Statistical Bias in the Hubble Constant and Mass Power Law Slope for Mock Strong Lenses

Abstract: Strong gravitational lensing offers constraints on the Hubble constant that are independent of other methods. However, those constraints are subject to uncertainties in lens models. Previous studies suggest that using an elliptical power law + external shear (EPL+XS) for the lensing galaxy can yield results that are precise but inaccurate. We examine such models by generating and fitting mock lenses which produces multiple images of a background quasar-like point source. Despite using the same model for input and output, we find statistical bias in the Hubble constant on the order of 3% to 5%, depending on whether the elliptical lenses have noise or not. The phase space distribution has a `flared' shape that causes the mass power law slope to be underestimated and the Hubble constant to be overestimated. The bias varies with image configuration, which we quantify through annulus length between images with the first and second time delays ($\Delta r_{1,2}$). The statistical bias is worse for configurations that have narrow annuli (e.g., symmetric cross configurations). Assuming a source at redshift 2.0 and an EPL+XS lens at redshift 0.3, we find that the bias can be reduced, but not eliminated, if we limit the sample to systems with annulus lengths $\Delta r_{1,2} \gtrsim 0.3$ arcsec. As lens samples grow, it may be helpful to prioritize this range of image configurations for follow-up observation and analysis.