Instrument Performance and Sensitivity

The performance of the SXRP is critically dependent on the effective area of the SODART telescope. Detailed evaluation of the performance of the SXRP will be presented after the SODART design is finalized.

The instrument sensitivity has been described in detail in a paper by Kaaret et al. (1994; SPIE, 2010, 22). Polarized radiation from a source will produce a modulation in the detected source count rate at twice the frequency of rotation of the polarization analyzers. THe count rate can be decomposed into a Fourier series in azimuthal angle given by

$$N(\phi)= \Sigma a_n \cos [n(\phi-\phi_n)].$$ (1)

The magnitude of the polarization of the source is then given as $P=a_2(r+b)/a_0 \mu r$ where $\mu$ is the modulation factor, r is the source counting rate, and b is the background counting rate. The modulation factor for is the modulation in the rate for 100% linearly polarized X-rays in the absence of background. The position angle of the polarization is given by $\phi_2$. In a time T, the minimum detectable polarization, MDP, that can be detected at 99% confidence can be expressed as:

$${\rm MDP}= \frac{4.29}{\mu r} \sqrt((r+b)/T.$$ (2)

The MDP given above corresponds to a $2.6\sigma$ detection.

The expected and measured telescope effective areas and detector efficiencies can be used to estimate MDP. The effective area of the lithium polarimeter has a maximum of $65{\rm cm}^{2}$ at 9keV. The modulation factor, mu, varies from 0.77 at 6keV to 0.71 at 20keV. The detector efficiency is calculated to be 79% at 2.6keV and 97% at 5.2 keV. For the Bragg crystal polarimeter, the modulation factor $\mu$ exceeds 99%. A spectrum of 10E^-2.05cm-2 photons cm-2 sec-1has been assumed along with an interstellar absorption of $3\times10^{21}$cm-2. This spectrum yields a flux of $2.4\times10^{-8}$ ergs cm-2 sec-1 in the 2-10 keV band. The background was assumed to be $3\times 10^{-3}$ cts cm-2 sec-1 keV-1. For the graphite polarimeter, the background was integrated over an image diameter of 14 arcminutes. For the lithium polarimter, the signal was integrated over an energy band of 6-12 keV. Note that a single integration will produce three polarization measurements: two in narrow energy bands at 2.6keV and 5.2keV and a broad band measurement from 6-12keV which in principle can be resolved in energy if sufficient statistics are available.