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Broad-Band Soft X-ray Polarimetry

We developed an instrument design capable of measuring linear X-ray polarization over a broad-band using conventional spectroscopic optics. A set of multilayer-coated flats reflects the dispersed X-rays to the instrument detectors. The intensity variation with position angle is measured to determine three Stokes parameters: I, Q, and U -- all as a function of energy. By laterally grading the multilayer optics and matching the dispersion of the gratings, one may take advantage of high multilayer reflectivities and achieve modulation factors>50% over the entire 0.2 to 0.8 keV band. This instrument could be used in a small orbiting mission or scaled up for the International X-ray Observatory. Laboratory work has begun that would demonstrate the capabilities of key components.


Introduction
The soft X-ray band (0.1-1.0 keV) should prove to be a fruitful region to explore for polarized emission. One concept, the Polarimeter for Low Energy X-ray Astrophysical Sources (PLEXAS), was proposed to use multilayercoated mirrors tuned to 0.25 keV as Bragg reflectors (9). As in similar Bragg reflection systems, the PLEXAS design had a narrow bandpass, reducing its attractiveness for astrophysical observations because one expects polarization to be energy dependent, so a wide bandpass is desired. Marshall (2007(8)) described a method to overcome this limitation by using transmission gratings to disperse in the incoming X-rays. Following up on this approach, Marshall (2008(7)) suggested an arrangement that can be used in missions ranging from a small explorer to the International X-ray Observatory (IXO).

Polarimetry with the Extreme Ultraviolet Explorer
For the record, it is worth noting that the first attempt to measure the polarization above 0.1 keV of an extragalactic source used the Extreme Ultraviolet Explorer (EUVE). However, the telescope was not designed for polarimetry. The expected modulation factor was small, 2.7%, so experiment failed due to systematic errors that could not be eliminated with existing calibration data.(10) Even using an in-flight null calibrator (a white dwarf) was insufficient. The program described here grew out of this attempt, so one might say that it was not a complete loss.

Science Goals
Here we describe two potential scientific studies to be performed with an X-ray polarimetry mission with sensitivity in the 0.1-1.0 keV band.
Probing the Relativistic Jets in BL Lac Objects -Blazars are all believed to contain parsec-scale jets with β ≡ v/c approaching 0.995. The jet and shock models make different predictions regarding the directionality of the magnetic field at X-ray energies: for knots in a laminar jet flow it should lie nearly parallel to the jet axis (5), while for shocks it should lie perpendicular (6). McNamara et al. (these proceedings) suggest that X-ray polarization data could be used to deduce the primary emission mechanism at the base, discriminating between synchrotron, self-Compton (SSC), and external Compton models. Their SSC models predict polarizations between 20% and 80%, depending on the uniformity of seed photons and the inclination angle (11). The X-ray spectra are usually very steep so that a small instrument operating below 1 keV can be quite effective.
Polarization in Disks of Active Galactic Nuclei and X-ray Binaries -Schnittmann & Krolik (these proceedings) show that the variation of polarization with energy could be used as a probe of the black hole spin and that the polarization position angle would rotate through 90 • between 1 and 2 keV in some cases, arguing that X-ray polarization measurements are needed both below and above 2 keV(12). As Blandford et al. (2002) noted "to understand the inner disk we need ultraviolet and X-ray polarimetry" (1).

