Probing dark matter structure down to 107 solar masses: flux ratio statistics in gravitational lenses with line-of-sight haloes

Strong lensing provides a powerful means of investigating the nature of dark matter as it probes dark matter structure on sub-galactic scales. We present an extension of a forward modelling framework that uses flux ratios from quadruply imaged quasars (quads) to measure the shape and amplitude of the halo mass function, including line-of-sight (LOS) haloes and main deflector subhaloes. We apply this machinery to 50 mock lenses - roughly the number of known quads - with warm dark matter (WDM) mass functions exhibiting free-streaming cut-offs parametrized by the half-mode mass m(hm). Assuming cold dark matter (CDM), we forecast bounds on m(hm) and the corresponding thermal relic particle masses over a range of tidal destruction severity, assuming a particular WDM mass function and mass-concentration relation. With significant tidal destruction, at 2 sigma we constrain , or a 4.4 (3.1) keV thermal relic, with image flux uncertainties from measurements and lens modelling of . With less severe tidal destruction we constrain , or an 8.2 (6.2) keV thermal relic. If dark matter is warm, with (5.1keV), we would favour WDM with over CDM with relative likelihoods of 22:1 and 8:1 with flux uncertainties of and , respectively. These bounds improve over those obtained by modelling only main deflector subhaloes because LOS objects produce additional flux perturbations, especially for high-redshift systems. These results indicate that similar to 50 quads can conclusively differentiate between WDM and CDM.