Cosmic Ray Transport Models Research Articles

Cosmic-Ray Feedback on Bistable Interstellar Medium Turbulence

While cosmic rays (E ≳ 1 GeV) are well coupled to a galaxy’s interstellar medium (ISM) at scales of L > 100 pc, adjusting stratification and driving outflows, their impact on small scales is less clear. Based on calculations of the cosmic-ray diffusion coefficient from observations of the grammage in the Milky Way, cosmic rays have little time to dynamically impact the ISM on those small scales. Using numerical simulations, we explore how more complex cosmic-ray transport could allow cosmic rays to couple to the ISM on small scales. We create a two-zone model of cosmic-ray transport, with the cosmic-ray diffusion coefficient set at the estimated Milky Way value in cold gas but smaller in warm gas. We compare this model to simulations with a constant diffusion coefficient. Quicker diffusion through cold gas allows more cold gas to form compared to a simulation with a constant, small diffusion coefficient. However, slower diffusion in warm gas allows cosmic rays to take energy from the turbulent cascade anisotropically. This cosmic-ray energization comes at the expense of turbulent energy which would otherwise be lost during radiative cooling. Finally, we show our two-zone model is capable of matching observational estimates of the grammage for some transport paths through the simulation.

Cosmic ray transport in large-amplitude turbulence with small-scale field reversals

ABSTRACT The nature of cosmic ray (CR) transport in the Milky Way remains elusive. The predictions of current microphysical CR transport models in magnetohydrodynamic (MHD) turbulence are drastically different from what is observed. These models usually focus on MHD turbulence with a strong guide field and ignore the impact of turbulent intermittency on particle propagation. This motivates our studying the alternative regime of large-amplitude turbulence with δB/B0 ≫ 1, in which intermittent small-scale magnetic field reversals are ubiquitous. We study particle transport in such turbulence by integrating trajectories in stationary snapshots. To quantify spatial diffusion, we use a set-up with continuous particle injection and escape, which we term the turbulent leaky box. We find that particle transport is very different from the strong guide-field case. Low-energy particles are better confined than high-energy particles, despite less efficient pitch-angle isotropization at small energies. In the limit of weak guide field, energy-dependent confinement is driven by the energy-dependent (in)ability to follow reversing magnetic field lines exactly and by the scattering in regions of ‘resonant curvature’, where the field line bends on a scale that is of the order of the local particle gyro-radius. We derive a heuristic model of particle transport in magnetic folds that approximately reproduces the energy dependence of transport found numerically. We speculate that CR propagation in the Galaxy is regulated by the intermittent field reversals highlighted here and discuss the implications of our findings for CR transport in the Milky Way.

Constraining cosmic ray transport with observations of the circumgalactic medium

ABSTRACT Recent theoretical studies predict that the circumgalactic medium (CGM) around low-redshift, ∼L* galaxies could have substantial non-thermal pressure support in the form of cosmic rays. However, these predictions are sensitive to the specific model of cosmic ray transport employed, which is theoretically and observationally underconstrained. In this work, we propose a novel observational constraint for calculating the lower limit of the radially averaged, effective cosmic ray transport rate, ${\kappa _{\rm eff}^{\rm min}}$. Under a wide range of assumptions (so long as cosmic rays do not lose a significant fraction of their energy in the galactic disc, regardless of whether the cosmic ray pressure is important or not in the CGM), we demonstrate a well-defined relationship between ${\kappa _{\rm eff}^{\rm min}}$ and three observable galaxy properties: the total hydrogen column density, the average star formation rate, and the gas circular velocity. We use a suite of Feedback in Realistic Environments 2 galaxy simulations with a variety of cosmic ray transport physics to demonstrate that our analytical model of ${\kappa _{\rm eff}^{\rm min}}$ is a robust lower limit of the true cosmic ray transport rate. We then apply our new model to calculate ${\kappa _{\rm eff}^{\rm min}}$ for galaxies in the COS-Halos sample, and confirm this already reveals strong evidence for an effective transport rate that rises rapidly away from the interstellar medium to values ${\kappa _{\rm eff}^{\rm min}}\gtrsim 10^{30\!-\!31}\, {\rm cm}^2\, {\rm s}^{-1}$ (corresponding to anisotropic streaming velocities of $v^{\rm stream}_{\rm eff} \gtrsim 1000\, {\rm km}\, {\rm s}^{-1}$) in the diffuse CGM, at impact parameters larger than 50–100 kpc. We discuss how future observations can provide qualitatively new constraints in our understanding of cosmic rays in the CGM and intergalactic medium.

