Galaxy radial profiles are often classified as exponential Types I, II or III according to whether the outer parts continue with the same scale length as the inner parts, continue with a shorter scale length (i.e., bend down a little) or continue with a larger scale length (bend up a little), respectively (Fig. 1). The Sersic profile with n = 1 corresponds to Type I; the other types do not have a constant Sersic index. For a review, see van der Kruit (2001), and for early surveys, see Pohlen and Trujillo (2006) and Erwin et al (2008).
Figure 1. Three types of exponential or piece-wise exponential profiles
Gutiérrez et al (2011) determined the proportion of the three exponential profile types for barred and non-barred galaxies of various Hubble types, including 183 large local face-on galaxies from three separate studies. For S0 and earlier, the three profile types are nearly evenly divided. For Sab to Sbc, Types II and III are about equal and Type I becomes relatively rare (10%). For Scd to Sdm, Type II dominates with ∼ 80% of the total. Herrmann et al (2013) continued this study to dIrrs and blue compact dwarfs (BCDs, see also Sect. 8.4). dIrr galaxies are dominated (80%) by Type IIs, while BCDs have steep inner parts from a starburst and are usually Type III.
A general caution should be mentioned about possible contamination at faint light levels from scattered light. Sandin (2015) showed R and I band radial profiles for NGC 4102 that were fit to a single exponential model with a broad point spread function from the instrument. The usual Type III profile for this galaxy turned into a Type I when the outer excess was corrected for the instrumental profile.