Migration rates for the nominal model (blue line), the growth track 2 times faster than the nominal one (violet line) and the growth tracks 0.25 and 0.15 times the nominal one (green and red line, respectively). The black dashed line represents the critical migration rate at which L₃ and L₄ start to merge and disappear v_crit ≈ 1.45qΩr (Ogilvie & Lubow 2006). The black dash-dotted line represents the lower limit for the migration rate to get an asymmetry comparable with the one observed and estimated in our simulations, that is v_lim ≈ 0.17qΩr.