Analysis of Galactic Cosmic Ray Anisotropy During the Time Period from 1996 to 2020

We study the influence of drift effects on the galactic cosmic ray anisotropy (GCRA) in different periods of solar activity (from 1996 to 2020) using data from the global network of neutron monitors. We analyze the GCRA in 1996, the last year of Solar Cycle 22 with positive polarity (A>0), Solar Cycles 23 and 24 with both positive (A>0) and negative polarities (A<0), and the 2020 onset of Solar Cycle 25 with positive polarity (A>0). We show that in positive polarity periods, a diffusion model with noticeably manifested drift is acceptable, whereas the diffusion-dominated model of galactic cosmic ray (GCR) transport is more acceptable in negative polarity periods.We found that the average radial component of the drift vector for A>0 practically points to 12 h, and for the A<0 polarity to 24 h, respectively. These results are consistent with the drift theory of modulation of GCRs. According to theory, during positive or negative polarity periods, a drift stream of GCRs is directed away from or toward the Sun, respectively, thus giving rise to long-term changes of the radial component of the GCRA.The calculated magnitudes of the radial and tangential components of the GCRA in different sectors of the heliospheric magnetic field were used to calculate the parameters that characterize the GCR modulation in interplanetary space.

Gamma-Ray and Neutrino Emissions from Starforming and Starburst Galaxies

Experimental observations have demonstrated a strong correlation between the star formation rate and the gamma-ray lumosities of starforming and starburst galaxies (SFGs and SBGs). However, the real origin of these emissions is still under debate. In this contribution, we present several updates on their non-thermal radiations, revisiting both their point-like and cumulative (diffuse) emission properties. From the point-like side, we discuss the potential- ities of future neutrino (KM3NeT/ARCA, IceCube-gen2) telescopes to quanti- tively scrutinize their expected properties from different cosmic-ray transport models. From the diffuse perspective, we investigate a model based on a data- driven blending of spectral indexes, hence taking into account the changes in the properties of individual emitters. Strikingly, SFGs and SBGs can explain 25% (up to 40%) of the diffuse High-Energy Starting Events (HESE) data, without overshooting the gamma-ray limits regarding non-blazar sources.

A new multi‐messenger description of starburst galaxies emission: perspectives for neutrino and gamma‐ray observations

AbstractStar‐forming and starburst galaxies (SBGs), which are well‐known cosmic‐ray (CR) reservoirs, are expected to emit gamma rays and neutrinos predominantly via hadronic collisions. In this work we analyze the 10‐year Fermi‐Low Energy Technique (LAT) spectral energy distributions of 13 nearby galaxies by means of a physical model that accounts for high‐energy proton transport in starburst nuclei and includes the contribution of primary and secondary electrons. In particular, we test the hypothesis that the observed gamma‐ray fluxes are mostly due to star‐forming activity, which is in agreement with the available star formation rates coming from infrared (IR) and ultraviolet (UV) observations. Through this observation‐based approach, we determine the most‐likely neutrino counterparts from star‐forming and SBGs and quantitatively assess the ability of current and upcoming neutrino telescopes to detect them as point‐like sources. We also generate mock gamma‐ray data to simulate the Cherenkov Telescope Array (CTA) performance in detecting these sources. Moreover, we propose a test to discriminate between the two different CR transport models for the starburst nuclei by looking at the different gamma‐ray expectations. We point out that current data already gives a slight preference to CR models, which are dominated by advection.

Galaxies at a Cosmic Ray Eddington Limit

Cosmic rays have been shown to be extremely important in the dynamics of diffuse gas in galaxies, helping to maintain hydrostatic equilibrium, and serving as a regulating force in star formation. In this paper, we address the influence of cosmic rays on galaxies by re-examining the theory of a cosmic ray Eddington limit, first proposed by Socrates et al. and elaborated upon by Crocker et al. and Huang & Davis. A cosmic ray Eddington limit represents a maximum cosmic ray energy density above which the interstellar gas cannot be in hydrostatic equilibrium, resulting in a wind. In this paper, we continue to explore the idea of a cosmic ray Eddington limit by introducing a general framework that accounts for the circumgalactic environment and applying it to five galaxies that we believe to be a good representative sample of the star-forming galaxy population, using different cosmic ray transport models to determine what gives each galaxy the best chance to reach this limit. We show that, while an Eddington limit for cosmic rays does exist, for our five galaxies, the limit either falls at star formation rates that are much larger or gas densities that are much lower than each galaxy’s measured values. This suggests that cosmic ray pressure is not the main factor limiting the luminosity of starburst galaxies.

