Gravitational lens magnification by Abell 1689: distortion of the background galaxy luminosity function

Gravitational lensing magnifies the observed flux of galaxies behind the le ns. We use this effect to constrain the total mass in the cluster Abell 168 9 by comparing the lensed luminosities of background galaxies with the lumi nosity function of an undistorted field. Under the assumption that these ga laxies are a random sample of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate ga laxy distance and intrinsic luminosity. Knowing the redshift distribution o f the background population allows us to lift the mass/background degenerac y common to lensing analysis. In this paper we use nine filters observed ov er 12 h with the Calar Alto 3.5-m telescope to determine the redshifts of 1 000 galaxies in the field of Abell 1689. Using a complete sample of 146 bac kground galaxies we measure the cluster mass profile. We find that the tota l projected mass interior to 0.25 h(-1) Mpc is M-2D(<0.25 h(-1) Mpc)=(0.48 +/-0.16)x10(15) h(-1) M., where our error budget includes uncertainties fro m the photometric redshift determination, the uncertainty in the offset cal ibration and finite sampling. This result is in good agreement with that fo und by number-count and shear-based methods and provides a new and independ ent method to determine cluster masses.