Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses. II.Observational constraints on the sub-galactic matter power spectrum

Stringent observational constraints on the sub-galactic matter power spectrum would allow one to distinguish between the concordance $\Lambda$CDM and the various alternative dark-matter models that predict significantly different properties of mass structure in galactic haloes. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to probe the sub-galactic mass structure in lens galaxies beyond the Local Group. Here, we demonstrate the first application of a novel methodology to observationally constrain the sub-galactic matter power spectrum in the inner regions of massive elliptical lens galaxies on 1-10 kpc scales from the power spectrum of surface-brightness anomalies in highly magnified galaxy-scale Einstein rings and gravitational arcs. The pilot application of our approach to Hubble Space Telescope (HST/WFC3/F390W) observations of the SLACS lens system SDSS J0252+0039 allows us to place the following observational constraints (at the 99 per cent confidence level) on the dimensionless convergence power spectrum $\Delta^{2}_{\delta\kappa}$ and the standard deviation in the aperture mass $\sigma_{\rm AM}$: $\Delta^{2}_{\delta\kappa}<1$ ($\sigma_{\rm AM}< 0.8 \times 10^8 M_\odot$) on 0.5-kpc scale, $\Delta^{2}_{\delta\kappa}<0.1$ ($\sigma_{\rm AM}< 1 \times 10^8 M_\odot$) on 1-kpc scale and $\Delta^{2}_{\delta\kappa}<0.01$ ($\sigma_{\rm AM}< 3 \times 10^8 M_\odot$) on 3-kpc scale. These first upper-limit constraints still considerably exceed the estimated effect of CDM subhaloes. However, future analysis of a larger sample of galaxy-galaxy strong lens systems can substantially narrow down these limits and possibly rule out dark-matter models that predict a significantly higher level of density fluctuations on the critical sub-galactic scales.