Prospects for detection of a galactic diffuse neutrino flux

A Galactic cosmic-ray transport model featuring non-homogeneous transport has been developed over the latest years. This setup is aimed at reproducing γ-ray observations in different regions of the Galaxy (with particular focus on the progressive hardening of the hadronic spectrum in the inner Galaxy) and was shown to be compatible with the very-high-energy γ-ray diffuse emission recently detected up to PeV energies. In this work, we extend the results previously presented to test the reliability of that model throughout the whole sky. To this aim, we compare our predictions with detailed longitude and latitude profiles of the diffuse γ-ray emission measured by Fermi-LAT for different energies and compute the expected Galactic ν diffuse emission, comparing it with current limits from the ANTARES collaboration. We emphasize that the possible detection of a Galactic ν component will allow us to break the degeneracy between our model and other scenarios featuring prominent contributions from unresolved sources and TeV halos.

Cosmic ray interstellar propagation tool using Itô Calculus (criptic): software for simultaneous calculation of cosmic ray transport and observational signatures

ABSTRACT We present criptic, the Cosmic Ray Interstellar Propagation Tool using Itô Calculus, a new open-source software package to simulate the propagation of cosmic rays through the interstellar medium and to calculate the resulting observable non-thermal emission. criptic solves the Fokker–Planck equation describing transport of cosmic rays on scales larger than that on which their pitch angles become approximately isotropic, and couples this to a rich and accurate treatment of the microphysical processes by which cosmic rays in the energy range ∼MeV to ∼PeV lose energy and produce emission. criptic is deliberately agnostic as to both the cosmic ray transport model and the state of the background plasma through which cosmic rays travel. It can solve problems where cosmic rays stream, diffuse, or perform arbitrary combinations of both, and the coefficients describing these transport processes can be arbitrary functions of the background plasma state, the properties of the cosmic rays themselves, and local integrals of the cosmic ray field itself (e.g. the local cosmic ray pressure or pressure gradient). The code is parallelized using a hybrid OpenMP-MPI paradigm, allowing rapid calculations exploiting multiple cores and nodes on modern supercomputers. Here, we describe the numerical methods used in the code, our treatment of the microphysical processes, and the set of code tests and validations we have performed.

The Isotopic Abundances of Galactic Cosmic Rays with Atomic Number 29 ≤ Z ≤ 38

The Cosmic Ray Isotope Spectrometer (CRIS) on the Advanced Composition Explorer spacecraft has been operating successfully in a halo orbit about the L1 Lagrange point since late 1997. We report here the isotopic composition of the Galactic cosmic ray (GCR) elements with 29 ≤ Z ≤ 38 derived from more than 20 years of CRIS data. Using a model of cosmic-ray transport in the Galaxy and the solar system (SS), we have derived from these observations the isotopic composition of the accelerated material at the GCR source (GCRS). Comparison of the isotopic fractions of these elements in the GCRS with corresponding fractions in the solar system gives no indication of GCRS enrichment in r-process isotopes. Since a large fraction of core-collapse supernovae (CCSNe) occur in OB associations, the fact that GCRs do not contain enhanced abundances of r-process nuclides indicates that CCSNe are not the principal source of lighter (Z ≤ 38) r-process nuclides in the solar system. This conclusion supports recent work that points to binary neutron-star mergers, rather than supernovae, as the principal source of galactic r-process isotopes.

Observable signatures of cosmic rays transport in Starburst Galaxies on gamma-ray and neutrino observations

ABSTRACT The gamma-ray emission from Starburst and Star-forming Galaxies (SBGs and SFGs) strongly suggests a correlation between star-forming activity and gamma-ray luminosity. However, the very nature of cosmic ray (CR) transport and the degree of their confinement within SBG cores are still open questions . We aim at probing the imprints left by CR transport on gamma-ray and neutrino observations of point-like SFGs and SBGs, looking into quantitative ways to discriminate among different transport models. We analyse the 10-yr Fermi-LAT spectral energy distributions of 13 nearby galaxies with two different CR transport models, taking into account the corresponding IR and UV observations. We also generate mock gamma-ray data to simulate the CTA performance in detecting these sources. In this way, we propose a test to discriminate between the two CR models, quantifying the statistical confidence at which one model can be preferred over the other. We point out that the current data already give a slight preference to CR models that are dominated by advection. Moreover, we show that CTA will allow us to firmly disfavour models dominated by diffusion over self-induced turbulence, compared to advection-dominated models, with Bayes factors, which can be as large as 107 for some of the SBGs. Finally, we estimate the diffuse gamma-ray and neutrino fluxes of SFGs and SBGs, showing that they can explain $25{{\,\rm per\ cent}}$ of the diffuse HESE data while remaining consistent with gamma-ray limits on non-blazar sources.

