We examine the temperature history of gas accreted by forming galaxies in smoothed particle hydrodynamics simulations. About half of the gas follows the track expected in the conventional picture of galaxy formation, shock heating to roughly the virial temperature of the galaxy potential well (T similar to 10(6) K for a Milky Way type galaxy) before cooling, condensing and forming stars. However, the other half radiates its acquired gravitational energy at much lower temperatures, typically T < 10(5) K, and the histogram of maximum gas temperatures is clearly bimodal. The 'cold mode' of gas accretion dominates for low-mass galaxies (baryonic mass M-gal <= 10(10.3) M-circle dot or halo mass M-halo < 10(11.4) M-circle dot), while the conventional 'hot mode' dominates the growth of high-mass systems. Cold accretion is often directed along filaments, allowing galaxies to efficiently draw gas from large distances, while hot accretion is quasispherical. The galaxy and halo mass dependence leads to redshift and environment dependence of cold and hot accretion rates, with the cold mode dominating at high redshift and in low-density regions today, and the hot mode dominating in group and cluster environments at low redshift. The simulations reproduce an important feature of the observed relation between the galaxy star formation rate (SFR) and the environment, namely a break in star formation rates at surface densities Sigma similar to 1 h(75)(2) Mpc(-2), outside the virial radii of large groups and clusters. The cosmic SFR tracks the overall history of gas accretion, and its decline at low redshift follows the combined decline of cold and hot accretion rates. The drop in cold accretion is driven by the decreasing infall rate on to haloes, while for hot accretion this slower mass growth is further modified by the longer cooling times within haloes. If we allowed hot accretion to be suppressed by conduction or active galactic nuclei feedback, then the simulation predictions would change in interesting ways, perhaps resolving conflicts with the colours of ellipticals and the cut-off of the galaxy luminosity function. The transition at M-halo similar to 10(11.4) M-circle dot between cold-mode domination and hot-mode domination is similar to that found by Birnboim & Dekel using one-dimensional simulations and analytic arguments. The corresponding baryonic mass is tantalizingly close to the scale at which Kauffmann et al. find a marked shift in galaxy properties, and we speculate on possible connections between these theoretical and observational transitions.
