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Restoring the Suzaku Source Position Accuracy and Point-Spread Function

We present an empirical correction of sky coordinates of X-ray photons obtained with the XIS aboard the Suzaku satellite to improve the source position accuracy and restore the point-spread function (PSF). The XIS images are known to have an uncertainty in position of up to 1 arcmin, and to show considerable degradations of the PSF. These problems are caused by a drifting of the satellite attitude due to thermal distortion of the side panel 7, where the attitude control system is mounted. We found that the position error averaged over a pointing observation can be largely reduced by using the relation between the deviation of the source position in the DETX direction and the ecliptic latitude of the pointing target. We parameterized the wobbling of the source position synchronized with the satellite orbital period with temperatures of onboard radiators and elapsed time since the night-day transition of the spacecraft. We developed software, aeattcor, to correct the image drift using these parameters, and applied it to 27 point-source images. We show that the radius of the 90% error circle of the source position was reduced to 19 arcsec and the PSF was sharpened. These improvements have enhanced the scientific capability of the Suzaku XIS.


Introduction
The X-ray Observatory Suzaku (Mitsuda et al. 2007), developed jointly by Japan and the US, has two active scientific payload, XIS (X-ray Imaging Spectrometer: Koyama et al. 2007) and HXD (Hard X-ray Detector: Takahashi et al. 2007). XIS consists of four X-ray imaging CCD cameras covering a field-of-view of 17. ′ 8 × 17. ′ 8; three are front-illuminated (0.4-12 keV), and one is a backilluminated CCD (0.2-12 keV). The XISs are located on the focal plane of the X-ray Telescopes, XRTs (Serlemitsos et al. 2007). Each X-ray photon recorded by the XIS can be localized with the CCD native pixels, each of which has dimensions of 1.04 ′′ × 1.04 ′′ . While the PSF of the XRTs has a broad distribution with a half-power diameter (HPD) of ∼ 2 ′ , it has a sharp core with a width of ∼ 10 ′′ . Thus, the sky positions of point-like sources with good photon statistics ( > ∼ 10 4 photons) are in principle determined with a precision of better than ∼ 10 ′′ , if we know the instantaneous pointing direction of the XRT perfectly. The positional information is crucial to search for coun-terparts in other wavelengths [e.g., a new supersoft source discovered by Suzaku; see Takei et al. (2007)] and also to construct source catalogs [e.g., Ueda et al. (2001) and Ueda et al. (2005) in the case of ASCA].
The celestial coordinates of each photon detected with the Suzaku XRT-XIS are calculated from the position coordinates of the CCD pixels defined on the XRT focal plane and the instantaneous pointing direction of the XRT. The arcsecond localizations of optical guide stars by a pair of star trackers (STTs) primarily determine the absolute pointing direction of the XRT. While guide stars are not available, a set of gyroscopes takes a role to determine the pointing direction. However, over the course of in-orbit calibrations of the Suzaku XRT, it was revealed that the calculated positions of X-ray sources have an error of 1 ′ (Serlemitsos et al. 2007), which is significantly larger than that expected in the pre-flight specifications, ∼ 10 ′′ . The deviation of the calculated source position from the true position is time-dependent and synchronized with the orbital motion of the spacecraft. Its behavior differs from one observation to another. The error of the [Vol. , source position can be as large as 1 ′ , and therefore the astrometric accuracy of the XIS images has been taken to be ∼ 1 ′ so far.
The cause of this problem has been identified with a thermal distortion of the satellite chassis, particularly the cross frames on the side panel #7 (see figure 1), as briefly stated in Serlemitsos et al. (2007). This panel is situated on the anti-Sun side of the spacecraft, where the dewar of the X-ray Spectrometer (XRS: Kelley et al. 2007) is placed. To expose the XRS dewar to space, the lower half of the panel #7 is skeletonized by cross frames made of aluminum [see figure 1 and also Mitsuda et al. (2007)]. The cross frames suffer from thermal distortion due mainly to Earth albedo illumination. Specifically, side panel #7 is forced to be tilted in the DETY direction as the cross frames expand, since the upper end of the panel is fixed at the side panels #6 and #8. Since the STT and gyroscopes are co-located on side panel #7, it causes a time-dependent misalignment between the XRT-XIS system and the attitude system, and consequently drifts the XRT pointing in the DETY direction. Also, an imbalance of thermal expansion between the cross frames induces rotation around the Y-axis (perpendicular to the side panel #7), resulting in drifts in the DETX direction.
We have investigated the characteristics of drift of the X-ray images to restore the pointing accuracy as close to the pre-flight specification as possible. Suzaku does not have onboard sensors for the temperatures of the cross frames, which are considered to be the most relevant parameters to the thermal distortion. We therefore have searched for relevant key parameters within the limited housekeeping data available on ground.
In the present work, we parameterize the drifts of the XRT pointing direction against the attitude control system with the spacecraft temperatures, the satellite orbital phase, and the average pointing direction relative to the ecliptic plane, and found a method to correct the position accuracy and the PSF in the observed XIS image using these parameters. We applied the method to point-source images taken in the initial scientific operation phase and derived the position accuracy currently achievable. The outline of this paper is as follows. We describe the data sets and basic reduction in section 2. The parameterization of drifts of the XRT pointing is presented in section 3, which is followed by a brief description of new software, aeattcor, developed for the position-error correction in section 4. We present the improvement on the PSF and the position accuracy in section 5. A summary is in section 6.

