The Statistical Uncertainties on X-Ray Flux and Spectral Parameters from Chandra ACIS-I Observations of Faint Sources: Application to the Cygnus OB2 Association

Abstract

We investigate the uncertainties of fitted X-ray model parameters and fluxes for relatively faint Chandra ACIS-I source spectra. Monte Carlo (MC) simulations are employed to construct a large set of 150,000 fake X-ray spectra in the low photon count statistics regime (from 10 to 350 net counts) using the XSPEC spectral model-fitting package. The simulations employed both absorbed thermal (APEC) and nonthermal (power-law) models, in concert with the Chandra ACIS-I instrument response and interstellar absorption. Simulated X-ray spectra were fit assuming a wide set of different input parameters and C-statistic minimization criteria to avoid numerical artifacts in the accepted solutions. Results provide an error estimate for each parameter (absorption, NH, plasma temperature, kT, or power-law slope, Γ, and flux) and for different background contamination levels. The distributions of these errors are studied as a function of the 1σ quantiles, and we show how these correlate with different model parameters, net counts in the spectra, and relative background levels. Maps of uncertainty in terms of the 1σ quantiles for parameters and flux are computed as a function of spectrum net counts. We find very good agreement between our estimated X-ray spectral parameter and flux uncertainties and those recovered from spectral fitting for a subset of the X-ray sources detected in the Chandra Cygnus OB2 Legacy Survey diagnosed to be association members and that have between 20 and 350 net counts. Our method can provide uncertainties for spectral parameters whenever formal X-ray spectral fits cannot be well constrained, or are unavailable, and predictions are useful for computing Chandra ACIS-I exposure times for observation planning.