The strong suppression of galactic cosmic rays reaching AU Mic b, c, and Prox Cen b

ABSTRACT The propagation of Galactic cosmic rays is well understood in the context of the Solar system but is poorly studied for M dwarf systems. Quantifying the flux of cosmic rays reaching exoplanets is important since cosmic rays are relevant in the context of life. Here, we calculate the Galactic cosmic ray fluxes in AU Mic and Prox Cen planetary systems. We propagate the Galactic cosmic rays using a 1D cosmic ray transport model. We find for Prox Cen b, AU Mic b, and AU Mic c that the Galactic cosmic ray fluxes are strongly suppressed and are lower than the fluxes reaching Earth. We include in our models, for the first time for a star other than the Sun, the effect of radial particle drift due to gradients and curvatures in the stellar magnetic field. For Prox Cen, we find that the inclusion of particle drift leads to less suppression of Galactic cosmic rays fluxes than when it is excluded from the model. In the case of AU Mic we explore two different wind environments, with a low and high stellar wind mass-loss rate. For AU Mic, the particle drift also leads to less suppression of the Galactic cosmic ray fluxes but it is only significant for the high mass-loss rate scenario. However, both wind scenarios for AU Mic suppress the Galactic cosmic rays strongly. Overall, careful modelling of stellar winds is needed to calculate the Galactic cosmic ray fluxes reaching exoplanets. The results found here can be used to interpret future exoplanet atmosphere observations and in atmospheric models.

Reconciling cosmic ray transport theory with phenomenological models motivated by Milky-Way data

ABSTRACT Phenomenological models of cosmic ray (CR) transport in the Milky Way can reproduce a wide range of observations assuming that CRs scatter off of magnetic-field fluctuations with spectrum ∝ k−δ and δ ∼ [1.4, 1.67]. We study the extent to which such models can be reconciled with current microphysical theories of CR transport, specifically self-confinement due to the streaming instability and/or extrinsic turbulence due to a cascade of magnetohydrodynamic (MHD) fast modes. We first review why it is that on their own neither theory is compatible with observations. We then highlight that CR transport is a strong function of local plasma conditions in the multiphase interstellar medium, and may be diffusive due to turbulence in some regions and streaming due to self-confinement in others. A multiphase combination of scattering mechanisms can in principle reproduce the main trends in the proton spectrum and the boron-to-carbon ratio. However, models with a combination of scattering by self-excited waves and fast-mode turbulence require significant fine-tuning due to fast-mode damping, unlike phenomenological models that assume undamped Kolmogorov turbulence. The assumption that fast modes follow a weak cascade is also not well justified theoretically, as the weak cascade is suppressed by wave steepening and weak-shock dissipation even in subsonic turbulence. These issues suggest that there may be a significant theoretical gap in our understanding of MHD turbulence. We discuss a few topics at the frontier of MHD turbulence theory that bear on this (possible) gap and that may be relevant for CR scattering.

A Numerical Study of the Solar Modulation of Galactic Protons and Helium from 2006 to 2017

Abstract With continuous measurements from space-borne cosmic-ray detectors such as AMS-02 and PAMELA, precise spectra of galactic cosmic rays over the 11 yr solar cycle have become available. For this study, we utilize proton and helium spectra below 10 GV from these missions from 2006 to 2017 to construct a cosmic-ray transport model for a quantitative study of the processes of solar modulation. This numerical model is based on Parker’s transport equation, which includes four major transport processes. The Markov Chain Monte Carlo method is utilized to search the relevant parameter space related to the drift and the diffusion coefficients by reproducing and fitting the mentioned observed spectra. The resulting best-fit normalized χ 2 is mainly less than 1. It is found that (1) when reproducing these observations the parameters required for the drift and diffusion coefficients exhibit a clear time dependence, with the magnitude of the diffusion coefficients anticorrelated with solar activity; (2) the rigidity dependence of the resulting mean free paths varies with time, and their rigidity dependence at lower rigidity can even have a larger slope than at higher rigidity; (3) using a single set of modulation parameters for each pair of observed proton and helium spectra, most spectra are reproduced within observational uncertainty; and (4) the simulated proton-to-helium flux ratio agrees with the observed values in terms of its long-term time dependence, although some discrepancy exists, and the difference is mostly coming from the underestimation of proton flux.

