Acceleration Of Ultra-high Energy Cosmic Rays Research Articles

Closing the Net on Transient Sources of Ultrahigh-energy Cosmic Rays

The arrival directions of ultrahigh-energy cosmic rays (UHECRs) observed above 4 × 1019 eV provide evidence of localized excesses that are key to identifying their sources. We leverage the 3D matter distribution from optical and infrared surveys as a density model of UHECR sources, which are considered to be transient. Agreement of the sky model with UHECR data imposes constraints on both the emission rate per unit matter and the time spread induced by encountered turbulent magnetic fields. Based on radio measurements of cosmic magnetism, we identify the Local Sheet as the magnetized structure responsible for the kiloyear duration of UHECR bursts for an observer on Earth and find that the turbulence amplitude must be within 0.5–20 nG for a coherence length of 10 kpc. At the same time, the burst-rate density must be above 50 Gpc−3 yr−1 for Local Sheet galaxies to reproduce the UHECR excesses and below 5000 Gpc−3 yr−1 (30,000 Gpc−3 yr−1) for the Milky Way (Local Group galaxies) not to outshine other galaxies. For the transient emissions of protons and nuclei to match the energy spectra of UHECRs, the kinetic energy of the outflows responsible for UHECR acceleration must be below 4 × 1054 erg and above 5 × 1050 erg (2 × 1049 erg) if we consider the Milky Way (or not). The only stellar-sized transients that satisfy both Hillas’ and our criteria are long-duration gamma-ray bursts.

A Detectable Ultra-high-energy Cosmic-Ray Outburst from GRB 221009A

Gamma-ray bursts (GRBs) have been proposed as one of the promising sources of ultra-high-energy cosmic rays (UHECRs), but observational evidence is still lacking. The nearby brightest of all time GRB 221009A, a once in 1000 yr event, is able to accelerate protons to ∼103 EeV, and then generate extremly energetic neutrons via the photomeson production interaction. Protons arriving at the Milky Way are dominated by neutron-decay-induced protons. The intergalactic magnetic fields would not yield a sizable delay of the ≥10 EeV cosmic rays if its strength is ≲10−13 G, while Galactic magnetic fields would cause a significant time delay. We predict that a UHECR burst from GRB 221009A would be detectable by the Pierre Auger Observatory and the TA×4, within ∼10 yr. The detection of such a UHECR outburst will provide the direct evidence for UHECR acceleration in GRBs.

Acceleration and Spectral Redistribution of Cosmic Rays in Radio-jet Shear Flows

A steady-state, semi-analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity obtained by Webb et al. is generalized to take into account more general cosmic-ray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution function f 0(r, p) at cylindrical radius r from the jet axis (assumed to lie along the z-axis) is given by convolving the particle momentum spectrum with the Green’s function , which describes the monoenergetic spectrum solution in which as r → ∞ . Previous work by Webb et al. studied only the Green’s function solution for . In this paper, we explore for the first time, solutions for more general and realistic forms for . The flow velocity u = u(r) e z is along the axis of the jet (the z-axis). u is independent of z, and u(r) is a monotonic decreasing function of r. The scattering time in the shear flow region 0 < r < r 2, and , where s > 0 in the region r > r 2 is outside the jet. Other original aspects of the analysis are (i) the use of cosmic ray flow lines in (r, p) space to clarify the particle spatial transport and momentum changes and (ii) the determination of the probability distribution that particles observed at (r, p) originated from r → ∞ with momentum . The acceleration of ultrahigh-energy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described.

