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Chapter 6 - Imaging Data Analysis
This chapter describes in more detail the astrometry GALEX of images, the GALEX point spread function, and the various artifacts present in GALEX images.
Astrometric Uncertainties
The positional errors listed in the GALEX photometric catalogs are the errors in the coordinates due simply to counting statistics. For faint sources, this is the dominant source of error. However, at the bright end, systematic uncertainties in the positions dominant the errors. This section briefly describes the absolute astrometric uncertainties of GALEX data.
We have matched sources using a 4 arcsec maximum search radius from the Medium Imaging Survey (MIS) and All-sky Imaging Survey (AIS) in the GALEX GR6 data release with objects identified as stars in the SDSS-DR7 catalogs (type = 6). We have further restricted the sample to stars detected in the NUV with aperture magnitudes in the range 15 < NUV 18, r-band PSF magnitude errors less than 0.05, PSF r-band magnitudes less than 20, and that are not saturated in the SDSS. The resulting sample consists of 9,000 stars in the MIS and 24,000 in the AIS. These stars are bright enough such that the statistical errors in their positions are small. We only used a NUV-selected sample as the final astrometry for each image in the GALEX pipeline was determined using the positions of stars on the NUV detector. As the astrometric accuracy of the SDSS is about 0.1” even for relatively faint stars, we can consider it essentially an “absolute” reference for our purposes (Pier et al. 2003, AJ, 125, 1559).
We noticed small systematic offsets of about 0.1-0.3 arcsec in the GALEX positions relative to the SDSS in some parts of the sky. The magnitude and direction of these offsets vary with position on the sky. These differences are ultimately due to reliance on the USNO-B catalogs (Monet et al. 2003, AJ, 125, 984) for the absolute astrometry in GALEX images. The USNO-B has small systematic offsets relative to the Tycho-2 catalog. Since the SDSS relies upon Tycho-2, the GALEX positions relative to the SDSS reflect these offsets as well.
| Figure 1 Histogram of the position differences between GALEX and the SDSS for bright stars with 15 < NUV < 18. The solid and dashed curves are refer to the MIS and AIS, respectively.
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| Figure 2 Cumulative histogram of the position differences between GALEX and the SDSS for bright stars with 15 < NUV < 18. The solid and dashed curves are refer to the MIS and AIS, respectively.
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In Figures 1 and 2 we plot the differential and cumulative histograms, respectively, of the radial position offsets between GALEX and the SDSS for our sample of bright stars. The radii containing 68.3%, 95.4%, and 99.7% of the matches within 4 arcsec are 0.7, 1.4, and 3.4 arcsec in the AIS. The corresponding radii for the MIS are 0.9, 1.9, and 3.6 arcsec. Similar results were reported in Morrissey et al. (2007 ApJS, 173, 682) who found the absolute positional uncertainty to be 0.5” (rms) based upon a sample of QSOs from the SDSS with detections by GALEX. The astrometry is slightly better in the AIS than in the MIS. This may be the result of small errors in the solution for the spacecraft dither pattern within each observation which tend to accumulate in the longer MIS exposures as compared to the AIS. Many MIS observations are co-adds of two or more exposures which can also degrade the astrometry slightly compared to individual visits.
Point Spread Function
We have characterized the GALEX point spread function (PSF) using various in-flight observations. Although the GALEX PSF is in general a complicated function of position on each detector, we begin by characterizing the average PSF in each band. These results were derived using the GALEX GR2 release but should remain valid for later releases as well.
In order to produce an average PSF, we have relied upon two data sets. The first is a set of field stars while the second relies upon averages of the numerous observations of the primary calibration star LDS 749B. The list of field stars was selected using an SQL search on the MAST CASJobs web site. We selected all observations of sources that have matches between the GALEX GR2 data release with the SDSS that were classified as point sources from the SDSS pipeline and within a relatively narrow range of UV magnitudes. For the NUV, we selected sources with aperture magnitudes satisfying 16.75 < NUV < 17.25. Due to the lack of bright stars in the FUV, we selected stars in a larger range with 15.75 < FUV < 17.00. These limits insure that the sources are well away from the level where sources become significantly saturated, i.e. for magnitudes NUV < 15.
| Figure 4 Contour plot of the NUV PSF. The NUV contours range from 5 x 10-5 to 0.5 in steps of a factor of 10. This PSF was genreated by averaging together many point sources from the Medium Imaging Survey in sky coordinates.
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| Figure 5 Contour plot of the FUV PSF. The FUV contours range from 2 x 10-4 to 0.2 in steps of a factor of 10. This PSF was generated by averaging together many point sources from the Medium Imaging Survey in sky coordinates.
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In each band, we subtracted a local background determined in a circular annulus around each star with an inner radius of 90” and a width of 30”. This background on average is about 3% fainter than the standard GALEX pipeline background in the NUV and about 5% brighter than the pipeline background in the FUV. After subtracting a local background, the profile or each star was scaled to unity total flux. Before stacking the stars together, each individual star was shifted to have it’s center always lie directly on top of a pixel using bilinear interpolation. This prevents the resulting average PSF from blurring just due to sub-pixel shifts in the centroid of each star. Finally, the stars were averaged to gether on a pixel by pixel basis using a clipped average. In the NUV, the counts at these magnitudes are large enough such that Gaussian statistics can be used while in the FUV, it was necessary to use the full Poisson distribution, similar to the clipping used in determining the sky background as described in the previous chapter.
