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We study the damping processes of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in a partially ionized medium. We start from the linear analysis of MHD waves, applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and the cutoff boundary of linear MHD waves is investigated. We find two branches of slow modes propagating in ions and neutrals, respectively, below the damping scale of slow MHD turbulence, and offer a thorough discussion of their propagation and dissipation behavior. Our analytical results are shown to be applicable in a variety of partially ionized interstellar medium (ISM) phases and the solar chromosphere. The importance of neutral viscosity in damping the Alfvenic turbulence in the interstellar warm neutral medium and the solar chromosphere is demonstrated. As a significant astrophysical utility, we introduce damping effects to the propagation of cosmic rays in partially ionized ISM. The important role of turbulence damping in both transit-time damping and gyroresonance is identified.
Context.
Tycho's supernova remnant (SNR) is associated with the historical supernova (SN) event SN 1572 of Type Ia. The explosion occurred in a relatively clean environment, and was visually observed, providing an age estimate. This SNR therefore represents an ideal astrophysical test-bed for the study of cosmic-ray acceleration and related phenomena. A number of studies suggest that shock acceleration with particle feedback and very efficient magnetic-field amplification combined with Alfvenic drift are needed to explain the rather soft radio spectrum and the narrow rims observed in X-rays.
Aims.
We show that the broadband spectrum of Tycho's SNR can alternatively be well explained when accounting for stochastic acceleration as a secondary process. The re-acceleration of particles in the turbulent region immediately downstream of the shock should be efficient enough to impact particle spectra over several decades in energy. The so-called Alfvenic drift and particle feedback on the shock structure are not required in this scenario. Additionally, we investigate whether synchrotron losses or magnetic-field damping play a more profound role in the formation of the non-thermal filaments.
Methods.
We solved the full particle transport equation in test-particle mode using hydrodynamic simulations of the SNR plasma flow. The background magnetic field was either computed from the induction equation or follows analytic profiles, depending on the model considered. Fast-mode waves in the downstream region provide the diffusion of particles in momentum space.
Results.
We show that the broadband spectrum of Tycho can be well explained if magnetic-field damping and stochastic re-acceleration of particles are taken into account. Although not as efficient as standard diffusive shock acceleration, stochastic acceleration leaves its imprint on the particle spectra, which is especially notable in the emission at radio wavelengths. We find a lower limit for the post-shock magnetic-field strength similar to 330 mu G, implying efficient amplification even for the magnetic-field damping scenario. Magnetic-field damping is necessary for the formation of the filaments in the radio range, while the X-ray filaments are shaped by both the synchrotron losses and magnetic-field damping.
Supernova remnants (SNRs) are discussed as the most promising sources of galactic cosmic rays (CR). The diffusive shock acceleration (DSA) theory predicts particle spectra in a rough agreement with observations. Upon closer inspection, however, the photon spectra of observed SNRs indicate that the particle spectra produced at SNRs shocks deviate from the standard expectation. This work suggests a viable explanation for a softening of the particle spectra in SNRs. The basic idea is the re-acceleration of particles in the turbulent region immediately downstream of the shock. This thesis shows that at the re-acceleration of particles by the fast-mode waves in the downstream region can be efficient enough to impact particle spectra over several decades in energy. To demonstrate this, a generic SNR model is presented, where the evolution of particles is described by the reduced transport equation for CR. It is shown that the resulting particle and the corresponding synchrotron spectra are significantly softer compared to the standard case. Next, this work outlines RATPaC, a code developed to model particle acceleration and corresponding photon emissions in SNRs. RATPaC solves the particle transport equation in test-particle mode using hydrodynamic simulations of the SNR plasma flow. The background magnetic field can be either computed from the induction equation or follows analytic profiles. This work presents an extended version of RATPaC that accounts for stochastic re-acceleration by fast-mode waves that provide diffusion of particles in momentum space. This version is then applied to model the young historical SNR Tycho. According to radio observations, Tycho’s SNR features the radio spectral index of approximately −0.65. In previous modeling approaches, this fact has been attributed to the strongly distinctive Alfvénic drift, which is assumed to operate in the shock vicinity. In this work, the problems and inconsistencies of this scenario are discussed. Instead, stochastic re-acceleration of electrons in the immediate downstream region of Tycho’s SNR is suggested as a cause for the soft radio spectrum. Furthermore, this work investigates two different scenarios for magnetic-field distributions inside Tycho’s SNR. It is concluded that magnetic-field damping is needed to account for the observed filaments in the radio range. Two models are presented for Tycho’s SNR, both of them feature strong hadronic contribution. Thus, a purely leptonic model is considered as very unlikely. Additionally, to the detailed modeling of Tycho’s SNR, this dissertation presents a relatively simple one-zone model for the young SNR Cassiopeia A and an interpretation for the recently analyzed VERITAS and Fermi-LAT data. It shows that the γ-ray emission of Cassiopeia A cannot be explained without a hadronic contribution and that the remnant accelerates protons up to TeV energies. Thus, Cassiopeia A is found to be unlikely a PeVatron.
