Precision Weak Gravitational Lensing Using Velocity Fields: Fisher Matrix Analysis

Weak gravitational lensing measurements based on photometry are limited by shape noise: the variance in the unknown unlensed orientations of the source galaxies. If the source is a disk galaxy with a well-ordered velocity field, however, velocity field data can support simultaneous inference of the shear, inclination, and position angle, virtually eliminating shape noise. We use the Fisher information matrix formalism to forecast the precision of this method in the idealized case of a perfectly ordered velocity field defined on an infinitesimally thin disk. For nearly face-on targets, one shear component, gamma(x), can be constrained to 0.003 90/I-0 25/n(pix), where I-0 is the signal-to-noise ratio of the central intensity pixel and n(pix) is the number of pixels across a diameter enclosing 80% of the light. This precision degrades with inclination angle by a factor of 3 by i = 50 degrees. The uncertainty on the other shear component, gamma(+), is about 1.5 (7) times larger than the gamma(x) uncertainty for targets at i = 10 degrees (50 degrees). For an arbitrary galaxy position angle on the sky, these forecasts apply not to gamma(+) and gamma(x) as defined on the sky but to two eigenvectors in (gamma(+), gamma(x), mu) space, where mu is the magnification. We also forecast the potential of less expensive partial observations of the velocity field, such as slit spectroscopy. We conclude by outlining some ways in which real galaxies depart from our idealized model and thus create random or systematic uncertainties not captured here. In particular, our forecast gamma(x) precision is currently limited only by the data quality rather than scatter in galaxy properties because the relevant type of scatter has yet to be measured.