Observations
We analyzed XIS data acquired during the Suzaku initial science-operation phase for the present work. We selected data of point sources whose celestial coordinates were cataloged with a precision of better than a few arcseconds, their X-ray fluxes were higher than 0.5 counts s −1 chip −1 , but less than 100 counts s −1 chip −1 because a too-high count-rate caused a significant pileup at the peak of the PSF and degraded the precision of the position determination. Table 1 lists the selected X-ray sources, consisting mainly of active galactic nuclei and X-ray binaries, used in this work. (For multi-epoch monitoring observations, we used only the data of the two latest epochs in order not to enhance statistical weights on these sources.) We retrieved the Suzaku XIS data with version 1.2 pipeline processing (V1.2), and utilized cleaned event data. We analyzed the XIS images using sky coordinates, X/Y columns (+X is directed to west and +Y is north) in the event files, which were calculated from the detector coordinates (DETX/Y) of the CCD pixels and the satellite attitude monitored by the STTs and gyroscopes . It is worth emphasizing that prior to the pipeline processing V1.0, the attitude determination with STTs and gyroscopes on ground had not been applied. We present results obtained from XIS-0, one of the three frontside illuminated CCDs, because the XIS-0 has the best PSF suited for our purpose. The drifts of all four XIS images due to the drifts of the satellite attitude were found to be almost identical. The results from XIS-0 are equally applicable to the other XIS data.

Position Drift of Suzaku XIS Image
In order to track a drift of a source position in the sky coordinates (X/Y), we determined the quasi-instantaneous peak of the sky image for every 200 second time bin by a two-dimensional Lorentzian fitting. The deviation of the peak position from the expected position (∆X, ∆Y ) was computed at each time bin. The expected pixel position is (768.5, 768.5) if the source was aimed to be placed at the XIS nominal position. They were then converted into the detector coordinate system, (∆X det , ∆Y det ), using the following transformation: where θ is the average roll angle, PA NOM, stored in the event file headers. A similar method was adopted in Gotthelf et al. (2000) for correcting the ASCA position accuracy.
To illustrate the characteristics of the drift of the XIS images, the time history of a source position obtained from data of Her X-1 (seq# 100035010) is shown in figure 2. It can be seen that the source position oscillates with amplitudes of 10 ′′ -30 ′′ in both ∆X det and ∆Y det synchronized with the satellite orbital motion of a 96-min period. Furthermore, the center of oscillation has an offset toward the −∆X det direction by ∼ 40 ′′ , which causes a large astrometric error in the Suzaku XRT-XIS system.
We found that the position drift of the Suzaku XIS image can be well described by a wobbling motion synchronized with the satellite orbital motion and an offset which changes slowly in a much longer timescale than the orbital period during a fixed pointing observation. The offset appears to differ from one pointing to another. We derived the offset in both the X det and Y det directions for each pointing by fitting the time-integrated XIS image with a two-dimensional Gaussian function. We denote the derived offsets as ∆X det and ∆Y det , though these quantities are not necessarily the average of the above deviations ∆X det and ∆Y det . The offsets would be a good measure of the center of oscillation.
In the left panel of figure 3 we show a scatter plot of the offset, ∆X det versus ∆Y det , derived for all of our samples. This plot represents the position accuracy of the Suzaku XIS image processed by the pipeline V1.2. We found that the dispersion of the offsets is larger in the DETX (X det ) direction, ∼ 70 ′′ . The dispersion of the offset in the DETY direction is relatively small and the distribution tends to be positive.

