From tchester Tue Oct 3 20:56:56 1995 From: Tom Chester Date: Tue, 3 Oct 95 20:54:16 PDT To: jarrett Subject: some results on completeness versus seeing Cc: tchester, chas, roc X-Lines: 284 Status: RO X-Mozilla-Status: 0001 Content-Length: 11705 For your amusements, this is still the unfinished memo, but there are a couple of conclusions already, and some numbers on the loss of completeness versus seeing, for point sources and galaxies. Comments are welcome, but not expected until this draft is finished. tchester Completeness of galaxy and point source catalog versus seeing, and reliability of the galaxy catalog versus seeing Seeing is an important variable to 2MASS. Changes in seeing cause many significant effects, among them: 1. An increase in seeing causes a loss of sensitivity in detecting point sources and in distinguishing small galaxies from point sources. 2. Flux errors for point sources result from seeing changes that are not identified and tracked in the processing. 3. Untracked seeing changes cause significant reliability problems for the galaxy catalog. We have found that the most sensitive indicator of the actual value of the seeing at any time is given by the parameters computed by the galaxy processor. In particular, the measured "shape" of a single point source in the coadd image with K < 13.5 mag determines the seeing to a one sigma accuracy of 16% at 1", 5% at 2"; and 2% at 3-4" seeing. The only problem is caused by the need to make sure that the group of sources used to determine the seeing are not contaminated by double stars, galaxies, and the like. Thus we currently demand that a group of 10 stars is needed in order to toss the outliers and robustly estimate the seeing. For about half of the sky at high galactic latitudes, this implies that a seeing determination can be made approximately every 30 seconds, which is the time to take the data for 2 or 3 coadd images. The seeing lore that we have picked up from infrared observers is that when the seeing is good, it is stable, and when the seeing is bad, it can change rapidly. The last prototype camera run was taken during moderately bad seeing, and the examination of about 10 scans supports this lore. The good seeing scans all show the canonical dispersion in the shape parameter, but the bad seeing scans all show much increased dispersion, indicating that the seeing has varied quite significantly within a scan. In particular, on the night of 95-04-23, the seeing varied from 2-4" on the 14 scans examined so far. The two scans with 2" seeing showed no significant change in the seeing within each scan. Of the 8 scans with 2.5-3" seeing, 7 had stable seeing, but 1 had very significant changes in seeing within the scan, ranging from 2-4", with changes from 2-4" happening within 15", faster than our ability to track the seeing change. The 4 scans with 3-4" seeing all had similar dramatic changes in seeing within each scan. Since the seeing can apparently vary more rapidly than our ability to track it, it is important to understand what effect such untracked changes have on the completeness and reliability of the point source and galaxy catalogs. We are able to identify that the seeing has changed more accurately than we can track the seeing, and thus knowing how such changes affect us allows us to identify and throw out scans that do not meet our quality requirements. Thus the purpose of this memo is to try to quantify the effects of changes in seeing, both tracked and untracked, so that we can begin the process of setting quality standards for acceptable data, in the form of an upper limit to the absolute acceptable seeing and an upper limit to the variability of the seeing within a scan. This memo is organized into 4 parts. We consider in order: The effect on completeness of changes in the seeing that are tracked. The effect on completeness of changes in the seeing that are not tracked. The effect on reliability of changes in the seeing that are tracked. The effect on reliability of changes in the seeing that are not tracked. The overall conclusions are as follows: 1. Changes in the seeing affect the completeness of point sources much more than galaxies. A change in the seeing from 1" to 2" causes a loss of 0.13 mag; from 1" to 3" causes a loss of 0.29 mag; and from 1" to 4" causes a loss of 0.46 mag. These changes in seeing result in only a small loss to the completeness of the galaxy catalog at its limiting magnitude. However, the small number of galaxies that are at the limit of being distinguished from point sources are affected nearly as much as point sources by an increase in the seeing. In particular, they are lost from the galaxy catalog, causing the completeness of the galaxy catalog at the threshold to vary from 100% at 1" seeing; to 98% at 2" seeing; to 96% at 3" seeing; and to 93% at 4" seeing. 2. Changes in the seeing that are tracked have no effect on the reliability of the point source or galaxy catalogs. 