\,\,,$$ with $$\begin{aligned}
p &=& x - (x^2 -1)^{1/2}\,\,,\\
x &=& \frac{R^2 + r^2 + z^2}{2Rr}\,\,.\end{aligned}$$ Here $K(p)$ and $E(p)$ are the complete elliptical integrals of the first and second kind. The equations are evaluated numerically. The equation of the density distribution $\rho(r,z)$ of the [ <span style="font-variant:small-caps;">HI</span> ]{}disc has been previously presented in Equation 15 in Paper II. We have presented the measured densities in Paper III. The equations for the stellar disc and bulge luminosity distributions have been previously presented in Equations 1 and 3 in Paper IV. We convert to a combined stellar mass distribution from these equations using $$\rho(r,z) = (M_*/L_R)\left(j_\textrm{disc}(R,z) + j_\textrm{bulge}(R,z)\right)\,\,.$$ The measurements for the stellar disc have been presented in Paper IV. Note that we adopt a single mass-to-light ratio $M_*/L_R$. While this may be a bit unrealistic, we noted in Paper IV that the fits for some of the bulges appear to supplement the stellar disc, rather than model a central component. Treating the two as distinct would therefore be invalid. A fixed $M_*/L_R$ ratio also has the advantage of limiting the complexity of the parameter space we will be fitting in.

### Vertical Tracer

We follow the method of @OBrien2010D to 