Cosmic Ray Transport Research Articles

Simulating Groups and the IntraGroup Medium: The Surprisingly Complex and Rich Middle Ground between Clusters and Galaxies

Galaxy groups are more than an intermediate scale between clusters and halos hosting individual galaxies, they are crucial laboratories capable of testing a range of astrophysics from how galaxies form and evolve to large scale structure (LSS) statistics for cosmology. Cosmological hydrodynamic simulations of groups on various scales offer an unparalleled testing ground for astrophysical theories. Widely used cosmological simulations with ∼(100 Mpc)3 volumes contain statistical samples of groups that provide important tests of galaxy evolution influenced by environmental processes. Larger volumes capable of reproducing LSS while following the redistribution of baryons by cooling and feedback are the essential tools necessary to constrain cosmological parameters. Higher resolution simulations can currently model satellite interactions, the processing of cool (T≈104−5 K) multi-phase gas, and non-thermal physics including turbulence, magnetic fields and cosmic ray transport. We review simulation results regarding the gas and stellar contents of groups, cooling flows and the relation to the central galaxy, the formation and processing of multi-phase gas, satellite interactions with the intragroup medium, and the impact of groups for cosmological parameter estimation. Cosmological simulations provide evolutionarily consistent predictions of these observationally difficult-to-define objects, and have untapped potential to accurately model their gaseous, stellar and dark matter distributions.

Intermediate-mass and heavy Galactic cosmic-ray nuclei: The case of new AMS-02 measurements

The recent measurement of the spectra of intermediate mass nuclei and iron nuclei carried out with the AMS-02 experiment provided us with the most complete set of data on cosmic ray fluxes to date, and allowed us to test the standard model for the transport of these particles through the Galaxy to the finest details. We show that the parameters derived from lighter primary and secondary elements in the cosmic radiation also lead to a good description of the data on heavier nuclei, with no need to invoke different injection spectra for such nuclei, provided the whole chain of fragmentation is properly accounted for. The only exception to this finding is represented by iron nuclei, which show a very unusual trend at rigidity $\lesssim 100$ GV. This trend reflects in a Fe/O ratio that is at odds with the results of the standard model of cosmic ray transport, and is in contradiction with data collected by HEAO, ACE-CRIS and Voyager at lower energy. We speculate on possible origins of such findings.

Cosmic ray protons and electrons from supernova remnants

Context.The spectrum of cosmic ray protons and electrons released by supernova remnants throughout their evolution is poorly known because of the difficulty in accounting for particle escape and confinement downstream of a shock front, where both adiabatic and radiative losses are present. Since electrons lose energy mainly through synchrotron losses, it is natural to ask whether the spectrum released into the interstellar medium may be different from that of their hadronic counterpart. Independent studies of cosmic ray transport through the Galaxy require that the source spectrum of electrons and protons be very different. Therefore, the above question acquires a phenomenological relevance.Aims.Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from the upstream region and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons, where in addition to adiabatic losses we take the radiative losses suffered behind the shock into account. These electrons are dominated by synchrotron losses in the magnetic field, which most likely is self-generated by cosmic rays accelerated at the shock.Methods.We use standard temporal evolution relations for supernova shocks expanding in different types of interstellar media together with an analytic description of particle acceleration and magnetic field amplification to determine the density and spectrum of cosmic ray particles. Their evolution in time is derived by numerically solving the equation describing advection with adiabatic and radiative losses for electrons and protons. The flux from particles continuously escaping the supernova remnants is also accounted for.Results.The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to nonresonant and resonant streaming instability and their saturation. The resulting field is compared with the available set of observational results concerning the dependence of the magnetic field strength upon shock velocity. We find that when the field is the result of the growth of the cosmic-ray-driven nonresonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different; however, such a difference becomes appreciable only at energies ≳100−1000 GeV, while observations of the electron spectrum require such a difference to be present at energies as low as ∼10 GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of supernova remnant evolution (shock velocity ≪1000 km s−1); this may not be due to streaming instability but rather hydrodynamical processes. We comment on the feasibility of such conditions and speculate on the possibility that the difference in spectral shape between electrons and protons may reflect either some unknown acceleration effect or additional energy losses in cocoons around the sources.

