Sensitivity of strong lensing observations to dark matter substructure: a case study with Euclid

We introduce a machine learning method for estimating the sensitivity of strong lens observations to dark matter subhaloes in the lens. Our training data include elliptical power-law lenses, Hubble Deep Field sources, external shear, and noise and PSF for the Euclid VIS instrument. We set the concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$ relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$ simulated strong lens observations with depth and resolution resembling Euclid VIS images. We find that, with a $3\sigma$ detection threshold, $2.35$ per cent of pixels inside twice the Einstein radius are sensitive to subhaloes with a mass $M_\mathrm{max}\leq 10^{10}M_\odot$, $0.03$ per cent are sensitive to $M_\mathrm{max}\leq 10^{9}M_\odot$, and, the limit of sensitivity is found to be $M_\mathrm{max}=10^{8.8\pm0.2}M_\odot$. Using our sensitivity maps and assuming CDM, we estimate that Euclid-like lenses will yield $1.43^{+0.14}_{-0.11}[f_\mathrm{sub}^{-1}]$ detectable subhaloes per lens in the entire sample, but this increases to $35.6^{+0.9}_{-0.9}[f_\mathrm{sub}^{-1}]$ per lens in the most sensitive lenses. Estimates are given in units of the inverse of the substructure mass fraction $f_\mathrm{sub}^{-1}$. Assuming $f_\mathrm{sub}=0.01$, one in every $70$ lenses in general should yield a detection, or one in every $\sim$ three lenses in the most sensitive sample. From $170,000$ new strong lenses detected by Euclid, we expect $\sim 2500$ new subhalo detections. We find that the expected number of detectable subhaloes in warm dark matter models only changes relative to cold dark matter for models which have already been ruled out, i.e., those with half-mode masses $M_\mathrm{hm}>10^8M_\odot$.