# X-ray Spectro-polarimetry with Photoelectric Polarimeters

## TL;DR

This paper extends X-ray spectroscopy fitting methods to include polarization data, enabling joint analysis of intensity and polarization spectra for next-generation space polarimeters.

## Contribution

It introduces a generalized forward fitting approach that incorporates polarization sensitivity through joint fitting of three spectra, including polarization parameters.

## Key findings

- Simulations demonstrate the method's effectiveness with PRAXyS parameters.
- The approach allows accurate modeling of polarization and intensity spectra.
- Discussion on calibration and operation of photoelectric polarimeters.

## Abstract

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.