Cosmic Ray Diffusion Research Articles

Anisotropic diffusion of high-energy cosmic rays in magnetohydrodynamic turbulence

The origin of cosmic rays (CRs) and how they propagate remain unclear. Studying the propagation of CRs in magnetohydrodynamic (MHD) turbulence can help to comprehend many open issues related to CR origin and the role of turbulent magnetic fields. To comprehend the phenomenon of slow diffusion in the near-source region, we study the interactions of CRs with the ambient turbulent magnetic field to reveal their universal laws. We numerically study the interactions of CRs with the ambient turbulent magnetic field, considering pulsar wind nebula as a general research case. Taking the magnetization parameter and turbulence spectral index as free parameters, together with radiative losses, we perform three group simulations to analyze the CR spectral, spatial distributions, and possible CR diffusion types. Our studies demonstrate that (1) CR energy density decays with both its effective radius and kinetic energy in the form of power-law distributions; (2) the morphology of the CR spatial distribution strongly depends on the properties of magnetic turbulence and the viewing angle; (3) CRs suffer a slow diffusion near the source and a fast or normal diffusion away from the source; (4) the existence of a power-law relationship between the averaged CR energy density and the magnetization parameter is independent of both CR energy and radiative losses; and (5) radiative losses can suppress CR anisotropic diffusion and soften the power-law distribution of CR energy density. The distribution law established between turbulent magnetic fields and CRs presents an intrinsic property, providing a convenient way to understand complex astrophysical processes related to turbulence cascades.

Life in the Bubble: How a Nearby Supernova Left Ephemeral Footprints on the Cosmic-Ray Spectrum and Indelible Imprints on Life

Abstract The Earth sits inside a 300 pc-wide void that was carved by a series of supernova explosions that went off tens of millions of years ago, pushing away interstellar gas and creating a bubble-like structure. The 60Fe peak deposits found in the deep-sea crust have been interpreted by the imprints left by the ejecta of supernova explosions occurring about 2–3 and 5–6 Myr ago. It is likely that the 60Fe peak at about 2–3 Myr originated from a supernova occurring in the Upper Centaurus Lupus association in Scorpius Centaurus (≈140 pc) or the Tucana-Horologium association (≈70 pc), whereas the ≈5–6 Myr peak is likely attributed to the solar system's entrance into the bubble. In this Letter, we show that the supernova source responsible for synthesizing the 60Fe peak deposits ≈2–3 Myr ago can consistently explain the cosmic-ray spectrum and the large-scale anisotropy between 100 TeV and 100 PeV. The cosmic-ray knee could then potentially be attributed entirely to a single nearby “PeVatron” source. Matching the intensity and shape of the cosmic-ray spectrum allows us to place stringent constraints on the cosmic-ray energy content from the supernova as well as on the cosmic-ray diffusion coefficient. Making use of such constraints, we provide a robust estimate of the temporal variation of terrestrial ionizing cosmic radiation levels and discuss their implications in the development of early life on Earth by plausibly influencing the mutation rate and, as such, conceivably assisting in the evolution of complex organisms.

Neural Network Constraints on the Cosmic-Ray Ionization Rate and Other Physical Conditions in NGC 253 with ALCHEMI Measurements of HCN and HNC

We use a neural network model and Atacama Large Millimeter/submillimeter Array (ALMA) observations of HCN and HNC to constrain the physical conditions, most notably the cosmic-ray ionization rate (CRIR, ζ), in the Central Molecular Zone (CMZ) of the starburst galaxy NGC 253. Using output from the chemical code UCLCHEM, we train a neural network model to emulate UCLCHEM and derive HCN and HNC molecular abundances from a given set of physical conditions. We combine the neural network with radiative transfer modeling to generate modeled integrated intensities, which we compare to measurements of HCN and HNC from the ALMA Large Program ALCHEMI. Using a Bayesian nested sampling framework, we constrain the CRIR, molecular gas volume and column densities, kinetic temperature, and beam-filling factor across NGC 253's CMZ. The neural network model successfully recovers UCLCHEM molecular abundances with ∼3% error and, when used with our Bayesian inference algorithm, increases the parameter-inference speed tenfold. We create images of these physical parameters across NGC 253's CMZ at 50 pc resolution and find that the CRIR, in addition to the other gas parameters, is spatially variable with ζ ∼ a few ×10−14 s−1 at r ≳ 100 pc from the nucleus, increasing to ζ > 10−13 s−1 at its center. These inferred CRIRs are consistent within 1 dex with theoretical predictions based on nonthermal emission. Additionally, the high CRIRs estimated in NGC 253's CMZ can be explained by the large number of cosmic-ray-producing sources as well as a potential suppression of cosmic-ray diffusion near their injection sites.

