• The final catalog of optical stars

For boresight calibration, we used the open star cluster NGC 2516. For this task, we need optical astrometry with a better than 0.2"-0.3" accuracy, so that this error component would be negligible compared to other AXAF coordinate errors (totaling about 1"). There are no accurate coordinates in the literature, so in April 1998 Scott Wolk has taken several short (6 s and 60 s) CCD exposures at the CTIO 0.9 m telescope in several spectral bands, covering a 25'x25' area in 4 pointings.

To achieve the required accuracy, we must use the Tycho Catalog coordinates as a reference frame and take the star proper motions into account whenever possible (some exceptional stars in this field have moved quite noticeably since the Tycho epoch of 1991; the effect of the proper motions will be discussed below). For a reference frame, I used a subset of the AXAF Guide Star Catalog (AGASC) with the star coordinates from the Tycho (with listed coordinate accuracies <0.1"), corrected for our CCD epoch of 1998 using the known proper motions listed in AGASC (originating from either the PPM or ACT catalogs) or left in the 1991 epoch if the proper motion was unknown. There were no stars with proper motions taken from the Tycho Catalog (which are claimed to be unreliable).

Each of the 6 s exposures have several m>9 Tycho stars that are not strongly saturated and can be used to establish a coordinate reference frame in the optical CCDs. In the 60 s exposures, all the Tycho stars are saturated and the coordinate solutions have to be found using the fainter stars from the 6 s exposures. On the other hand, the 60 s exposures are deep enough to detect stars down to m>21. In analyzing these exposures, my aim was to generate a catalog of accurate star coordinates in the field for subsequent identification with X-ray sources. I have chosen a rather conservative flux limit for the source detection (about 200 photons in the 60 s exposures, or about m=21). If some X-ray sources would not be identified, one can go back to the CCDs and look for fainter sources using the coordinate solutions already found.

Scott Wolk has provided images with initial reduction (flat-fielding, background subtraction, crude coordinate solutions) done. I used IRAF for detecting the sources in the CCDs and finding the accurate coordinate solutions. The source chip coordinates were determined using the centroid method with the square window width of 8 pixels (to accommodate the unsaturated regions of the bright star images and at the same time to avoid excessive background contribution for the faintest stars). The chip scale is 0.4"/pixel and the PSF FWHM is about 1.6". The statistical accuracy of the centering for the faintest sources in the final catalog was better than 0.15" (rms), while for typical sources it is negligible.

Coordinate frame for the 6 second exposures

Is the linear coordinate solution sufficient?

The coordinate solution for each pointing (and each spectral band) was fitted by a 6-parametric linear transformation using the IRAF task images.imcoords.ccmap. It appears that there is no need to introduce nonlinear terms; the residual deviations of individual reference stars (covering all of the chip) from their best-fit positions were all smaller than 0.2" with rms deviation of about 0.1".

Proper motions.

Of the useful Tycho reference stars (13-15 per each of the 4 pointings), only 2/3 have measured proper motions (hereafter PM). Given the limited number of the available reference stars, it is advantageous to use all of them, including those without the PM. For 90% of all the stars with known PM in the r=40' field around the cluster, the PM (radial value) is <0.02"/yr (translating to <0.14" since the Tycho epoch of 1991), and the median value is 0.01"/yr. Ignoring such PM would be acceptable. However, 3 stars (3%) have very large PM, 0.15"-0.50"/yr (these stars are outside the field covered by our exposures).

To check if there are such fast-moving stars among those with unknown PM in our field, I calculated the chip coordinate solutions using only those reference stars that have known PM and using all reference stars. Both solutions were nearly identical. When the former solutions were applied to the remaining Tycho stars with unknown PM, the difference of their measured and cataloged coordinates was acceptably small: the rms deviation (radius) was 0.11"-0.16" in individual pointings and the maximum deviation was 0.14"-0.23". Only one star in one pointing deviated by 0.28". Therefore, I have decided to exclude this one star but otherwise use all stars, with and without the PM, as reference stars.

For another check, I have used the reference star coordinates for the 1991 epoch without the PM correction; the residual deviations were slightly worse, which means that the PM are noticeable (although insignificant) and the PM correction is of the right sign.

Different chip quadrants.

The chip physically consists of 4 adjacent quadrants, for which, ideally, individual coordinate solutions should be found. However, examination of the residuals along the quadrant boundaries showed that there is no need for that -- no systematic differences were apparent at the level of our accuracy.

Different spectral bands.

