Effects of the central luminosity, L_★, on the alignment timescales in our radiative transfer models at 0.87 mm, with the fixed parameters of a_max = 50 µm and f_high−J = 1. Each column is associated with a central luminosity value, L_★. While the plots in the three first rows represent the alignment timescales as a function of grain size, the plots in the last row represent the polarization fraction. The timescales are computed in specific locations, i.e., toward the equatorial mid-plane (first row), at an outflow cavity wall (second row), and in the middle of an outflow cavity (third row), in the central 2D slice of the model. These locations are indicated by the three colored circles in the polarization fraction maps, with the dark point for the first row (equatorial plane), the blue point for the second row (outflow cavity wall), and the green point for the third row (outflow cavity). In each plot of the first three rows, we present the Larmor precession timescale, τ_Larmor (with a dotted line for a grain without super-paramagnetic inclusions and with dot-dash and solid blue lines, respectively, for two values of N_cl, the number of atoms per cluster, 10³ and 10⁵), the radiative precession timescale, τ_rad, the collisional gaseous damping time of the grain, τ_gas (solid brown line), and the rotational disruption timescale, τ_disr (for an S_max value of 10⁵ erg cm⁻³, in solid dark yellow lines). We show the minimum grain size of aligned grains, a_align, with the vertical dotted green line. The range of grain size affected by rotationally disruption (a_disr − a_disr,max) for S_max = 10⁵ erg cm⁻³ is shown by the horizontal dark line. At a given grain size, the shortest precession timescale between τ_Larmor and τ_rad dictates the direction of alignment for the grains aligned at low J, i.e., with the magnetic field or the radiation field.