Direct Shear Mapping: Prospects for weak lensing studies of individual galaxy-galaxy lensing systems

We have investigated, using both a theoretical and an empirical approach, the frequency of low redshift galaxy-galaxy lensing systems in which the signature of weak lensing might be directly detectable. We find good agreement between these two approaches. In order to make a theoretical estimate of the weak lensing shear, $\gamma$, for each galaxy in a catalogue, we have made an estimate of the asymptotic circular velocity from the stellar mass using three different approaches: from a simulation based relation, from an empirically-derived relation, and using the baryonic Tully-Fisher relation. Using data from the Galaxy and Mass Assembly redshift survey we estimate the frequency of detectable weak lensing at low redshift. We find that to a redshift of $z\sim 0.6$, the probability of a galaxy being weakly lensed by at least $\gamma = 0.02$ is $\sim 0.01$. A scatter in the $M_*-M_h$ relation results in a shift towards higher measured shears for a given population of galaxies. Given this, and the good probability of weak lensing at low redshifts, we have investigated the feasibility of measuring the scatter in the $M_*-M_h$ relation using shear statistics. This is a novel measurement, and is made possible because DSM is able to make individual \itshape direct~\upshape shear measurements, in contrast to traditional weak lensing techniques which can only make statistical measurements. We estimate that for a shear measurement error of $\Delta\gamma = 0.02$ (consistent with the sensitivity of DSM), a sample of $\sim$50,000 spatially and spectrally resolved galaxies would allow a measurement of the scatter in the $M_*-M_h$ relation to be made. While there are no currently existing IFU surveys of this size, there are upcoming surveys which will provide this data (e.g The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), surveys with Hector, and the Square Kilometre Array (SKA)).