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there has been significant recent progress in the study of galaxy formation within a cosmological context , mainly due to a phenomenological approach to this problem .
the idea is to start with a structure formation model that describes where and when galactic dark haloes form . a simple description of gas dynamics and star formation provides a means to calculate the amount of stars forming in these haloes .
stellar population synthesis models then provide the spectral evolution , i.e.  luminosities and colours , of these galaxies .
many physical processes are modelled as simple functions of the circular velocity of the galaxy halo . therefore
, the tully - fisher relation is the most obvious observational relation to try and predict , as it relates the total luminosity of a galaxy to its halo circular velocity .
however , most phenomenological galaxy formation models do not simultaneously fit the i - band tully - fisher relation and the b or k band luminosity function .
when one sets the model parameters such that the tully - fisher relation has the right normalization , the luminosity functions generally overshoot ( e.g.  kauffmann , white & guiderdoni 1993 ; kauffmann , colberg , diaferio & white 1999 ) , certainly for the @xmath0 , @xmath1 km s@xmath2 mpc@xmath2 standard cdm cosmology ( in the form given by davis et al .  1985 ) that we consider in this paper .
alternatively , when making sure that the luminosity functions matches by changing some of the model parameters , the tully - fisher relation ends up significantly shifted with respect to the observed relation ( e.g.  cole et al .  1994 ; heyl et al .
1995 ) .    in order to keep the modelling as analytical as possible , an extension to the press & schechter ( 1974 ) prescription for the evolution of galaxy haloes ( e.g.  bond et al . 1991
; bower 1991 ; lacey & cole 1993 ; kauffmann & white 1993 ) has been a popular ingredient for implementations of a phenomenological theory of galaxy formation .
however , the eps formalism is designed to identify collapsed systems , irrespective of whether these contain surviving subsystems .
this ` overmerging ' of subhaloes into larger embedding haloes is relevant to the problem of matching both the galaxy luminosity function and the tully - fisher relation , as the central galaxy in an overmerged halo is the focus of a much larger cooling gas reservoir than the reservoir that galaxy is to focus of in case its parent subhalo survives .
traditional n - body simulations suffer from a similar overmerging problem ( e.g.  white 1976 ) , which is of a purely numerical nature , caused by two - body heating in dense environments when the mass resolution is too low ( carlberg 1994 ; van kampen 1995 ) .    in order to circumvent these problems , we use an n - body simulation technique that includes a built - in recipe for galaxy halo formation , designed to prevent overmerging ( van kampen 1995 , 1997 ) , to generate the halo population and its formation and merger history .
this resolves most of the discrepancy sketched above , _ and _  allows us to make the modelling more realistic by adding chemical evolution and a merger - driven bursting mode of star formation to the modelling . once stars are formed , we apply the stellar population synthesis models of jimenez et al .
( 1998 ) to follow their evolution .
we have enhanced these models with a model for the evolution of the average metallicity of the population , which depends on the starting metallicity .
feedback to the surrounding material means that cooling properties of that material will change with time , affecting the star formation rate , and thus various other properties of the parent galaxy .
the key ingredients of the model are described below .
we refer to van kampen et al .
( 1999 ) for a much more detailed description and discussion of the model , and a list of the choices for the various parameters involved .
this is often treated by monte - carlo realizations of the analytic ` extended press - schechter ' formalism , which ignores substructure .
we use a special n - body technique to prevent galaxy - scale haloes undergoing ` overmerging ' owing to inadequate numerical resolution .
each halo contains a single galaxy at formation .
when haloes merge , a criterion based on dynamical friction is used to decide how many galaxies exist in the newly merged halo .
the most massive of those galaxies becomes the single central galaxy to which gas can cool , while the others become its satellites .
when a halo first forms , it is assumed to have an isothermal - sphere density profile .
a fraction @xmath3 of this is in the form of gas at the virial temperature , which can cool to form stars within a single galaxy at the centre of the halo .
application of the standard radiative cooling curve shows the rate at which this hot gas cools below @xmath4  k , and is able to form stars .
energy output from supernovae reheats some of the cooled gas back to the hot phase .
when haloes merge , all hot gas is stripped and ends up in the new halo .
the star formation rate is equal the ratio of the amount of cold gas available and the star - formation timescale .
the amount of cold gas available depends on the merger history of the halo , the star formation history , and the how much cold gas has been reheated by feedback processes .
we also model star bursts , i.e.  the star - formation rate may suffer a sharp spike following a major merger event .      the energy released from young stars heats cold gas in proportion to the amount of star - formation , returning it to the reservoir of hot gas .
our work assumes the spectral models of jimenez et al .
