POLARIZATION MEASUREMENTS

The SXRP exploits the polarization dependence of Bragg reflection from a graphite crystal, and of Thomson scattering from a target of metallic lithium. A "physicist's view" of the instrument is shown in Figure 1. The polarization analyzers for the SXRP consist of a very thin mosaic graphite crystal mounted above a cylindrical lithium scattering target. The graphite crystal and lithium target are centered on the optical axis of the SODART X-ray telescope and are surrounded by four imaging proportional counters (IPCs) that detect the Bragg reflected and Thomson scattered X-rays.

The portion of the SXRP shown in Figure 1 rotates about the optical axis of the telescope with a period of approximately 2 minutes. We have found that a very thin mosaic graphite crystal can be used to efficiently reflect X-rays meeting the Bragg condition, while allowing the X-rays that do not satisfy the Bragg condition to pass through the crystal with only moderate attenuation. This stacked grapite-lithium configuration permits us to obtain data from both polarization elements simultaneously, greatly improving the observing efficiency of the instrument.

LITHIUM POLARIMETER

The angular distribution of X-rays scattered from the lithium target depends on the polarization of the incident X-rays according to the Thomson scattering cross-section:

where theta is the polar angle measured from the direction of propagation and phi is the azimuthal angle measured from the direction of the photon electric field vector. Maximum scattering occurs when the photon is scattered through an azimuthal angle that is perpendicular to the photon electric field vector. Therefore, if the incident radiation is polarized, the count rate will be modulated at twice the rotation frequency of the polarimeter. The energy band pass for the lithium polarimeter extends from 5 keV, limited by photoelectric absorption, up to 15 keV, limited by the reflectivity of the SODART telescope.

GRAPHITE POLARIMETER

The signature of polarization is a modulation in the count rate of the detectors as the instrument rotates. The graphite crystal, oriented at 45° with respect to an incoming X-ray beam, will reflect only those X-rays with energies satisfying the Bragg condition and with electric vectors lying in the plane of the crystal. If the incident radiation is polarized, the count rate will be modulated at twice the rotation frequency of the polarimeter. The graphite polarimeter is sensitive in two narrow bands corresponding to the first and second order Bragg diffraction peaks at 2.6 and 5.2 keV.

IPCs

The IPCs are gas-filled multi-wire proportional counters with a single amplification stage, a wedge and strip cathode, and a rear anticoincidence region. The IPC bodies are made of stainless steel, and the 103.8 mm by 113.3 mm IPC windows are made of beryllium. The IPC gas mixture is 50% xenon, 40% argon, and 10% methane. This mixture was chosen to give favorable X-ray and background rejection efficiency.

Several IPC characteristics are crucial to the successful operation of the SXRP including X-ray efficiency, energy resolution, and position resolution. To match the energy band pass of the graphite and lithium polarization analyzers, the IPCs must be efficient in an energy band extending from 2 to 15 keV. The X-ray energy is not significantly changed by Compton scattering or Bragg reflection. Therefore, the accuracy with which the energy of incoming X-rays can be measured is determined by the energy resolution of the IPCs.

We have concluded that the basic scientific objectives of the SXRP can be met with an energy resolution (delta E/E) near 25% at 6 keV. Using detectors with imaging capabilities increases the polarization sensitivity of the SXRP by a factor of three over an instrument with non-imaging detectors. Our design goal is a position resolution of 4 mm (fwhm) for the graphite reflected (2.6 keV) X-rays. The IPC energy resolution can be determined from data collected when a source producing X-rays of known energy illuminates the face of the IPC.

Figure 3 shows the IPC response to illumination by 5.9 keV X-rays from 55Fe. For this IPC, the energy resolution at 5.9 keV is 20%. An energy resolution around 20% is typical for the SXRP flight model IPCs surpassing the stated energy resolution requirement. The IPC positioning capabilities are tested by illuminating the face of the IPC obscured by a hole pattern. During this test, the IPC sits about 4 meters from the X-ray source. The hole pattern is adjacent to the IPC and has 0.5 mm diameter holes between 6.26 mm spacing.

Figure 4a shows the IPC response to this test, where each point on the graph corresponds to an X-ray detection. Since the true hole positions are known, data taken in this configuration can be used to calculate a position correction matrix which can then be applied to the data taken during an actual observation. Figure 4b shows the IPC position response after the application of the position correction matrix. For the flight model IPCs, the mean position resolution across the face of the IPC is about 3.3 mm in the x-direction (as defined in Figure 4) and about 2.6 mm in the y-direction for 2.8 keV X-rays. Thus, the flight model IPCs meet our goal of 4 mm position resolution.(For an in depth look of the IPC and its function, see the IPC Report.)

POLARIZATION SENSITIVITY

The sensitivity of the SXRP is limited by systematic and statistical errors. Our goal is to reduce the systematic error in a polarization measurement below the 1% level. The statistical error in a polarization measurement is determined by the minimum detectable polarization (MDP) of the instrument. The MDP is defined to be the minimum source polarization which can be detected at a 99% statistical confidence level. For an observation where r is the count rate from the source, b is the background count rate, is the modulation factor of the polarimeter, and T is the total observation time, the MDP is given by:

Figure 5 shows the MDP of the SXRP for sources with spectra similar to the Crab nebula assuming T = 10^ 5 seconds and a background flux of 3 × 10^ -3 counts/cm^ 2 sec keV. We have used a source spectrum of 10.0E^ -2.05 photons/cm^ 2 sec keV with an interstellar column density with standard cosmic abundances of 3 × 10^ 21 cm^ -2 for the Crab. Table 1 shows the calculated MDP for a number of potential target objects with an assumed background flux of 2.3 × 10^ -3 counts/cm^ 2 sec keV.

SXRP-EM CALIBRATION

The SXRP engineering model prototype was tested at Lawrence Livermore National Labs in late 1993. During the tests, the lithium polarimeter was tested using a polarized 9.7 keV beam and an unpolarized 8.4 keV beam. The graphite polarimeter was tested using polarized and unpolarized 2.7 keV beams. Figure 2 shows modulation curves for all four beam types.

In order to determine the polarization of an X-ray source from a modulation curve, the detector count rate (N) is decomposed into its Fourier components according to:

The magnitude of polarization is given by:

where r and b are the source and the background count rates, respectively, and µ is the modulation factor defined as the modulation in the count for a beam of 100% polarized X-rays with no background. Thus, the curves on the left hand side of Figure 2 indicate the value of the modulation factor for the lithium and graphite polarimeters. The curves on the right hand side of Figure 2 provide an estimate of instrumental, or systematic, errors in polarization measurements.