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This work introduces a new fitting formalism for isophotes which enables moreaccurate modelling of galaxies with non-elliptical shapes, such as diskgalaxies viewed edge-on or galaxies with X-shaped/peanut bulges. Within thisscheme, the angular parameter which defines quasi-elliptical isophotes istransformed from the commonly used, but inappropriate, polar co-ordinate to the`eccentric anomaly'. This provides a superior description of deviations fromellipticity, better capturing the true isophotal shape. Furthermore, this makesit possible to accurately recover both the surface brightness profile, usingthe correct azimuthally-averaged isophote, and the two-dimensional model of anygalaxy: the hitherto ubiquitous, but artificial, cross-like features inresidual images are completely removed. The formalism has been implemented intothe IRAF tasks $Ellipse$ and $Bmodel$ to create the new tasks `$Isofit$', and`$Cmodel$'. The new tools are demonstrated here with application to fivegalaxies, chosen to be representative case-studies for several areas where thistechnique makes it possible to gain new scientific insight. Specifically:properly quantifying boxy/disky isophotes via the fourth harmonic order inedge-on galaxies, quantifying X-shaped/peanut bulges, higher-order Fouriermoments for modelling bars in disks, and complex isophote shapes. Higher order(n > 4) harmonics now become meaningful and may correlate with structuralproperties, as boxyness/diskyness is known to do. This work also illustrateshow the accurate construction, and subtraction, of a model from a galaxy imagefacilitates the identification and recovery of over-lapping sources such asglobular clusters and the optical counterparts of X-ray sources.

Beyond Ellipse(s): Accurately Modelling the Isophotal Structure of Galaxies with $Isofit$ and $Cmodel$