The planetary mass-luminosity relation during the formation phase for cold gas accretion (cold-nominal population). The luminosity L is the sum of the internal luminosity L_int and (for accreting planets) the accretion shock luminosity L_shock. The planets with a small black dot in the center have L_shock/L_int > 1, i.e., their luminosity is dominated by the accretion shock luminosity. Red, yellow, and green dots correspond to planets with a fractional contribution of the deuterium burning luminosity of L_D/L_int of at least 0.5, 0.1, and 0.05, respectively. In the panel at 3 Myr the gray dotted (dashed) lines show the linear (quadratic) M−L relations discussed in the text. In the two bottom panels, the gray solid line shows the mass-luminosity relation in the classical hot start tracks of Burrows et al. (1997), while the black dashed line shows the classical cold start simulations of Marley et al. (2007). Despite the cold gas accretion, the synthetic planets have luminosities almost as high as in the hot start models, a consequence of the core-mass effect. At 5 Myr, the luminosity of HD 100546 b (Quanz et al. 2015) is shown.