Images made with different filters (I, R, V, B for almost all the pointings) were analyzed separately. The plate scale in different bands is found to be different by about 0.1%. Therefore, I have calculated the individual coordinate solutions for each spectral band and then averaged the final sky coordinates of the detected stars over the bands. The difference between the coordinates of the same star (a detected star, not a reference star) in different bands of the same pointing was small, with the median of 0.04"-0.07" and the maximum deviations of 0.3" for the 6 s exposures and 0.4" for the 60 s exposures. In the B band, the fluxes and the accuracy are lower; therefore, I have chosen not to use this band (although the coordinate solutions are calculated for those images as well).

Overlapping regions of different pointings.

The fields of view of the 4 pointings have a 1' overlap, which allows a useful check of the final coordinate accuracy. For the stars detected in more than one pointing, the coordinate differences between the pointings were small, with the median 0.05"-0.13" and a maximum deviation of 0.25" (for both the 6 s and 60 s exposures). Coordinates for stars in overlapping regions were averaged between the pointings.

Source detection

Stars in the CCD images were detected as enhancements of the surface brightness above a certain threshold, using the IRAF task digiphot.daophot.daofind. For the 6 s exposures, I have chosen this threshold to correspond to the total flux of 1000 photons in the V band (since these exposures are only necessary for a transfer of the coordinate frame to the deeper exposures), and for the 60 s exposures, about 200 photons. The sources were detected in the V band only; these same sources were then identified and re-centered in other bands, except for several cases when a source fell on a CCD defect in one of the bands and was omitted. All exposures were examined by eye and all defects detected as sources, as well as poorly resolved double stars, were removed. The source exact positions and fluxes were then determined in each band by the task digiphot.apphot.phot, using the same algorithm (centroid in the 8-pixel window) as that used for the reference stars, to ensure that the PSF shape has the same effect on both measurements and is properly taken into account in the coordinate solution.

Transfer of the coordinate frame to the 60 second exposures

Stars with fluxes greater than 10^6 photons have saturated brightness peaks in the CCDs. Therefore, to establish the coordinate frame for the 60 s exposures, I have used all stars from the 6 s images that have fluxes between 2000-10^5 photons (per 6 s). There are 287 such stars in the entire field. These stars were identified in the 60 s images, their exact coordinates found by the task digiphot.apphot.center, and a linear coordinate solution was found similarly to the 6 s exposures, for each band separately. The residual deviations for these stars were small, with rms about 0.05".

After that, other sources in the 60 s exposures were detected and their coordinates averaged between the different bands (all 60 s pointings have I,R,V data) and between the different pointings in the overlapping areas. For the 60 s exposures, only those sources whose coordinates in different bands were within r=0.3" were included in the final list (that excluded several faintest stars).

The final source catalog

Stellar magnitude scale.

For reference, approximate V magnitudes were determined from the V-band CCD fluxes, using the average conversion coefficient calculated for several unsaturated Tycho Catalog stars in our list.

Combined list.

The brightest stars can only be measured in the 6 s exposures, but intermediate-flux stars were detected in both the 6 s and 60 s exposures. The agreement of their coordinates is very good: the maximum deviation is 0.15". For those stars whose flux in the 60 s exposure is greater than 20000 photons, I have chosen to use the 6 s coordinates. This results in 356 stars with coordinates from the 6 s exposures and 1979 stars with those from the 60 s exposures.

Finally, 6 bright Tycho stars that are in the field but are too bright and saturated even in the 6 s exposures, were manually inserted in the final list. Unfortunately, for 2 of them, including the brightest, there are no measured proper motions, and their coordinates, taken from AGASC, correspond to the 1991 epoch. The final list of 2341 objects can be found here.

Preliminary identification of X-ray sources

About 85% of the X-ray sources seen in the ROSAT PSPC image have one or more (up to 4) optical counterparts in the above list within r=15" (the PSPC PSF). Since the PSPC coordinates are rather inaccurate and the sources are confused, it would be useful to look at the HRI image (proprietary at this moment). It is possible to detect fainter sources in the CCD images to try to identify the rest of the X-ray sources; however, since stars are strongly variable in X-rays, I think it is better to do it after the AXAF images are obtained.

In addition, I would consider taking longer exposures (say, 600 s) of the same pointings to be on the safe side (since the sources fainter in the optical than those in my catalog would have a nonnegligible statistical uncertainty of their position).

ADDED ON 3/9/99:

Paul Green has advised me to estimate the faintest reasonable V magnitude for possible counterparts of our X-ray sources using

log fx/fv= -0.5 = log fx(0.3-3.5 keV) + V/2.5 + 5.37