Galaxy-wide IMF power-law index, α^gal (Eq. (15)), for OSGIMF (colored thin lines) and IGIMF (black lines) for SFR = 10^-5, 10^-4 ... 10⁵M_⊙/yr from upper to lower lines. For the SFR = 10⁵M_⊙/yr case, only the IGIMF index is plotted because a star-by-star sampling costs too much computational time. Below 1 M_⊙, the plot reproduces the canonical IMF indexes of 1.3 and 2.3 as defined in Eq. (2). Between 1 and 1.1 M_⊙, α^gal follows the variable α₃ defined in Eq. (5). At higher masses, α^gal varies with SFR. The OSGIMF index deviates from the IGIMF index at roughly 1 M_⊙. This result may lead to a large observational scatter at intermediate and high mass ranges. The large α^gal scatter for the OSGIMF at the low mass end and low SFR has been explained in the text for Fig. 4. The vertical dashed line at m = 1.3M_⊙ divides the IGIMF into two parts as mentioned in Sect. 5.1.