(An)isotropy of the Hubble diagram: comparing hemispheres

We test the isotropy of the Hubble diagram. At small redshifts, this is possible without assumptions on the cosmic inventory and provides a fundamental test of the cosmological principle. At higher redshift we check for the self-consistency of the LambdaCDM model. At small redshifts, we use public supernovae (SNe) Ia data to determine the deceleration parameter q_0 and the SN calibration on opposite hemispheres. For the complete data sets we fit Omega_M and the SN calibration on opposite hemispheres. A statistically significant anisotropy of the Hubble diagram at redshifts z 95% C.L.). While data from the North Galactic hemisphere favour the accelerated expansion of the Universe, data from the South Galactic hemisphere are not conclusive. The hemispheric asymmetry is maximal toward a direction close to the equatorial poles. The discrepancy between the equatorial North and South hemispheres shows up in the SN calibration. For the LambdaCDM model fitted to all available SNe, we find the same asymmetry. The alignment of discrepancies between hemispheric Hubble diagrams with the equatorial frame seems to point toward a systematic error in the SN search, observation, analysis or data reduction. We also find that our model independent test cannot exclude the case of the deceleration of the expansion at a statistically significant level.Comment: 13 pages, 8 figures; several corrections - conclusions unchanged; matches published versio

A Generalized Diffusion Tensor for Fully Anisotropic Diffusion of Energetic Particles in the Heliospheric Magnetic Field

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulas to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the 'traditional' diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we motivate the choice of the Frenet-Serret trihedron which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and the Parker field. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard 3D model for the modulation of galactic protons. For this we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the 'traditional' one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.Comment: 8 pages, 6 figures, accepted in Ap

Simulating Heliospheric and Solar Particle Diffusion using the Parker Spiral Geometry

Cosmic Ray transport in curved background magnetic fields is investigated using numerical Monte-Carlo simulation techniques. Special emphasis is laid on the Solar system, where the curvature of the magnetic field can be described in terms of the Parker spiral. Using such geometries, parallel and perpendicular diffusion coefficients have to be re-defined using the arc length of the field lines as the parallel displacement and the distance between field lines as the perpendicular displacement. Furthermore, the turbulent magnetic field is incorporated using a WKB approach for the field strength. Using a test-particle simulation, the diffusion coefficients are then calculated by averaging over a large number of particles starting at the same radial distance from the Sun and over a large number of turbulence realizations, thus enabling one to infer the effects due to the curvature of the magnetic fields and associated drift motions.Comment: accepted for publication at Journal of Geophysical Research - Space Physic