We use the observed sizes and star formation rates of Lyman-break galaxies ( LBGs ) to understand their properties expected in the hierarchical scenario of galaxy formation .
The observed size distribution constrains the masses ( or circular velocities ) of the host haloes of LBGs from below , because small haloes can only host galaxies with small sizes .
The observed star-formation distribution constrains the masses from above , because the number density of massive haloes in duty cycle is too low to host all the observed galaxies .
Assuming a flat CDM model with a cosmological constant ( \Omega _ { \Lambda } = 0.7 ) , we find that consistency with observations requires the circular velocities of LBG host haloes to be in the range 100 – 300 { km s ^ { -1 } } .
The star formation in these haloes is quite efficient ; a large fraction of all the gas in them can form stars on a time scale of about 10–20 per cent of the Hubble time at redshift of 3 .
The predicted comoving correlation length of these objects is \sim 3 h ^ { -1 } { Mpc } , and the predicted velocity dispersion of their stellar contents is typically 70 { km s ^ { -1 } } .
It is likely that these LBGs are the progenitors of galactic bulges and faint ellipticals .

The same prescription applied to larger haloes in the CDM cosmogony predicts the existence of galaxies with star formation rates \sim 1000 { M _ { \odot } yr ^ { -1 } } at redshift z \sim 3 .
We explore the possibility of identifying these galaxies to be the bright sub-millimeter ( sub-mm ) sources detected by SCUBA .
The model predicts that the host haloes of these sub-mm sources are massive , with typical circular velocity \sim 350 { km s ^ { -1 } } .
The typical star formation timescale in these systems is about 10 per cent of the Hubble time at redshift 3 , and the comoving number density of galaxies ( in their duty cycle ) is 10 ^ { -5 } – 10 ^ { -4 } h ^ { 3 } { Mpc ^ { -3 } } .
These galaxies are predicted to be strongly correlated , with a comoving correlation length of \sim 7 h ^ { -1 } { Mpc } .
They are also predicted to be strongly correlated with LBG population at the same redshift , with a cross-correlation length ( 4 - 5 ) h ^ { -1 } { Mpc } .
The descendants of the bright sub-mm sources should reside in clusters of galaxies at the present time , and it is likely that these objects are the progenitors of giant ellipticals .
We estimate that about 15 per cent of the observed sub-mm background is contributed by this population of objects in the redshift range 2.5 – 3.5 ; a comparable contribution is made by LBGs in the same redshift range .
The model predicts the existence of a relatively bright and red population of galaxies at z \sim 3 , which may be observed in the K-band .