Glow in the Dark Matter: Observing galactic halos with scattered light

We consider the observation of diffuse halos of light around the discs of spiral galaxies, as a probe of the interaction cross section between Dark Matter and photons. Using the galaxy M101 as an example, we show that for a scattering cross section at the level of 10^(-23) x (m/GeV) cm^2 or greater Dark Matter in the halo will scatter light out from the more luminous centre of the disc to larger radii, contributing to an effective increased surface brightness at the edges of the observed area on the sky. This allows us to set an upper limit on the DM-photon cross section using data from the Dragonfly instrument. We then show how to improve this constraint, and the potential for discovery, by combining the radial profile of DM-photon scattering with measurements at multiple wavelengths. Observation of diffuse light presents a new and potentially powerful way to probe the interactions of Dark Matter with photons, which is complimentary to existing searches.Comment: 6 pages, 3 figures: v2 matches version accepted to PRL, with an extended discussion of potential background

Casimir force in the O(n -> infinity) model with free boundary conditions

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness $L$ subject to free boundary conditions and described by the $n\to\infty$ limit of the $O(n)$ model. These results extend over all temperatures, including the critical regime near the bulk critical temperature $T_c$, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone's modes contributions. The temperature behavior when the absolute temperature, $T$, is a finite distance below $T_c$, up to a logarithmic-in-$L$ proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble - but do not duplicate - the experimental curve behavior for the force obtained for $^4$He films.Comment: 16 pages, 3 figures, accepted for publication in Physical Review E. Abstract and author order changed to reflect the manuscript as rewritten, and comments changed to reflect the current status of the manuscript. Now publishe

Reply to Comment on "Casimir force in the O(n→∞)O(n\to\infty) model with free boundary conditions"

The proceeding comment raises a few points concerning our paper Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014). In this reply we stress that while Refs. Diehl \textit{et al.} EPL {\bf 100}, 10004 (2012) and Phys. Rev. E. {\bf 89}, 062123 (2014) use three different models to study the the Casimir force for the $O(n \rightarrow \infty)$ model with free boundary conditions we study a single model over the entire range of temperatures, from above the bulk critical temperature, $T_c$, to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the comment, we make no claim for the superiority of our model over any of those considered by Diehl \textit{et al}. We also present additional evidence supporting our conclusion in Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014) that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, while $T$ remains well outside of the critical region.Comment: 3 pages, 1 tabl

Moeglin's theorem and Goldie rank polynomials in Cartan type A

We use the theory of finite W-algebras associated to nilpotent orbits in the Lie algebra g = gl_N(C) to give another proof of Moeglin's theorem about completely prime primitive ideals in the enveloping algebra U(g). We also make some new observations about Joseph's Goldie rank polynomials in Cartan type A.Comment: final version; minor changes and some additions to bibliography; 32 page