( 1998 ) ; for solar metallicity , the results are not greatly different from those of other workers .
the imf is generally taken to be salpeter , but any choice is possible . unlike other workers , we take it as established that the population of brown dwarfs makes a negligible contribution to the total stellar mass density , and we do not allow an adjustable @xmath5 ratio , @xmath6 , for the stellar population
.      the evolution of the metals must be followed , for two reasons : ( i ) the cooling of the hot gas depends on metal content ; ( ii ) for a given age , a stellar population of high metallicity will be much redder .
the models of jimenez et al .
( 1998 ) allow synthetic stellar populations of any metallicity to be constructed .
with the set - up described above we match both the b and k band luminosity function and the i - band tully - fisher relation , for an @xmath0 standard cdm structure formation scenario . resolving
the overmerging problem is the major contributor to this result , but the inclusion of chemical evolution and starbursts are also important ingredients .
the new ingredients we have added to the modelling of galaxy formation are needed in order to make the models more realistic , and are not introduced simply in order to give yet more free parameters . nevertheless , our resolution to the tully - fisher / luminosity function discrepancy may well not be unique , and various other changes to the ingredients of the phenomenological galaxy formation recipe might produce similar results .
for example , we have not studied the influence cosmological parameters have on the model galaxy populations , where @xmath7 , @xmath8 , and @xmath9 are likely to be the important parameters .
other types of ingredients are possible as well : somerville & primack ( 1998 ) resolve some of the discrepancy using a dust extinction model plus a halo - disk approach to feedback .
one way of resolving the worries about degeneracies in the cosmological / physical parameter space will be to include data at intermediate and high redshifts , which is being gathered with increasing speed and ease , and at increasingly higher redshifts . in this contribution
we show a preliminary comparison of the correlation properties of galaxies at redshift @xmath10 .
recently , giavalisco et al .  ( 1998 ) gave an estimate for the galaxy - galaxy correlation function @xmath11 for a sample of lyman - break galaxies at this redshift .
they found @xmath12mpc and @xmath13 .
we selected our model galaxies in exactly the same way as giavalisco et al .
( 1998 ) did , and compared two of the models produced by van kampen et al .
( 1999 ) , models @xmath14 and @xmath15 , to the observational data . the first model ( @xmath14 ) , which is as close as possible to the model by cole et al .  ( 1994 ) , but with the mass - to - light parameter @xmath16 , gives @xmath17mpc and @xmath18 . the second model ( @xmath15 ) , which includes starbursts and chemical evolution , gives @xmath19mpc and @xmath20 .
both models fit the correlation function at @xmath21 very well , and can not be distinguished from each other .    as the observed correlation data are still relatively uncertain at this moment in time
, it is premature to rule out models on the basis of this data .
the two models discussed above have similar predictions for low redshifts , but predict different clustering properties at high - redshift .
however , the differences are not large , so one needs either really good data , or a much larger variety of observational characteristics of the high - redshift galaxy population .    many thanks for the loud vocal support from outside the conference building during my presentation .
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most phenomenological galaxy formation models show a discrepancy between the predicted tully - fisher relation and the luminosity function . 
 we show that this is mainly due to overmerging of galaxy haloes , which is inherent in both the press - schechter formalism and dissipationless n - body simulations . 
 this overmerging problem be circumvented by including a specific galaxy halo formation recipe into an otherwise standard n - body code . resolving the overmerging 
 also allows us to include models for chemical evolution and starbursts , which improves the match to observational data _ and _ renders the modelling more realistic . 
 we use high - redshift clustering data to try and distinguish models which predict similar results at low redshifts for different sets of parameters .