Discriminating power of milli-lensing observations for dark matter models

Abstract: The nature of dark matter (DM) is still under intense debate. Sub-galactic scales are particularly critical, as different, currently viable DM models make diverse predictions on the expected abundance and density profile of DM haloes on these scales. We investigate the ability of sub-galactic DM haloes to act as strong lenses on background compact sources, producing gravitational lensing events on milli-arcsecond scales (milli-lenses), for different DM models. For each DM scenario, we explore whether a sample of $\sim$ 5000 distant sources is sufficient to detect at least one milli-lens. We develop a semi-analytical model to estimate the milli-lensing optical depth as a function of the source's redshift for various DM models. We employ the Press-Schechter formalism, as well as results from recent N-body simulations to compute the halo mass function, taking into account the appropriate spherically averaged density profile of haloes for each DM model. We treat the lensing system as a point-mass lens and invoke the effective surface mass density threshold to calculate the fraction of a halo that acts as a gravitational lens. We study three classes of dark matter models: cold DM, warm DM, and self-interacting DM. We find that haloes consisting of warm DM turn out to be optically thin for strong gravitational milli-lensing (zero expected lensing events). CDM haloes may produce lensing events depending on the steepness of the concentration-mass relation. Self-interacting DM haloes can efficiently act as gravitational milli-lenses only if haloes experience gravothermal collapse, resulting in highly dense central cores.