Probing the dark dimension with Auger data

By combining swampland conjectures with observational data, it was recently pointed out that our universe could stretch off in an asymptotic region of the string landscape of vacua. Within this framework, the cosmological hierarchy problem (i.e. the smallness of the cosmological constant in Planck units: Λ∼10−122MPl4) can be naturally resolved by the addition of one mesoscopic (dark) dimension of size ∼λΛ−1/4∼1μm. The Planck scale of the higher dimensional theory, MUV∼λ−1/3Λ1/12MPl2/3∼1010GeV, is tantalizingly close to the energy above which the Telescope Array (TA) and the Pierre Auger collaborations found conclusive evidence for a sharp cutoff of the flux of ultra-high-energy cosmic rays (UHECRs). It was recently suggested that since physics becomes strongly coupled to gravity beyond MUV, universal features deep-rooted in the dark dimension could control the energy cutoff of the source spectra ∝E−γexp(−E/MUV), where E is the cosmic ray energy and γ a free parameter. Conversely, in the absence of phenomena inborn within the dark dimension, we would expect a high variance of the cosmic ray maximum energy Emax characterizing the source spectra ∝E−γexp(−E/Emax), reflecting the many different properties inherent to the most commonly assumed UHECR accelerators. The most recent analysis of Auger and TA data exposed strong evidence for a correlation between UHECRs and nearby starburst galaxies, with a global significance post-trial of 4.7σ. Since these galaxies are in our cosmic backyard, the flux attenuation factor due to cosmic ray interactions en route to Earth turns out to be negligible. This reasoning implies that for each source, the shape of the observed spectrum should roughly match the emission spectrum by the starburst, providing a unique testing ground for the dark dimension hypothesis. Using Auger data, we carry out a maximum likelihood analysis to characterize the shape of the UHECR emission from the galaxies dominating the anisotropy signal. We show that the observed spectra from these sources could be universal only if λ≲10−3.

Nuclear and electromagnetic cascades induced by ultra-high-energy cosmic rays in radio galaxies: implications for Centaurus A

ABSTRACT Very high energy (VHE) γ-rays ($\gtrsim\!\! 0.1\rm ~TeV$) and neutrinos are crucial for identifying accelerators of ultra-high-energy cosmic rays (UHECRs), but this is challenging especially for UHECR nuclei. In this work, we develop a numerical code to solve the transport equation for UHECRs and their secondaries, where both nuclear and electromagnetic cascades are taken into account self-consistently, considering steady UHECR accelerators such as radio galaxies. In particular, we focus on Centaurus A, which has been proposed as one of the most promising UHECR sources in the local Universe. Motivated by observations of extended VHE γ-ray emission from its kiloparsec-scale jet by the High Energy Stereoscopic System (H.E.S.S.), we study interactions between UHECRs accelerated in the large-scale jet and various target photon fields including blazar-like beamed core emission, and present a quantitative study on VHE γ-ray signatures of UHECR nuclei, including the photodisintegration and Bethe–Heitler pair production processes. We show that VHE γ-rays from UHECR nuclei could be detected by the ground-based γ-ray telescopes given that the dominant composition of UHECRs consists of intermediate-mass (such as oxygen) nuclei.

Further evidence for ultrahigh-energy cosmic ray acceleration in starburst-driven superwinds

Very recently, the Pierre Auger and Telescope Array collaborations reported strong evidence for a correlation between the highest energy cosmic rays and nearby starburst galaxies, with a global significance post-trial of $4.7\ensuremath{\sigma}$. It is well-known that the collective effect of supernovae and winds from massive stars in the central region of these galaxies drives a galactic-scale superwind that can shock heat and accelerate ambient interstellar or circumgalactic gas. In previous work we showed that, for reasonable source parameters, starburst-driven superwinds can be the carriers of ultrahigh-energy cosmic ray acceleration. In this paper we assess the extent to which one can approach the archaeological ``inverse'' problem of deciphering properties of superwind evolution from present-day IR emission of their host galaxies. We show that the Outer Limits galaxy NGC 891 could provide ``smoking-gun evidence'' for the starburst-driven superwind model of ultrahigh-energy cosmic rays.

