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Galaxy-scale gravitational lenses are often modeled with two-component massprofiles where one component represents the stellar mass and the second is anNFW profile representing the dark matter. Outside of the spherical case, theNFW profile is costly to implement, and so it is approximated via two differentmethods; ellipticity can be introduced via the lensing potential (NFWp) or viathe mass by approximating the NFW profile as a sum of analytical profiles(NFWm). While the NFWp method has been the default for lensing applications, itgives a different prescription of the azimuthal structure, which we showintroduces ubiquitous gradients in ellipticity and boxiness in the massdistribution rather than having a constant elliptical shape. Because unmodeledazimuthal structure has been shown to be able to bias lens model results, weexplore the degree to which this introduced azimuthal structure can affect themodel accuracy. We construct input profiles using composite models using boththe NFWp and NFWm methods and fit these mocks with a power-law elliptical massdistribution (PEMD) model with external shear. As a measure of the accuracy ofthe recovered lensing potential, we calculate the value of the Hubble parameter$H_0$ one would determine from the lensing fit. We find that the fits to theNFWp input return $H_0$ values which are systematically biased by about $3\%$lower than the NFWm counterparts. We explore whether such an effect isattributable to the mass sheet transformation (MST) by using an MST-independentquantity, $\xi_2$. We show that, as expected, the NFWm mocks are degeneratewith PEMD through an MST. For the NFWp, an additional bias is found beyond theMST due to azimuthal structures {\it exterior to the Einstein radius}. Werecommend modelers use an NFWm prescription in the future, such that azimuthalstructure can be introduced explicitly rather than implicitly.

On the ellipticity parameterization for an NFW profile: an overlooked angular structure in strong lens modeling