Plots for a set of regions offset in 5 degree increments of galactic latitude are as follows:
This document describes some tests designed to determine whether the flux uncertainties quoted by PROPHOT take proper account of all of the various sources of error in different parts of the sky and over the range of observing conditions. The PROPHOT error model takes explicit account of the following sources of error:
(1) Poisson noise.
(2) Read noise.
(3) PSF error.
(4) Confusion noise.
With the exception of the confusion noise term (obtained from the standard deviation of sky pixels surrounding the source), the error model is descibed mathematically in the 2nd release documentation.
Downstream from PROPHOT, other sources of error are included, such as the flat fielding error and the uncertainty in the absolute flux calibration. Estimates of the relative contributions of the various error sources have been made by Gizis (2000).
In the present study, the estimated RMS flux errors are compared with the uncertainties quoted by PROPHOT, both to verify that the four effects listed above have been adequately taken into account, and to determine whether there are circumstances under which any of the neglected sources of error become significant.
Repeatability tests represent our primary tool for investigating the validity of the quoted uncertainties. Previous work, involving sets of calibration scans (see Cutri (2001)), has shown that the RMS flux dispersion is less than the quoted flux uncertainty for signal-to-noise ratios down to 10, but starts to exceed it at lower S/N. The reason for the latter is unknown.
Some effects which are not probed by the repeatability of calibration scans of the same region on the same night are:
(1) Cross-scan flux bias due to focal-plane distortion.
(2) Errors of absolute calibration.
The present analysis, using overlapping survey scan data, is aimed at probing such effects.
The selection criteria for point sources within each circular window were:
(1) Read-2 detection in all 3 bands.
(2) Confusion flags all null (i.e. nominally free of artifacts)
Repeated observations of the same source are available from the same night (because of overlapping scans) and from different nights (during a second observational pass through the region).
The flux differences of the various apparitions of each source were calculated, and the RMS flux difference calculated for various subsets of the sources in a given region. This RMS flux difference was then divided by the theoretical sigma, corresponding to the quadrature sum of the quoted PROPHOT flux uncertainties for the two apparitions.
The relative RMS fluxes are plotted against J, H, and K magnitude in Figure 1a, using data taken from the high density region centered on Baade's window. Filled circles represent data from the same night, and open circles represent data from different nights. The magnitude plot for a lower density region (offset 15 degrees in longitude from Baade's window, away from the Galactic center) is shown in Figure 1b.
Plots of RMS flux difference as a function of cross-scan position for the brightest sources are shown in Figure 2a and Figure 2b for the same two regions, respectively. The magnitude selection criteria are indicated on the plots.
Some conclusions which may be drawn from these plots are:
(1) The flux dispersions of observations on the same night are less than the quoted PROPHOT uncertainties for all except the faint end of the magnitude range, consistent with conservative estimates for the uncertainties. Even for the faintest sources, the RMS dispersion only slightly exceeds the quoted uncertainty.
(2) There is a significant increase in flux dispersion for observations on different nights; this increase will presumably be properly accounted for by the incorporation of the uncertainties in absolute calibration (in the msigcom parameter in the catalog).
(3) No trend is apparent with cross-scan position, indicating that the cross-scan bias has been successfully removed from the magnitudes quoted in the database.
For obvious reasons, confusion errors cannot be assessed using repeatability analyses; we need some knowledge of the statistical properties of the true fluxes for this purpose. One suitable property arises from the fact that normal stars have well-defined color-color relations, and it is this property which is exploited in the present analysis. Specifically, we use the width of the color-color relation as a probe of the validity of the quoted PROPHOT flux errors with particular regard to its dependence on source density.
(J-H) versus (H-K) plots were made for point sources in several regions in the vicinity of Baade's window, each of which corresponded to a circular patch of radius 1 degree. The same selection criteria were used as for the repeatability tests described in Section 2. The standard deviations of H-K at selected reference values of J-H were then evaluated and compared with the expected values based on the quoted sigmas, with the values for the two bands added in quadrature in each case.
The color-color plot for the region centered on Baade's window is as follows:
Plots for a set of regions offset in 5 degree increments of galactic latitude
are as follows:
Delta-b = +5 deg
Delta-b = +10 deg
Delta-b = +15 deg
Delta-b = +20 deg
The analagous plots for the longitude offsets (at 0 deg latitude offset) are as follows:
Delta-l = -5 deg
Delta-l = -10 deg
Delta-l = -15 deg
Delta-l = -20 deg
For both the latitude and longitude offsets, the direction of the offset was AWAY from the Galactic Center.
It is apparent that the color-color plot of the central region is much cleaner (in terms of scatter) than the ones which are offset in galactic longitude (see, for example, the plot for Delta-l = -5 deg). The latter show the existence of a component with a large dispersion of H-K values. This component represents the faint end of the magnitude distribution, corresponding to H magnitudes in the range 14-16. The reason that this component is absent from the plot for the central region is that the latter is devoid of stars fainter than about H = 14; this is due to a thresholding effect in the detection step preceding PROPHOT, whereby the detection threshold is set higher (in terms of flux) in dense fields.
Since the detection threshold is related to the standard deviation of the local sky background, the limiting magnitude should be strongly correlated with the latter quantity, and this is indeed the case, as shown by the following plot of H cutoff magnitude versus sky sigma. In this plot, the ordinate is defined as the H magnitude at which the histogram of magnitude values has fallen to 10% of its value at the peak, and the absissa represents the standard deviation of local sky background, estimated by PROPHOT in an annulus surrounding the source.
The sky sigma is closely related to the source density itself, since faint unresolved sources contribute to the statistical properties of the sky background. The the density-dependence of the limiting magnitude is shown in the plot of H cutoff magnitude versus source density, where the latter quantity is defined as the number of 3-band detected sources per square degree whose H magnitudes are brighter than 13, with appropriate allowance being made for duplicate observations of the same source.
For each region, the values of RMS color dispersion were calculated along various slices through the color-color plot, each slice representing a narrow strip of width 0.05 magnitudes. Only the H-K dispersion was calculated, since the intrinsic dispersion in J-H was too large to be useful for error evaluation.
The RMS dispersion of H-K was calculated at two separate reference values of J-H, namely 0.5 and 0.74 (the latter of which was chosen based on the peak density of points in color-color space for the central region). So, for example, in the former case, the RMS dispersion of H-K was calculated using all sources for which 0.475 < J-H < 0.525.
The resulting RMS values of H-K have been plotted as a function of source density in the RMS color plot, for three magnitude ranges, namely H = 13-14, 14-15, and 15-16. In this plot, the filled and open circles represent the values obtained using J-H reference colors of 0.5 and 0.74, respectively. Also shown for comparison are the corresponding sigmas from PROPHOT, represented by the horizontal bars.
The following conclusions can be drawn from the above results:
(1) The values of RMS dispersion of H-K colors are, in all cases, less than or comparable to the corresponding PROPHOT-derived sigmas, consistent with the assertion that the PROPHOT flux sigmas are reasonable.
(2) The RMS values do not increase with increasing source density, indicating that we are not in the confusion-limited regime. Since regions of higher density will be similarly limited by the dependence of detection threshold on sky sigma, there would be no point in extending the analysis to denser regions. Sources faint enough to be confusion limited would have been automatically excluded from the database.