External Inverse-compton and Proton Synchrotron Emission from the Reverse Shock as the Origin of VHE Gamma Rays from the Hyper-bright GRB 221009A

The detection of the hyper-bright gamma-ray burst (GRB) 221009A enables us to explore the nature of the GRB emission and the origin of very high-energy gamma rays. We analyze the Fermi Large Area Telescope (Fermi-LAT) data of this burst and investigate the GeV–TeV emission in the framework of the external reverse-shock model. We show that the early ∼1–10 GeV emission can be explained by the external inverse-Compton mechanism via upscattering MeV gamma rays by electrons accelerated at the reverse shock, in addition to the synchrotron self-Compton component. The predicted early optical flux could have been brighter than that of the naked-eye GRB 080319B. We also show that proton synchrotron emission from accelerated ultrahigh-energy cosmic rays (UHECRs) is detectable and could potentially explain ≳TeV photons detected by LHAASO or constrain the UHECR acceleration mechanism. Our model suggests that the detection of photons with energies up to ∼18 TeV is possible for reasonable models of the extragalactic background light without invoking new physics and predicts anticorrelations between MeV photons and TeV photons, which can be tested with the LHAASO data.

Ultrahigh-energy cosmic-ray signature in GRB 221009A

The brightest long gamma-ray burst (GRB) detected so far by the Swift-BAT and Fermi-GBM telescopes, GRB 221009A, provides an unprecedented opportunity for understanding the high-energy processes in extreme transient phenomena. We find that the conventional leptonic models for the afterglow emission from this source, synchrotron and synchrotron-self-Compton, have difficulties explaining the observation of ≳10 TeV γ rays (as high as 18 TeV) by the LHAASO detector. We modeled the γ-ray spectrum estimated in the energy range 0.1–1 GeV by the Fermi-LAT detector. The flux predicted by our leptonic models is severely attenuated at &gt; 1 TeV due to γγ pair production with extragalactic background light, and hence an additional component is required at ≳10 TeV. Ultrahigh-energy cosmic rays can be accelerated in the GRB blast wave, and their propagation induces an electromagnetic cascade in the extragalactic medium. The line-of-sight component of this flux can explain the emission at ≳10 TeV detected by LHAASO, which requires a fraction of the GRB blast wave energy to be in ultrahigh-energy cosmic rays. This could be an indication of ultrahigh-energy cosmic-ray acceleration in GRBs.

Constraints on the Hosts of UHECR Accelerators

Interactions of ultra-high-energy cosmic rays (UHECRs) in the surroundings of their accelerators can naturally explain the observed spectrum and composition of UHECRs, including the abundance of protons below the ankle. Here we show that astrophysical properties of the UHECR source environment such as the temperature, size, and magnetic field can be constrained by UHECR and neutrino data. Applying this to candidate sources with a simple structure shows that starburst galaxies are consistent with these constraints, but galaxy clusters are in tension with them. For multicomponent systems like active galactic nuclei and gamma-ray bursts, the results are indicative, but a customized analysis is needed for definitive conclusions.

Active Galactic Nuclei as Potential Sources of Ultra-High Energy Cosmic Rays

Active Galactic Nuclei (AGNs) and their relativistic jets belong to the most promising class of ultra-high-energy cosmic ray (UHECR) accelerators. This compact review summarises basic experimental findings by recent instruments, and discusses possible interpretations and astrophysical constraints on source energetics. Particular attention is given to potential sites and mechanisms of UHECR acceleration in AGNs, including gap-type particle acceleration close to the black hole, as well as first-order Fermi acceleration at trans-relativistic shocks and stochastic shear particle acceleration in large-scale jets. It is argued that the last two represent the most promising mechanisms given our current understanding, and that nearby FR I type radio galaxies provide a suitable environment for UHECR acceleration.

Searches for Neutrinos from Gamma-Ray Bursts Using the IceCube Neutrino Observatory

Gamma-ray bursts (GRBs) are considered as promising sources of ultra-high-energy cosmic rays (UHECRs) due to their large power output. Observing a neutrino flux from GRBs would offer evidence that GRBs are hadronic accelerators of UHECRs. Previous IceCube analyses, which primarily focused on neutrinos arriving in temporal coincidence with the prompt gamma-rays, found no significant neutrino excess. The four analyses presented in this paper extend the region of interest to 14 days before and after the prompt phase, including generic extended time windows and targeted precursor searches. GRBs were selected between 2011 May and 2018 October to align with the data set of candidate muon-neutrino events observed by IceCube. No evidence of correlation between neutrino events and GRBs was found in these analyses. Limits are set to constrain the contribution of the cosmic GRB population to the diffuse astrophysical neutrino flux observed by IceCube. Prompt neutrino emission from GRBs is limited to ≲1% of the observed diffuse neutrino flux, and emission on timescales up to 104 s is constrained to 24% of the total diffuse flux.

