Subsections

• 5.13.1 Overlap Rejection
• 5.13.2 Optimization for Source Validity ($P_B$)
• 5.13.3 Optimization for Source Position
• 5.13.4 Optimization for Timing Analysis
• 5.13.5 Optimization for Photometry and Spectral Fitting

5.13 Discarding Observations

In a multi-observation analysis, single-observation extractions are combined to form multi-ObsId data products and source properties, as described in the previous sections. In some cases, combining all the observations of a source will not produce the highest quality results, due to the highly-variable PSF size across the Chandra focal plane..

5.13.1 Overlap Rejection

The ae_make_catalog tool now computes an OVERLAP metric for each source, quantifying how much its extraction region overlaps its nearest neighbor (closely-spaced sources can still overlap substantially even though AE automatically reduces the extraction region to minimize overlap; this is because we have imposed a floor in that reduction so that we never have an extraction region containing <40% of the full PSF). The MERGE stage now accepts an OVERLAP_LIMIT metric which will discard observations that have excessive overlap. This provides a blunt control over source crowding. Our justification for explicitly limiting overlap is that source photometry and our background algorithm (ae_better_backgrounds) are both expected to lose accuracy as neighboring sources share more and more counts in their apertures.

5.13.2 Optimization for Source Validity ($P_B$)

The MERGE stage also has a /MERGE_FOR_PB option which seeks to choose, for each source, the subset of the observations which gives the smallest (most significant) PROB_NO_SOURCE value (the probability that the source is just a background fluctuation). For a constant source, this should tend to optimally discard far off-axis observations (which have high background in their large apertures) when on-axis observations are present. For variable sources this should tend to discard observations when the source is weak. This should provide an increased sensitivity to flaring sources (since you can ignore the non-flaring observations). The cost you pay for such an optimization, of course, should be an increased false detection rate--the PROB_NO_SOURCE statistic is computed on several different subsets of the data and thus Mr. Poisson has several random chances to score a passing grade.

5.13.3 Optimization for Source Position

The MERGE stage also has a /MERGE_FOR_POSITIONS option which seeks to choose, for each source, the subset of the observations which gives the smallest position error estimate. The position error computation involves both the PSF sizes and number of counts in each observation. For example, an off-axis observation may add value to an on-axis observation if the former has many more counts (due to the length of the observation, or due to a flare).

5.13.4 Optimization for Timing Analysis

Ideally, no observation selection is desired for timing analysis since even off-axis extractions with high background carry useful timing information for that epoch. Thus we propose that the only selection criterion applied in the merge used for timing analysis will be the "overlap rejection" described above.

5.13.5 Optimization for Photometry and Spectral Fitting

When the source property of interest is photometry (whether derived via SRC_COUNTS or via spectral fitting), one could similarly devise a selection procedure that seeks to maximize the signal-to-noise (SNR) ratio (or some other metric) of the merged data. However, such a procedure will produced biased photometry estimates--it will tend to accept observations where the source appears brighter than average, and tend to reject observations where it appears weaker. If your sources are truly variable, and your goal is to estimate their average flux, then obviously this procedure will bias that estimate. Even if your sources are truly constant, their observed flux will vary from observation to observation due to Poisson variation; if your algorithm is allowed to ``cherry pick'' the brighter observations, then your flux estimate will be biased.

Note that bias arises because you are allowing the algorithm to optimize an observed quantity (e.g. SNR). The Source Validity pruning procedure (above) has the same problem; however we embrace the resulting bias (i.e. an increased false detection rate) in our quest for increased sensitivity to variable sources. The Source Position pruning procedure (above) also optimizes an observed quantity (position error); however since we assume that all data from a source come from the same point in the sky then cherry picking a subset of the data should not bias our positions.

When the goal is computing photometry, however, optimizing any observed quantity is not at all acceptable. Only a blind selection procedure of some kind--one that chooses whether to retain or discard each ObsId without considering the events actually observed in its aperture or background region--can avoid photometry bias. One can readily imagine two categories of unbiased procedures that attempt to optimize photometry by selecting observations:

• One could predict the number of counts that should be observed in each extraction of the source (SRC_CNTS and BKG_CNTS) based on a constant model of the source flux and background surface brightness. (For example, the model might be derived from a merge of all the source's extractions.) The algorithm would compute which combination of those predicted extractions would optimize some metric of the merged data (e.g. SNR), and would then proceed to merge those actual observations and perform photometry. Under this procedure, when background is important to SNR (i.e. for weak sources), high-background extractions (e.g. from large off-axis apertures) will be discarded. But when background is not important (i.e. for bright sources), then all extractions will be retained.

• One could devise some set of rules for deciding which extractions to merge that is based only on the properties of the extraction regions (e.g. the size of the regions, off-axis angle, exposure time, etc.). Such a procedure would necessarily be tuned to some particular situation the rule-maker had in mind; it could never ``do the right thing'' for both weak and bright sources, or for both low and high background regimes.

Alas, any such blind (unbiased) photometry merge will sometimes have a severe problem with variable sources--the observations we choose to discard may in fact have very high-quality data (e.g. a beautiful flare).

The AE team has so far been unable to devise a satisfactory procedure for discarding observations when merging for photometry and spectral analysis. Assuming that unbiased photometry is important to the observer, we recommend that photometry and spectral analysis should be performed on a simple merge (i.e. one that omits the /MERGE_FOR_PB and /MERGE_FOR_POSITIONS options).