Revisiting the Equipartition Assumption in Star-forming Galaxies

Energy equipartition between cosmic rays and magnetic fields is often assumed to infer magnetic field properties from the synchrotron observations of star-forming galaxies. However, there is no compelling physical reason to expect the same. We aim to explore the validity of the energy equipartition assumption. After describing popular arguments in favour of the assumption, we first discuss observational results which support it at large scales and how certain observations show significant deviations from equipartition at scales smaller than $\approx 1 \, {\rm kpc}$, probably related to the propagation length of the cosmic rays. Then we test the energy equipartition assumption using test-particle and MHD simulations. From the results of the simulations, we find that the energy equipartition assumption is not valid at scales smaller than the driving scale of the ISM turbulence ($\approx 100 \, {\rm pc}$ in spiral galaxies), which can be regarded as the lower limit for the scale beyond which equipartition is valid. We suggest that one must be aware of the dynamical scales in the system before assuming energy equipartition to extract magnetic field information from synchrotron observations. Finally, we present ideas for future observations and simulations to investigate in more detail under which conditions the equipartition assumption is valid or not.Comment: Invited review article for the special issue "New Perspectives on Galactic Magnetism" of the journal "Galaxies", accepted for publicatio

Seed magnetic fields in turbulent small-scale dynamos

Magnetic fields in galaxies and galaxy clusters are amplified from a very weak seed value to the observed $\mu{\rm G}$ strengths by the turbulent dynamo. The seed magnetic field can be of primordial or astrophysical origin. The strength and structure of the seed field, on the galaxy or galaxy cluster scale, can be very different, depending on the seed-field generation mechanism. The seed field first encounters the small-scale dynamo, thus we investigate the effects of the strength and structure of the seed field on the small-scale dynamo action. Using numerical simulations of driven turbulence and considering three different seed-field configurations: 1) uniform field, 2) random field with a power-law spectrum, and 3) random field with a parabolic spectrum, we show that the strength and statistical properties of the dynamo-generated magnetic fields are independent of the details of the seed field. We demonstrate that, even when the small-scale dynamo is not active, small-scale magnetic fields can be generated and amplified linearly due to the tangling of the large-scale field. In the presence of the small-scale dynamo action, we find that any memory of the seed field for the non-linear small-scale dynamo generated magnetic fields is lost and thus, it is not possible to trace back seed-field information from the evolved magnetic fields in a turbulent medium.Comment: 12 pages, 9 figures, 1 table, accepted for publication in MNRA

Cosmic ray propagation in turbulent galactic magnetic fields

PhD ThesisCosmic rays and magnetic fields are important non-thermal components of the interstellar medium in galaxies. This thesis explores the intermittent structure of the magnetic field generated by a fluctuation dynamo and the interaction of cosmic rays with small-scale random magnetic fields. First, the nonlinear state of fluctuation dynamo is described in terms of the statistical and structural properties of magnetic and velocity fields. Using three-dimensional fluctuation dynamo simulations, we study their properties in the kinematic and saturated stages. The alignment of the magnetic field, electric current density, and velocity field are analyzed to suggest a possible saturation mechanism for the fluctuation dynamo. Furthermore, we also study the change in the diffusion of magnetic fields by calculating local magnetic Reynolds number in the kinematic and saturated stages. We show that both the amplification and diffusion of magnetic fields are affected by nonlinearity. The dynamo-generated magnetic field is intermittent, i.e., concentrated in filaments, ribbons, and sheets. Minkowski functionals are used to characterize the shape of the magnetic structures and study its dependence on magnetic Reynolds number. We find that all three length scales of magnetic structures decreases on saturation. We also propose that observing magnetic fields in elliptical galaxies, via a grid of the Faraday rotation measures from background polarized sources, would serve as a probe of the fluctuation dynamo action in a galactic environment. Next, the effect of magnetic field intermittency on cosmic ray propagation is studied. Using test-particle simulations, it is shown that the diffusivity of low energy cosmic rays is enhanced when the magnetic field is intermittent. It is demonstrated that the cosmic ray diffusion in any random magnetic field (Gaussian or intermittent) can be better described as a correlated random walk rather the usual Brownian motion. Then, the energy equipartition between magnetic fields and cosmic rays usually assumed to infer magnetic field strength from synchrotron intensity observations is discussed. Using test-particle and magnetohydrodynamic simulations, it is shown that the cosmic ray and magnetic field energy densities are not correlated on scales less than the driving scale of the turbulence. Even when the cosmic ray and magnetic field energy densities are uncorrelated, small-scale structures are seen in the spatial distribution of cosmic rays as they are trapped between random magnetic mirrors. These results exclude the possibility of local energy equipartition between cosmic rays and magnetic fields