Impact of inhomogeneous diffusion on secondary cosmic ray and antiproton local spectra

Recent γ-ray and neutrino observations seem to favor the consideration of non-uniform diffusion of cosmic rays (CRs) throughout the Galaxy.In this study, we investigate the consequences of spatially-dependent inhomogeneous propagation of CRs on the fluxes of secondary CRs and antiprotons detected at Earth. A comparison is made among different scenarios in search of potential features that may guide us toward favoring one over another in the near future. We also examine both the influence of inhomogeneous propagation in the production of secondary CRs from interactions with the gas, and the effects of this scenario on the local fluxes of antiprotons and light antinuclei produced as final products of dark matter annihilation. Our results indicate that the consideration of an inhomogeneous diffusion model could improve the compatibility of the predicted local antiproton flux with that of B, Be and Li, assuming only secondary origin of these particles. In addition, our model predicts a slightly harder local antiproton spectrum, making it more compatible with the high energy measurements of AMS-02.Finally, no significant changes are expected in the predicted local flux of antiprotons and antinuclei produced from dark matter among the different considered propagation scenarios.

Suprathermal corrections on galactic cosmic rays driven magnetohydrodynamic waves and gravitational instability in astrophysical plasmas

The interaction of two populations of highly energetic cosmic rays (CRs) and suprathermal kappa gas in the astrophysical systems manifests exciting features of low-frequency magnetohydrodynamic (MHD) waves and instabilities. Contrary to the previous works on waves and instability analysis in Maxwellian gas, this paper investigates the effects of suprathermal corrections on the CR driven MHD waves and gravitational (Jeans) instability using the kappa distribution function. The equation of state for a kappa gas, including spectral κ− index, is considered in the CR-plasma interactions using the hydrodynamic fluid–fluid approach. The modified dispersion properties of fast, slow, and pure Alfvén waves and Jeans instability have been discussed in a suprathermal gas in astrophysical environments. The suprathermal corrections enhance the phase speed of the fast mode of MHD waves which is found to be greater in the suprathermal gas (κ>3/2) and smaller in the Maxwellian gas (κ→∞). In the absence of CR diffusion, the Jeans instability criterion is modified due to the simultaneous presence of CR pressure and suprathermal corrections. However, in the presence of CR diffusion, only suprathermal corrections modify the Jeans instability criterion. The suprathermal gases with higher degrees of freedom require large values of the Jeans wavenumber to produce gravitational instability and make the system more unstable. The suprathermal corrections along with modified thermal speed stabilize the growth rate of Jean instability, supporting the gravitational collapse of non-thermal gas in astrophysical systems.

Cosmic Ray Diffusion in Magnetic Fields Amplified by Nonlinear Turbulent Dynamo

The diffusion of cosmic rays (CRs) in turbulent magnetic fields is fundamental to understanding various astrophysical processes. We explore the CR diffusion in the magnetic fluctuations amplified by the nonlinear turbulent dynamo in the absence of a strong mean magnetic field. Using test particle simulations, we identify three distinct CR diffusion regimes: mirroring, wandering, and magnetic moment scattering (MMS). With highly inhomogeneous distribution of the dynamo-amplified magnetic fields, we find that the diffusion of CRs is also spatially inhomogeneous. Our results reveal that lower-energy CRs preferentially undergo the mirror and wandering diffusion in the strong-field regions, and the MMS diffusion in the weak-field regions. The former two diffusion mechanisms play a more important role toward lower CR energies, resulting in a relatively weak energy dependence of the overall CR mean free path (MFP). In contrast, higher-energy CRs predominantly undergo the MMS diffusion, for which the incomplete particle gyration, i.e., the limit case of mirroring, in strong fields has a more significant effect than the scattering by small-scale field tangling/reversal. Compared with lower-energy CRs, they are more poorly confined in space and their MFPs have a stronger energy dependence. We stress the fundamental role of magnetic field inhomogeneity of nonlinear turbulent dynamo in causing the different diffusion behavior of CRs compared to that in sub-Alfvénic magnetohydrodynamic turbulence.

