Constraints from Faraday rotation on the magnetic field structure in the Galactic halo

We examine the constraints imposed by Faraday rotation measures of extragalactic point sources on the structure of the magnetic field in the halo of our Galaxy. Guided by radio polarization observations of external spiral galaxies, we look in particular into the possibility that field lines in the Galactic halo have an X shape. We employ the analytical models of spiraling, possibly X-shape magnetic fields derived in a previous paper to generate synthetic all-sky maps of the Galactic Faraday depth, which we fit to an observational reference map with the help of Markov Chain Monte Carlo simulations. We find that the magnetic field in the Galactic halo is slightly more likely to be bisymmetric (azimuthal wavenumber, $m = 1$) than axisymmetric ($m = 0$). If it is indeed bisymmetric, it must appear as X-shaped in radio polarization maps of our Galaxy seen edge-on from outside, but if it is actually axisymmetric, it must instead appear as nearly parallel to the Galactic plane.Comment: 23 pages, 23 figure

Analytical models of X-shape magnetic fields in galactic halos

External spiral galaxies seen edge-on exhibit X-shape magnetic fields in their halos. Whether the halo of our own Galaxy also hosts an X-shape magnetic field is still an open question. We would like to provide the necessary analytical tools to test the hypothesis of an X-shape magnetic field in the Galactic halo. We propose a general method to derive analytical models of divergence-free magnetic fields whose field lines are assigned a specific shape. We then utilize our method to obtain four particular models of X-shape magnetic fields in galactic halos. In passing, we also derive two particular models of predominantly horizontal magnetic fields in galactic disks. All our field models have spiraling field lines with spatially varying pitch angle. Our four halo field models do indeed lead to X patterns in synthetic synchrotron polarization maps. Their precise topologies can all be explained by the action of a wind blowing outward from the galactic disk or from the galactic center. In practice, our field models may be used for fitting purposes or as inputs to various theoretical problems.Comment: 16 pages, 14 figure

Transport of positrons in the interstellar medium

This work investigates some aspects of the transport of low-energy positrons in the interstellar medium (ISM). We consider resonance interactions with magnetohydrodynamic waves above the resonance threshold. Below the threshold, collisions take over and deflect positrons in their motion parallel to magnetic-field lines. Using Monte-Carlo simulations, we model the propagation and energy losses of positrons in the different phases of the ISM until they annihilate. We suggest that positrons produced in the disk by an old population of stars, with initial kinetic energies below 1 MeV, and propagating in the spiral magnetic field of the disk, can probably not penetrate the Galactic bulge.Comment: 4 pages, 3 figures, accepted for publication in the proceeding of the 6th INTEGRAL worksho

The focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superposition

We consider the logarithmic Schrödinger equation in the focusing regime. For this equation, Gaussian initial data remains Gaussian. In particular, the Gausson - a time-independent Gaussian function - is an orbitally stable solution. In the general case in dimension d = 1, the solution with Gaussian initial data is periodic, and we compute some approximations of the period in the case of small and large oscillations, showing that the period can be as large as wanted for the latter. The main result of this article is a principle of nonlinear superposition: starting from an initial data made of the sum of several standing Gaussian functions far from each other, the solution remains close (in L^2) to the sum of the corresponding Gaussian solutions for a long time, in square of the distance between the Gaussian functions

Convergence rate in Wasserstein distance and semiclassical limit for the defocusing logarithmic Schrödinger equation

We consider the dispersive logarithmic Schrödinger equation in a semi-classical scaling. We extend the results about the large time behaviour of the solution (dispersion faster than usual with an additional logarithmic factor, convergence of the rescaled modulus of the solution to a universal Gaussian profile) to the case with semi-classical constant. We also provide a sharp convergence rate to the Gaussian profile in Kantorovich-Rubinstein metric through a detailed analysis of the Fokker-Planck equation satisfied by this modulus. Moreover, we perform the semiclassical limit of this equation thanks to the Wigner Transform in order to get a (Wigner) measure. We show that those two features are compatible and the density of a Wigner Measure has the same large time behaviour as the modulus of the solution of the logarithmic Schrödinger equation. Lastly, we discuss about the related kinetic equation (which is the Kinetic Isothermal Euler System) and its formal properties, enlightened by the previous results and a new class of explicit solutions

Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Comment: 29 page