4 Proper motions

The heart of this investigation is to use the measured proper motions to separate out the bulge and cluster stars. Our chosen method to find the proper motion for each star consists of the following steps:

1.

find the transformation, x- and y-shifts as well as rotation (small in our case), between the two epochs of observations using a small number of bright stars;

2.

transform the positions on the new images (the deep drizzled F555W images in our case) to the reference frame of the old images;

3.

re-center the transformed positions on the old image (in our case we used the deep image combined from both filters for this);

4.

inspect the x- and y-shifts found in the re-centering, select only stars that have small shifts relative to the centre of the distribution of shifts;

5.

using only those stars selected in the previous item find a new, improved transformation between the epochs;

6.

apply the new solution and re-center the stars on the old image;

7.

if deemed necessary iterate.

We only needed to iterate a few times to find our solutions. Since the WF chips in the WFPC2 over time slowly drift relative to each other, Fruchter & Mutchler (1998), the transformations between the new and the old reference frames have to be found separately for each WF-chip.

For the short exposures we first applied the transformation found from the deep images. However, since it appears that the new short exposure is not perfectly aligned with the new deep images we iterated the solution for the transformation once.