Acceleration of ultrahigh-energy cosmic rays in the early afterglows of gamma-ray bursts: Concurrence of jet dynamics and wave-particle interactions

The origin of ultra-high energy cosmic rays $($UHECRs$)$ remains a mystery. It has been suggested that UHECRs can be produced by the stochastic acceleration in relativistic jets of gamma-ray bursts $($GRBs$)$ at the early afterglow phase. Here, we develop a time-dependent model for proton energization by cascading compressible waves in GRB jets considering the concurrent effect of the jet's dynamics and the mutual interactions between turbulent waves and particles. Considering fast mode of magnetosonic wave as the dominant particle scatterer and assuming interstellar medium $($ISM$)$ for the circumburst environment, our numerical results suggest that protons can be accelerated up to $\textrm{10}^{\textrm{19}}\,$eV during the early afterglow. An estimation shows ultra-high energy nuclei can easily survive photodisintegration in the external shocks in most cases, thus allowing the acceleration of $\textrm{10}^{\textrm{20}}\,$eV cosmic-ray nuclei in the proposed frame. The spectral slope can be as hard as $\textrm{d}\textit{N}/\textrm{d}\textit{E} \propto \textit{E}^\textrm{0}$, which is consistent with the requirement for the interpretation of intermediate-mass composition of UHECR as measured by the Pierre Auger Observatory.

Scrutinizing FR 0 radio galaxies as ultra-high-energy cosmic ray source candidates

Fanaroff-Riley (FR) 0 radio galaxies compose a new class of radio galaxies, which are usually weaker but much more numerous than the well-established class of FR 1 and FR 2 galaxies. The latter classes have been proposed as sources of the ultra-high-energy cosmic rays (UHECRs) with energies reaching up to ∼1020 eV. Based on this conjecture, the possibility of UHECR acceleration and survival in an FR 0 source environment is examined in this work.In doing so, an average spectral energy distribution (SED) based on data from the FR 0 catalog (FR0CAT) is compiled. The resulting photon fields are used as targets for UHECRs, which suffer from electromagnetic pair production, photo-disintegration, photo-meson production losses, and synchrotron radiation. Multiple mechanisms are discussed to assess the UHECR acceleration probability, including Fermi-I order and gradual shear accelerations, and particle escape from the source region.This work shows that in a hybrid scenario, combining Fermi and shear accelerations, FR 0 galaxies can contribute to the observed UHECR flux, as long as Γj≳1.6, where shear acceleration starts to dominate over escape. Even in less optimistic scenarios, FR 0s can be expected to contribute to the cosmic-ray flux between the knee and the ankle. Our results are relatively robust with respect to the realized magnetic turbulence model and the speed of the accelerating shocks.

Constraining Low-luminosity Gamma-Ray Bursts as Ultra-high-energy Cosmic Ray Sources Using GRB 060218 as a Proxy

Abstract We study the connection between low-luminosity gamma-ray bursts (llGRBs) and ultra-high-energy cosmic rays (UHECRs) using the canonical low-luminosity GRB 060218 as a proxy. We focus on the consequential synchrotron emission from electrons that are coaccelerated in the UHECR acceleration region, comparing this emission to observations. Both the prompt and afterglow phases are considered. For the prompt phase, we assume the coaccelerated electrons are injected with a power-law distribution instantaneously (without additional heating or reacceleration), which results in bright optical-UV emission in tension with observations. For the afterglow phase, we constrain the total kinetic energy of the blast wave by comparing electron thermal synchrotron radiation to available radio data at ∼ 3 days. Considering mildly relativistic outflows with bulk Lorentz factor Γ ≳ 2 (slower transrelativistic outflows are not treated), we find that the limited available energy does not allow for GRB 060218-like afterglows to be the main origin of UHECRs. This analysis independently constrains the prompt phase as a major UHECR source as well, given that the prompt energy budget is comparable to that of the afterglow kinetic energy. More generally, our study demonstrates that synchrotron emission from thermal electrons is a powerful diagnostic of the physics of mildly relativistic shocks.