Influence of Ion–Neutral Damping on the Cosmic-Ray Streaming Instability: Magnetohydrodynamic Particle-in-cell Simulations

Abstract We explore the physics of the gyroresonant cosmic-ray streaming instability (CRSI) including the effects of ion–neutral (IN) damping. This is the main damping mechanism in (partially ionized) atomic and molecular gas, which are the primary components of the interstellar medium (ISM) by mass. Limitation of CRSI by IN damping is important in setting the amplitude of Alfvén waves that scatter cosmic rays (CRs) and control galactic-scale transport. Our study employs the magnetohydrodynamic (MHD)–particle-in-cell hybrid fluid-kinetic numerical technique to follow linear growth as well as post-linear and saturation phases. During the linear phase of the instability—where simulations and analytical theory are in good agreement—IN damping prevents wave growth at small and large wavelengths, with the unstable bandwidth lower for higher IN collision rates ν in. Purely MHD effects during the post-linear phase extend the wave spectrum toward larger k. In the saturated state, the CR distribution evolves toward greater isotropy (lower streaming velocity) by scattering off of Alfvén waves excited by the instability. In the absence of low-k waves, CRs with sufficiently high momentum are not isotropized. The maximum wave amplitude and rate of isotropization of the distribution function decrease at higher ν in. When the IN damping rate approaches the maximum growth rate of CRSI, wave growth and isotropization are suppressed. Implications of our results for CR transport in partially ionized ISM phases are discussed.

The Earth-like Galactic cosmic ray intensity in the habitable zone of the M dwarf GJ 436

ABSTRACT Galactic cosmic rays are energetic particles important in the context of life. Many works have investigated the propagation of Galactic cosmic rays through the Sun’s heliosphere. However, the cosmic ray fluxes in M dwarf systems are still poorly known. Studying the propagation of Galactic cosmic rays through the astrospheres of M dwarfs is important to understand the effect on their orbiting planets. Here, we focus on the planetary system GJ 436. We perform simulations using a combined 1D cosmic ray transport model and 1D Alfvén-wave-driven stellar wind model. We use two stellar wind set-ups: one more magnetically dominated and the other more thermally dominated. Although our stellar winds have similar magnetic field and velocity profiles, they have mass-loss rates two orders of magnitude different. Because of this, they give rise to two different astrosphere sizes, one 10 times larger than the other. The magnetically dominated wind modulates the Galactic cosmic rays more at distances $\lt 0.2\,$ au than the thermally dominated wind due to a higher local wind velocity. Between 0.2 and 1 au the fluxes for both cases start to converge. However, for distances $\gt 10\,$ au, spatial diffusion dominates, and the flux of GeV cosmic rays is almost unmodulated. We find, irrespective of the wind regime, that the flux of Galactic cosmic rays in the habitable zone of GJ 436 (0.2–0.4 au) is comparable with intensities observed at Earth. On the other hand, around GJ 436 b (0.028 au), both wind regimes predict Galactic cosmic ray fluxes that are approximately 104 times smaller than the values observed at Earth.

Cosmic rays and non-thermal emission in simulated galaxies − I. Electron and proton spectra compared to Voyager-1 data

ABSTRACT 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.

Cosmic rays and non-thermal emission in simulated galaxies – II. γ-ray maps, spectra, and the far-infrared–γ-ray relation

ABSTRACT The γ-ray emission of star-forming (SF) galaxies is attributed to hadronic interactions of cosmic ray (CR) protons with the interstellar gas and contributions from CR electrons via bremsstrahlung and inverse Compton (IC) scattering. The relative importance of these processes in different galaxy types is still unclear. We model these processes in three-dimensional magnetohydrodynamical (MHD) simulations of the formation of isolated galactic discs using the moving-mesh code arepo, including dynamically coupled CR protons and adopting different CR transport models. We calculate steady-state CR spectra and also account for the emergence of secondary electrons and positrons. This allows us to produce detailed γ-ray maps, luminosities, and spectra of our simulated galaxies at different evolutionary stages. Our simulations with anisotropic CR diffusion and a low CR injection efficiency at supernovae (SNe; $\zeta_\mathrm{SN}=0.05$) can successfully reproduce the observed far-infrared (FIR)–γ-ray relation. Starburst galaxies are close to the calorimetric limit, where CR protons lose most of their energy due to hadronic interactions and hence, their γ-ray emission is dominated by neutral pion decay. However, in low SF galaxies, the increasing diffusive losses soften the CR proton spectra due to energy-dependent diffusion, and likewise steepen the pionic γ-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to ∼40 per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed γ-ray spectra of starburst galaxies, we require a weaker energy dependence of the CR diffusion coefficient, $D\propto E^{0.3}$, in comparison to Milky Way-like galaxies.

