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We use high-resolution ($\simeq$ 35pc) hydrodynamical simulations of galaxyformation to investigate the relation between gas accretion and star formationin galaxies hosted by dark matter haloes of mass $10^{12}$ $\mathrm{M_\odot}$at $z = 2$. At high redshift, cold-accreted gas is expected to be readilyavailable for star formation, while gas accreted in a hot mode is expected torequire a longer time to cool down before being able to form stars. Contrary tothese expectations, we find that the majority of cold-accreted gas takesseveral hundred Myr longer to form stars than hot-accreted gas after it reachesthe inner circumgalactic medium (CGM). Approximately 10% of the cold-accretedgas flows rapidly through the inner CGM onto the galactic disc. The remaining90% is trapped in a turbulent accretion region that extends up to $\sim$ 50 percent of the virial radius, from which it takes several hundred Myr for the gasto be transported to the star-forming disc. In contrast, most hot shock-heatedgas avoids this 'slow track', and accretes directly from the CGM onto the discwhere stars can form. We find that shock-heating of cold gas after accretion inthe inner CGM and supernova-driven outflows contribute to, but do not fullyexplain, the delay in star formation. These processes combined slow down thedelivery of cold-accreted gas to the galactic disc and consequently limit therate of star formation in Milky Way mass galaxies at $z > 2$.

Hot gas accretion fuels star formation faster than cold accretion in high redshift galaxies