The Structure of Galaxies: II. Fitting Functions and Scaling Relations for Ellipticals

Surface photometry of 311 ellipticals from the 2MASS imaging database is analyzed with respect to the two most common fitting functions; the r^1/4 law and the Sersic r^1/n model. The advantages and disadvantages of each fitting function are examined. In particular, the r^1/4 law performs well in the middle regions, but is inadequate for the core (inner 5 kpcs) and the outer regions (beyond the half-light radius) which do not have r^1/4 shapes. It is found that the Sersic r^1/n model produce good fits to the core regions of ellipticals (r < r_half), but is an inadequate function for the entire profile of an elliptical from core to halo due to competing effects on the Sersic n index and the fact that the interior shape of an elliptical is only weakly correlated with its halo shape. In addition, there are a wide range of Sersic parameters that will equally describe the shape of the outer profile, degrading the Sersic models usefulness as a describer of the entire profile. Empirically determined parameters, such as half-light radius and total luminosity, have less scatter than fitting function variables. The scaling relations for ellipticals are often non-linear, but for ellipticals brighter than M_J < -23 the following structural relations are found: L propto r^0.8 \pm 0.1, L propto Sigma^-0.5 \pm 0.1 and Sigma propto r^-1.5 \pm 0.1.