First Observations of Anomalous Cosmic Rays in to 36 Solar Radii

Abstract NASA’s Parker Solar Probe mission continues to travel closer to the Sun than any prior human-made object, with an expected closest approach of <10 solar radii (<0.046 au) by 2024. On board, the Integrated Science Investigation of the Sun instrument suite makes unprecedented in situ measurements of energetic particles in the near-Sun environment. The current low level of solar activity offers a prime opportunity to measure cosmic rays closer to the Sun than ever before. We present the first observations of anomalous cosmic rays in to 36 solar radii (0.166 au), focusing specifically on helium. Our results indicate a strong radial intensity gradient of ∼25 ± 5%/au over energies of ∼4 to ∼45 MeV/nuc. These values are larger than prior observations, further out in the heliosphere, and come at a unique time in our understanding and modeling of particle transport and acceleration, particularly as both Voyagers have crossed the heliopause and IBEX has accumulated a full solar cycle of observations. Thus, continued measurements of cosmic rays by Parker Solar Probe will play a critical role in linking past observations with our present knowledge and significantly advancing our understanding of cosmic ray transport in the heliosphere.

Galactic cosmic ray transport in the heliosphere: Forbush ion chamber data analysis

The study of ratio α (=λ⊥/λ||) of galactic cosmic ray (GCR) free paths normal (λ⊥) and parallel (λ||) to the mean interplanetary magnetic field (IMF) B is continued with annual mean GCR solar diurnal anisotropy (SDA) data of the Cheltenham/Fredericksburg shielded ion chamber (CH-IC) for 1936–1977 previously analyzed by Bieber and Chen (1991) but not corrected for atmospheric temperature effect. This study uses CH-IC data corrected for temperature effect to calculate α for the first time assuming negligible latitudinal density gradient. Solar activity dependence of α shown by Bieber and Chen (BC) remains qualitatively unchanged. Present GCR modulation theories do not provide guidance for α, its rigidity or solar cycle dependence. Flat heliosphere current sheet (HCS) and Master equations derived by Ahluwalia and Dorman (1997) are used for computing α and study its rigidity dependence and correlation with solar activity for positive (p) and negative (n) polarity intervals of B at 1 AU; B points outward/ inward from the Sun during p/n interval in Northern hemisphere, IMF polarity changes sign near sunspot number (SSN) maximum. CH-IC median rigidity of response (Rm) for GCR differential spectrum is 67 GV. We show that computed α is high for p- and low for n-intervals, also α is low near SSN maximum and high near SSN minimum when effective limiting GCR rigidity (Rc) for SDA is known to be <100 GV. The results are consistent with those reported earlier by Ahluwalia and Modzelewska (2020) for NagV-MT (Rm = 60 GV) for 1971–2017; they challenge validity of present conceptual understanding of GCR modulation processes in the heliosphere, pointing to a great need to develop an acceptable modulation theory to explain empirical results reported in this paper.

Stellar versus Galactic: the intensity of cosmic rays at the evolving Earth and young exoplanets around Sun-like stars

ABSTRACT Energetic particles, such as stellar cosmic rays, produced at a heightened rate by active stars (like the young Sun) may have been important for the origin of life on Earth and other exoplanets. Here, we compare, as a function of stellar rotation rate (Ω), contributions from two distinct populations of energetic particles: stellar cosmic rays accelerated by impulsive flare events and Galactic cosmic rays. We use a 1.5D stellar wind model combined with a spatially 1D cosmic ray transport model. We formulate the evolution of the stellar cosmic ray spectrum as a function of stellar rotation. The maximum stellar cosmic ray energy increases with increasing rotation, i.e. towards more active/younger stars. We find that stellar cosmic rays dominate over Galactic cosmic rays in the habitable zone at the pion threshold energy for all stellar ages considered ($t_*=0.6\!-\!2.9\,$ Gyr). However, even at the youngest age, $t_*=0.6\,$ Gyr, we estimate that $\gtrsim \, 80$ MeV stellar cosmic ray fluxes may still be transient in time. At ∼1 Gyr when life is thought to have emerged on Earth, we demonstrate that stellar cosmic rays dominate over Galactic cosmic rays up to ∼4 GeV energies during flare events. Our results for t* = 0.6 Gyr (Ω = 4 Ω⊙) indicate that ≲GeV stellar cosmic rays are advected from the star to 1 au and are impacted by adiabatic losses in this region. The properties of the inner solar wind, currently being investigated by the Parker Solar Probe and Solar Orbiter, are thus important for accurate calculations of stellar cosmic rays around young Sun-like stars.

