Using data from the COSMOS survey , we perform the first joint analysis of galaxy-galaxy weak lensing , galaxy spatial clustering , and galaxy number densities .
Carefully accounting for sample variance and for scatter between stellar and halo mass , we model all three observables simultaneously using a novel and self-consistent theoretical framework .
Our results provide strong constraints on the shape and redshift evolution of the stellar-to-halo mass relation ( SHMR ) from z = 0.2 to z = 1 .
At low stellar mass , we find that halo mass scales as M _ { h } \propto M _ { * } ^ { 0.46 } and that this scaling does not evolve significantly with redshift from z = 0.2 to z = 1 .
The slope of the SHMR rises sharply at M _ { * } > 5 \times 10 ^ { 10 } ~ { } { M } _ { \odot } and as a consequence , the stellar mass of a central galaxy becomes a poor tracer of its parent halo mass .
We show that the dark-to-stellar ratio , M _ { h } / M _ { * } , varies from low to high masses , reaching a minimum of M _ { h } / M _ { * } \sim 27 at M _ { * } = 4.5 \times 10 ^ { 10 } ~ { } { M } _ { \odot } and M _ { h } = 1.2 \times 10 ^ { 12 } ~ { } { M } _ { \odot } .
This minimum is important for models of galaxy formation because it marks the mass at which the accumulated stellar growth of the central galaxy has been the most efficient .
We describe the SHMR at this minimum in terms of the “ pivot stellar mass ” , M _ { * } ^ { piv } , the “ pivot halo mass ” , M _ { h } ^ { piv } , and the “ pivot ratio ” , ( M _ { h } / M _ { * } ) ^ { piv } .
Thanks to a homogeneous analysis of a single data set spanning a large redshift range , we report the first detection of mass downsizing trends for both M _ { h } ^ { piv } and M _ { * } ^ { piv } .
The pivot stellar mass decreases from M _ { * } ^ { piv } = 5.75 \pm 0.13 \times 10 ^ { 10 } ~ { } { M } _ { \odot } at z = 0.88 to M _ { * } ^ { piv } = 3.55 \pm 0.17 \times 10 ^ { 10 } ~ { } { M } _ { \odot } at z = 0.37 .
Intriguingly , however , the corresponding evolution of M _ { h } ^ { piv } leaves the pivot ratio constant with redshift at ( M _ { h } / M _ { * } ) ^ { piv } \sim 27 .
We use simple arguments to show how this result raises the possibility that star formation quenching may ultimately depend on M _ { h } / M _ { * } and not simply M _ { h } , as is commonly assumed .
We show that simple models with such a dependence naturally lead to downsizing in the sites of star formation .
Finally , we discuss the implications of our results in the context of popular quenching models , including disk instabilities and AGN feedback .