Contour plots of the resulting average PSF are shown in Figures 4 and 5 for the NUV and FUV, respectively. Although the GALEX PSFs in general are somewhat elliptical, the PSFs shown in the figures are very axisymmetric since the sources were averaged together in sky coordinates and were selected regardless of their location on the detector. Relative radial profiles for the PSFs in both bands are shown in Figure 6 where the peak of each PSF has been scaled to unity. The PSFs consist of a more or less Gaussian core with extended wings. For the cores of these PSFs the full width half maxima are 4.9” and 4.2” for the NUV and FUV, respectively. The wings of the FUV PSF appear to extend smoothly with radius while the NUV has a “shelf” which extends out to a radius of about 45”, beyond which it falls off more rapidly.
The average PSFs used in these plots can be found in the following two FITS files: PSFnuv_faint.fits (NUV) and PSFfuv.fits (FUV).
| Figure 6 Radial profiles of the FUV (blue) and NUV (red) PSFs.
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The corresponding encircled energy curves are shown in Figures 7 and 8 in black for the PSFs generated from the field star sample whereas the dashed red lines show the encircled energy for our primary calibration star LDS 749B from Morrissey et al. (2007). The curves for LDS 749B have the same overall shape as for the field stars although they are a bit broader, particularly in the FUV. This is likely due to two effects. The average for the LDS 749B data does not account for sub-pixel shifts in the centers of each individual observation whereas the field star average does take this into account. A second possibility is that the LDS 749B data are slightly saturated in parts of the detector, particularly in the NUV, leading to a broader encircled energy curve. As is obvious from this section, in order to include all of the light for a given source, a rather large aperture should be used. For faint sources, using a large aperture can greatly increase the error due to sky noise. Often it is advantageous to measure the flux in a smaller aperture and then use an average PSF to compute an aperture correction to account for light lost outside the aperture. We have used the average field star PSF to compute aperture corrections for the radii employed by the GALEX pipeline when computing aperture magnitudes. In Table 1 we list the aperture corrections in magnitudes for the standard GALEX aperture measurements.
| Figure 7 Encircled energy curve for the NUV PSF. The solid black line is the curve for the average field star PSF whereas the corresponding curve for the white dwarf calibration star LDS 749B is shown as the red dashed line.
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| Figure 8 Encircled energy curve for the FUV PSF. The solid black line is the curve for the average field star PSF whereas the corresponding curve for the white dwarf calibration star LDS 749B is shown as the red dashed line.
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| Table 1: Aperture corrections for the average field star PSFs
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| Aperture No. | radius (arcsec) | FUV aperutre correction (mag) | NUV aperture correction (mag)
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| 1 | 1.5 | 1.65 | 1.33
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| 2 | 2.3 | 0.77 | 0.62
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| 3 | 3.8 | 0.20 | 0.21
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| 4 | 6.0 | 0.10 | 0.12
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| 5 | 9.0 | 0.07 | 0.08
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| 6 | 12.8 | 0.05 | 0.06
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| 7 | 17.3 | 0.04 | 0.04
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Since the GALEX PSF varies with position within each detector and in principle from observation to observation, the aperture corrections listed in Table 1 may not apply to a particular observation. If possible, we recommend using bright stars within the image to determine aperture corrections appropriate for that particular image. The PSF tends to become broader near the edge of the field of view. (See Figures 9 and 10 of Morrissey et al. (2007) for more details).
Image Artifacts
GALEX images contain a number of artifacts particularly around bright stars. This section describes these artifacts and gives example images.
- Diffuse Reflections: Bright stars just outside of the field-of-view can create various large diffuse reflections within the field. The shapes of these artifacts vary but the most common shapes are either horse-shoes as shown in Figure 8 below or long thin cones. These diffuse reflections are not flagged automatically by the GALEX pipeline. The reflection itself can be detected as a source (or sources) by the GALEX pipeline and can also bias the local background.
| Figure 8 Example of a so called "diffuse reflection." The horse-shoe shaped emission visible in the middle of this image is due to scattered light from a bright star just off of the field-of-view. These diffuse reflections are not automatically flagged by the GALEX pipeline.
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- Dichroic and window reflections: Bright stars that fall within the field-of-view also generate image artifacts. An example is shown in Figure 9 below. The large diffuse circular reflection is due to the NUV detector window. These ghosts are always radially offset from the star towards the outer part of the detector. The other smaller elliptically shaped artifact is due to the dichroic beam splitter. It is offset along the detector y-axis and will thus appear to move on the sky relative to the star for different space craft roll angles. In the flags map, the regions flagged as being part of a window reflection are set to 2 (10 in binary notation) while the dichroic reflection is flagged with the value 4 (100 in binary notation).
| Figure 9 Example of artifacts due to bright stars within the field of view. The large diffuse circle seen to the North-east of the star is the detector window reflection while the smaller circle to the north is due to the dichroic beam splitter.
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- FUV bright star halo: Very bright stars in the FUV will sometimes scatter light off of wires that are on the FUV detector window, resulting in a spray of faint light around the star. An example of this is shown in Figure 10 below. These reflections are not flagged by the GALEX pipeline.
| Figure 10 Example of FUV bright star halo due to scattering off of the grid wires on the FUV detector window.
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- Hot spot: Normally masked out in the pipeline, new hotspots not already in the hotspot mask will appear as a spiral dither pattern. Hot spots are fixed in detector coordinates and thus will appear to move around on the sky due to the space craft dither motion. An example of an unmasked FUV hot spot is shown in Figure 11. The shape of the hot spot artifact in the image will vary depending upon the particular space craft dither for the particular observation. Unmasked hot spots can occur in both FUV and NUV images.
| Figure 11 Example of an unmasked FUV hot spot.
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- NUV edge reflection: The NUV window has a beveled interior surface required to locate the photocathode surface close to the microchannel plate surface. Total internal reflection causes light from stars within 5 arcminutes of the edge to reflect into the field of view. This can result in elongated artifacts pointing inward from the edge of the field towards the center of the detector as shown in Figure 12 below.
| Figure 12 Example of NUV edge reflection.
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