On the classical approach to describing the diffusion of cosmic rays in a turbulent medium

The inhomogeneous structure of the interstellar medium (ISM) is characterized by largescale fluctuations that significantly affect the cosmic ray propagation process. Accounting for this influence can not only lead to adjustments in the diffusion process parameters but even to pass from differential operators to integral ones. The most crucial characteristics of a turbulent medium is its power spectrum. Including appropriate approximations of this spectrum allows us to consider this problem in the framework of the traditional diffusion approach [1, 2]. This article explores the analytical representations of this spectrum applied in the cosmic ray transfer theory, including the four-parameter Uchaikin—Zolotarev approximation, derived from the generalized Ornstein—Zernike equation. Testing of the latter revealed that, with carefully chosen parameters, it accurately replicates numerical modeling results both in the inertial interval and beyond. Therefore, it can be effectively employed in addressing cosmic ray transfer issues within a turbulent interstellar medium.

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.

Past activity of Sgr A⋆ is unlikely to affect the local cosmic-ray spectrum up to the TeV regime

Context The presence of kiloparsec-sized bubble structures on both sides of the Galactic plane suggests active phases of Sgr A⋆, the central supermassive black hole of the Milky Way in the last 1–6 Myr. We investigated the contribution of such events to the cosmic-ray (CR) flux measured in the solar neighborhood with numerical simulations. Aims. We evaluate whether the population of high-energy charged particles emitted by the Galactic center could be sufficient to significantly impact the CR flux measured in the solar neighborhood. Methods. We present a set of 3D magnetohydrodynamical simulations following the anisotropic propagation of CRs in a Milky Way-like Galaxy. We followed independent populations of CRs through time. We followed CRs originating from two different source types, namely supernovae and the Galactic center. To assess the evolution of the CR flux spectrum properties, we split these populations into two independent energy groups of 100 GeV and 10 TeV. Results. We find that the anisotropic nature of CR diffusion dramatically affects the amount of CR energy received in the solar neighborhood. The typical timescale required to observe measurable changes in the CR spectrum slope is of the order 10 Myr, largely surpassing estimated ages of the Fermi bubbles in the active galactic nuclei (AGN) jet-driven scenario. Conclusions. We conclude that a CR outburst from the Galactic center in the last few million years is unlikely have produced any observable feature in the local CR spectrum in the TeV regime within times consistent with current estimates of the age of the Fermi bubbles.

Cosmic ray diffusion in molecular clouds: some problems of theoretical models

Cosmic ray diffusion in molecular clouds: some problems of theoretical models

The Coherent Magnetic Field of the Milky Way

We present a suite of models of the coherent magnetic field of the Galaxy based on new divergence-free parametric functions describing the global structure of the field. The model parameters are fit to the latest full-sky Faraday rotation measures (RMs) of extragalactic sources and polarized synchrotron intensity (PI) maps from the Wilkinson Microwave Anisotropy Probe and Planck. We employ multiple models for the density of thermal and cosmic-ray electrons in the Galaxy, needed to predict the sky maps of RMs and PI for a given Galactic magnetic field (GMF) model. The robustness of the inferred properties of the GMF is gauged by studying many combinations of parametric field models and electron density models. We determine the pitch angle of the local magnetic field (11° ± 1°), explore the evidence for a grand-design spiral coherent magnetic field (inconclusive), determine the strength of the toroidal and poloidal magnetic halo fields below and above the disk (magnitudes the same for both hemispheres within ≈10%), set constraints on the half-height of the cosmic-ray diffusion volume (≥2.9 kpc), investigate the compatibility of RM- and PI-derived magnetic field strengths (compatible under certain assumptions), and check if the toroidal halo field could be created by the shear of the poloidal halo field due to the differential rotation of the Galaxy (possibly). A set of eight models is identified to help quantify the present uncertainties in the coherent GMF spanning different functional forms, data products, and auxiliary input. We present the corresponding sky maps of rates for axion–photon conversion in the Galaxy and deflections of ultrahigh-energy cosmic rays.

