The free streaming length of dark matter particles determines the abundance of structure on sub-galactic scales .
We present a statistical technique , amendable to any parameterization of subhalo density profile and mass function , to probe dark matter on these scales with quadrupole image lenses .
We consider a warm dark matter particle with a mass function characterized by a normalization and free streaming scale m _ { hm } .
We forecast bounds on dark matter warmth for 120-180 lenses , attainable with future surveys , at typical lens ( source ) redshifts of 0.5 ( 1.5 ) in early-type galaxies with velocity dispersions of 220-270 km/sec .
We demonstrate that limits on m _ { hm } deteriorate rapidly with increasing uncertainty in image fluxes , underscoring the importance of precise measurements and accurate lens models .
For our forecasts , we assume the deflectors in the lens sample do not exhibit complex morphologies , so we neglect systematic errors in their modeling .
Omitting the additional signal from line of sight halos , our constraints underestimate the true power of the method .
Assuming cold dark matter , for a low normalization , corresponding the destruction of all subhalos within the host scale radius , we forecast 2 \sigma bounds on m _ { hm } ( thermal relic mass ) of 10 ^ { 7.5 } ( 5.0 ) , 10 ^ { 8 } ( 3.6 ) , and 10 ^ { 8.5 } ( 2.7 ) M _ { \odot } \left ( keV \right ) for flux errors of 2 \% , 4 \% , and 8 \% .
With a higher normalization , these constraints improve to 10 ^ { 7.2 } ( 6.6 ) , 10 ^ { 7.5 } ( 5.3 ) , and 10 ^ { 7.8 } ( 4.3 ) M _ { \odot } \left ( keV \right ) with 120 systems .
We are also able to measure the normalization of the mass function , which has implications for baryonic feedback models and tidal stripping .