  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 20 to 350 net counts) using the
XSPEC spectral model fitting package. The simulations employed both absorbed
thermal (APEC) and non-thermal (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, Gamma, and flux, and for different
background contamination levels. The distributions of these errors are studied
as a function of the 1 sigma quantiles and we show how these correlate with
different model parameters, net counts in the spectra and relative background
level. Maps of uncertainty in terms of the 1 sigma 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 useful for
computing Chandra ACIS-I exposure times for observation planning.
