Single-exposure (L1) vs Multiframe (L3) photometric comparisons

1. L3 vs averaged L1 photometry

All-sky Catalog (L3) wpro extractions were queried from a 3 square degree region centered on the ELAIS-N1 field, then matched against the single-exposure (L1) all-sky database using a match radius of 1.5 arcsec. The following constraints were used:

 * L3 w1rchi2 & w2rchi2 < 1.15 (to minimize contamination
   from extended/resolved sources and skewing the profile-fit
   estimates; ~98% of sources in this field satisfied this limit)
 * L3 na = 0 (to further minimize possible ambiguities and
   keep estimates relatively 'clean')
 * L1 and L3 w?sigmpro.ne.'null' (to avoid upper limits in the
   band of interest)			      

To avoid abnormally lo/hi L1 fluxes, outliers, etc for each L3 extraction, the minimum and maximum measurements were blindly tossed from each stack. Given the median depth-of-coverage was ~67 for this field, this operation did not significantly impact the L1 stack statistics. The stacked (min/max clipped) L1 fluxes for each L3 extraction were then averaged, medianed and a standard-deviation was computed. The WISE single-exposure photometric zero-points were then used to convert to magnitudes.

Results are shown in Figures 1 - 4 for each respective band. Given the L1 extractions correspond to a higher signal-detection limit than the L3, the averaged L1 fluxes will be biased high beyond some flux limit when the L1 S/N is low. I.e., we are likely to catch the high tail of the L1 flux distribution, comprising only those sources that made it above the L1 detection limit. To enable an 'unbiased' comparison with the L3 fluxes, the L1 limiting fluxes above which measurements should be compared were determined by first computing a proxy for the L1 S/N (characteristic of this field):

(S/N)_L1 ~ <L1 fluxes> / StdDev(L1 fluxes; unbiased estimate of pop sigma).

This proxy is plotted as a function of magnitude below. The limiting L1 fluxes (magnitude) values for comparing <L1> and L3 fluxes are indicated by the vertical blue lines in Figures 1 - 4. These limits where determined from the L1 S/N vs <L1> plots below, i.e., just before the abrupt 'artificial' turnovers in S/N. These correspond to S/N values of ~ 3.8-4.5 across all bands.

Conclusion: to limiting magnitudes where it makes sense to compare L1 and L3 measurements (due to differences in detection limits), it appears the L3 wpro fluxes are starting to be biased low relative to averaged or medianed L1 fluxes. This is seen in bands W1 and W2. W3 is inconclusive and there's a slight hint of a bias in W4. The W1 and W2 results are consistent with those found in W? - K band UKIDDS colors vs L1 magnitudes for the EN1 field (see below).

Figure 1 - W1: left to right: averaged L1 fluxes, medianed L1 fluxes, and L1 S/N proxy from Std-Dev.

Figure 2 - W2: left to right: averaged L1 fluxes, medianed L1 fluxes, and L1 S/N proxy from Std-Dev.

Figure 3 - W3: left to right: averaged L1 fluxes, medianed L1 fluxes, and L1 S/N proxy from Std-Dev.

Figure 4 - W4: left to right: averaged L1 fluxes, medianed L1 fluxes, and L1 S/N proxy from Std-Dev.

2. L1 Wpro photometry vs UKIDDS K-band

Figure 5 shows color-density plots involving K-W1 and K-W2 colors where the W1, W2 photometry is from the single-exposure (L1) all-sky database, and K band photometry is from UKIDDS for an area in the ELAIS N1 field. Here are the filters used:

 * ukidds K < 18.0 (to select mostly stars)
 * ukidds J - K < 1.0 (blue limit; also to select mostly stars)
 * ukidds - wise match sepn = 1.5 arcsec.
 * L1 w?snr >= 3
 * w?sigmpro not 'null' (to avoid uppper limits)

Overall, the L1 photometry for W1,W2 does not appear to show any significant bias towards the faint end as seen in multiframe photometry. I.e., the K - W? colors do not appear to get bluer with decreasing W? flux.

Figure 5 - left: K - W1 color vs W1 magnitude from single exposure photometry for a region in the ELAIS N1 field; right: similar for K - W2 vs W2.

3. Reduced chi-squares from profile-fit photometry

Figure 6 shows the "w1chi2" values from multiframe profile-fit photometry for the same ELAIS N1 region examined in Section 2, and with the same filtering metrics. The observed drop in reduced chi-square for faint sources (at W1 >~ 16) means photometric uncertainties are being over-estimated by ~ (1/√0.87) - 1 ~ 7%. At the time of writing, it is not known whether this applies to the entire all-sky catalog.

Also, it is unclear how the trend in w1chi2 at faint fluxes is related to the multiframe flux bias, if at all.

Figure 6 - Reduced chi-square from multiframe profile-fit photometry (wpro) as a function of W1 magnitude for the same region in ELAIS N1 used in Section 2; left: as a scatter plot; right: as a color-density plot.