The following figure shows the RMS residuals to the nightly northern (left column) and southern (right column) J, H and Ks photometric zero point fits, plotted as a function of survey day number. The two vertical lines in each column represent the survey days at which new secondary standard stars were introduced into the pipeline calibration.
Figure 1 - J, H and Ks nightly zero point residuals plotted as a function of time. For the J-band plot, residuals to a constant zero point fit are shown in red, and residuals to the linear zero point are shown in black.
This plot illustrates the improvement in the statistical accuracy of the nightly zero points with the introduction of secondary standard stars in the calibration fields. The mean northern residuals drop significantly with the introduction of the first set of secondary standards used to process survey day 427 onward. The second delivery of secondary standards were predominantly for the southern calibration fields, so the improvement in residuals is primarly in the southern nights.
The following three figures show histograms of the RMS residuals of the nightly J, H and Ks photometric zero point fits, respectively. Northern residuals are denoted by the black lines in these plots, and southern residuals are denoted in red. These histograms include only RMS residuals from survey days >427 (having secondary standards), and from nights in which the photometric interval was >5 hours, so there are more than 5 cal sets going into a solution. The J-band plot shows the distribution of residuals to the linear fits.
Figure 2 - J-band Zero Point Fit Residuals
Figure 3 - H-band Zero Point Fit Residuals
Figure 4 - Ks-band Zero Point Fit Residuals
Discussions are ongoing about how to weight individual calibration scan zero point data in the computation of the nightly zero point fits. Airmass is one weighting factor that has been discussed, but it was not certain if the degradation of seeing and increase of backgrounds with increasing airmass naturally results in decreased scan-wise zero point measurements, rendering a separate airmass weight unnecessary. Figures 5 and 6 show for every nominally photometric calibration scan taken after 980501 UT (north) and 980503 UT (south) the RMS uncertainty in the zero point offset measurement plotted versus the starting airmass of the scan. The zero point offset measurement for each scan is the mean difference between the instrumental magnitudes and "catalog" magnitudes for all primary and secondary standard stars in the scan, corrected for atmospheric extinction. The RMS uncertainty of the scan-wise zero point measurement is the population standard deviation. Only calibration scans that had secondary standards are included in this analysis.
The small, colored points represent individual scans. Figures 2 and 3 show that the integrated residual distributions have tails towards larger values. Simple scatter plots, such as those below, don't indicate well where "ridgeline" of sources fall. Since I don't have the ability to generate density (or Hess) plots, I instead have added to each plot, in black, the 2 sigma-clipped average zero point uncertainties in 0.05 airmass bins. The vertical error bars on these points represent the RMS difference from the mean of the trimmed sample in each bin.
Figure 5 - Northern Scan Zero Point Uncertainties Plotted as a Function of Scan Airmass
Figure 6 - Southern Scan Zero Point Uncertainties Plotted as a Function of Scan Airmass
The two figures above show a weak dependence of zero point measurement uncertainty on airmass. Linear fits of the trimmed average sigma versus airmass, weighted by the RMS in each bin yields the following relationships for each band. Sigma is the mean zero point uncertainty, in magnitudes, X is the airmass. The first two numbers in parentheses are the uncertainties in each term in the fit, and the third is the reduced chi-squared. The fits were limited to bins containing >50 scans, which translates approximately to an airmass of 2.025.
North: J: Sigma = 0.011917 + 0.002146*X (0.004070, 0.002816, 1.664610) H: Sigma = 0.009751 + 0.007934*X (0.006440, 0.004681, 1.086577) Ks: Sigma = 0.015648 + 0.003222*X (0.006244, 0.004299, 2.727485)South: J: Sigma = 0.004723 + 0.008107*X (0.004611, 0.003038, 0.653533) H: Sigma = 0.010164 + 0.007178*X (0.005828, 0.003814, 0.465303) Ks: Sigma = 0.012987 + 0.007093*X (0.007260, 0.004729, 1.284591)
These linear fits for each hemisphere are included in Figures 5 and 6. The weak dependence of zero point uncertainties on airmass does not appear to be sufficient to de-emphasize the high airmass calibration scan measurements.
