A Comparative Study of Density Field Estimation for Galaxies: New
  Insights into the Evolution of Galaxies with Environment in COSMOS out to z~3
  It is well-known that galaxy environment has a fundamental effect in shaping
its properties. We study the environmental effects on galaxy evolution, with an
emphasis on the environment defined as the local number density of galaxies.
The density field is estimated with different estimators (weighted adaptive
kernel smoothing, 10$^{th}$ and 5$^{th}$ nearest neighbors, Voronoi and
Delaunay tessellation) for a K$_{s}<$24 sample of $\sim$190,000 galaxies in the
COSMOS field at 0.1$<$z$<$3.1. The performance of each estimator is evaluated
with extensive simulations. We show that overall, there is a good agreement
between the estimated density fields using different methods over $\sim$2 dex
in overdensity values. However, our simulations show that adaptive kernel and
Voronoi tessellation outperform other methods. Using the Voronoi tessellation
method, we assign surface densities to a mass complete sample of quiescent and
star-forming galaxies out to z$\sim$3. We show that at a fixed stellar mass,
the median color of quiescent galaxies does not depend on their host
environment out to z$\sim$3. We find that the number and stellar mass density
of massive ($>$10$^{11}$M$_{\odot}$) star-forming galaxies have not
significantly changed since z$\sim$3, regardless of their environment. However,
for massive quiescent systems at lower redshifts (z$\lesssim$1.3), we find a
significant evolution in the number and stellar mass densities in denser
environments compared to lower density regions. Our results suggest that the
relation between stellar mass and local density is more fundamental than the
color-density relation and that environment plays a significant role in
quenching star formation activity in galaxies at z$\lesssim$1.
