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Galaxy Mass-Luminosity Relationships

Antonuccio-Delogu, 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 N-body simulations. First, we have undertaken a critical reappraisal of the derivation of this M-L relationship. We have restricted the mass range only to include galaxy-sized 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. $\delta_{8}$ is the average overdensity in spheres of $8 h^{-1}$ Mpc, $\delta_{cic}$ is the overdensity estimated in N-body simulations using a CIC estimator with 64 neighbours. The inputs MFs were derived for two different simulations with comparable mass resolution
\begin{figure}\centerline{\psfig{file=cosmology/fig1.eps,width=8cm}}\end{figure}
As a second constraint we have taken explicitly into account an observational relationship between Mass and Luminosity, i.e. the Tully-Fisher relation, to restrict the domain of validity of the M-L 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 $J$: $\Phi(<M_{J})dM_{J}$, with the Mass Function (hereafter MF) derived from N-body simulations, : $\Psi
(m_{halo})dm_{halo}$, so that we obtain an equation for the dependence of the magnitude on the mass:
\begin{displaymath}
\frac{dM_{J}}{dm_{halo}} = c_{b}\frac{\Phi\left(<M_{J}\left[m_{halo}\right]\right)}{\Psi
(m_{halo})}
\end{displaymath} (1)

This equation is solved as an initial value problem, and a series of M-L 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 M-L relation derived above in conjunction with Mass Functions for galaxy-sized halos in different environments derived from N-body 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.
next up previous contents index
Next: Simulations of Weak Lensing Up: Cosmology and Large-Scale Structure Previous: Cosmology and Large-Scale Structure   Contents   Index
Innocenza Busa' 2005-11-14