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

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