Propagation Of Cosmic Rays Research Articles

On the Contribution of Unresolved Pulsars to the Ultra-high-energy Galactic Diffuse Gamma-Ray Emission

Abstract The ultra-high-energy (UHE) Galactic diffuse gamma-ray emission holds important information on the propagation of cosmic rays in the Galaxy. However, its measurements suffer from a contamination from unresolved sources whose contribution remains unclear. In this Letter, we propose a novel data-driven estimate of the contribution of unresolved pulsar wind nebulae and TeV halos based on the information present in the Australia Telescope National Facility and the LHAASO catalogs. We find that in the inner Galaxy, this contribution is limited to ∼38% ± 10% of the diffuse flux measured by LHAASO at ∼20 TeV in the case where all sources associated to pulsars contribute as unresolved sources, and this fraction drops to less than 21% ± 6% above 100 TeV. In the outer Galaxy, this contribution is always subdominant. In particular, it reaches at most ∼18% ± 2% at 10 TeV and is less than ∼7% ± 1% above ∼25 TeV. We conclude that the UHE Galactic diffuse gamma-ray emission cannot be dominated by unresolved pulsar sources above a few tens of TeV.

Radio-FIR correlation: A probe into cosmic ray propagation in the nearby galaxy IC 342

Resolved studies of the correlation between the radio and far-infrared (FIR) emission from galaxies at different frequencies can unveil the interplay between star formation and the relativistic interstellar medium (ISM). Thanks to the LOFAR LoTSS observations combined with VLA, Herschel, and WISE data, we study the role of cosmic rays and magnetic fields in the radio--FIR correlation on scales of grtsim 200 pc in the nearby galaxy IC342. The thermal emission traced by the 22 mu m emission, constitutes about 6<!PCT!>, 13<!PCT!>, and 30<!PCT!> of the observed radio emission at 0.14, 1.4, and 4.8 GHz, respectively, in star-forming regions and less in other parts . The nonthermal spectral index becomes flatter at frequencies lower than 1.4\,GHz ($ nu alpha_n $) than between 1.4 and 4.8\,GHz ($ 0.19$) on average, and this flattening occurs not only in star-forming regions but also in the diffuse ISM . The radio--FIR correlation holds at all radio frequencies; however, it is tighter at higher radio frequencies. A multi-scale analysis shows that this correlation cannot be maintained on small scales due to diffusion of cosmic ray electrons (CREs). The correlation breaks at a larger scale (simeq 320 pc) at 0.14 GHz than at 1.4 GHz (simeq 200 pc), indicating that the CREs traced at lower frequencies have diffused a longer path in the ISM. We find that the energy index of CREs becomes flatter in star-forming regions, in agreement with previous studies. Cooling of CREs due to the magnetic field is evident globally only after compensating for the effect of star formation activity that both accelerates CREs and amplifies magnetic fields. Compared with other nearby galaxies, we show that the smallest scale of the radio--FIR correlation is proportional to the propagation length of the CREs on which the ordered magnetic field has an important effect.

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.

Contribution of the Cygnus Bubble to the Galactic Cosmic Ray Spectrum and Diffuse γ-Ray Emissions

Since the discovery of cosmic rays (CRs) over a century ago, their origin has remained a mystery and a key research question. Recently, the LHAASO experiment identified the first CR superacceleration source, the Cygnus bubble, which can accelerate CRs to energies exceeding 10 PeV. A pertinent question is how much the Cygnus bubble contributes to the CR spectrum observed on Earth. With the aim of answering that question, a 3D propagation analysis was conducted on CRs in this study. The Cygnus bubble was incorporated into our propagation model in order to determine its contributions to the observed spectra. First, we calculated the spectrum and spatial morphology of the Cygnus bubble to reproduce the observed LHAASO data. Subsequently, we calculated the diffuse γ-ray emissions produced by the CRs from the Cygnus bubble and the energy spectrum of the CR particles near Earth after propagation. Finally, we utilized a CR spatial-dependent propagation model to calculate the large-scale CR energy spectrum and the resulting diffuse γ-ray emissions. Our results indicate that (1) the Cygnus bubble contributes minimally to the CR spectrum observed on Earth, (2) the emissions produced by the CR particles from the Cygnus bubble dominate the diffuse γ-ray emissions in that region, and (3) the structural fluctuations of the diffuse γ-ray emissions observed by LHAASO are likely due to the local CR halo. We anticipate that LHAASO will identify more CR halo sources to validate our model.

