The observed surface densities of dark matter halos are known to follow a simple scaling law , ranging from dwarf galaxies to galaxy clusters , with a weak dependence on their virial mass .
Here we point out that this can not only be used to provide a method to determine the standard relation between halo mass and concentration , but also to use large samples of objects in order to place constraints on dark matter self-interactions that can be more robust than constraints derived from individual objects .
We demonstrate our method by considering a sample of about 50 objects distributed across the whole halo mass range , and by modelling the effect of self-interactions in a way similar to what has been previously done in the literature .
Using additional input from simulations then results in a constraint on the self-interaction cross section per unit dark matter mass of about \sigma / m _ { \chi } \lesssim 0.3 cm ^ { 2 } /g .
We expect that these constraints can be significantly improved in the future , and made more robust , by i ) an improved modelling of the effect of self-interactions , both theoretical and by comparison with simulations , ii ) taking into account a larger sample of objects and iii ) by reducing the currently still relatively large uncertainties that we conservatively assign to the surface densities of individual objects .
The latter can be achieved in particular by using kinematic observations to directly constrain the average halo mass inside a given radius , rather than fitting the data to a pre-selected profile and then reconstruct the mass .
For a velocity-independent cross-section , our current result is formally already somewhat smaller than the range 0.5 - 5 cm ^ { 2 } /g that has been invoked to explain potential inconsistencies between small-scale observations and expectations in the standard collisionless cold dark matter paradigm .