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Paper text:
the luminosity function ( lf ) is the basic statistic used to understand galaxy properties , giving the relative frequency of galaxies of a given luminosity in a given volume . since starlight at 3.6 @xmath0 m very nearly follows the rayleigh - jeans limit of blackbody emission for @xmath3 k , the colors of both early- and late - type stars are similar .
there is virtually no dust extinction at this wavelength either , since any standard extinction law predicts only a few percent of the extinction of optical wavelengths .
the 3.6 @xmath0 m light therefore traces the stellar mass distribution free of dust obscuration effects ( pahre et al .
thus , a useful approach to understanding how galaxies form is to track their growing stellar mass , measured through the evolution of the 3.6 @xmath0 m lf .
several studies found lf results consistent with the behavior of a simple , passive luminosity evolution model in which galaxies form all their stars at high redshift and thereafter passively evolve .
however , seldom these studies address which models data exclude . what it actually interesting is whether some plausible scenario can be rejected by the data , because sometime a ( wrong ) scenario can not be rejected simply because of the low information content of the data in hand .
furthermore , previous works rarely address the topic of sample representativity .
specifically , clusters in the sample are typical or atypical clusters ?
all types of clusters are included in the studied sample ?
some type of cluster is over- or under- represented in the sample ?
the above questions are closely related to the following one : can a result found to hold on a sample of unknown representativity ( the studied sample of clusters ) be generalized to the parent distribution ( i.e. to clusters ) ?
results obtained on uncontrolled sample rarely hold in general ( and when they hold , they hold by good chance ) .    throughout this paper
we assume @xmath4 , @xmath5 and @xmath6 km s@xmath7 mpc@xmath7 .
ir data were obtained with the irac ( fazio et al .
2004 ) on the spitzer space telescope ( werner et al . 2004 ) .
optical data come from the wide field imager mosaic - ii at the 4 m ctio .
details on data ( and more ) can be found in andreon ( 2006 ) .
the cluster sample studied in this paper consists of 32 colour  selected clusters , all spectroscopically confirmed .
the availability of spectroscopic redshifts is an essential difference from some previous works having photometric redshift only . in works lacking a cluster spectroscopic confirmation , errors on lf parameters ( and evolution )
are unduly kept small by ignoring the uncertainty due to the contamination in the cluster sample by other , often only apparent , structures ( e.g. line of sight superpositions ) . as shown in yamada et al .
( 2005 ) with a few examples , this occurs frequently to works lacking a cluster spectroscopic confirmation . working with spectroscopically confirmed clusters , we are not affected by the uncertainty due to unrelated structures entering in the sample . furthermore , we are not affected by uncertainties on cluster distances that instead affect works using photometric redshifts .
the clusters were detected as spatially localized galaxy overdensities of similar optical colour , as described in andreon et al .
( 2003 ; 2004a , b ) .
the studied cluster sample is not a volume complete sample , nevertheless it densely samples the explored universe volume , up to @xmath8 , that should make the studied sample representative of typical clusters , and our results of high generalization power .
most of our clusters are at the bottom of the abell richness scale and are not rich systems .
this is unsurprisingly , because the mass ( richness ) function of clusters is steep .
instead , other samples studied in literature consider rich ( and therefore rare ) clusters , biasing the representativity of them with respect to clusters of modest richness and larger abundance .
the 32 clusters are distributed in redshift as shown in fig 1 . in particular , 6 clusters
have @xmath9 and 8 clusters have @xmath10 .
these clusters are essential to discriminate among different histories of star formation and mass assembly , because over a short redshift range different histories do not differ too much ( see right panel of fig 2 ) . to our best knowledge ,
no previous work scores better than our work in the number of clusters at @xmath9 or @xmath10 .
the determination of the lf uses state of the art statistical methods : an improved likelihood function ( andreon , punzi & grado 2004 ) and bayesian methods for model selection .
incongrounces , logical contradictions , circular arguments , arbitrary bins , unphysical values for quantities , all have been avoided by a rigorous statistical analysis ( see andreon et al .
2006 and andreon 2006 ) .
for example , in order to determine @xmath11 our statistical analysis do nt oblige us to keep fixed the nuisance parameter @xmath12 , because unconstrained , as instead other analysis oblige .
if @xmath12 is unconstrained , what statistical theorem allows other works to keep it to be a fixed ( and arbitrary ) value ? by the way , keeping nuisance parameters fixed contradicts the sum rule of probabilities and underestimates the uncertainty on @xmath11 ( the latter as re - discovered by andreon 2004 ) .
furtheremore , other works bin clusters in redshift bins , and forget to investigate whether the found / missed effect is related to some binning choices ( bin size , bin location , sub - optimal binning strategy , etc . ) . instead , we do nt bin clusters in redshift bins and therefore we are not affected by bin resolution / choice
. the analysis also account for the younger age of the universe ( and therefore of stars ) at hight redshift .
full details are described in andreon ( 2006 ) , where a traditional analysis is also presented for old - fashioned readers .
grasil ( silva et al . 1998 ) models are used to convert light in stellar mass and to convert apparent to absolute luminosities .
astronomical results are summarized in the abstract section .
shortly , only a model is viable for the evolution of cluster galaxies : a model in which there is almost no mass growth during the last two third of the universe age .
all the remaining considered models are rejected by the data .
figure 2 is a pictorial excerpt of the results .
a full report , including methodological details , is presented in andreon ( 2006 ) .
andreon , s. , willis , j. , quintana , h. , valtchanov , i. , pierre , m. , & pacaud , f.  2004b , in the proceeding of ` rencontres de moriond : exploring the universe .
contents and structure of the universe ' ( astro - ph/0405574 )
we have measured the 3.6 @xmath0 m luminosity and mass evolution of about 1000 galaxies in 32 clusters at @xmath1 with a special attention to methodological issues , as emphasized in this proceeding contribution . 
 we find that the luminosity of our galaxies evolves as an old and passively evolving population formed at high redshift without any need for additional redshift - dependent evolution . 
 models with a prolonged stellar mass growth are rejected by the data with high confidence . 
 the data also reject models in which the age of the stars is the same at all redshifts . 
 similarly , the characteristic stellar mass evolves , in the last two thirds of the universe age , as expected for a stellar population formed at high redshift . 
 together with the old age of stellar populations derived from fundamental plane studies , our data seems to suggest that massive early - type cluster galaxies have been completely assembled at high redshift , and not only that their stars are old . 
 the quality of the data allows us to derive the lf and mass evolution homogeneously over the whole redshift range , using a single estimator . 
 the schechter function describes the galaxy luminosity function well . 
 the characteristic luminosity at @xmath2 is found to be 16.30 mag , with an uncertainty of 10 per cent .