Origin of the break in the cosmic-ray electron plus positron spectrum at ∼1 TeV

Recent measurements of the cosmic-ray electron plus positron spectrum in several experiments have confirmed the presence of a break at ∼1 TeV. The origin of the break is still not clearly understood. In this work, we explored different possibilities for the origin, which include an electron source spectrum with a broken power law, a power law with an exponential or super-exponential cutoff, and the absence of potential nearby cosmic-ray sources. Based on the observed electron plus positron data from the DAMPE and the H.E.S.S experiments, and considering supernova remnants as the main sources of cosmic rays in the Galaxy, we find statistical evidence in favor of the scenario with a broken power-law source spectrum, with the best-fit source parameters obtained as Γ = 2.39 for the source spectral index, E0 ≈ 1.6 TeV for the break energy, and f = 1.59 × 1048 ergs for the amount of supernova kinetic energy injected into cosmic-ray electrons. This power-law break in the spectrum has been predicted for electrons confined inside supernova remnants after acceleration via diffusive shock acceleration process, and also indicated by the multi-wavelength study of supernova remnants. All of this evidence shows that the observed spectral break provides a strong indication of a direct link between cosmic-ray electrons and their sources. Our findings further show that electrons must undergo spectral changes while escaping the source region in order to reconcile the difference between the spectral index of electrons observed inside supernova remnants and that obtained from Galactic cosmic-ray propagation studies.

Cosmic-ray propagation models elucidate the prospects for antinuclei detection

Tentative observations of cosmic-ray antihelium by the AMS-02 collaboration have re-energized the quest to use antinuclei to search for physics beyond the standard model. However, our transition to a data-driven era requires more accurate models of the expected astrophysical antinuclei fluxes. We use a state-of-the-art cosmic-ray propagation model, fit to high-precision antiproton and cosmic-ray nuclei (B, Be, Li) data, to constrain the antinuclei flux from both astrophysical and dark matter annihilation models. We show that astrophysical sources are capable of producing 𝒪(1) antideuteron events and 𝒪(0.1) antihelium-3 events over 15 years of AMS-02 observations. Standard dark matter models could potentially produce higher levels of these antinuclei, but showing a different energy-dependence. Given the uncertainties in these models, dark matter annihilation is still the most promising candidate to explain preliminary AMS-02 results. Meanwhile, any robust detection of antihelium-4 events would require more novel dark matter model building or a new astrophysical production mechanism.

Fifty years of studying the GCR intensity during inversion of the heliospheric magnetic fields. II. HMF inversion on the inner heliospheric boundary

Phenomena in the outer layer of the solar atmosphere, the heliosphere, including the supersonic solar wind, the heliospheric magnetic field (HMF) carried by it, and cosmic rays propagating in the heliosphere are important for many processes occurring in this layer. For some of these processes such as geomagnetic activity or propagation of cosmic rays, not only the strength, but also the direction of the field is significant. Nonetheless, if in this regard the situation during periods of low sunspot activity is quite clear — the heliosphere is divided into two hemispheres with opposite polarity (toward the Sun/away from the Sun), — during periods of high sunspot activity when the HMF inversion occurs, there is no simple model of this phenomenon. The paper is a sequel to the study of the HMF inversion phenomenon and associated effects in the intensity of galactic cosmic rays (GCR). Previously, general ideas about the 22-year cyclicity in the characteristics of the Sun, heliosphere, and cosmic rays have been formulated, and the effects observed in the GCR intensity, which we associate with the HMF inversion, have been discussed in detail. This paper deals with a model of HMF inversion, associated only with the evolution of the magnetic field in the layer between the photosphere and the base of the heliosphere due to changes in the distribution of photospheric fields from one solar rotation to the next one, and shows that this is not enough to explain the main effects in the GCR intensity. In this layer, the magnetic field is the main energy factor. A more complete model of HMF inversion, including the transformation of its characteristics due to the interaction of different-speed solar wind streams in the heliosphere itself, where the solar wind is the main energy factor, will be discussed in the next paper.