During the nightly photometric calibration process, a zero point offset is measured for every scan by calculating the mean difference between the catalog (i.e. true) and atmospheric extinction-corrected instrumental magnitudes for all primary and secondary standard stars in the the scan. The nightly zero point offsets in each band are derived from either the mean or linear fit versus time of the individual scan offsets. Individual scan zero point offsets can obviously differ from the nightly values. The RMS to the nightly zero point offset fits provide a measure of the average difference between the nightly fits and scan offsets.
Figures 7a-7c show histograms of the residual differences between individual scan offsets and the nightly values for northern and southern calibration scans that are nominally considered to be in photometric periods. In each figure, the green and red lines show the distribution of differences for H and Ks, respectively. For J-band, the blue curve shows the differences between the scan offsets and night J-band average zero points and the cyan curve shows the differences between scan and nightly J-band linear fit zero points. Linear fits are calculated for all J-band solutions, but are used in calibration only if there are more than four contiguous calibration sets going into the fits. The residuals for all of the linear fits are shown in the figures. Figure 7a shows the residual differences for all 75,957 scans that are nominally in photometric periods. Figures 7b and 7c show the differences for calibration scans with airmasses less than 1.4 and 1.1, respectively.
Figure 7a - Histogram of differences between scan zero point offsets and nightly zero point offset values for all northern and southern calibration scans.
Figure 7b - Histogram of differences between scan zero point offsets and nightly zero point offset values for northern and southern calibration scans with airmass <1.4, which includes most equatorial observations.
Figure 7c - Histogram of differences between scan zero point offsets and nightly zero point offset values for northern and southern calibration scans with airmass <1.1, which is mostly restricted observations near the zenith.
Figures 8a-8c show the same residual distributions within the airmass limits of Figures 7a-7c, but are limited to those scans that are from nights with photometric intervals longer than 8 hours, and from survey days after number 429. The former constraint should draw primarily nights with robust fits, and the latter limits the residuals from nights that had secondary standard stars available.
Figure 8a - Histogram of differences between scan zero point offsets and nightly zero point offset values for northern and southern calibration scans from survey days after number 429, and photometric intervals longer than eight hours.
Figure 8b - Histogram of differences between scan zero point offsets and nightly zero point offset values for northern and southern calibration scans with airmass <1.4, from survey days after number 429, and photometric intervals longer than eight hours.
Figure 8c - Histogram of differences between scan zero point offsets and nightly zero point offset values for northern and southern calibration scans with airmass <1.1, from survey days after number 429, and photometric intervals longer than eight hours.
The following figures show the scan offset residuals by band broken down by hemisphere. For the data in each hemisphere, three curves are presented that show the residual distribution for all cal scans in photometric periods (black lines), cal scans that fall within photometric periods longer than 4 hours ( blue lines), and cal scans within >4hr photometric intervals and taken after 980503 UT so that they contain secondary standards (red lines). Two sets of figures are shown for J-band; the first shows the residuals from the nightly average zero point and the second shows the residuals from the nightly linear-fit zero point offsets.
Figure 9 - Histograms of Northern and Southern J-band scan zero point offset residuals with respect nightly average zero point offsets.
Figure 10 - Histograms of Northern and Southern J-band scan zero point offset residuals with respect nightly linear-fit zero point offsets.
Figure 11 - Histograms of Northern and Southern H-band scan zero point offset residuals with respect to nightly average zero point offsets.
Figure 12 - Histograms of Northern and Southern Ks-band scan zero point offset residuals with respect to nightly average zero point offsets.
The southern residual plots show less difference between the full, >4hr, and secondary standard sets because most southern cal sets were processed with secondary standards in place and because there are generally longer contiguous photometric periods on most nights than in the north.