The Limited Contribution of Low- and High-luminosity Gamma-Ray Bursts to Ultra-high-energy Cosmic Rays

Abstract The acceleration site for ultra-high-energy cosmic rays (UHECRs) is still an open question despite extended research. In this paper, we reconsider the prompt phase of gamma-ray bursts (GRBs) as a possible candidate for this acceleration and constrain the maximum proton energy in optically thin synchrotron and photospheric models, using properties of the prompt photon spectra. We find that neither of the models favors acceleration of protons to 1020 eV in high-luminosity bursts. We repeat the calculations for low-luminosity GRBs (llGRBs) considering both protons and completely stripped iron and find that the highest obtainable energies are &lt;1019 eV and &lt;1020 eV for protons and iron respectively, regardless of the model. We conclude therefore that for our fiducial parameters, GRBs, including low-luminosity bursts, contribute little to nothing to the UHECRs observed. We further constrain the conditions necessary for an association between UHECRs and llGRBs and find that iron can be accelerated to 1020 eV in photospheric models, given very efficient acceleration and/or a small fractional energy given to a small fraction of accelerated electrons. This will necessarily result in high prompt optical fluxes, and the detection of such a signal could therefore be an indication of successful UHECR acceleration at the source.

Ultrahigh energy cosmic rays from shocks in the lobes of powerful radio galaxies

The origin of ultra-high energy cosmic rays (UHECRs) has been an open question for decades. Here, we use a combination of hydrodynamic simulations and general physical arguments to demonstrate that UHECRs can in principle be produced by diffusive shock acceleration (DSA) in shocks in the backflowing material of radio galaxy lobes. These shocks occur after the jet material has passed through the relativistic termination shock. Recently, several authors have demonstrated that highly relativistic shocks are not effective in accelerating UHECRs. The shocks in our proposed model have a range of non-relativistic or mildly relativistic shock velocities more conducive to UHECR acceleration, with shock sizes in the range 1-10kpc. Approximately 10% of the jet's energy flux is focused through a shock in the backflow of $M>3$. Although the shock velocities can be low enough that acceleration to high energy via DSA is still efficient, they are also high enough for the Hillas energy to approach $10^{19-20}$eV, particularly for heavier CR composition and in cases where fluid elements pass through multiple shocks. We discuss some of the more general considerations for acceleration of particles to ultra-high energy with reference to giant-lobed radio galaxies such as Centaurus A and Fornax A, a class of sources which may be responsible for the observed anisotropies from UHECR observatories.

A Multimessenger Picture of the Flaring Blazar TXS 0506+056: Implications for High-energy Neutrino Emission and Cosmic-Ray Acceleration

Abstract Detection of the IceCube-170922A neutrino coincident with the flaring blazar TXS 0506+056, the first and only ∼3σ high-energy neutrino source association to date, offers a potential breakthrough in our understanding of high-energy cosmic particles and blazar physics. We present a comprehensive analysis of TXS 0506+056 during its flaring state, using newly collected Swift, NuSTAR, and X-shooter data with Fermi observations and numerical models to constrain the blazar’s particle acceleration processes and multimessenger (electromagnetic (EM) and high-energy neutrino) emissions. Accounting properly for EM cascades in the emission region, we find a physically consistent picture only within a hybrid leptonic scenario, with γ-rays produced by external inverse-Compton processes and high-energy neutrinos via a radiatively subdominant hadronic component. We derive robust constraints on the blazar’s neutrino and cosmic-ray emissions and demonstrate that, because of cascade effects, the 0.1–100 keV emissions of TXS 0506+056 serve as a better probe of its hadronic acceleration and high-energy neutrino production processes than its GeV–TeV emissions. If the IceCube neutrino association holds, physical conditions in the TXS 0506+056 jet must be close to optimal for high-energy neutrino production, and are not favorable for ultrahigh-energy cosmic-ray acceleration. Alternatively, the challenges we identify in generating a significant rate of IceCube neutrino detections from TXS 0506+056 may disfavor single-zone models, in which γ-rays and high-energy neutrinos are produced in a single emission region. In concert with continued operations of the high-energy neutrino observatories, we advocate regular X-ray monitoring of TXS 0506+056 and other blazars in order to test single-zone blazar emission models, clarify the nature and extent of their hadronic acceleration processes, and carry out the most sensitive possible search for additional multimessenger sources.