Пятьдесят лет исследования поведения интенсивности ГКЛ в периоды инверсии гелиосферного магнитного поля. II. Инверсия ГМП на внутренней границе гелиосферы

Phenomena in the outer layer of the solar atmosphere, the heliosphere, including the supersonic solar wind, the heliospheric magnetic field (HMF) carried by it, and cosmic rays propagating in the heliosphere are important for many processes occurring in this layer. For some of these processes such as geomagnetic activity or propagation of cosmic rays, not only the strength, but also the direction of the field is significant. Nonetheless, if in this regard the situation during periods of low sunspot activity is quite clear — the heliosphere is divided into two hemispheres with opposite polarity (toward the Sun/away from the Sun), — during periods of high sunspot activity when the HMF inversion occurs, there is no simple model of this phenomenon. The paper is a sequel to the study of the HMF inversion phenomenon and associated effects in the intensity of galactic cosmic rays (GCR). Previously, general ideas about the 22-year cyclicity in the characteristics of the Sun, heliosphere, and cosmic rays have been formulated, and the effects observed in the GCR intensity, which we associate with the HMF inversion, have been discussed in detail. This paper deals with a model of HMF inversion, associated only with the evolution of the magnetic field in the layer between the photosphere and the base of the heliosphere due to changes in the distribution of photospheric fields from one solar rotation to the next one, and shows that this is not enough to explain the main effects in the GCR intensity. In this layer, the magnetic field is the main energy factor. A more complete model of HMF inversion, including the transformation of its characteristics due to the interaction of different-speed solar wind streams in the heliosphere itself, where the solar wind is the main energy factor, will be discussed in the next paper.

Studies on the temperature dependent drift velocity for the HELIX Drift Chamber Tracker

HELIX (High Energy Light Isotope eXperiment) is a ballon experiment designed to measure abundance of cosmic ray isotopes from hydrogen to neon, with a particular interest in abundances of beryllium isotopes. HELIX aim to provide essential data to study the cosmic ray propagation in our galaxy. The Drift Chamber Tracker (DCT) in HELIX is a multi-wire gas drift chamber designed to measure the position of incident cosmic rays. It is located inside a magnet, bending the trajectory of incoming particles through 72-layers of tracking, enabling the measurement of the momentum of incoming particles.Before the data can be used for scientific analysis, the background must be taken out, and the instrument must be well calibrated. In order to exclude electronic noise from the DCT data it was necessary to determine the maximum drift velocity of each wire over a short period of time. To do this I developed an algorithm to be able to identify the maximum drift velocity for each wire over each dataset. This revealed a position dependence of the data within the detector. In order to attempt to characterize this dependence, so it can be accounted for in the calibration stage, I preformed a study on the temperature dependence of the drift velocities analyzing at data from different time periods over the course of the flight. To characterize this dependence I built a predicted heat map of the gas within the detector over the course of the flight. This involved calibrating the thermistors based on data collected when the experiment was on the ground. This helped confirm that the predicted temperature was reasonable and that the variation was temperature dependent. This algorithms and this study can now be applied to the full data set to develop a calibration method.

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.

Interactions of cosmic rays with the primordial photons of the Universe

Understanding the physical processes involved in the propagation of cosmic rays in the intergalactic media is one of the biggest problems in astrophysics today. It is an important topic because one first tries to identify the sources and later to understand the physical processes that occur when the particles are accelerated to ultra-high energies (E>1018eV). And because cosmic rays are charged particles, they are deflected in the existing magnetic fields as they propagate to Earth, making it very difficult to correlate their direction of arrival with astrophysical sources. Moreover, cosmic rays consist mainly of atomic nuclei interacting with the cosmic microwave background (CMB) and the extragalactic background light (EBL) during their propagation, and a significant part of their energy is consumed in these processes (for a proton with E∼1021 eV, its energy is approximately halved over a distance of 20 Mpc). In this article, we describe the main processes between background photons and ultrahigh-energy cosmic rays. We have also used the equations for comparison with the most commonly used programme in this field to illustrate the physical processes addressed. We conclude that the result of the equations leads to well-established results in the field, such as the importance of EBL for the process of photodesintegration (Allard, 2012).

