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AntonuccioDelogu, Becciani, and Coppola have studied the relationship between
halo Mass and galaxy Luminosity in a given photometric band using
data coming from the 2dF and the Sloan Digital Sky surveys, in conjunction with
results from high resolution Nbody simulations. First, we have undertaken a
critical reappraisal of the derivation of this ML relationship. We have
restricted the mass range only to include galaxysized halos. This allows
us to avoid specifying a multiplicity function, thus diminishing the
uncertainties connected to its modelling.
Figure 1.24:
Luminosity functions for different environments. The
continuous curves are Schechter fits to data from Croton et
al. (2004), while filled points and triangles are predictions from
our model for field (points) and ''void'' (open triangles)
environments, respectively. is the average overdensity
in spheres of Mpc, is the overdensity
estimated in Nbody simulations using a CIC estimator with 64
neighbours. The inputs MFs were derived for two different
simulations with comparable mass resolution

As a second constraint we have taken explicitly into account an
observational relationship between Mass and Luminosity, i.e. the
TullyFisher relation, to restrict the domain of validity of the ML
relationship. Because the TF relationship applies only to disc
galaxies, we consistently impose this constraint within a magnitude
interval for each photometric band where disc galaxies dominate in
number density over elliptical, at least in the nearby Universe.
We then follow Vale & Ostriker (2003) and identify
the LF in a given band :
, with the Mass
Function (hereafter MF) derived from Nbody simulations, :
, so that we obtain an equation for the dependence of the
magnitude on the mass:

(1) 
This equation is solved as an initial value problem, and a series of ML relationships can be derived.
We have applied this
formalism to two independent problems: the derivation of the
Mass Function (MF) of Sab galaxies and the dependence of the LF on
local density. Both these tests give very encouraging results. In
particular, using the ML relation derived above in conjunction with
Mass Functions for galaxysized halos in different environments
derived from Nbody simulations, one can derive luminosity
functions for different environments. An example is given in
Figure 1.24. The agreement is very satisfactory,
particularly if one considers the circumstance that it was derived
under a very small set of basic hypotheses. This fact implies then
the validity of the two implicit assumptions of this model: the
existence of a universal ML relation for galaxies and the
circumstance that environmental properties can be entirely described
by local variations of the MF.
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Innocenza Busa'
20051114