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When modelling strong gravitational lenses, i.e., where there are multipleimages of the same source, the most widely used parameterisation for the massprofile in the lens galaxy is the singular power-law model $\rho(r)\proptor^{-\gamma}$. This model may be insufficiently flexible for very accurate work,for example measuring the Hubble constant based on time delays between multipleimages. Here we derive the lensing properties - deflection angle, shear, andmagnification - of a more adaptable model where the projected mass surfacedensity is parameterised as a continuous two-dimensional broken power-law(2DBPL). This elliptical 2DBPL model is characterised by power-law slopes$t_1$, $t_2$ either side of the break radius $\theta_\mathrm{B}$. The key tothe 2DBPL model is the derivation of the lensing properties of the truncatedpower law (TPL) model, where the surface density is a power law out to thetruncation radius $\theta_\mathrm{T}$ and zero beyond. This TPL model is alsouseful by itself. We create mock observations of lensing by a TPL profile wherethe images form outside the truncation radius, so there is no mass in theannulus covered by the images. We then show that the slope of the profileinterior to the images may be accurately recovered for lenses of moderateellipticity. This demonstrates that the widely-held notion that lensingmeasures the slope of the mass profile in the annulus of the images, and isinsensitive to the mass distribution at radii interior to the images, isincorrect.

Galaxy mass profiles from strong lensing III: The two-dimensional broken power-law model