  We examine the duty cycle and the history of star formation (SFH) for
high-redshift galaxies at z>=6 using cosmological hydrodynamic simulations. We
find that, even though individual galaxies have bursty SFH, the averaged SFH
between z~15 to z=6 can be characterized well by either an exponentially
increasing functional form with characteristic time-scales of 70 Myr to 200 Myr
for galaxies with stellar masses Ms~10^6 Msun to >10^10 Msun respectively, or
by a simple power-law form which exhibits a similar mass dependent time-scales.
Using the SFH of individual galaxies, we measure the duty cycle of star
formation (DC_SFH); i.e., the fraction of time a galaxy of a particular mass
spends above a star formation rate (SFR) threshold which would make it
observable to the Hubble Space Telescope (HST) during a given epoch. We also
examine the fraction of galaxies at a given redshift that are brighter than a
rest-frame UV magnitude (Muv ~ -18), which is sufficient enough to make them
observable (DC_Muv). We find that both DC_SFH and DC_Muv make a sharp
transition from zero (for galaxies with Ms <= 10^7 Msun) to unity (for Ms >
10^9 Msun). The measured duty cycle is also manifested in the intrinsic scatter
in the Ms-SFR relationship (~ 1 dex) and Ms-Muv relationship (\Delta Muv ~ +-1
mag). We provide analytic fits to the DC as a function of Ms using a sigmoid
function, which can be used to correct for catalogue incompleteness. We
consider the effects of duty cycle to the observational estimate of galaxy
stellar mass functions (GSMF) and the star formation rate density (SFRD), and
find that it results in a much shallower low-mass end slopes of the GSMF and a
reduction of >~ 70% of our intrinsic SFRD, making our simulation results more
compatible with observational estimates.