The origin of cosmic rays was the subject of several studies for over a century. The investigations done within this dissertation are one small step to shed some more light on this mystery.
Locating the sources of cosmic rays is not trivial due to the interstellar magnetic field. However, the Hillas criterion allows us to arrive at the conclusion that supernova remnants are our main suspect for the origin of galactic cosmic rays. The mechanism by which they are accelerating particles is found within the field of shock physics as diffusive shock acceleration. To allow particles to enter this process also known as Fermi acceleration pre-acceleration processes like shock surfing acceleration and shock drift acceleration are necessary. Investigating the processes happening in the plasma shocks of supernova remnants is possible by utilising a simplified model which can be simulated on a computer using Particle-in-Cell simulations.
We developed a new and clean setup to simulate the formation of a double shock, i.e., consisting of a forward and a reverse shock and a contact discontinuity, by the collision of two counter-streaming plasmas, in which a magnetic field can be woven into. In a previous work, we investigated the processes at unmagnetised and at magnetised parallel shocks, whereas in the current work, we move our investigation on to magnetised perpendicular shocks.
Due to a much stronger confinement of the particles to the collision region the perpendicular shock develops much faster than the parallel shock. On the other hand, this leads to much weaker turbulence. We are able to find indications for shock surfing acceleration and shock drift acceleration happening at the two shocks leading to populations of pre-accelerated particles that are suitable as a seed population to be injected into further diffusive shock acceleration to be accelerated to even higher energies. We observe the development of filamentary structures in the shock ramp of the forward shock, but not at the reverse shock. This leads to the conclusion that the development of such structures in the shock ramp of quasi-perpendicular collisionless shocks might not necessarily be determined by the existence of a critical sonic Mach number but by a critical shock speed.
The results of the investigations done within this dissertation might be useful for further studies of oblique shocks and for studies using hybrid or magnetohydrodynamic simulations. Together with more sophisticated observational methods, these studies will help to bring us closer to an answer as to how particles can be accelerated in supernova remnants and eventually become cosmic rays that can be detected on Earth.
Current-day cosmic ray (CR) propagation studies use static Milky Way models and fit parametrized source distributions to data. Instead, we use three-dimensional magnetohydrodynamic (MHD) simulations of isolated galaxies with the moving-mesh code arepo that self-consistently accounts for hydrodynamic effects of CR protons. In post-processing, we calculate their steady-state spectra, taking into account all relevant loss processes. We show that this steady-state assumption is well justified in the disc and generally for regions that emit non-thermal radio and gamma rays. Additionally, we model the spectra of primary electrons, accelerated by supernova remnants, and secondary electrons and positrons produced in hadronic CR proton interactions with the gas. We find that proton spectra above 10 GeV only weakly depend on galactic radius, while they acquire a radial dependence at lower energies due to Coulomb interactions. Radiative losses steepen the spectra of primary CR electrons in the central galactic regions, while diffusive losses dominate in the outskirts. Secondary electrons exhibit a steeper spectrum than primaries because they originate from the transported steeper CR proton spectra. Consistent with Voyager-1 and AMS-02 data, our models (i) show a turnover of proton spectra below GeV energies due to Coulomb interactions so that electrons start to dominate the total particle spectra and (ii) match the shape of the positron fraction up to 10 GeV. We conclude that our steady-state CR modelling in MHD CR galaxy simulations is sufficiently realistic to capture the dominant transport effects shaping their spectra, arguing for a full MHD treatment to accurately model CR transport in the future.
