OBSERVATIONS

In astrophysical contexts, the primary processes which lead to polarized X-ray emission are non-thermal radiation and electron scattering of thermal X-rays in non-spherically symmetric geometries. The magnitude and position angle of polarization from a source is highly dependent on source geometry. For example, deviations from spherical symmetry can arise in systems with accretion disks or strong magnetic fields. Polarization measurements provide a direct probe of source geometry and a means of distinguishing between different emission processes. We plan to use the SXRP to look at accreting pulsars, radio pulsars, SNRs, LMXBs, and systems containing accretion disks including SXTs. The following focuses on systems with accretion disks and accreting pulsars and discusses what is expected to be learned from SXRP observations of these systems.

SYSTEMS WITH ACCRETION DISCS

There is significant evidence that Cyg X-1 is a black hole onto which matter is accreting from a disk. For Cyg X-1, the X-ray luminosity between 10 and 200 keV has been observed to be between 3 × 10^36 and 3 × 10^37 ergs/s. It is possible to characterize the spectrum from 10 to 250 keV by a single power-law with a spectral index near 1.0. These observations indicate that there is a significant hard X-ray component to the emission.

An accretion disk model which is able to produce the hard X-ray luminosity of Cyg X-1 is the "two-temperature" disk model. This model assumes that the inner region of the disk is geometrically thick and optically thin and the outer region of the disk is optically thick. Soft X-rays are produced, possibly in the outer region, which illuminate the inner region up to the soft X-ray cutoff energy, Es. Typical values assumed for Es are between 0.5 keV and 5 keV. The X-rays with energies above Es are produced by Comptonization of soft X-rays by electrons in the inner region. Figure 6 shows the expected X-ray polarization based on the model of Shapiro, Lightman, and Eardley (1976).

Due to electron scattering in the disk, polarization is expected to be produced in both the inner and outer regions of the accretion disk. The soft X-rays coming from the optically thick outer region of the disk are polarized parallel to the plane of the disk, while the X-rays with energies greater than Es are produced in the optically thin inner region and are polarized perpendicular to the plane of the disk. In Figure 6, P>0 indicates a polarization parallel to the disk, while P<0 indicates a polarization perpendicular to the disk.

For Cyg X-1, a 2 ×10^ 5 second SXRP observation will provide constraints on the values of the soft X-ray cutoff energy and the viscosity parameter. The inclination of the accretion disk (defined as the angle between the line of sight and the normal to the disk) for Cyg X-1 is near 41°. Table 2 (within Figure 6) shows that the expected polarization magnitudes for both the inner and outer regions of the disk increase with inclination angle. In systems where the inclination angle is near or above 60°, the SXRP will be sensitive enough to distinguish between all four cases presented in Figure 6.

Soft X-ray Transients are also systems where it is thought that matter is flowing onto a compact object from an accretion disk. Table 1 shows that polarization measurements of SXTs during outbursts could be made in significantly less time than required for Cyg X-1, due to the high X-ray luminosity of these objects during outbursts. The other advantage to making measurements of SXTs compared to constant sources is that, during quiescence, it is possible to make optical measurements of the secondary to determine the orbital parameters of the binary. This is important because these observations allow for good constraints on the inclination angle of the accretion disk (defined as the angle between the line of sight and the normal to the disk).

In Table 3 (within Figure 6), it is shown that the observed polarization varies greatly with inclination angle. Thus, the inclination angle must be known to reasonably good accuracy to make a comparison between observation and theory based on polarization measurements. It should be noted that measurements of the inclination of the orbital plane are only useful in determining expected polarizations if the accretion disk and the orbital plane are roughly coincident. The combination of high photon flux during outbursts and the ability to place good constraints on the inclination angle of the disk make SXTs very good candidates for polarization measurements.

ACCRETING PULSARS

Her X-1, Cen X-3, and the other binary pulsars listed in Table 1 are examples of accreting pulsars. The standard model for these systems has accreting matter funneled by the magnetic field onto the magnetic pole of the pulsar. It is generally assumed that the X-ray radiation originates at or near the magnetic poles. The fact that the observed emission is pulsed is explained by models where the emission is beamed and the pulsar magnetic moment and rotation axis are not aligned. Below, two models for beamed emission will be discussed (the pencil and fan beam models) and it will be shown that X-ray polarization measurements will allow for distinction between the two models.

Figure 7 illustrates the fan and pencil beam emission geometries. Accreting pulsar models assume two different accretion geometries which lead to a fan beam in one case and a pencil beam in the other. To produce the fan beam, it is assumed that matter falls onto the magnetic pole in an accretion column. To produce the pencil beam, it is assumed that matter falls onto the magnetic pole along the stellar surface (slab accretion geometry). As shown in Figure 7a, the X-ray emission is parallel to the magnetic dipole (M) for the pencil beam, while for the fan beam, X-rays are emitted in the plane perpendicular to M (shown in Figure 7b).

The pencil and fan beam models both are able to produce the pulse profiles observed from accreting pulsars. The observed emission is expected to be polarized because a strong magnetic field will produce significant anisotropies in the Thomson scattering cross section for X-rays propagating in the pulsar atmosphere. The expected polarization magnitudes and directions have been calculated for the two models and are displayed for X-ray energies of 1.6 and 9.0 keV in Figure 8. In producing the curves in Figure 8, a cyclotron energy of 38 keV (B = 3.3 × 10^ 12 G), a Thomson optical depth of 20 and a density of 0.5 g/cm^ 3 are assumed. Also, it is important to note that the curves are for the case where the angles between the magnetic dipole and the pulsar rotation axis (omega) and between the line of sight and the pulsar rotation axis are 45°.

Figure 8 shows that the variation of the polarization magnitude (Pmag) and the polarization angle (chi) with pulse phase are distinctly different for the pencil and fan beam models at both 1.6 and 9.0 keV. For the pencil beam, minima in Pmag correspond to flux maxima, while in the fan beam case, the maxima and minima for Pmag and the flux are coincident. This is true for both energies. Also, there are jumps in the value of chi at flux maxima for the pencil beam, while the jumps in chi occur at flux minima for the fan beam. With appropriate pulse phase binning, the SXRP could distinguish between the pencil and fan beam models from measurements of either the polarization magnitude or the polarization angle.

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