Measuring the Mass of Missing Baryons in the Halo of Andromeda Galaxy with Gamma-Ray Observations

Abstract It has been suggested that a huge amount of baryon resides in the circumgalactic medium (CGM) extending out to the virial radii of galaxies. In this work we attempt to measure the baryon mass in the CGM with a novel method based on the gamma-ray observations of the extended halo of the Andromeda galaxy Messier 31 (M31). Since cosmic-ray particles generated inside the galaxy will eventually escape to the CGM, they will produce gamma-ray emission via the proton–proton collision with the CGM and produce gamma-rays. Different from some traditional measurements that are sensitive only to certain metallic ions in specific temperature range, the hadronic gamma-ray flux is sensitive to baryonic gases in all phases and does not rely on the metallicity in the halo, hence the measured gamma-ray flux from the galaxy’s halo can be used to constrain the mass of the CGM. By dealing with the cosmic-ray transport in the halo and calculating the hadronic gamma-ray intensity, we find that the total baryon mass contained within the virial radius is less than (1.4–5) × 1010 M ⊙ according to the gamma-ray intensity obtained with a model-dependent analysis. It implies that the CGM of Andromeda galaxy may not account for more than 30% of the missing baryons, but the result is subject to uncertainties from the gamma-ray intensity upper limit, diffusion coefficient of the cosmic-rays in the halo, as well as the stellar mass and dark matter halo mass of the galaxy. This method will become more constraining provided better understandings on these issues and more sensitive gamma-ray telescopes in the future.

Particle acceleration in winds of star clusters

ABSTRACT The origin of cosmic rays in our Galaxy remains a subject of active debate. While supernova remnant (SNR) shocks are often invoked as the sites of acceleration, it is now widely accepted that the difficulties of such sources in reaching PeV energies are daunting and it seems likely that only a subclass of rare remnants can satisfy the necessary conditions. Moreover, the spectra of cosmic rays escaping the remnants have a complex shape that is not obviously the same as the spectra observed at the Earth. Here, we investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters’ winds in the interstellar medium. While the main limitation to the maximum energy in SNRs comes from the need for effective wave excitation upstream so as to confine particles in the near-shock region and speed up the acceleration process, at the termination shock of star clusters the confinement of particles upstream is guaranteed by the geometry of the problem. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for powerful clusters in the high end of the luminosity tail for these sources. A crucial role in this problem is played by the dissipation of energy in the wind to magnetic perturbations. Under reasonable conditions, the spectrum of the accelerated particles has a power-law shape with a slope 4/4.3, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.

Implementation of Cosmic Ray Energy Spectrum (CRESP) Algorithm in PIERNIK MHD Code. I. Spectrally Resolved Propagation of Cosmic Ray Electrons on Eulerian Grids

Abstract We present an efficient algorithm to follow spectral evolution of cosmic rays (CR) coupled with an MHD system on Eulerian grids. The algorithm is designed for studies of CR energy spectrum evolution in MHD simulations of a galactic interstellar medium. The base algorithm for CR transport relies on the two-moment piece-wise power-law method, known also as coarse-grained momentum finite volume (CGMV), for solving the Fokker–Planck CR transport equation, with a low number of momentum bins extending over several decades of the momentum coordinate. We propose an extension of the CGMV with a novel feature that allows momentum boundaries to change in response to CR momentum gains or losses near the extremes of the population distribution. Our extension involves a special treatment of momentum bins containing spectral cutoff. Contrary to the regular bins of fixed width, those bins have variable width, and their outer edges coincide with spectral cutoffs. The cutoff positions are estimated from the particle number density and energy density in the outer bins for an assumed small value of an additional parameter representing the smallest physically significant level of CR spectral energy density. We performed a series of elementary tests to validate the algorithm and demonstrated, whenever possible, that results of the test simulations correspond, with a reasonable accuracy, to the results of analogous analytical solutions. In a more complex test of the galactic CR-driven wind problem, we obtained results consistent with expectations regarding the effects of advection, diffusion, adiabatic, and synchrotron cooling of a CR population.