Parametrization of Drift
We searched for related parameters to the offset and the wobbling motion of the X-ray image to recover the image that should be obtained in a condition free from the drift of the satellite attitude. We here assume that the long-timescale offset is constant during a fixed pointing observation.

Long-timescale offset
First, we found that the offset in DETX, ∆X det , has a clear correlation with the ecliptic latitude of the source, β ecl . In figure 4 we present the distribution of ∆X det of each observation against β ecl . A linear relation between the DETX offset ∆X det and the ecliptic latitude β ecl is clearly seen. The ecliptic latitude β ecl represents the angle of the XRT pointing direction from the ecliptic plane, and characterizes the way of illumination by the bright Earth. The strong correlation suggests that the geometry between the Sun, Earth, and the satellite, plays an essential roll in determining the long-timescale offset of the XRT pointing in the DETX direction. The configuration of side panel #7 relative to the ecliptic plane is considered to somehow control the thermal distortion of the cross frames.
The following linear relation is found to reasonably fit these data: This relation gives a DETX offset for a given observation using the ecliptic latitude of the target. It can be seen that ∆X det ≃ 0 for β ecl ≃ −14 • . This is simply because the nominal position has been calibrated by MCG−6−30-15 (seq# 100004010), which has an ecliptic latitude of β ecl ≃ −22. • 5.

Wobbling with satellite orbital period
We next explored the wobbling motion synchronized with the orbital motion of the satellite. After inspecting correlations with various parameters stored in the satellite housekeeping data, we arrived at two parameters related with the wobbling motion. One is a difference of temperature between radiators at the side panels #8 and #6, where HK XIS RAD8 T1 CAL and HK XIS RAD6 T1 CAL are temperatures of radiators at the side panel #8 and #6, respectively. The newly introduced parameter is found to be a good indicator of the wobbling motion in the DETX direction. The temperature difference T 86 represents a temperature gradient in side panel #7 in the DETX direction. The other parameter is the elapsed time after a night-day transition, T DY (in units of second), defined by where day-time means a period in which Sun light irradiates the satellite. We make use of the parameter T DY to parameterize the wobbling motion in the DETY direction because it is supposed to be coupled with thermal cycling of the orbiting spacecraft. Figure 5 shows a correlation between T 86 and ∆X det , after removing the offset of ∆X det . In the plot, we utilized only bright sources with a flux higher than 2 counts s −1 among the samples in table 1, because the source position has to be determined for each 200-sec bin. For a fixed value of T 86 in a given observation, ∆X det was found to have a scatter of about 10 pixels. We averaged ∆X det for each temperature bin over each observation. There is a tendency that the source position deviates from the nominal position to the +DETX direction as the temperature difference T 86 increases. We therefore parametrized ∆X det (pix) by the combination of a linear function of T 86 and ∆X det (β ecl ) in equation (3) as In figure 6 we demonstrate a correlation seen between T DY and ∆Y det . It appears that ∆Y det increases as T DY increase for T DY ≤ 2000 and then starts to fall. We approximated the relation between ∆Y det (pix) and T DY with a broken line: No. ]

Restoration of Suzaku Astrometry 5
These empirical relations give an instantaneous deviation from the nominal position at each event time for a given observation, thus allowing corrections in the DETY direction. Note however that the absence of a direct measurement of the cross frame temperatures makes the corrections difficult.

Software Implementation
We have developed a program, aeattcor, to correct the parameters of the satellite attitude using the parameterization of drift of the XIS image described above.
The program first calculates the expected deviation of the XRT pointing direction from that aimed at each event time using equations (6) and (7). The deviation corresponds to the error of the satellite attitude caused by any misalignment between the XRT-XIS system and the attitude control system. The program calculates Euler angles of the satellite attitude for the XRT-XIS system from those monitored on the attitude control system, and then updates the attitude file in which the Euler angles are stored. If one simply converts detector coordinates (DETX, DETY) to sky coordinates (X,Y) using the updated attitude file, the corrected sky coordinates (X,Y) can be obtained. A detailed description of the conversion scheme is given by Ishisaki et al. (2007).
The program is now included in FTOOLS, the official analysis software released form the Suzaku Guest Observer Facility, and will be applied to the XIS event files released through the pipeline processing V2.0 or the later versions.

