Gravitational lensing and structural stability of dark matter caustic rings

Abstract

Gravitational lensing by the dual cusp (A −3 ) catastrophes of the cold dark matter (CDM) caustic rings at cosmological distances may provide the tantalizing opportunity to detect CDM indirectly, and discriminate between axions and weakly interacting massive particles (WIMPs). The infall of CDM onto isolated galaxies such as our own produces discrete number of flows and caustics in the halo CDM distribution. Caustics are places where the CDM particles are naturally focussed. In the CDM cosmology, caustics in the distribution of dark matter are plentiful once density perturbations enter the nonlinear regime. Our focus is upon the caustic rings which are closed tubes whose cross-section is an elliptic umbilic (D −4 ) catastrophe with three dual cusps. We call this cross-section a "tricusp." Caustic rings are located near where the particles with the most angular momentum in a given inflow reach their distance of closest approach to the galactic center before going back out. We reparameterize the CDM flow near a caustic ring, and obtain the ring equations in space, as single valued functions of an angular variable parameterizing the tricusp. A caustic ring has a specific density profile, a specific geometry and, therefore, precisely calculable gravitational lensing signatures that vary on the caustic surface, depending on the location of the line of sight. We calculate the image magnification of point-like sources as a function of the angular parameter of the tricusp for the line of sights that are parallel to the galactic plane of the caustic ring and near tangent to the surface. The magnification monotonically increases 1 as the line of sight approaches to the cusps where it diverges in the limit of zero velocity dispersion. If the velocity dispersion is small but nonzero, the divergence is cut off, because the caustic surface gets smeared over some distance in space and the cusps are smoothed out. The lensing effects are no longer infinite at the cusps, but merely large. To estimate the magnification numerically, for the rings at cosmological distances and for the ring closest to us (the fifth caustic ring of the Milky Way), we choose sample points near the cusps. We find that the lensing effects are largest at the outer cusp which lies in (or, near) the galactic plane.Around the outer cusp, the surface is curved toward the side with two extra flows. We call such a surface concave. In the limit of zero velocity dispersion, at a sample point near the outer cusp, we find 37% magnification for the CDM caustic rings at cosmological distances. This is about 250 times stronger than the lensing effect we predicted for the concave folds (considering the A 2 catastrophes enveloping the galaxy), and 37 times stronger than the largest lensing effect we predicted for the CDM caustics (considering the convex folds of the rings) before. In the presence of finite velocity dispersion, the lower and upper bounds of the effective velocity dispersions of the axion and WIMP flows in galactic halos may be used to constrai...

Caustics, Cold Flows, and Annual Modulation

“…Two mechanisms were found by which the star density could be enhanced in the vicinity of an inner caustic, and these may have played a role in the formation of the Monoceros ring. Authors [24][25][26][27] examined the possibility of observing caustics by gravitational lensing, while [28][29][30][31][32][33][34] have studied dark matter annihilation in caustics. These possibilities however require high densities in the vicinity of the caustic.…”

Weakly interacting massive particle annihilation in caustics

“…Previous work on particle annihilation in caustics includes [10,11,12,13,14]. For the possibility of detecting caustics by gravitational lensing, see [15,16,17]. Caustics and their associated cold flows are also relevant to direct detection experiments [18,19,20,21,22].…”