Connecting turbulent velocities and magnetic fields in galaxy cluster simulations with active galactic nuclei jets

ABSTRACT The study of velocity fields of the hot gas in galaxy clusters can help to unravel details of microphysics on small scales and to decipher the nature of feedback by active galactic nuclei (AGN). Likewise, magnetic fields as traced by Faraday rotation measurements (RMs) inform about their impact on gas dynamics as well as on cosmic ray production and transport. We investigate the inherent relationship between large-scale gas kinematics and magnetic fields through non-radiative magnetohydrodynamical simulations of the creation, evolution, and disruption of AGN jet-inflated lobes in an isolated Perseus-like galaxy cluster, with and without pre-existing turbulence. In particular, we connect cluster velocity measurements with mock RM maps to highlight their underlying physical connection, which opens up the possibility of comparing turbulence levels in two different observables. For single-jet outbursts, we find only a local impact on the velocity field, i.e. the associated increase in velocity dispersion is not volume-filling. Furthermore, in a setup with pre-existing turbulence, this increase in velocity dispersion is largely hidden. We use mock X-ray observations to show that at arcmin resolution, the velocity dispersion is therefore dominated by existing large-scale turbulence and is only minimally altered by the presence of a jet. For the velocity structure of central gas uplifted by buoyantly rising lobes, we find fast, coherent outflows with low velocity dispersion. Our results highlight that projected velocity distributions show complex structures, which pose challenges for the interpretation of observations.

A finite volume method for two-moment cosmic ray hydrodynamics on a moving mesh

ABSTRACT 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 Alfvén 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.

The impact of astrophysical dust grains on the confinement of cosmic rays

ABSTRACT We argue that charged dust grains could significantly impact the confinement and transport of galactic cosmic rays. For sub-GeV to ∼103 GeV cosmic rays, small-scale parallel Alfvén waves, which isotropize cosmic rays through gyro-resonant interactions, are also gyro-resonant with charged grains. If the dust is nearly stationary, as in the bulk of the interstellar medium, Alfvén waves are damped by dust. This will reduce the amplitude of Alfvén waves produced by the cosmic rays through the streaming instability, thus enhancing cosmic ray transport. In well-ionized regions, the dust damping rate is larger by a factor of ∼10 than other mechanisms that damp parallel Alfvén waves at the scales relevant for ∼GeV cosmic rays, suggesting that dust could play a key role in regulating cosmic ray transport. In astrophysical situations in which the dust moves through the gas with super-Alfvénic velocities, Alfvén waves are rendered unstable, which could directly scatter cosmic rays. This interaction has the potential to create a strong feedback mechanism where dust, driven through the gas by radiation pressure, then strongly enhances the confinement of cosmic rays, increasing their capacity to drive outflows. This mechanism may act in the circumgalactic medium around star-forming galaxies and active galactic nuclei.

Cosmic rays across the star-forming galaxy sequence – I. Cosmic ray pressures and calorimetry

ABSTRACT In the Milky Way (MW), cosmic rays (CRs) are dynamically important in the interstellar medium (ISM), contribute to hydrostatic balance, and may help regulate star formation. However, we know far less about the importance of CRs in galaxies whose gas content or star formation rate (SFR) differ significantly from those of the MW. Here, we construct self-consistent models for hadronic CR transport, losses, and contribution to pressure balance as a function of galaxy properties, covering a broad range of parameters from dwarfs to extreme starbursts. While the CR energy density increases from ∼1 eV cm−3 to ∼1 keV cm−3 over the range from sub-MW dwarfs to bright starbursts, strong hadronic losses render CRs increasingly unimportant dynamically as the SFR surface density increases. In MW-like systems, CR pressure is typically comparable to turbulent gas and magnetic pressure at the galactic mid-plane, but the ratio of CR to gas pressure drops to ∼10−3 in dense starbursts. Galaxies also become increasingly CR calorimetric and gamma-ray bright in this limit. The degree of calorimetry at fixed galaxy properties is sensitive to the assumed model for CR transport, and in particular to the time CRs spend interacting with neutral ISM, where they undergo strong streaming losses. We also find that in some regimes of parameter space hydrostatic equilibrium discs cannot exist, and in Paper II of this series we use this result to derive a critical surface in the plane of star formation surface density and gas surface density beyond which CRs may drive large-scale galactic winds.

