Efstathiou-Lake-Negroponte criterion: quantity v_c, max/(αM_discG)^1/2, calculated at t = 0, for all thin+thick disc models as a function of maximum bar strength (S​_bar, max). Left panels: evolution for the rthickS models, and the middle and right panels show the evolution for models rthickE and rthickG, respectively. The points are colour-coded by the corresponding thick-disc fraction, f_thick (see the colour bar). The different symbols represent thin+thick models with different scale heights. The horizontal line (in black) denotes v_c, max/(αM_discG)^1/2 = 1.1, which serves as a boundary for the bar instability phase. For details, see the text.