After reduction, there is one more decision to take before photometry can begin. That is how to combine the data from the individual frames. One can do one of two things. The first is to take all of the frames in a given filter for a given object, combine them into a single master frame, and measure that. The other option is measure each frame individually and then take a weighted average of the photometry over all frames for each object.
The first option is attractive for a number of reasons. To begin with, it allows one to reject cosmic rays, preferably by implementing some kind of sigma clipping algorithm. As anyone who has attempted PSF photometry can attest, cosmic rays are one of the banes of a PSF photometrist’s life. Secondly, combining is a much less time consuming task than PSF photometry, which is one of the other banes of a PSF photometrist’s life. (Though the second benefit was not reaped in this study, since the photometry of every individual frame was needed in order to study the variable stars.)
The first option was thus adopted for Leo IV. In a universe without cosmic rays, one could simply take all of one’s frames for any given object and filter and sum them. Un- fortunately, that is not this universe. In order to reject cosmic rays, frames of the same exposure time and nearly the same alignment were averaged by threes and a sigma clipping algorithm applied, using IRAF task imcombine of package immatch. (That algorithm is named “ccdclip”. It involves taking the median of each pixel across frames, calculating the expected spread in valuesσbased on Poisson statistics, and then iteratively rejecting pixels some number ofσaway from the median.) Some images had to be shifted slightly in order to align them correctly for averaging. This was done with IRAF task imshift of package immatch. Finally, the averaged frames, having been cleaned of cosmic rays, were combined by a simple sum, againinimcombine.
cosmic rays, as well as to get a good average, one needs at least three frames of the same filter and exposure time that are unaffected by thin cirrus, or at least equally affected. Most of the images of Boötes II do not fit this bill.
The frames from the night of May 16, 2007 were of either 300 s or 1200 s exposure times. There are not a total of three of each for each filter across the three nights of Boötes II observations.
The frames of the night of June 17, 2007, were heavily affected by thin cirrus. Careful examination of the radial profile plots of stars and sky statistics for the frames of that night show the brightnesses of stars and sky to vary greatly between frames of the same exposure time and filter. If the stellar images of any one frame were found to be dimmer than those in another image, they were found to be so by a fraction constant across the field. This was coupled with what was often abrightersky value in the frame with thedimmerstars. This is consistent with thin cirrus, which dims the stars, but can result in a brighter sky because of reflected light. Unfortunately, the stellar brightnesses varied so much between frames that averaging was out of the question. Fortunately, the dimming was found to be constant across any given frame by examination of the stellar profiles and photon counts of bright stars, so that photometry could still be usefully performed on those frames, and the dimming taken into account by constant magnitude offset (which is to say a multiplicative factor in flux.)
Only the frames of the night of May 16, 2007 were suitable for averaging. That was done. The rest of the frames were measured individually. The photometry of all frames, both obtained by measuring individual frames and obtained by measuring the combined frames, were averaged together to obtain the final photometry. (See §4.5 and §4.7 for details concerning the averaging.)
The Leo IV control field frames were also done in a similar fashion - individually for the most part, with some frames combined. The 1200 second exposure I band frames of
the night of May 16/17, 2007 were averaged. The two 300 second dSphsband frames of the night of March 22/23, 2007, and the 300 s frame I band frame of the night of May 17/18 were also averaged. Then these two averaged frames were summed. The rest of the frames were not suitable for combining for various reasons.
Attempts were made to average and measure the 1200 s V frames of the night of May 16/17, 2007, but the results were poor. The fields appear to be aligned, but combining them as is yields odd looking stellar radial profiles. After slight re-alignment to address this, photometry on the resulting averaged frame produced poor results, as shown by examin- ing residuals of subtracted stars (see §4.4.) Thus it was decided to measure these frames individually. Those results turned out well.
The 300 s V frames from the nights of March 22/23, 2007 and May 17/18, 2007 were not averaged because the first frame from March 22/23 was found to have elongated stellar profiles, owing to tracking issues. All three frames were successfully measured individually, as DAOPHOT can handle elongated profiles. For the remaining frames, there were not three of the same exposure time in any filter, so they too were measured individually.