Empirical model of magnetic field line spreading in isotropic turbulence with varying mean field

In many astrophysical phenomena, understanding the diffusion of the magnetic eld line random walk (FLRW) is central to understand cosmic ray transport. In 3D uctuations, the behavior of the FLRW can be characterized by the Kubo number R = (b/B 0)(l ⫽⃥ /l ∧ ) [1], where the parameters b and B 0 are the rms magnetic uctuation and the large-scale mean eld, respectively. The parameters l ∥ and l ∧ are coherence scales parallel and perpendicular to B 0, respectively. For isotropic turbulence, in which l ∥ = l ∧ , Sonsrettee et al. [2] found that Corrsin-based theories can be applied to study the FLRW’s behavior for a whole range of R by varying b/B 0. Sonsrettee et al. [2] used Corrsin-based theory with three models of eld line spreading to examine the R-scaling of the asymptotic diffusion coefficients for the FLRW. The models are the diffusive decorrelation (DD) model [3{5], the random ballistic decorrelation (RBD) model [6], and the ordinary differential equation (ODE) model [7]. To improve the theory of the FLRW in isotropic turbulence with B 0 = 0, Sonsrettee [8] proposed the empirical (EMP) model of magnetic eld line spreading to determine the asymptotic diffusion coefficients. Benchmarked against the previous models, the EMP model is the best model to predict computer simulation results (with ≤ 0:9% error). In this work, we extend the previous works [2, 8] by formulating the EMP model to explore the R scaling FLRW behavior in isotropic magnetic turbulence by varying B 0. In the limit of very low R, we obtain the the closed-form solution of the FLRW for the EMP model. In order to develop the closed-form solution at any R, we employ the Padé approximants to the EMP model. The EMP model predicts that, with increasing R, the FLRW behavior transits from quasilinear diffusion to Bohm diffusion. This work shows that the theoretical results of the EMP model match the computer simulation results for the FLRW in Kolmogorov turbulence better than the other models significantly.

Testing physical models for cosmic ray transport coefficients on galactic scales: self-confinement and extrinsic turbulence at ∼GeV energies

ABSTRACT The microphysics of ∼ GeV cosmic ray (CR) transport on galactic scales remain deeply uncertain, with almost all studies adopting simple prescriptions (e.g. constant diffusivity). We explore different physically motivated, anisotropic, dynamical CR transport scalings in high-resolution cosmological Feedback In Realistic Environment (FIRE) simulations of dwarf and ∼L* galaxies where scattering rates vary with local plasma properties motivated by extrinsic turbulence (ET) or self-confinement (SC) scenarios, with varying assumptions about e.g. turbulent power spectra on un-resolved scales, Alfvén-wave damping, etc. We self-consistently predict observables including γ-rays (Lγ), grammage, residence times, and CR energy densities to constrain the models. We demonstrate many non-linear dynamical effects (not captured in simpler models) tend to enhance confinement. For example, in multiphase media, even allowing arbitrary fast transport in neutral gas does not substantially reduce CR residence times (or Lγ), as transport is rate-limited by the ionized WIM and ‘inner CGM’ gaseous halo (104–106 K gas within $\lesssim 10\!-\!30\,$ kpc), and Lγ can be dominated by trapping in small ‘patches’. Most physical ET models contribute negligible scattering of ∼1–10 GeV CRs, but it is crucial to account for anisotropy and damping (especially of fast modes) or else scattering rates would violate observations. We show that the most widely assumed scalings for SC models produce excessive confinement by factors ≳100 in the warm ionized medium (WIM) and inner CGM, where turbulent and Landau damping dominate. This suggests either a breakdown of quasi-linear theory used to derive the CR transport parameters in SC, or that other novel damping mechanisms dominate in intermediate-density ionized gas.

Effects of different cosmic ray transport models on galaxy formation

ABSTRACT Cosmic rays (CRs) with ∼GeV energies can contribute significantly to the energy and pressure budget in the interstellar, circumgalactic, and intergalactic medium (ISM, CGM, IGM). Recent cosmological simulations have begun to explore these effects, but almost all studies have been restricted to simplified models with constant CR diffusivity and/or streaming speeds. Physical models of CR propagation/scattering via extrinsic turbulence and self-excited waves predict transport coefficients which are complicated functions of local plasma properties. In a companion paper, we consider a wide range of observational constraints to identify proposed physically motivated cosmic ray propagation scalings which satisfy both detailed Milky Way (MW) and extragalactic γ-ray constraints. Here, we compare the effects of these models relative to simpler ‘diffusion+streaming’ models on galaxy and CGM properties at dwarf through MW mass scales. The physical models predict large local variations in CR diffusivity, with median diffusivity increasing with galactocentric radii and decreasing with galaxy mass and redshift. These effects lead to a more rapid dropoff of CR energy density in the CGM (compared to simpler models), in turn producing weaker effects of CRs on galaxy star formation rates (SFRs), CGM absorption profiles, and galactic outflows. The predictions of the more physical CR models tend to lie ‘in between’ models which ignore CRs entirely and models which treat CRs with constant diffusivity.