Data-driven constraints on cosmic-ray diffusion: Probing self-generated turbulence in the Milky Way

Data-driven constraints on cosmic-ray diffusion: Probing self-generated turbulence in the Milky Way

Importance of Cosmic-Ray Propagation on Sub-GeV Dark Matter Constraints

We study sub-GeV dark matter (DM) particles that may annihilate or decay into Standard Model particles producing an exotic injection component in the Milky Way that leaves an imprint in both photon and cosmic-ray (CR) fluxes. Specifically, the DM particles may annihilate or decay into e + e −, μ + μ −, or π + π − and may radiate photons through their e ± products. The resulting e ± products can be directly observed in probes such as Voyager 1. Alternatively, the e ± products may produce bremsstrahlung radiation and upscatter the low-energy Galactic photon fields via the inverse Compton process, generating a broad emission from X-ray to γ-ray energies observable in experiments such as XMM-Newton. We find that we get a significant improvement in the DM annihilation and decay constraints from XMM-Newton (excluding thermally averaged cross sections of 10−31 cm3 s−1 ≲ 〈σ v〉 ≲ 10−26 cm3 s−1 and decay lifetimes of 1026 s ≲ τ ≲ 1028 s, respectively) by including best-fit CR propagation and diffusion parameters. This yields the strongest astrophysical constraints for this mass range of DM of 1 MeV to a few GeV and even surpasses cosmological bounds across a wide range of masses as well.

Radiation pressure and galactic cosmic rays-driven gravitational instability in rotating and magnetized viscoelastic fluids

This paper studies the combined effects of radiation and galactic cosmic ray pressures on the gravitational instability of magnetized and rotating viscoelastic fluids. The dispersion relations are derived using the normal mode analysis and discussed in the hydrodynamic (weakly coupled fluid) and kinetic (strongly coupled fluid) limits. These dispersion relations are analyzed separately for transverse and longitudinal wave propagation modes. Jeans instability criteria are obtained for kinetic and hydrodynamic limits for both modes of wave propagation, and it is found that the critical Jeans wavenumbers in each case are modified due to the presence of viscoelastic effects, radiation and cosmic rays pressures, and Alfvên wave velocity. It is also observed that the radiation pressure, cosmic ray pressure and viscoelastic parameters suppress the growth rate and thus have stabilizing effects on the Jeans instability. However, cosmic ray diffusion has a destabilizing effect on the onset of gravitational instability. The effects of various parameters on the growth rate of instability are calculated numerically and the outcomes are depicted graphically. The results of the present analysis shall be helpful in understanding the impact of cosmic rays and radiative mechanisms on the gravitational collapse in the viscoelastic region of molecular cloud clumps.

Cosmic-ray diffusion in two local filamentary clouds

Context. Hadronic interactions between cosmic rays (CRs) and interstellar gas have been probed in γ rays across the Galaxy. A fairly uniform CR distribution is observed up to a few hundred parsecs from the Sun, except in the Eridu cloud, which shows an unexplained 30–50% deficit in GeV to TeV CR flux. Aims. To explore the origin of this deficit, we studied the Reticulum cloud, which shares notable traits with Eridu: a comparable distance in the low-density region of the Local Valley and a filamentary structure of atomic hydrogen extending along a bundle of ordered magnetic-field lines that are steeply inclined to the Galactic plane. Methods. We measured the γ-ray emissivity per gas nucleon in the Reticulum cloud in the 0.16–63 GeV energy band using 14 years of Fermi-LAT data. We also derived interstellar properties that are important for CR propagation in both the Eridu and Reticulum clouds, at the same parsec scale. Results. The γ-ray emissivity in the Reticulum cloud is fully consistent with the average spectrum measured in the solar neighbourhood, but this emissivity, and therefore the CR flux, is 1.57 ± 0.09 times larger than in Eridu across the whole energy band. The difference cannot be attributed to uncertainties in gas mass. Nevertheless, we find that the two clouds are similar in many respects: both have magnetic-field strengths of a few micro-Gauss in the plane of the sky; both are in approximate equilibrium between magnetic and thermal pressures; they have similar turbulent velocities and sonic Mach numbers; and both show magnetic-field regularity with a dispersion in orientation lower than 10°–15° over large zones. The gas in Reticulum is colder and denser than in Eridu, but we find similar parallel diffusion coefficients around a few times 1028 cm2 s−1 in both clouds if CRs above 1 GV in rigidity diffuse on resonant, self-excited Alfvén waves that are damped by ion-neutral interactions. Conclusions. The loss of CRs in Eridu remains unexplained, but these two clouds provide important test cases to further study how magnetic turbulence, line tangling, and ion-neutral damping regulate CR diffusion in the dominant gas phase of the interstellar medium.

