Constrained simulations of the magnetic field in the local Universe and the propagation ofultrahigh energy cosmic rays

Abstract

We use simulations of large-scale structure formation to study the build-up ofmagnetic fields (MFs) in the intergalactic medium. Our basic assumption is thatcosmological MFs grow in a magnetohydrodynamical (MHD) amplificationprocess driven by formation of structure from a magnetic seed field present athigh red-shift. This approach is motivated by previous simulations of the MFs ingalaxy clusters which, under the same hypothesis as we adopt here, succeeded inreproducing Faraday rotation measurements (RMs) in clusters of galaxies. OurΛCDM initial conditions for the dark matter density fluctuations have been statisticallyconstrained by the observed large-scale density field within a sphere of 110 Mpcaround the Milky Way, based on the IRAS 1.2-Jy all-sky red-shift survey. As aresult, the positions and masses of prominent galaxy clusters in our simulationcoincide closely with their real counterparts in the local Universe. We find excellentagreement between RMs of our simulated galaxy clusters and observational data. Theimproved numerical resolution of our simulations compared to previous workalso allows us to study the MFs in large-scale filaments, sheets and voids. Bytracing the propagation of ultrahigh energy (UHE) protons in the simulated MFs weconstruct full-sky maps of expected deflection angles of protons with arrival energiesE = 1020 eVand 4 × 1019 eV, respectively. Accounting only for the structures within 110 Mpc, we find that strongdeflections are only produced if UHE protons cross galaxy clusters. The total area on thesky covered by these structures is however very small. Over still larger distances,multiple crossings of sheets and filaments may give rise to noticeable deflectionsover a significant fraction of the sky; the exact amount and angular distributiondepends on the model adopted for the magnetic seed field. On the basis of ourresults we argue that over a large fraction of the sky the deflections are likelyto remain smaller than the present experimental angular sensitivity. Therefore,we conclude that forthcoming air shower experiments should be able to locatesources of UHE protons and shed more light on the nature of cosmological MFs.