Gravitational lenses on galaxy scales are plausibly modelled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires kn
owledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasising that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential. We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modelled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.
In this review, we discuss the role of the various experimental programs taking part in the broader effort to identify the particle nature of dark matter. In particular, we focus on electroweak scale dark matter particles and discuss a wide range of
search strategies being carried out and developed to detect them. These efforts include direct detection experiments, which attempt to observe the elastic scattering of dark matter particles with nuclei, indirect detection experiments, which search for photons, antimatter and neutrinos produced as a result of dark matter annihilations, and collider searches for new TeV-scale physics. Each of these techniques could potentially provide a different and complementary set of information related to the mass, interactions and distribution of dark matter. Ultimately, it is hoped that these many different tools will be used together to conclusively identify the particle or particles that constitute the dark matter of our universe.
