  X-ray sources with very few counts can be identified with low-noise X-ray
detectors such as ACIS onboard the Chandra X-ray Observatory. These sources are
often too faint for parametric spectral modeling using well-established methods
such as fitting with XSPEC. We discuss the estimation of apparent and intrinsic
broad-band X-ray fluxes and soft X-ray absorption from gas along the line of
sight to these sources, using nonparametric methods. Apparent flux is estimated
from the ratio of the source count rate to the instrumental effective area
averaged over the chosen band. Absorption, intrinsic flux, and errors on these
quantities are estimated from comparison of source photometric quantities with
those of high S/N spectra that were simulated using spectral models
characteristic of the class of astrophysical sources under study. The concept
of this method is similar to the long-standing use of color-magnitude diagrams
in optical and infrared astronomy, with X-ray median energy replacing color
index and X-ray source counts replacing magnitude. Our nonparametric method is
tested against the apparent spectra of 2000 faint sources in the Chandra
observation of the rich young stellar cluster in the M17 HII region. We show
that the intrinsic X-ray properties can be determined with little bias and
reasonable accuracy using these observable photometric quantities without
employing often uncertain and time-consuming methods of non-linear parametric
spectral modeling. Our method is calibrated for thermal spectra characteristic
of stars in young stellar clusters, but recalibration should be possible for
some other classes of faint X-ray sources such as extragalactic AGN.