Compact Geiger Counters as Additional Tools for Verifying Models of Cosmic Ray Transport through the Earth’s Atmosphere

Compact Geiger Counters as Additional Tools for Verifying Models of Cosmic Ray Transport through the Earth’s Atmosphere

Galactic cosmic ray propagation through M dwarf planetary systems

ABSTRACT Quantifying the flux of cosmic rays reaching exoplanets around M dwarfs is essential to understand their possible effects on exoplanet habitability. Here, we investigate the propagation of Galactic cosmic rays as they travel through the stellar winds (astrospheres) of five nearby M dwarfs, namely: GJ 15A, GJ 273, GJ 338B, GJ 411, and GJ 887. Our selected stars each have one or two detected exoplanets and they all have wind mass-loss rates constrained by Lyman α observations. Our simulations use a combined 1D magnetohydrodynamic (MHD) Alfvén-wave-driven stellar wind model and 1D cosmic ray transport model. We find that GJ 411 and GJ 887 have Galactic cosmic rays fluxes comparable with Earth’s at their habitable zones. On the other hand, GJ 15A, GJ 273, and GJ 338B receive a lower Galactic cosmic ray flux in their habitable zones. All exoplanets in our sample, with exception of GJ 15A c and GJ 411 c, have a significantly lower flux of Galactic cosmic rays than values observed at the Earth because they orbit closer-in. The fluxes found here can be further used for chemical modelling of planetary atmospheres. Finally, we calculate the radiation dose at the surface of the habitable-zone planet GJ 273 b, assuming it has an Earth-like atmosphere. This planet receives up to 209 times less 15 MeV energy cosmic ray fluxes than values observed at Earth. However, for high-energy cosmic rays (∼GeV), the difference in flux is only 2.3 times smaller, which contributes to GJ 273 b receiving a significant surface radiation dose of 0.13 mSv yr−1 (40 per cent of the annual dose on Earth’s surface).

Charting nearby stellar systems: the intensity of Galactic cosmic rays for a sample of solar-type stars

ABSTRACT Cosmic rays can penetrate planetary atmospheres driving the formation of prebiotic molecules, which are important for the origin of life. We calculate the Galactic cosmic ray fluxes in the habitable zone (HZ) of five nearby, well-studied solar-type stars and at the orbits of two known exoplanets. We model the propagation of Galactic cosmic rays through the stellar winds using a combined 1.5D stellar wind and 1D cosmic ray transport model. We find that the HZ of 61 Cyg A has comparable Galactic cosmic ray fluxes to present-day Earth values. For the other four systems (ϵ Eri, ϵ Ind, ξ Boo B, and π1 UMa), the fluxes are orders of magnitude smaller than Earth values. Thus, it is unlikely that any as-of-yet undetected Earth-like planets in their HZs would receive a higher radiation dose than is received on Earth. $\epsilon \,$Ind b, a Jupiter-like planet orbiting at ∼11 au, receives higher Galactic cosmic ray fluxes than Earth. We find the suppression of Galactic cosmic rays is influenced by whether diffusion or advection dominates at GeV energies and at distances where the wind has reached its’ terminal velocity. For advectively dominated winds (∼younger systems), varying the astrospheric size influences the suppression significantly. For diffusion-dominated systems (∼older systems), the astrospheric size, and therefore knowledge of the interstellar medium properties, are not very important. This reduces the Galactic cosmic ray flux uncertainties in the HZ for diffusion-dominated systems. Whether a system is advection- or diffusion-dominated can be determined from the stellar wind properties.

Ice mantles on dust grains: dramatic variation of thickness with grain size

ABSTRACT We compute the desorption rate of icy mantles on dust grains as a function of the size and composition of both the grain and the mantle. We combine existing models of cosmic ray (CR)-related desorption phenomena with a model of CR transport to accurately calculate the desorption rates in dark regions of molecular clouds. We show that different desorption mechanisms dominate for grains of different sizes and in different regions of the cloud. We then use these calculations to investigate a simple model of the growth of mantles, given a distribution of grain sizes. We find that modest variations of the desorption rate with grain size lead to a strong dependence of mantle thickness on grain size. Furthermore, we show that freeze-out is almost complete in the absence of an external ultraviolet (UV) field, even when photodesorption from CR-produced UV is taken into consideration. Even at gas densities of $10^4\, {\rm cm^{-3}}$, less than 30 per cent of the CO remain in the gas phase after 3 × 105 yr for standard values of the CR ionization rate.

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.

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.