Optimal Galaxy Shape Measurements for Weak Lensing Applications Using theHubble Space TelescopeAdvanced Camera for Surveys

We present three-epoch multiband ($V_{606}$, $i_{775}$, $z_{850}$)measurements of galaxy shapes using the ``polar shapelet'' orLaguerre-expansions method with the Hubble Space Telescope ($HST$) AdvancedCamera for Surveys (ACS) data, obtained as part of the {\it Great ObservatoriesOrigin Deep Survey} (GOODS). We take advantage of the unique features of theGOODS/ACS Fields to test the reliability of this relatively new method ofgalaxy shape measurement for weak lensing analysis and to quantify the impactof the ACS Point Spread Function (PSF) on $HST$/ACS data. We estimate the biasintroduced by the sharp PSF of the ACS on shape measurement. We show that thebias in the tangential shear due to galaxy-galaxy lensing can be safelyneglected provided only well-resolved galaxies are used, while it would becomparable to the signal level (1--3%) for cosmic shear measurements. Theseresults should of be general utility in planning and analyzing weak lensingmeasurements with $HST$/ACS data.Comment: 12 pages, 3 figures. Accepted for ApJ