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

Dependence on the environment of the abundance function of light-cone simulation dark matter haloes