Top: Arbitrary Gaussian, Lorentzian, and double Gaussian profiles that demonstrate how a Lorentzian can mimic a double Gaussian without the extra model parameters. The Gaussian (blue line) and Lorentzian (black line) profiles have a FWHM of 2 au, while the double Gaussian (orange dotted line) is composed of one Gaussian with a FWHM of 1.7 au and another with a FWHM of 6 au. Bottom: Various exponential forms with different ζ (colored lines, ζ values annotated on the panel). The wings of the Lorentzian (black line) are closely matched with an exponential with ζ = 1. All profiles are normalized to the same maximum value.