Demonstration
In this section we demonstrate the developed program, aeattcor, in application to the XIS images of sample sources. We show how degree the program improves the PSF and the position accuracy.

Restored Image and PSF
The left panel of figure 7 shows time-integrated XIS-0 image of Her X-1 before the attitude-error correction, as extracted from the V1.2 event files. The image before the attitude-error correction looks as if there are two pointlike sources separated by 30 ′′ . It is because the position of Her X-1 is oscillated with the satellite orbital period, and the source visibility is limited in selected orbital phases for Earth occultation (see figure 2).
The right panel of figure 7 is an image after the attitudeerror correction. One can realize that the deviation of the peak from the nominal position is improved, and the double-peak profile of the image before the correction disappears in the corrected image. In figure 2, we present a time sequence of the source position after the correction, where the large amplitude in the DETY is reduced.
To quantify the improvement of the PSF core, we introduce a new parameter, "core sharpness" S, defined as the ratio of the averaged count per pixel within an inner circle of 10-pix radius to that within an outer annulus between 10-pix and 20-pix radii. Here we determined the source centroid by fitting with a 2-dimentional Gaussian function. If the PSF is perfectly flat within 20 pixels from the center, the core sharpness is 1.0. For the instantaneous PSF free from the time-variable pointing direction, we expect S ≃ 2. We note that the "core sharpness" depends on each XIS because each XRT has a slightly different PSF. We here present the results of XIS-0. Figure 8 shows the distributions of S for the sources listed in table 1, before and after the attitude-error correction.
The sources with a flux higher than 50 counts exposure −1 chip −1 are shown separately with red histograms, because those bright sources are expected to severely suffer from pileup effects. It is clear that the [Vol. , PSFs of the corrected image are sharpened and the core sharpness becomes close to 2, the value expected for the PSF free from the attitude error.

Improved Position Accuracy
We determined the offset of the source centroid from the expected position for all sample sources before/after the attitude-error correction, in order to evaluate the im-provement on the source position accuracy. The distributions of these offsets ( ∆X det , ∆Y det ) before/after the attitude-error correction are plotted separately in figure 3. The improvement of the position accuracy is clearly seen from the difference of the two distributions.
To quantify the position accuracy, figure 9 shows the distributions of ∆r ≡ ∆X det 2 + ∆Y det 2 , i.e., the distance between the source centroid and the expected position, separately before/after the attitude-error correction. Without the attitude-error correction, the deviation from the nominal position has a 90% error circle of ∆r ≃ 50 ′′ radius. The aeattcor restores the pointing accuracy to ∆r ≤ 19 ′′ (a 90% error circle). The improvement is brought mainly by the successful parameterization of the large DETX offsets. The residual position error after the attitude-error correction is somewhat worse compared with the preflight specification, ∼ 10 ′′ , and the position accuracy of ASCA, ≃ 12 ′′ (Gotthelf et al. 2000). Given a lack of direct measurements of the temperatures of the cross frames, which are the most relevant parameters, we do not expect that further improvements can be easily made. We will monitor the Suzaku pointing accuracy to check its validity over the course of the mission.

Summary
We have developed an empirical method to restore the position accuracy and the PSF in the observed Suzaku XIS image. We analyzed 27 pointing observations of point-like sources using the XIS-0 data of the pipeline processing V1.2 to investigate the characteristics of the drift of the XIS image which degrades the position accuracy and the PSF. We found that the deviation of the source centroid from the expected position, averaged over one pointing observation, can be well characterized by the relation between the deviation in the DETX direction and the ecliptic latitude of the pointing target. It is also found that the oscillation of the source position synchronized with the satellite orbital period can be parameterized to some extent by the temperatures of the onboard radiators and the elapsed time since the night-day transition of the satellite. Based on the parameterization of the drifts of the XIS image, we have implemented new software, aeattcor, to correct the XRT pointing direction with respect to the attitude control system at each event time. By applying the attitude-error corrections to the XIS data of our sample, we demonstrated that the distorted core of PSF can be sharpened and showed that a 90% error circle of the sky position of a point-like source is reduced to 19 ′′ in radius. The results presented in this paper describe the current accuracy of performing astrometry with the Suzaku XIS.