5.3 Source Positions

Obviously, the extraction region will be most effective in maximizing a source's signal and minimizing the background if it is positioned accurately on the source. AE can compute three types of source position estimates:

• The most straightforward position estimate provided is the mean position of events in a specified energy band that are found in the source's extraction regions (§7.16). Obviously, this estimator will be biased if the extraction region(s) are offset from the true position; thus, iterative repositioning of the source is recommended. This estimator should also be biased if the local background is sloped (e.g. if the source sits in the wing of a bright neighbor). This estimator should also be biased if the PSF is asymmetric.

  A standard error on the mean data position estimate is computed for each axis using the variances of the PSF and flat background within the extraction region of each observation. The resulting 2-D error ellipse is then approximated by the so-called ``1 deviation root mean square'' (dRMS or 1DRMS) error radius, $dRMS = \sqrt{\sigma_X^2 + \sigma_Y^2}$.⁶ The integral of the error ellipse inside this dRMS radius (i.e. the significance of this circular confidence region) varies from 63% for equal errors in X and Y (a circular ellipse) to 68% for a highly eccentric ellipse.

• When the PSF is asymmetric the mean data position estimate should be biased. Thus, AE provides a second position estimate by correlating the neighborhood around the source (not just the extracted counts) with the source's PSF (§7.17). In a multi-observation reduction, a multi-ObsId data image and multi-ObsId PSF are constructed and correlated. This estimator should be biased if the local background is sloped (e.g. if the source sits in the wing of a bright neighbor). Currently no uncertainty estimate is available for the correlation position.

• Both the mean data and PSF correlation estimators above implicitly assume the observed data are explained by a single source, and then seek to estimate the best position for that source. In a crowded field, the wings of bright neighboring sources will tend to bias these estimators. For such situations, AE provides a third position estimate by performing image reconstruction on the neighboring field, and then estimating the position of any nearby peak in the reconstruced image (§7.17). Currently no uncertainty estimate is available for the reconstruction position.

The responsibility for choosing which position estimate should be adopted for each source is left with the observer.