Quantitative Analysis of Galaxy‐Galaxy Lensing

Abstract

Gravitational light deflection due to mass along the line of sight will distort the images of background sources. Although an individual galaxy is not massive enough to cause a detectable lensing distortion in the background population, this effect can be measured statistically for a population of galaxies, and a first detection was claimed recently by Brainerd, Blandford, & Smail (BBS). BBS modeled their observations by describing galaxy halos as isothermal spheres of velocity dispersion sigma , truncated at a radius s, where sigma and s scale with the luminosity of the galaxy. Through Monte Carlo simulations they predicted the mean image polarization as a function of radius and compared it to the observations. In this paper we follow up on this discovery by developing a maximum-likelihood analysis that can constrain the halo properties of distant galaxy populations through "galaxy-galaxy" lensing; with it we show that the mean masses and sizes of halos can be estimated accurately, without excessive data requirements. The proposed maximum-likelihood analysis contains several important new elements: (1) it takes full account of the actual image ellipticities, positions, and apparent magnitudes, and as a consequence, it provides more efficient parameter estimation; (2) it provides automatically the proper relative weight for images of different ellipticities; (3) it uses a redshift probability distribution for each galaxy image and does not require a foreground lens--background image dichotomy; (4) it provides a rigorous means to investigate the covariances among the parameters that describe the halo model. We apply this analysis technique to simulated observations, using for ease of comparison the same lens model as BBS, and determine the best-fitting values, sigma * and s*, corresponding to an L* galaxy. We explore two different observing strategies: (1) taking deep images (e.g., with HST) on small fields, and (2) using shallower images on larger fields. From these simulations we find that sigma * can be determined to