The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius R L and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 10 6 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10 −2 R L /l c 10 3 , where l c is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for R L /l c ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

In this white paper we introduce the IMAGINE Consortium and its scientific background, goals and structure. The purpose of the consortium is to coordinate and facilitate the efforts of a diverse group of researchers in the broad areas of the interstellar medium, Galactic magnetic fields and cosmic rays, and our overarching goal is to develop more comprehensive insights into the structures and roles of interstellar magnetic fields and their interactions with cosmic rays within the context of Galactic astrophysics. The ongoing rapid development of observational and numerical facilities and techniques has resulted in a widely felt need to advance this subject to a qualitatively higher level of self-consistency, depth and rigour. This can only be achieved by the coordinated efforts of experts in diverse areas of astrophysics involved in observational, theoretical and numerical work. We present our view of the present status of this research area, identify its key unsolved problems and suggest a strategy that will underpin our work. The backbone of the consortium is the Interstellar MAGnetic field INference Engine, a publicly available Bayesian platform that employs robust statistical methods to explore the multi-dimensional likelihood space using any number of modular inputs. This tool will be used by the IMAGINE Consortium to develop an interpretation and modelling framework that provides the method, power and flexibility to interfuse information from a variety of observational, theoretical and numerical lines of evidence into a self-consistent and comprehensive picture of the thermal and non-thermal interstellar media. An important innovation is that a consistent understanding of the phenomena that are directly or indirectly influenced by the Galactic magnetic field, such as the deflection of ultra-high energy cosmic rays or extragalactic backgrounds, is made an integral part of the modelling. The IMAGINE Consortium, which is informal by nature and open to new participants, hereby presents a methodological framework for the modelling and understanding of Galactic magnetic fields that is available to all communities whose research relies on a state of the art solution to this problem.

We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields, and cosmic rays are all initially in a magnetohydrostatic equilibrium. This is done for different choices of initial cosmic-ray density and magnetic field. The growth rates and characteristic scales obtained from the models, as well as their dependences on the density of cosmic rays and magnetic fields, are in broad agreement with previous (linearized, ideal) analytical work. However, this nonideal instability develops a multimodal 3D structure, which cannot be quantitatively predicted from the earlier linearized studies. This 3D signature of the instability will be of importance in interpreting observations. As a preliminary step toward such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure (RM) maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from RM maps are a possible probe for the cosmic-ray content of a given galaxy. Our calculations highlight the importance of cosmic rays in these measures, making them an essential ingredient of realistic models of the interstellar medium.

We study the cosmic evolution of the magnetic fields of a large sample of spiral galaxies in a cosmologically representative volume by employing a semi-analytic galaxy formation model and numerical dynamo solver in tandem. We start by deriving timeand radius-dependent galaxy properties using the galform galaxy formation model, which are then fed into the nonlinear mean-field dynamo equations. These are solved to give the large-scale (mean) field as a function of time and galactocentric radius for a thin disc, assuming axial symmetry. A simple prescription for the evolution of the small-scale (random) magnetic field component is also adopted. We find that, while most massive galaxies are predicted to have large-scale magnetic fields at redshift z = 0, a significant fraction of them is expected to contain negligible large-scale field. Our model indicates that, for most of the galaxies containing large-scale magnetic fields today, the mean-field dynamo becomes active at z < 3. Moreover, the typical magnetic field strength at any given galactic stellar mass is predicted to decline with time up until the present epoch, in agreement with our earlier results. We compute the radial profiles of pitch angle, and find broad agreement with observational data for nearby galaxies.

We explore the parameter space of the semi-analytic galaxy formation model GALFORM, studying the constraints imposed by measurements of the galaxy stellar mass function (GSMF) and its evolution. We use the Bayesian Emulator method to quickly eliminate vast implausible volumes of the parameter space and zoom in on the most interesting regions, allowing us to identify a set of models that match the observational data within model uncertainties. We find that the GSMF strongly constrains parameters related to quiescent star formation in discs, stellar and AGN feedback and threshold for disc instabilities, but weakly restricts other parameters. Constraining the model using local data alone does not usually select models that match the evolution of the GSMF well. Nevertheless, we show that a small subset of models provides acceptable match to GSMF data out to redshift 1.5. We explore the physical significance of the parameters of these models, in particular exploring whether the model provides a better description if the mass loading of the galactic winds generated by starbursts (β 0,burst ) and quiescent disks (β 0,disc ) is different. Performing a principal component analysis of the plausible volume of the parameter space, we write a set of relations between parameters obeyed by plausible models with respect to GSMF evolution. We find that while β 0,disc is strongly constrained by GSMF evolution data, constraints on β 0,burst are weak. Although it is possible to find plausible models for which β 0,burst = β 0,disc , most plausible models have β 0,burst > β 0,disc , implying -for these -larger SN feedback efficiency at higher redshifts.