Propagation and fluxes of ultra-high energy cosmic rays in f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{f(R)}$$\\end{document} gravity theory

In this work, we study the effect of diffusion of ultra-high energy cosmic ray (UHECR) protons in the presence of turbulent magnetic fields (TMFs) in the light of the f(R) theory of gravity. The f(R) theory of gravity is a successful modified theory of gravity in explaining the various aspects of the observable Universe including its current state of expansion. For this work, we consider two most studied f(R) gravity models, viz., the power-law model and the Starobinsky model. With these two models, we study the diffusive character of the propagation of UHECR protons in terms of their density enhancement. The density enhancement is a measure of how the density of CRs changes due to their diffusion in the intergalactic medium and interaction with the cosmic microwave background (CMB) radiation. Ankle, instep and Greisen–Zatsepin–Kuzmin (GZK) cutoff are all spectrum characteristics that extragalactic UHECRs acquire when they propagate through the CMB. We analyse all these characteristics through the diffusive flux as well as its modification factor. Model dependence of the modification factor is minimal compared to the diffusive flux. We compare the UHECR proton spectra calculated for the considered f(R) gravity models with the available data of the Telescope Array (TA) and Pierre Auger Observatory (PAO). We see that both models of f(R) gravity predict energy spectra of UHECRs with all experimentally observed features, which lay well within the range of combined data of both experiments throughout the energy range of concern. It is to be noted that our present work is only to investigate the possible effects of f(R) gravity theory on the UHECRs propagation, using pure proton composition as a simplified case study since protons are least affected by magnetic fields. Hence, at this stage, our results cannot be used to favor or disfavor f(R) cosmology over Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM cosmology as more work is needed in this regard.

Study of Magnetic Field and Turbulence in the TeV Halo around the Monogem Pulsar

Magnetic fields are ubiquitous in the interstellar medium, including extended objects such as supernova remnants and diffuse halos around pulsars. Its turbulent characteristics govern the diffusion of cosmic rays and the multiwavelength emission from pulsar wind nebulae (PWNe). However, the geometry and turbulence nature of the magnetic fields in the ambient region of PWN is still unknown. Recent gamma-ray observations from HAWC and synchrotron observations suggest a highly suppressed diffusion coefficient compared to the mean interstellar value. In this study, we present the first direct observational evidence of the orientation of the mean magnetic field and turbulent characteristics by employing a recently developed statistical parameter “Y turb” in the extended halo around the Monogem pulsar. Our study points to two possible scenarios: nearly aligned toward the line of sight (LOS) with compressible modes dominance or high inclination angle toward the LOS and characterized by Alfvénic turbulence. The first scenario appears consistent with other observational signatures. Furthermore, we report that the magnetic field has an observed correlation length of approximately 3 ± 0.6 pc in the Monogem halo. Our study highlights the pivotal role of magnetic field and turbulence in unraveling the physical processes in TeV halos and cosmic-ray transport.