Properties of Cosmic Deuterons Measured by the Alpha Magnetic Spectrometer.

Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of the deuteron (D) flux are presented. The measurements are based on 21×10^{6} D nuclei in the rigidity range from 1.9 to 21GV collected from May 2011 to April 2021. We observe that over the entire rigidity range the D flux exhibits nearly identical time variations with the p, ^{3}He, and ^{4}He fluxes. Above 4.5GV, the D/^{4}He flux ratio is time independent and its rigidity dependence is well described by a single power law ∝R^{Δ} with Δ_{D/^{4}He}=-0.108±0.005. This is in contrast with the ^{3}He/^{4}He flux ratio for which we find Δ_{^{3}He/^{4}He}=-0.289±0.003. Above ∼13 GV we find a nearly identical rigidity dependence of the D and p fluxes with a D/p flux ratio of 0.027±0.001. These unexpected observations indicate that cosmic deuterons have a sizable primarylike component. With a method independent of cosmic ray propagation, we obtain the primary component of the D flux equal to 9.4±0.5% of the ^{4}He flux and the secondary component of the D flux equal to 58±5% of the ^{3}He flux.

Exploring cosmic ray energy loss mechanisms: Insights from Bethe-Bloch, modified bethe-bloch, and inverse compton scattering equations

This study delves into the intricate dynamics of cosmic ray energy loss mechanisms, employing three distinct mathematical approaches: the Bethe-Bloch equation, the modified Bethe-Bloch equation, and the inverse compton scattering equation. The Bethe-Bloch equation elucidates the ionization and bremsstrahlung processes governing cosmic ray interactions with plasma mediums, providing foundational insights into energy loss phenomena. Expanding upon this, the modified Bethe-Bloch equation integrates additional factors such as medium density and magnetic fields, refining our understanding of cosmic ray propagation in diverse astrophysical environments. Moreover, the inverse Compton scattering equation uncovers the energy loss mechanisms associated with cosmic ray interactions with photons in the interstellar medium, contributing essential insights into high-energy astrophysical phenomena. Through mathematical derivations, numerical computations, and graphical analyses, our investigation reveals the intricate dependencies of final cosmic ray energy on various parameters, including initial energy, target photon density, and magnetic field strength. Furthermore, our findings have broader implications for astrophysical processes such as gamma-ray emission and cosmic-ray acceleration mechanisms. By elucidating the complex interplay between cosmic rays and their surrounding environments, this study advances our understanding of high-energy astrophysical phenomena and provides a framework for future research in this field.

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.

Modified Temperature–Redshift Relation and Ultra-high-energy Cosmic Ray Propagation

We reexamine the interactions of ultra-high-energy cosmic rays (UHECRs) with photons from the cosmic microwave background (CMB) under a changed, locally nonlinear temperature–redshift relation T(z). This changed temperature–redshift relation has recently been suggested by the postulate of subjecting thermalized and isotropic photon gases such as the CMB to an SU(2) rather than a U(1) gauge group. This modification of ΛCDM is called SU(2)CMB, and some cosmological parameters obtained by SU(2)CMB seem to be in better agreement with local measurements of the same quantities, in particular H 0 and S8. In this work, we apply the reduced CMB photon density under SU(2)CMB to the propagation of UHECRs. This leads to a higher UHECR flux just below the ankle in the cosmic ray spectrum and slightly more cosmogenic neutrinos under otherwise equal conditions for emission and propagation. Most prominently, the proton flux is significantly increased below the ankle (5 × 1018 eV) for hard injection spectra and without considering the effects of magnetic fields. The reduction in CMB photon density also favors a decreased cosmic ray source evolution than the best fit using ΛCDM. In consequence, it seems that SU(2)CMB favors sources that evolve like the star formation rate, such as starburst galaxies and gamma-ray bursts, over active galactic nuclei as origins of UHECRs. We conclude that the question about the nature of primary sources of UHECRs is directly affected by the assumed temperature–redshift relation of the CMB.

