We measure the average mass properties of a sample of 41 strong gravitational lenses at moderate redshift ( z \sim 0.4 – 0.9 ) , and present the lens redshift for 6 of these galaxies for the first time .
Using the techniques of strong and weak gravitational lensing on archival data obtained from the Hubble Space Telescope , we determine that the average mass overdensity profile of the lenses can be fit with a power-law profile ( \Delta \Sigma \propto R ^ { -0.86 \pm 0.16 } ) that is within 1- \sigma of an isothermal profile ( \Delta \Sigma \propto R ^ { -1 } ) with velocity dispersion \sigma _ { v } = 260 \pm 20 km s ^ { -1 } .
Additionally , we use a two-component de Vaucouleurs+NFW model to disentangle the total mass profile into separate luminous and dark matter components , and determine the relative fraction of each component .
We measure the average rest frame V-band stellar mass-to-light ratio ( \Upsilon _ { V } = 4.0 \pm 0.6 ~ { } h~ { } M _ { \odot } / L _ { \odot } ) and virial mass-to-light ratio ( \tau _ { V } = 300 \pm 90 ~ { } h~ { } M _ { \odot } / L _ { \odot } ) for our sample , resulting in a virial-to-stellar mass ratio of M _ { vir } / M _ { * } = 75 \pm 25 .
Relaxing the NFW assumption , we estimate that changing the inner slope of the dark matter profile by \sim 20 % yields a \sim 30 % change in stellar mass-to-light ratio .
Finally , we compare our results to a previous study using low redshift lenses , to understand how galaxy mass profiles evolve over time .
We investigate the evolution of M _ { vir } / M _ { * } ( z ) = \alpha ( 1 + z ) ^ { \beta } , and find best fit parameters of \alpha = 51 \pm 36 and \beta = 0.9 \pm 1.8 , constraining the growth of virial to stellar mass ratio over the last \sim 7 Gigayears .
We note that , by using a sample of strong lenses , we are able to constrain the growth of M _ { vir } / M _ { * } ( z ) without making any assumptions about the IMF of the stellar population .