Stars form out of molecular gas and supply dust grains during their last evolutionary stages ; in turn hydrogen molecules ( H _ { 2 } ) are produced more efficiently on dust grains .
Therefore , dust can drastically accelerate H _ { 2 } formation , leading to an enhancement of star formation activity .
In order to examine the first formation of stars and dust in galaxies , we model the evolution of galaxies in the redshift range of 5 < z < 20 .
In particular , we focus on the interplay between dust formation in Type II supernova ejecta and H _ { 2 } production on dust grains .
Such effect causes an enhancement of star formation rate by an order of magnitude on a timescale ( \sim 3 –5 galactic dynamical times ) shorter than the Hubble timescale .
We also find that about half of the radiative energy from stars is reprocessed by dust grains and is finally radiated in the far infrared ( FIR ) .
For example , the typical star formation rate , FIR and ultraviolet ( UV ) luminosity of a galaxy with M _ { vir } = 10 ^ { 11.5 } ~ { } M _ { \odot } ( virial mass ) and z _ { vir } = 5 ( formation redshift ) are 3 M _ { \odot } yr ^ { -1 } , 4 \times 10 ^ { 9 } ~ { } L _ { \odot } , and 3 \times 10 ^ { 9 } ~ { } L _ { \odot } , respectively .
This object will be detected by both ALMA and NGST .
Typical star formation rates and luminosities ( FIR , UV and metal-line luminosities ) are calculated for a large set of ( M _ { vir } , z _ { vir } ) .
Using these results and the Press-Schechter formalism , we calculate galaxy number counts and integrated light from high-redshift ( z > 5 ) galaxies in sub-millimetre and near-infrared bands .
We find that : i ) ALMA can detect dust emission from \mbox { several } \times 10 ^ { 3 } galaxies per square degree , and ii ) NGST can detect the stellar emission from 10 ^ { 6 } galaxies per square degree .
Further observational checks of our predictions include the integrated flux of metal ( oxygen and carbon ) lines ; these lines can be used to trace the chemical enrichment and the gas density in early galactic environments .
We finally discuss possible color selection strategies for high-redshift galaxy searches .