Effect of cosmic rays and ionizing radiation on observational ultraviolet plasma diagnostics in the circumgalactic medium

ABSTRACT The relevance of some galactic feedback mechanisms, in particular cosmic-ray (CR) feedback and the hydrogen ionizing radiation field, has been challenging to definitively describe in a galactic context, especially far outside the galaxy in the circumgalactic medium (CGM). Theoretical and observational uncertainties prevent conclusive interpretations of multiphase CGM properties derived from ultraviolet (UV) diagnostics. We conduct three-dimensional magnetohydrodynamic simulations of a section of a galactic disc with star formation and feedback, including radiative heating from stars, a UV background, and CR feedback. We utilize the temperature phases present in our simulations to generate Cloudy models to derive spatially and temporally varying synthetic UV diagnostics. We find that radiative effects without additional heating mechanisms are not able to produce synthetic diagnostics in the observed ranges. For low CR diffusivity $\kappa _{\rm {cr}}=10^{28} \rm {cm}^2 \rm {s}^{-1}$, CR streaming heating in the outflow helps our synthetic line ratios roughly match observed ranges by producing transitional temperature gas (T ∼ 105–106 K). High CR diffusivity $\kappa _{\rm {cr}}=10^{29} \rm {cm}^2 \rm {s}^{-1}$, with or without CR streaming heating, produced transitional temperature gas. The key parameter controlling the production of this gas phase remains unclear, as the different star formation history and outflow evolution itself influences these diagnostics. Our work demonstrates the use of UV plasma diagnostics to differentiate between galactic/circumgalactic feedback models.

Origin of 60Fe nuclei in cosmic rays: the contribution of local OB associations

ABSTRACT The presence of live 60Fe nuclei (lifetime of 3.8 Myr) in cosmic rays detected by the Advanced Composition Explorer/Cosmic Ray Isotope Spectrometer instrument suggests a nearby nucleosynthesis source. 60Fe is primarily produced in core-collapse supernovae, and we aim to clarify whether the detected 60Fe nuclei can be associated with a particular local supernova. We consider 25 OB associations and subgroups located within 1 kpc of the Solar system based on recent Gaia census. A model is developed that combines stellar population synthesis within these OB associations, cosmic ray acceleration within associated superbubbles, and cosmic ray transport to the Solar system. The most critical model parameter impacting 60Fe cosmic ray production is the explodability criterion, which determines if a massive star ends its life as a supernova. Our study points to the Scorpius–Centaurus (Sco–Cen) OB association as the most probable origin of the observed 60Fe nuclei, particularly suggesting they were accelerated in the Sco–Cen superbubble by a young supernova aged ≤500 kyr with a progenitor mass of approximately 13–20 M⊙. A less likely source is the supernova at the origin of the Geminga pulsar 342 kyr ago, if the progenitor originated in the Orion OB1 association. The contribution of local OB associations to the cosmic ray density of stable 56Fe is estimated to be around 20 per cent, with some sensitivity to cosmic ray acceleration efficiency and diffusion coefficient. These findings shed light on the origins of cosmic ray nuclei, connecting them to nucleosynthesis events within our local cosmic neighbourhood.

Are odd radio circles virial shocks around massive galaxies? Implications for cosmic-ray diffusion in the circumgalactic medium

ABSTRACT Recently, a new population of circular radio (∼GHz) objects has been discovered at high Galactic latitudes, called the odd radio circles (ORCs). A fraction of the ORCs encircles massive galaxies in the sky with stellar mass ∼1011 M⊙ situated at z = 0.2–0.6, suggesting a possible physical connection. In this paper, we explore the possibility that these radio circles originate from the accretion shocks/virial shocks around massive (${\gtrsim} 10^{13}\, \ {\rm M}_\odot$) dark matter halo at z ∼ 0.5. We found that the radio flux density of the emitting shell is marginally consistent with the ORCs. We also find that pure advection of electrons from the shock results in a radio-emitting shell that is considerably narrower than the observed one due to strong inverse-Compton cooling of electrons. Instead, we show that the diffusion of cosmic-ray (CR) electrons plays a significant role in increasing the width of the shell. We infer a diffusion coefficient, $D_{\rm cr} \sim 10^{30}\ {\rm cm^2\, s^{-1}}$, consistent with the values expected for low-density circumgalactic medium (CGM). If ORCs indeed trace virial shocks, then our derived CR diffusion coefficient represents one of the few estimations available for the low-density CGM. Finally, we show that the apparent discrepancy between ORC and halo number density can be mitigated by considering an incomplete halo virialization and the limited radiation efficiency of shocks. This study therefore opens up new avenues to study such shocks and non-thermal particle acceleration within them. Furthermore, our results suggest that low-mass galaxies (≲1013 M⊙) may not show ORCs due to their significantly lower radio surface brightness.