Fitting Gravitational Lenses: Truth or Delusion

The observables in a strong gravitational lens are usually just the image positions and sometimes the flux ratios. We develop a new and simple algorithm which allows a set of models to be fitted exactly to the observations. Taking our cue from the strong body of evidence that early-type galaxies are close to isothermal, we assume that the lens is scale-free with a flat rotation curve. However, our algorithm allows full flexibility as regards the angular structure of the lensing potential. Importantly, all the free parameters enter linearly into the model and so the lens and flux ratio equations can always be solved by straightforward matrix inversion. The models are only restricted by the fact that the surface mass density must be positive. The transmission of the errors in the observations to uncertainties in the fitted parameters can be followed exactly and the full covariance matrix can be readily generated. We use this new algorithm to examine some of the claims made for anomalous flux ratios. It has been argued that such anomalies betray the presence of substantial amounts of substructure in the lensing galaxy.We demonstrate by explicit construction that some of the lens systems for which substructure has been claimed can be well-fit by smooth lens models. This is especially the case when the systematic errors in the flux ratios (caused by microlensing or scatter-broadening or differential extinction) are taken into account. However, there is certainly one system (B1422+231) for which the existing smooth models are definitely inadequate and for which substructure may be implicated. Within a few tens of kpc of the lensing galaxy centre, dynamical friction is very efficient at dissolving any substructure. Very little substructure ( ∼ < 1% of the mass) is projected within the Einstein radius. The numbers of strong lenses for which substructure is currently being claimed are so large that this contradicts rather than supports cold dark matter theories.