Growth of halo mass and efficiency of star formation. The contours show the efficiency of star formation, , as a function of redshift and halo mass, for the set of parameters that fit best the galaxy mass function (Sect. 3.1 and Table 1). The horizontal dash-dotted line shows the critical halo mass for shock heating, M_halo = M_shock. Baryons make stars efficiently only in the horizontal band of the diagram shown by the shaded region. The red irregular lines show the mass growth of four haloes, whose present masses are about 10¹¹, 10¹², 10¹³ and 10¹⁴ h^-1   M_⊙. They are backwards tracks for the most massive progenitors. The diagonal dashed line shows the characteristic mass scale M_nl on which density fluctuations become non-linear at redshift z, i.e. where σ(M_nl,z) = 1.68. The horizontal green line shows the mass resolution M_res = 1.5 × 10⁹ h^-1   M_⊙ of the N-body simulation.