Very high-energy gamma-ray signature of ultrahigh-energy cosmic ray acceleration in Centaurus A

Abstract The association of at least a dozen ultrahigh-energy cosmic ray (UHECR) events with energy ≳ 55 EeV detected by the Pierre Auger Observatory from the direction of Centaurus-A, the nearest radio galaxy, supports the scenario of UHECR acceleration in the jets of radio galaxies. In this work, we model radio to very high energy (VHE,≳ 100 GeV) γ-ray emission from Cen A, including GeV hardness detected by Fermi–LAT and TeV emission detected by the High Energy Stereoscopic System (HESS). We consider two scenarios: (i) two-zone synchrotron self-Compton (SSC) and external-Compton (EC) models, (ii) two-zone SSC, EC, and photohadronic emission from cosmic ray interactions. The GeV hardness observed by Fermi–LAT can be explained using these two scenarios, where zone 2 EC emission is very important. Hadronic emission in scenario (ii) can explain VHE data with the same spectral slope as obtained through fitting UHECRs from Cen A. The peak luminosity in cosmic ray proton at 1 TeV, to explain the VHE γ-ray data is ≈2.5 × 1046 erg s−1. The bolometric luminosity in cosmic ray protons is consistent with the luminosity required to explain the origin of 13 UHECR signal events that are correlated with Cen A.

Acceleration of ultrahigh-energy cosmic rays in starburst superwinds

The sources of ultrahigh-energy cosmic rays (UHECRs) have been stubbornly elusive. However, the latest report of the Pierre Auger Observatory provides a compelling indication for a possible correlation between the arrival directions of UHECRs and nearby starburst galaxies. We argue that if starbursts are sources of UHECRs, then particle acceleration in the large-scale terminal shock of the superwind that flows from the starburst engine represents the best known concept model in the market. We investigate new constraints on the model and readjust free parameters accordingly. We show that UHECR acceleration above about $1{0}^{11}\text{ }\text{ }\mathrm{GeV}$ remains consistent with observation. We also show that the model could accommodate hard source spectra as required by Auger data. We demonstrate how neutrino emission can be used as a discriminator among acceleration models.

Constraints on Physical Conditions for the Acceleration on Ultra-high-energy Cosmic Rays in Nearby Active Galactic Nuclei (AGNs) Observed with the Fermi Large Area Telescope

Abstract We investigated the possibility of acceleration of ultra-high-energy cosmic rays (UHECRs) in nearby active galactic nuclei (AGNs) using archival multi-wavelength observational data, and then we constrained their physical conditions, i.e., the luminosity of the synchrotron radiation and the size of the acceleration site. First, we investigated the spatial correlation between the arrival directions of UHECRs and the positions of nearby AGNs in the Fermi third gamma-ray source catalog. We selected 27 AGNs as candidates of accelerators of UHECRs. Then, we evaluated the physical conditions in the acceleration regions of these AGNs via the Pe’er and Loeb method, which uses the peak luminosity of synchrotron radiation and the peak flux ratio of inverse Compton scattering to synchrotron radiation. From the evaluation, we found that six AGNs have the ability to accelerate ultra-high-energy (UHE) protons in the AGN cores. Furthermore, we found that the minimum acceleration size must be more than a few kpc for acceleration of UHE protons in the AGN lobes.