3. ... THE EFFECT ON COMPLETENESS OF UNIFORM CHANGES IN THE SEEING A simple model can illustrate how seeing affects the completeness of the galaxy and point source catalog. The model is unrealistic in several detailed assumptions, such as the profile of galaxies. (Assume the cow is spherical!) However, it is useful in understanding how seeing affects the detection of galaxies, and is probably fairly accurate. The model assumes: 1. Only the effect of galaxy size is considered in discriminating stars from galaxies. 2. Galaxies have an intrinsic gaussian profile with intrinsic widths (shapes), denoted r0, in each axis of 1" - 7" at K=11 (values derived from the perseus and ngp data). 3. The distribution of galaxy shapes is uniform between the above two limiting values. 4. Galaxies observed at different magnitudes are these same galaxies merely placed at different distances, with magnitudes corresponding to the distances. 5. The width of the observed galaxy profile is the root sum square of the intrinsic galaxy profile and the seeing. Calculations: Shape(point sources)^2 = 0.65 + (seeing/4)^2, where seeing and all constants are measured in arcseconds. Numbers and formula come from simulation results. The one sigma value for shape(point sources) = 0.05", derived from undersampling and dithering pattern. Value derives from actual data. The threshold for galaxy detection is 3 sigma = 0.15" above shape(point sources). Observed galaxy shape^2 = intrinsic galaxy shape^2 + shape(point sources)^2. (Result of gaussian profile assumption - not quite true for real profile.) Intrinsic galaxy shape at mag K = (intrinsic galaxy shape at K=11) * 10^( (K-11)/5). (Simple distance scaling. For example, if K=16 and thus the source is 5 magnitudes fainter than K=11, the observed galaxy shape unconvolved with seeing is 10 times smaller since the galaxy is 10 times farther away.) Final formulae: shape threshold = 0.15" + sqrt(0.65 + (seeing/4)^2). observed galaxy shape = sqrt( (0.65 + (seeing/4)^2) + r0^2 * 10^(-0.4*(K-11)) ). A galaxy will be at the threshold by equating the observed galaxy shape and the shape threshold: K(threshold) = 11 - 2.5 * log ( (0.02 + 0.3 * sqrt(0.65 + (seeing/4)^2) ) / r0^2 ) Results: K threshold versus seeing: seeing r0 1" 2" 3" 4" 1.00 12.41 12.29 12.14 11.98 2.00 13.91 13.80 13.64 13.49 3.00 14.79 14.68 14.52 14.37 4.00 15.42 15.30 15.15 14.99 5.00 15.90 15.79 15.63 15.48 6.00 16.30 16.18 16.03 15.87 7.00 16.63 16.52 16.36 16.21 --------------------------------- pt src 14.00 13.87 13.71 13.54 (normalized to 14 at 1" seeing) change in K threshold versus seeing normalized to 1": seeing r0 1" 2" 3" 4" 1.00 0.00 -0.12 -0.27 -0.43 2.00 0.00 -0.12 -0.27 -0.43 3.00 0.00 -0.12 -0.27 -0.43 4.00 0.00 -0.12 -0.27 -0.43 5.00 0.00 -0.12 -0.27 -0.43 6.00 0.00 -0.12 -0.27 -0.43 7.00 0.00 -0.12 -0.27 -0.43 --------------------------------- pt src 0.00 -0.13 -0.29 -0.46 Thus for an increase in seeing of 1", we lose about 0.1 mag in the galaxy catalog for those galaxies at the threshold of discrimination from stars. Of course, most detected galaxies have r0 values large enough so that they are unaffected by increased seeing. For comparison, the noise for point sources scales as the width. The point source threshold change is given in the last line of the above table, scaling 1" seeing to K = 14.00 mag. Note that galaxies at the threshold are affected nearly as much as point sources by worse seeing. Another way to view the effect of the threshold change is to derive overall galaxy completeness numbers versus seeing. The following table gives r0 values at which the K threshold is 13.5 mag, and the corresponding completeness numbers at K = 13.5 mag if galaxies have a uniform distribution between 1 and 7", normalized such that the completeness at 1" is one (ie, eliminating galaxies that are too star-like with 1" seeing from the sample): 1" 2" 3" 4" r0 1.65 1.75 1.87 2.01 (values in arcsec) C 1.00 0.98 0.96 0.93 Thus in going from 2" seeing to 3" seeing, we lose about 2% of the galaxies at K = 13.5 mag, whereas we raise the threshold for all the point sources by 0.16 mag, losing all of those sources that were within 0.16 mag of the given SNR threshold. THE EFFECT ON COMPLETENESS OF VARIABLE SEEING WITHIN A SCAN THE EFFECT ON RELIABILITY OF UNIFORM CHANGES IN THE SEEING The reliability of the galaxy catalog is unaffected by uniform changes in seeing! A change in seeing simply causes the stellar ridge to rise or fall uniformly, with the sigma about that ridge constant with seeing. Thus the thresholding at the stellar mean plus three sigma will always eliminate stars in the same manner independent of seeing. Likewise, the reliability of the point source catalog should be unaffected by uniform changes in seeing. "Problem" sources, such as double stars, sources in high source density regions, will increase with worse seeing, but these already are exceptions to the reliability calculation, since the reliability standard does not apply to such problem sources.