• methods: numerical;
  • stars: formation;
  • galaxies: evolution;
  • galaxies: formation;
  • cosmology: theory


We examine the duty cycle (DC) and the star formation history (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 and 6 can be characterized well by either an exponentially increasing functional form with characteristic time-scales of 70–200 Myr for galaxies with stellar masses Ms ∼ 106 to >1010 M, respectively, or a simple power-law form which exhibits similar mass-dependent time-scales. Using the SFH of individual galaxies, we measure the DC 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 ultraviolet magnitude (Muv ∼ −18), which is sufficient to make them observable (inline image). We find that both DC SFH and inline image make a sharp transition from zero (for galaxies with inline image) to unity (for inline image). The measured DC is also manifested in the intrinsic scatter in the Ms - SFR relationship (∼1 dex) and Ms - Muv relationship (ΔMuv ∼ ±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 DC to the observational estimate of galaxy stellar mass functions (GSMF) and the SFR density (SFRD), and find that it results in much shallower low-mass end slopes of the GSMF and a reduction of ≳70 per cent of our intrinsic SFRD, making our simulation results more compatible with observational estimates.