  We derive a generalization of forward fitting for X-ray spectroscopy to
include linear polarization of X-ray sources, appropriate for the anticipated
next generation of space-based photoelectric polarimeters. We show that the
inclusion of polarization sensitivity requires joint fitting to three observed
spectra, one for each of the Stoke's parameters, I(E), U(E), and Q(E). The
equations for Stoke's I(E) (the total intensity spectrum) are identical to the
familiar case with no polarization sensitivity, and for which the
model-predicted spectrum is obtained by a convolution of the source spectrum,
F(E'), with the familiar energy response function, e(E')*R(E', E), where e(E')
and R(E', E) are the effective area and energy redistribution matrix,
respectively. In addition to the energy spectrum, the two new relations for
U(E) and Q(E) include the source polarization fraction and position angle
versus energy, a(E'), and psi'_0(E'), respectively, and the model-predicted
spectra for these relations are obtained by a convolution with the "modulated"
energy response function, m(E')*e(E')R(E, E'), where m(E') is the
energy-dependent modulation fraction that quantifies a polarimeter's angular
response to 100% polarized radiation. We present results of simulations with
response parameters appropriate for the proposed PRAXyS Small Explorer
observatory to illustrate the procedures and methods, and we discuss some
aspects of photoelectric polarimeters with relevance to understanding their
calibration and operation.
