Rigidity of spherical codes

A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configuration of the Coxeter-Todd lattice is not jammed, despite being locally jammed (each individual cap is held in place if its neighbors are fixed); in this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic lattice in three dimensions. By contrast, we find that many other packings have jammed kissing configurations, including the Barnes-Wall lattice and all of the best kissing configurations known in four through twelve dimensions. Jamming seems to become much less common for large kissing configurations in higher dimensions, and in particular it fails for the best kissing configurations known in 25 through 31 dimensions. Motivated by this phenomenon, we find new kissing configurations in these dimensions, which improve on the records set in 1982 by the laminated lattices.Comment: 39 pages, 8 figure

How the Universe got its Spots

The universe displays a three-dimensional pattern of hot and cold spots in the radiation remnant from the big bang. The global geometry of the universe can be revealed in the spatial distribution of these spots. In a topologically compact universe, distinctive patterns are especially prominent in spatial correlations of the radiation temperature. Whereas these patterns are usually washed out in statistical averages, we propose a scheme which uses the universe's spots to observe global geometry in a manner analogous to the use of multiple images of a gravitationally lensed quasar to study the geometry of the lens. To demonstrate how the geometry of space forms patterns in observations of the microwave sky, we develop a simple real-space approximation to estimate temperature correlations for any set of cosmological parameters and any global geometry. We present correlated spheres which clearly show geometric pattern formation for compact flat universes as well as for the compact negatively curved space introduced by Weeks and another discovered by Best. These examples illustrate how future satellite-based observations of the microwave background can determine the full geometry of the universe.Comment: 16 pages, 26 figure

Pulse profiles from thermally emitting neutron stars

The problem of computing the pulse profiles from thermally emitting spots on the surface of a neutron star in general relativity is reconsidered. We show that it is possible to extend Beloborodov (2002) approach to include (multiple) spots of finite size in different positions on the star surface. Results for the pulse profiles are expressed by comparatively simple analytical formulas which involve only elementary functions.Comment: 8 pages, 6 figures, accepted for publication in Ap

On the Nature of the X-ray Emission from the Accreting Millisecond Pulsar SAX J1808.4-3658

The pulse profiles of the accreting X-ray millisecond pulsar SAX J1808.4-3658 at different energies are studied. The two main emission component, the black body and the Comptonized tail that are clearly identified in the time-averaged spectrum, show strong variability with the first component lagging the second one. The observed variability can be explained if the emission is produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth ~0.3-1 at the neutron star surface. The emission patterns of the black body and the Comptonized radiation are different: a "knife"- and a "fan"-like, respectively. We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild spacetime. We present also accurate analytical formulae for computations of the light curves from rapidly rotating neutron stars using formalism recently developed by Beloborodov (2002). Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. We constrain the compact star mass to be bounded between 1.2 and 1.6 solar masses. By fitting the observed profiles, we determine the radius of the compact object to be R~11 km if M=1.6 M_sun, while for M=1.2 M_sun the best-fitting radius is ~6.5 km, indicating that the compact object in SAX J1808.4-3658 can be a strange star. We obtain a lower limit on the inclination of the system of 65 degrees.Comment: 11 pages, 7 figures, submitted to MNRA

Towards a holographic realization of the quarkyonic phase

Large-N_c QCD matter at intermediate baryon density and low temperatures has been conjectured to be in the so-called quarkyonic phase, i.e., to have a quark Fermi surface and on top of it a confined spectrum of excitations. It has been suggested that the presence of the quark Fermi surface leads to a homogeneous phase with restored chiral symmetry, which is unstable towards creating condensates breaking both the chiral and translational symmetry. Motivated by these exotic features, we investigate properties of cold baryonic matter in the single flavor Sakai-Sugimoto model searching for a holographic realization of the quarkyonic phase. We use a simplified mean-field description and focus on the regime of parametrically large baryon densities, of the order of the square of the 't Hooft coupling, as they turn out to lead to new physical effects similar to the ones occurring in the quarkyonic phase. One effect, the appearance of a particular marginally stable mode breaking translational invariance and linked with the presence of the Chern-Simons term in the flavor brane Lagrangian, is known to occur in the deconfined phase of the Sakai-Sugimoto model, but turns out to be absent here. The other, completely new phenomenon that we, preliminarily, study using strong simplifying assumptions are density-enhanced interactions of the flavor brane gauge field with holographically represented baryons. These seem to significantly affect the spectrum of vector and axial mesons and might lead to approximate chiral symmetry restoration in the lowest part of the spectrum, where the mesons start to qualitatively behave like collective excitations of the dense baryonic medium. We discuss the relevance of these effects for holographic searches of the quarkyonic phase and conclude with a discussion of various subtleties involved in constructing a mean-field holographic description of a dense baryonic medium.Comment: 31 pages, 16 figures; v2: inset plot in Fig. 10 removed, coloring in Fig. 13 fixed, typos fixed, matches published versio