Transport parameters from AMS-02 F/Si data and fluorine source abundance

The AMS-02 collaboration recently released cosmic ray F/Si data with an unprecedented accuracy. Cosmic ray fluorine is predominantly produced by fragmentation of heavier progenitors, while silicon is mostly accelerated at source. This ratio is thus maximally sensitive to cosmic ray propagation. We study the compatibility of the transport parameters derived from the F/Si ratio with those obtained from the lighter Li/C, Be/C, and B/C ratios. We also inspect the cosmic ray source abundance of F, which is one of the few elements that has a high first ionisation potential but is only moderately volatile and is a potentially key element to study the acceleration mechanism of cosmic rays. We used the 1D diffusion model implemented in the code and performed $ analyses accounting for several systematic effects (energy correlations in data, nuclear cross sections, and solar modulation uncertainties). We also took advantage of the nuclear database to update the F production cross sections for its most important progenitors (identified to be 56Fe, 32S, 28Si, 27Al, 24Mg, 22Ne, and 20Ne). The transport parameters obtained from AMS-02 F/Si data are compatible with those obtained from AMS-02 (Li,Be,B)/C data. The combined fit of all of these ratios leads to a $ 1.1$, with $ 10<!PCT!>$ adjustments of the B and F production cross sections (which are based on very few nuclear data points and would strongly benefit from new measurements). The F/Si ratio is compatible with a pure secondary origin of F, with a best-fit relative source abundance F/^ Si) CRS $ and an upper limit of $ $. Unfortunately, this limit is not sufficient to test global acceleration models of cosmic ray nuclei, for which values at the level of $ $ are required. Such levels could be attained with F/Si data with a few percent of accuracy at a few tens of TV, which is possibly within reach for the next generation of cosmic ray experiments.

Inelastic Scattering of Dark Matter with Heavy Cosmic Rays

We investigate the impact of inelastic collisions between dark matter (DM) and heavy cosmic ray (CR) nuclei on CR propagation. We approximate the fragmentation cross-sections for DM-CR collisions using collider-measured proton-nuclei scattering cross-sections, allowing us to assess how these collisions affect the spectra of CR boron and carbon. We derive new CR spectra from DM-CR collisions by incorporating their cross-sections into the source terms and solving the diffusion equation for the complete network of reactions involved in generating secondary species. In a specific example with a coupling strength of b χ = 0.1 and a DM mass of m χ = 0.1 GeV, considering a simplified scenario where DM interacts exclusively with oxygen, a notable modification in the boron-to-carbon spectrum due to the DM-CR interaction is observed. Particularly, the peak within the spectrum, spanning from 0.1 to 10 GeV, experiences an enhancement of approximately 1.5 times. However, in a more realistic scenario where DM particles interact with all CRs, this peak can be amplified to twice its original value. Utilizing the latest data from AMS-02 and DAMPE on the boron-to-carbon ratio, we estimate a 95% upper limit for the effective inelastic cross-section of DM-proton as a function of DM mass. Our findings reveal that at m χ ≃ 2 MeV, the effective inelastic cross-section between DM and protons must be less than O(10−32)cm2 .

Antiproton bounds on dark matter annihilation from a combined analysis using the DRAGON2 code

Early studies of the AMS-02 antiproton ratio identified a possible excess over the expected astrophysical background that could be fit by the annihilation of a weakly interacting massive particle (WIMP). However, recent efforts have shown that uncertainties in cosmic-ray propagation, the antiproton production cross-section, and correlated systematic uncertainties in the AMS-02 data, may combine to decrease or eliminate the significance of this feature. We produce an advanced analysis using the DRAGON2 code which, for the first time, simultaneously fits the antiproton ratio along with multiple secondary cosmic-ray flux measurements to constrain astrophysical and nuclear uncertainties. Compared to previous work, our analysis benefits from a combination of: (1) recently released AMS-02 antiproton data, (2) updated nuclear fragmentation cross-section fits, (3) a rigorous Bayesian parameter space scan that constrains cosmic-ray propagation parameters.We find no statistically significant preference for a dark matter signal and set strong constraints on WIMP annihilation to bb̅, ruling out annihilation at the thermal cross-section for dark matter masses below ∼ 200 GeV. We do find a positive residual that is consistent with previous work, and can be explained by a ∼ 70 GeV WIMP annihilating below the thermal cross-section. However, our default analysis finds this excess to have a local significance of only 2.8σ, which is decreased to 1.8σ when the look-elsewhere effect is taken into account.

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.