John W. Fowler
A preliminary error tree has been derived that includes all currently identified error sources that could affect the analysis of 2MASS data by the processing pipeline under development at IPAC. In order to make it clear which error sources are contained in the bookkeeping, some phenomena are included whose contributions are expected to be negligible.
The error sources are presented below as a list of numbered items broken down into ``input errors", which occur prior to any processing by software, and ``derived errors", which result from propagation of input errors and prior derived errors. The derived errors are listed with the item numbers of their constituent errors shown in parentheses. The list herein is composed of that presented in the January 27-28 review expanded by the addition of three items suggested by R. Cutri; the numbering has been adjusted accordingly.
The purpose in deriving this error tree is to aid in understanding the fundamental limits of photometric and astrometric accuracy. Because of the complexity in the computations required to achieve the project objectives, however, the error propagation is generally not modeled well by simple convolutions (i.e., error variances combining ``in quadrature", etc.), and error reduction is likewise not well modeled by typical averaging processes (i.e., variance reduction by 1/N, etc.). Only by high-fidelity simulation can the error propagation be studied. The error tree is immediately useful, therefore, in determining requirements on the simulation.
To illustrate the difficulty in tracing the error propagation, and to look more closely at one part of the error tree, one example will be discussed, namely that of the error in the final position of a point source. This is error number 29, whose contributors are errors 22, 27, and 28, namely the frame-to-frame offset errors, the astrometric catalog errors, and the band-merged point-source frame coordinate errors. The astrometric catalog error is treated as an input error; the other two are derived, as shown in the tree, but we will treat them each as single errors in this example.
Simulations using realistic conditions (source density, centroid errors) have shown that a frame-to-frame offset error of 0.12 arcseconds is reasonable. This propagates over the scan via a random walk, so that the end of a 260-frame scan has a one-sigma error of 0.76 arcseconds relative to the beginning. This is not 0.12 arcseconds multiplied by the square root of 259, because the same stars are used over five frame pairs, introducing correlations that must be taken into account.
A typical error in band-merged point source frame coordinates is 0.16 arcseconds. The northern Position and Proper Motion (PPM) Catalog has one- sigma errors of 0.34 arcsecond per star, including the proper motion errors incurred in applying this catalog to 2MASS protocamera data. A typical case with seven PPM stars per scan is processed by the position reconstruction software to obtain celestial positions with one-sigma errors of 0.5 arcseconds. Even with the astrometric catalog error variance reduced by 1/7 (which effectively takes place during the processing), the final error is much smaller than what is obtained by combining the input errors in quadrature. This is due to the nonlinear fitting that the software does to remove the lower-frequency component of the random walk.