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Evaluation of Calibration Field Completeness

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The images linked in the table below show comparisons in the completeness fraction for various selections from the calibration database. These statistics arise from the frequency of occurance of fiducial stars in a "catalog working" subset of the calibration WSDB. This subset derives from running same SQL query that produced the point source working catalog database (i.e. same snr/msig cuts, etc.). Completeness statistics for stars are computed on a tile-by-tile basis within this database. For a given tile the following steps lead to the final statistics:

1. Find the observation with the best sensitivity (i.e. the lowest PSP value in the selected band.

2. Use all stars detected in one scan with this PSP value as the "fiducial" set.

3. Find all occurrences of these "fiducial" stars in all of the other scans of this calibration tile based on positional coincidence within 3".

4. Calculate a mean magnitude for each "fiducial" star based on all legitimate detections (rd_flg contains [123] cc_flg does not contain [A-Z]).

5. Count the number of detections of the fiducial star and compare with the number of opportunities to detect the fiducial star.

6. Make plots of the completeness fraction for each star vs. the mean magnitude of interest.

1. Completeness within the entire working release dataset

2. Completeness for stars with photometric quality (ph_qual) flag set to "A" in the database - where the "A" classification arose from the scan with best sensitivity. These are the panels with "ja" at the top.

3. Completeness for stars with photometric quality (ph_qual) flag set to "A" in the database - where the "A" classification arose from the scan with worst sensitivity. These are the panels with "jab" at the top.

4. Completeness for stars with photometric quality "AAA". These are the panels with "jaaa" at the top.

1. 90161 -- a high galactic latitude field observed from the North.
2. 90312 -- a field in the galactic plane observed from the South

Observations:

1. Completeness fraction is a well defined function of magnitude. Changing observing conditions have only a modest effect. This may be a bit illusory as the best PSP values (best seeing in particular) tend to dominate in the database. Ultimately the variation in completeness with PSP will be used to translate all-sky PSP maps into all-sky completeness maps (see future work below).

2. The "catalog" as defined by a source having an "A" in any one band is complete to a depth approximately 0.5 mag brighter than the entire release dataset. Completeness in this case is defined by asking how many times a "fiducial" source which received an "A" also received an "A" in its other apparitions.

   • For the J-band, the entire release is 99% complete to J-mag=16.2. The "A" selection is 99% complete to J=15.7. These numbers are to be compared to the J-band Level 1 spec of 99% in the 1/2 magnitude bin brightward of J=15.8.

   	J-band	H-band	Ks-band
   Level 1	15.8	15.1	14.3
   "A" level	15.7	14.8	14.5
   Release	16.1	15.5	15.1

3. The definition of completeness (in terms of the ph_qual flag) is muddled. Completeness is well defined -- i.e. the number of times a source got an "A". What is not well defined is the bulk completeness of the integrated catalog (i.e. what is the average completeness in each magnitude bin for all sources which received an "A").

   • If the sample was observed under excellent sensitivity conditions, then the sample turns out to be relatively incomplete, because faint stars that would otherwise get "B"'s get "A's". All of their other apparitions are necessarily "B" which makes them appear incomplete.

   • At the other extreme, sources which receive an "A" when conditions are poor necessarily receive an "A" in all of their other apparitions. This is the difference between the "ja" and "jab" plots. They show the same points, but the "fiducial" list of stars is different because one was chosen in poor conditions, the other in good conditions.

4. "AAA" sources are very difficult to characterize in terms of completeness vs. mag (see plots labeled "jaaa"). This fuzzyness results from hybridization of the results from various bands. Some sources have their completeness determined by their J-band others by their K-band. The result is a poorly characterized turnover in completeness. Those interested in working with a sample with well-characterized completeness are strongly advised to stay away from the "AAA" sample. Of course this was exactly our motivation in going from a single encompassing ph_qual flag for each source to a band-specific ph_qual flag - an excellent choice in retrospect.

Future work:

1. Compare southern and northern fields with similar source density.

2. Divide according to PSP ranges to examine how completeness maps to this variable.

Addendum

Tom Chester pointed out that the fainter sources will suffer from flux overestimation as their detection is biased by positive noise fluctuations. Roc Cutri provided Ks-band photometry from a deep image stack of the P161 calibration field compared with the average photometry from the cal scan detections. It shows that

• Down to Ks=15.5 the photometry is largely unbiased.
• The faintest detected sources are actually Ks=16.5 (and one real one at K=17!)
• When compensating for this flux bias, the plots above will look the same down to Ks=15.5 and then the remainder will be expanded into the Ks=15.5-16.5 range.
• Completeness falls off less sharply with magnitude than the plots indicate.
• The conclusions for the 90% completeness levels are unaltered.
• Flux overestimation does not affect conclusions at the magnitude level of the Leve1 specifications and does not affect the completeness curves for "A" sources.

Roc's comments on the plot:

The attached plot shows the difference between the aperture mags
measured from a "deep" stack of ~1300 northgoing scans and your mean
mags for the P161D field.  The deep mags are from simple aperture
photometry using IRAF.  Mags are for 4" radius apertures
curve-of-growth corrected to "infinite" aperture.  The
c.o.g. correction was -0.067 mags, larger than the typical correction
from the pipeline..  The corrected-aperture mags were then normalized
to the mean cal-scan mags using the trimmed average offset for stars
having 8 < Ks < 14, where there is no systematic bias.

The points scattered downward off the general curve are
due to confusion - I let IRAF recenter the apertures, so for
some fainter stars, the apertures were pulled off the nominal
star positions towards brighter objects.  They can be disregarded.

The effects of flux-overestimation in the single scans is clear
and dramatic.  The result is that your completeness curves
will be stretched out somewhat.  It is also rather amazing that there are
some real detections and measurements of Ks>16 mag objects!

Also notice the rising offset for the two stars brighter
than Ks=8.  Must be some saturated samples that snuck into the
stacks.