Multiphase Neutral Interstellar Medium: Analyzing Simulation with H I 21cm Observational Data Analysis Techniques

Several different methods are regularly used to infer the properties of the neutral interstellar medium (ISM) using atomic hydrogen (H I) 21cm absorption and emission spectra. In this work, we study various techniques used for inferring ISM gas phase properties, namely the correlation between brightness temperature and optical depth $(T_B(v)$, $\tau(v))$ at each channel velocity $(v)$, and decomposition into Gaussian components, by creating mock spectra from a 3D magnetohydrodynamic simulation of a two-phase, turbulent ISM. We propose a physically motivated model to explain the $T_B(v)-\tau(v)$ distribution and relate the model parameters to properties like warm gas spin temperature and cold cloud length scales. Two methods based on Gaussian decomposition -- using only absorption spectra and both absorption and emission spectra -- are used to infer the column density distribution as a function of temperature. In observations, such analysis reveals the puzzle of large amounts (significantly higher than in simulations) of gas with temperature in the thermally unstable range of $\sim200\mathrm{\ K}$ to $\sim2000\mathrm{\ K}$ and a lack of the expected bimodal (two-phase) temperature distribution. We show that, in simulation, both methods are able to recover the true gas distribution till temperatures $\lesssim2500\mathrm{\ K}$ (and the two-phase distribution in general) reasonably well. We find our results to be robust to a range of effects such as noise, varying emission beam size, and simulation resolution. This shows that the observational inferences are unlikely to be artifacts, thus highlighting a tension between observations and simulations. We discuss possible reasons for this tension and ways to resolve it.Comment: 21 pages (including appendixes), 15 figures, 3 tables, Submitted to MNRAS, Comments are welcom

Growth or decay: universality of the turbulent dynamo saturation

The small-scale turbulent dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy $E_{\rm kin}$ into magnetic energy $E_{\rm mag}$, and is often used to explain how an initially weak magnetic field with $E_{\rm mag} \ll E_{\rm kin}$ is amplified, and then maintained at a level $E_{\rm mag} \lesssim E_{\rm kin}$. Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this study, using three-dimensional, non-ideal magnetohydrodynamical turbulence simulations, we show that the same saturated state can also be achieved if initially $E_{\rm mag} \gg E_{\rm kin}$ or $E_{\rm mag} \sim E_{\rm kin}$. This is realised through a two-stage exponential decay (1. a slow backreaction that converts $E_{\rm mag}$ into $E_{\rm kin}$, and 2. Ohmic dissipation concentrated in anisotropic current sheets) into the saturated state, for which we provide an analytical model. This means that even if there are temporary local enhancements of $E_{\rm mag}$ in the ISM, such that $E_{\rm mag} > E_{\rm kin}$, e.g., through amplifications such as compressions, over a long enough time the field will decay into the saturated state set by the SSD, which is determined by the turbulence and magnetic dissipation. However, we also provide analytical models for the decay times and utilise wait-time statistics from compressive supernova events to show that if the magnetic field is enhanced above the saturated state, it will not have enough time to decay the field before the next supernova event. Hence, unless there exists a mechanism for destroying magnetic fields that is not in our non-ideal MHD models, the amplitudes of interstellar magnetic fields may also be a... (abridged).Comment: 18 pages. 14 figures. Submitted to MNRAS. Comments welcom

Saturation mechanism of the fluctuation dynamo at Pr-M >= 1

The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially), persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.We acknowledge financial support of the STFC (Grant No. ST/N000900/1, Project 2) and the Leverhulme Trust (Grant No. RPG-2014-427)