Observed high mass end power-law index of the galaxy-wide IMF resulting from the calculated IGIMF, (i.e., α^gal in Eq. (15) for m> 1 M_⊙), for a constant SFR over δt = 10 Myr in dependence of the galaxy-wide SFR. In Fig. 5, values diverge for different SFRs and also vary for different m at the high mass end. As at each m value there exists a different –SFR relation, we plot solid lines for log ₁₀(m/M_⊙) = 0.2, 0.4, ..., 2, i.e., 1.58, 2.51, ..., 100 M_⊙ from black to gray (top to bottom) for the fiducial model and dotted lines for the corresponding SolarMetal model defined in Sect. 2.1. The blue squares are data from the GAMA galaxy survey (Gunawardhana et al. 2011). The red triangles and red dash-dotted line are data from Weidner et al. (2013b); the left triangle is for the MW field, the middle three triangles are galaxy studies, the right triangle is for the bulges of the MW and M 31, and the dash-dotted line is their IGIMF model assuming β = 2. A recent study has suggested that the 2 M_⊙/yr SFR for MW is overestimated (Chomiuk & Povich 2011), but we leave this data point the same as in Weidner et al. (2013b). Gargiulo et al. (2015) report consistency between their IGIMF model assuming β = 2 (thick yellow dashed line) and the [α/Fe] abundance ratios of elliptical galaxies. The purple diamond is an individual analysis for the dwarf galaxy NGC 2915 (Bruzzese et al. 2015). Green stars are based on the Lee et al. (2009) 11HUGS observations of dwarf galaxies. The black circle is an observation for the solar neighborhood from Rybizki & Just (2015) with adopted MW SFR from Robitaille & Whitney (2010) as an upper limit of the solar neighborhood SFR because the Sun is located in an inter-arm region where the relevant SFR is significantly smaller (toward the direction indicated by the arrow; see Sect. 4.6 for further details). The thin horizontal dashed line represents the canonical IMF index α₂ = α₃ = 2.3.