Dependence on the environment of the abundance function of light-cone
  simulation dark matter haloes
  Aims.We study the dependence of the halo abundance function (AF) on different
environments in a whole-sky $\Lambda$CDM light-cone halo catalogue extending to
z < 0.65, using a simple and well-defined halo isolation criterion. Methods.
The isolation status of each individual dark matter halo is determined by the
distance to its nearest neighbour, which defines the maximum spherical region
devoid of halos above a threshold mass around it (although the true size of
such region may be much larger since it is not necessarily spherical). A
versatile double power-law Schechter function is used to fit the dark matter
halo AF, and its derived parameters are studied as a function of halo isolation
status. Results. (a) Our function fits the halo abundances for all halo
isolation statuses extremely well, while the well-established theoretical mass
functions, integrated over the volume of the light-cone, provide an adequate
but poorer fit than our phenomenological model. (b) As expected, and in
agreement with other studies based on snap-shot simulations, we find
significant differences of the halo abundance function as a function of halo
isolation, indicating different rates of halo formation. The slope of the power
law and the characteristic mass of the Schechter-like fitting function decrease
with isolation, a result consistent with the formation of less massive haloes
in lower density regions. (c) We find an unexpected upturn of the
characteristic mass of the most isolated haloes of our sample. This upturn
originates and characterises only the higher redshift regime (z > 0.45), which
probably implies a significant and recent evolution of the isolation status of
the most isolated and most massive haloes.