An extinction-free estimator of the star formation rate (SFR) of galaxies is critical for understanding the high-redshift universe. To this end, the nearly linear, tight correlation of far-infrared (FIR), and radio luminosity of star-forming galaxies is widely used. While the FIR is linked to massive star formation, which also generates shock-accelerated cosmic-ray (CR) electrons and radio synchrotron emission, a detailed understanding of the underlying physics is still lacking. Hence, we perform three-dimensional magnetohydrodynamical (MHD) simulations of isolated galaxies over a broad range of halo masses and SFRs using the moving-mesh code AREPO, and evolve the CR proton energy density self-consistently. In post-processing, we calculate the steady-state spectra of primary, shock-accelerated and secondary CR electrons, which result from hadronic CR proton interactions with the interstellar medium. The resulting total radio luminosities correlate with the FIR luminosities as observed and are dominated by primary CR electrons if we account for anisotropic CR diffusion. The increasing contribution of secondary emission up to 30 per cent in starbursts is compensated by the larger bremsstrahlung and Coulomb losses. CR electrons are in the calorimetric limit and lose most of their energy through inverse Compton interactions with star light and cosmic microwave background (CMB) photons while less energy is converted into synchrotron emission. This implies steep steady-state synchrotron spectra in starbursts. Interestingly, we find that thermal free-free emission flattens the total radio spectra at high radio frequencies and reconciles calorimetric theory with observations while free-free absorption explains the observed low-frequency flattening towards the central regions of starbursts.
Cosmic rays (CRs) constitute an important component of the interstellar medium (ISM) of galaxies and are thought to play an essential role in governing their evolution. In particular, they are able to impact the dynamics of a galaxy by driving galactic outflows or heating the ISM and thereby affecting the efficiency of star-formation. Hence, in order to understand galaxy formation and evolution, we need to accurately model this non-thermal constituent of the ISM. But except in our local environment within the Milky Way, we do not have the ability to measure CRs directly in other galaxies. However, there are many ways to indirectly observe CRs via the radiation they emit due to their interaction with magnetic and interstellar radiation fields as well as with the ISM.
In this work, I develop a numerical framework to calculate the spectral distribution of CRs in simulations of isolated galaxies where a steady-state between injection and cooling is assumed. Furthermore, I calculate the non-thermal emission processes arising from the modelled CR proton and electron spectra ranging from radio wavelengths up to the very high-energy gamma-ray regime.
I apply this code to a number of high-resolution magneto-hydrodynamical (MHD) simulations of isolated galaxies, where CRs are included. This allows me to study their CR spectra and compare them to observations of the CR proton and electron spectra by the Voyager-1 satellite and the AMS-02 instrument in order to reveal the origin of the measured spectral features.
Furthermore, I provide detailed emission maps, luminosities and spectra of the non-thermal emission from our simulated galaxies that range from dwarfs to Milk-Way analogues to starburst galaxies at different evolutionary stages. I successfully reproduce the observed relations between the radio and gamma-ray luminosities with the far-infrared (FIR) emission of star-forming (SF) galaxies, respectively, where the latter is a good tracer of the star-formation rate. I find that highly SF galaxies are close to the limit where their CR population would lose all of their energy due to the emission of radiation, whereas CRs tend to escape low SF galaxies more quickly. On top of that, I investigate the properties of CR transport that are needed in order to match the observed gamma-ray spectra.
Furthermore, I uncover the underlying processes that enable the FIR-radio correlation (FRC) to be maintained even in starburst galaxies and find that thermal free-free-emission naturally explains the observed radio spectra in SF galaxies like M82 and NGC 253 thus solving the riddle of flat radio spectra that have been proposed to contradict the observed tight FRC.
