We discuss how current and future data on the clustering and number density of z \sim 3 Lyman-break galaxies ( LBGs ) can be used to constrain their relationship to dark matter haloes .
We explore a three-parameter model in which the number of LBGs per dark halo scales like a power-law in the halo mass : N ( M ) = ( M / { M } _ { 1 } ) ^ { S } for M > { M } _ { min } .
Here , { M } _ { min } is the minimum mass halo that can host an LBG , { M } _ { 1 } is a normalization parameter , associated with the mass above which haloes host more than one observed LBG , and S determines the strength of the mass dependence .
We show how these three parameters are constrained by three observable properties of LBGs : the number density , the large-scale bias , and the fraction of objects in close pairs .
Given these three quantities , the three unknown model parameters may be estimated analytically , allowing a full exploration of parameter space .
As an example , we assume a \Lambda CDM cosmology and consider the observed properties of a recent sample of spectroscopically confirmed LBGs .
We find that the favored range for our model parameters is { M } _ { min } \simeq ( 0.4 - 8 ) \times 10 ^ { 10 } { h ^ { -1 } } { M } _ { { } _ { \mathord { \odot } } } , M _ { 1 } \simeq ( 6 - 10 ) \times 10 ^ { 12 } { h ^ { -1 } } { M } _ { { } _ { \mathord { \odot } } } , and 0.9 \la S \la 1.1 .
The preferred region in { M } _ { min } expands by an order of magnitude and slightly shallower slopes are acceptable if the allowed range of b _ { g } is permitted to span all recent observational estimates .
We also discuss how the observed clustering of LBGs as a function of luminosity can be used to constrain halo occupation , although due to current observational uncertainties we are unable to reach any strong conclusions .
Our methods and results can be used to constrain more realistic models that aim to derive the occupation function N ( M ) from first principles , and offer insight into how basic physical properties affect the observed properties of LBGs .