Basis of a Soft X-ray Polarimeter
The approach to this polarimeter design was inspired by a new blazed transmission grating design, called the Critical Angle Transmission (CAT) grating (4), and the corresponding application to the Con-X mission in the design of a transmission grating spectrometer (3). This type of grating can provide very high efficiency in first order in the soft X-ray band. For a spectrometer, one places detectors on the Rowland torus, which is slightly ahead of the telescope's imaging surface.
A dispersive spectrometer becomes a polarimeter by placing multilayercoated flats on the Rowland circle that redirect and polarize the spectra. The flats are tilted about the spectral dispersion axis by an angle θ. For this design (7), the graze angle θ was chosen to be 40 • . The detectors are then oriented toward the mirrors at an angle 90 − 2θ = 10 • to the plane perpendicular to the optical axis of the telescope. Fig. 1.1 shows how the optics might look. In this case, the entrance aperture is divided into eight sectors, with gratings aligned to each other in each sector and along the average radial direction to the optical axis. This approach generates seven spectra that are reflected by four polarizing flats to four detectors. See Marshall (2008) for details (7).
The fundamental requirement of this approach is to vary the multilayer spacing, d, on the polarizing flats laterally, along the dispersion, in order to provide optimal reflection at graze angle θ. The multilayer period varies linearly with x, providing high reflectivity in a narrow bandpass at large graze angles (7). At Brewster's angle, θ = 45 • , reflectivity is minimized when the E-vector is in the plane containing the incident ray and the surface normal (p-polarized) and maximized when the E-vector is in the surface plane (spolarized). The polarization position angle (PA) is the average orientation in sky coordinates of the E-vector for the incoming X-rays. Sampling at least 3 PAs is required in order to measure three Stokes parameters (I, Q, U) uniquely, so one would require at least three separate detector systems with accompanying multilayer-coated flats. For this study, four detector-flat combinations are assumed, as shown in figure 1.1.
Critical angle transmission (CAT) gratings have excellent prospects for high efficiency in first order, up to 50% over a wide band.(4) The CAT gratings are free-standing (so no support membrane is needed) and have higher intrinsic efficiency than the gratings used on the Chandra program, making them excellent candidates for use in X-ray spectrometers as well as a possible X-ray polarimeter.
A CAT grating spectrometer has been proposed as one of two approaches to use on the IXO, so there is a development path for this type of soft Xray polarimeter. Sampling at least 3 PAs is required in order to measure three Stokes parameters (I, Q, U) uniquely, so one would require at least three separate detector systems with accompanying multilayer-coated flats, as shown in fig. 1.3.  7)). A small set of nested mirror shells focusses X-rays through gratings that disperse to an array of detectors about 2 m from the entrance aperture. Top left: View from the front aperture. Gratings are placed behind the mirror with the grating bars oriented along the average radius to the mirror axis. The gratings are blazed in the directions shown. Top right: The view from above the detectors and polarizers. Spectra from the gratings are incident on multilayer-coated flats that are tilted along the dispersion axis which contains the zeroth order (dot in center). The angle of the tilt is the same for all mirrors and always redirects the X-rays to the adjacent detector in a clockwise direction. The multilayer coating spacing, D, increases linearly outward from zeroth order, just as the wavelength increases, in order to match the first order wavelength to the peak of the multilayer reflectivity. The detectors could be aligned to the appropriate Rowland torus (as shown in the side view) or be tilted to face the corresponding mirror. Measuring the intensity at a given wavelength as a function of clocking angle then provides I(λ), Q(λ), and U (λ).

A Soft X-ray Polarimeter Prototyping Facility
We have recently recommissioned the X-ray grating evaluation facility (X-GEF), a 17 m beamline that was developed for testing transmission gratings fabricated at MIT for the Chandra project (2). With MKI technology development funding, we will soon adapt the existing source to produce polarized X-rays at the O-Kα line (0.525 keV). A new chamber will house a Polarized Source MultiLayer mirror, provided by Reflective X-ray Optics (RXO). The source will be mounted in the chamber at 90 • to the existing beamline. A rotatable flange will connect the PSML chamber output to the vacuum 17m facility so that the polarization vector may be rotated with respect to the grating and its dispersion direction. This prototyping effort will help us demonstrate the viability of soft X-ray polarimetry and show how a broadband version can be developed. A proposal to expand the facility to 4 or 5 more energies between 0.25 and 0.8 keV is under consideration by NASA.  7)). When used as a spectrometer (pink lines), the zeroth order of the spectrometer is centered in the dark red square, representing an IXO wide-field imager. When used as a polarimeter (gray lines), the zeroth order is placed at the location of the gray dot so that the dispersed spectrum first intercepts the laterally graded multilayer mirror that is angled at 30 • to the incoming X-rays. The lines leading to zeroth order are all the same length, showing that specific wavelengths appear at different distances from the near end of the mirror but are at the same distances when used as a spectrometer. Right: Side view of the CCD housing where the dispersion is perpendicular to the plane of the drawing and the multilayer mirror is oriented 30 • to the incoming, dispersed X-rays.