equally well and can use data where S/N$\gtrsim$3 to constrain the fit. For an input of about 100 absorption line systems, the number of systems is recovered to $\approx$14%. This investigation examined the O VII X-ray absorption line distribution, but the approach should be broadly applicable for statistically well-behaved data.