Lastly, I scrutinise the steady-state modelling of the CR proton component by investigating for the first time the influence of spectrally resolved CR transport in MHD simulations on the hadronic gamma-ray emission of SF galaxies revealing new insights into the observational signatures of CR transport both spectrally and spatially.
The standard model for GRB afterglow emission treats the accelerated electron population as a simple power law, N(E) proportional to E-p for p greater than or similar to 2. However, in standard Fermi shock acceleration, a substantial fraction of the swept-up particles do not enter the acceleration process at all. Additionally, if acceleration is efficient, then the nonlinear back-reaction of accelerated particles on the shock structure modifies the shape of the nonthermal tail of the particle spectra. Both of these modifications to the standard synchrotron afterglow impact the luminosity, spectra, and temporal variation of the afterglow. To examine the effects of including thermal particles and nonlinear particle acceleration on afterglow emission, we follow a hydrodynamical model for an afterglow jet and simulate acceleration at numerous points during the evolution. When thermal particles are included, we find that the electron population is at no time well fitted by a single power law, though the highest-energy electrons are; if the acceleration is efficient, then the power-law region is even smaller. Our model predicts hard-soft-hard spectral evolution at X-ray energies, as well as an uncoupled X-ray and optical light curve. Additionally, we show that including emission from thermal particles has drastic effects (increases by factors of 100 and 30, respectively) on the observed flux at optical and GeV energies. This enhancement of GeV emission makes afterglow detections by future gamma-ray observatories, such as CTA, very likely.
We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh AREPO code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretized using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of AREPO. The interaction of CRs and gyroresonant Alfven waves is described by short time-scale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magnetohydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetized discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magnetohydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.
Cosmic rays (CRs) are a ubiquitous and an important component of astrophysical environments such as the interstellar medium (ISM) and intracluster medium (ICM). Their plasma physical interactions with electromagnetic fields strongly influence their transport properties. Effective models which incorporate the microphysics of CR transport are needed to study the effects of CRs on their surrounding macrophysical media. Developing such models is challenging because of the conceptional, length-scale, and time-scale separation between the microscales of plasma physics and the macroscales of the environment. Hydrodynamical theories of CR transport achieve this by capturing the evolution of CR population in terms of statistical moments. In the well-established one-moment hydrodynamical model for CR transport, the dynamics of the entire CR population are described by a single statistical quantity such as the commonly used CR energy density. In this work, I develop a new hydrodynamical two-moment theory for CR transport that expands the well-established hydrodynamical model by including the CR energy flux as a second independent hydrodynamical quantity. I detail how this model accounts for the interaction between CRs and gyroresonant Alfvén waves. The small-scale magnetic fields associated with these Alfvén waves scatter CRs which fundamentally alters CR transport along large-scale magnetic field lines. This leads to the effects of CR streaming and diffusion which are both captured within the presented hydrodynamical theory. I use an Eddington-like approximation to close the hydrodynamical equations and investigate the accuracy of this closure-relation by comparing it to high-order approximations of CR transport. In addition, I develop a finite-volume scheme for the new hydrodynamical model and adapt it to the moving-mesh code Arepo. This scheme is applied using a simulation of a CR-driven galactic wind. I investigate how CRs launch the wind and perform a statistical analysis of CR transport properties inside the simulated circumgalactic medium (CGM). I show that the new hydrodynamical model can be used to explain the morphological appearance of a particular type of radio filamentary structures found inside the central molecular zone (CMZ). I argue that these harp-like features are synchrotron-radiating CRs which are injected into braided magnetic field lines by a point-like source such as a stellar wind of a massive star or a pulsar. Lastly, I present the finite-volume code Blinc that uses adaptive mesh refinement (AMR) techniques to perform simulations of radiation and magnetohydrodynamics (MHD). The mesh of Blinc is block-structured and represented in computer memory using a graph-based approach. I describe the implementation of the mesh graph and how a diffusion process is employed to achieve load balancing in parallel computing environments. Various test problems are used to verify the accuracy and robustness of the employed numerical algorithms.