Quantitative Analysis of Galaxy‐Galaxy Lensing

In this paper we explore a quantitative and efficient method to constrain thehalo properties of distant galaxy populations through ``galaxy--galaxy" lensingand show that the mean masses and sizes of halos can be estimated accurately,without excessive data requirements. Specifically, we propose amaximum-likelihood analysis which takes full account of the actual imageellipticities, positions and apparent magnitudes. We apply it to simulatedobservations, using the same model for the lensing galaxy population as in BBS,where the galaxy halos are described by isothermal spheres with velocitydispersion $\sigma$, truncated at a radius $s$. Both parameters are assumed toscale with the luminosity of the galaxy. The best fitting values are thendetermined with the maximum-likelihood analysis. We explore two differentobserving strategies, (a) taking deep images (e.g., with HST) on small fields,and (b) using shallower images on larger fields. We find that $\sigma_*$ can bedetermined to $\lesssim$10\% accuracy if a sample of about 5000 galaxies withmeasured ellipticities are available, down to $R\lesssim 23$. Alternatively,the same accuracy in the determination of $\sigma_*$ can be achieved from aboutten, moderately deep WFPC2 fields, on which galaxy shapes can be measured toabout $R\sim 25$ and for which ground-based images are available on which theWFPC2 fields are centered. Firm lower limits can be set on the radial extent ofthe halo, but the maximal halo extent is poorly constrained. We show that thelikelihood approach can also be used to constrain other parameters of thegalaxy population, such as the Tully-Fischer index, or the mean redshift of thegalaxies as a function of apparent magnitude. Finally we show how multi-colorinformation, constraining the redshift of individual galaxies, can dramaticallyComment: 20 pages, Plain-Tex, no macros needed, including 8 figures, submitted to Astrophysical Journa