Models Of Particle Acceleration Research Articles

Nonresonant particle acceleration in strong turbulence: Comparison to kinetic and MHD simulations

Collisionless, magnetized turbulence offers a promising framework for the generation of nonthermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D particle-in-cell, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of nonresonant particle acceleration in strongly magnetized turbulence [Lemoine, Phys. Rev. D 104, 063020 (2021)], which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, in the spirit of the original Fermi model. To do so, we compare, for a large number of particles that were tracked in the simulations, the predicted and the observed histories of particles momenta. The predicted history is that derived from the model, after extracting from the simulations, at each point along the particle trajectory, the three force terms that control acceleration: the acceleration of the field line velocity projected along the field line direction, its shear projected along the same direction, and its transverse compressive part. Overall, we find a clear correlation between the model predictions and the numerical experiments, indicating that this nonresonant model can successfully account for the bulk of particle energization through Fermi-type processes in strongly magnetized turbulence. We also observe that the parallel shear contribution tends to dominate the physics of energization in the particle-in-cell simulations, while in the magnetohydrodynamic incompressible simulation, both the parallel shear and the transverse compressive term provide about equal contributions.

A nonlinear model of diffusive particle acceleration at a planar shock

We study the process of nonlinear shock acceleration based on a nonlinear diffusion–advection equation. The nonlinearity is introduced via a dependence of the spatial diffusion coefficient on the distribution function of accelerating particles. This dependence reflects the interaction of energetic particles with self-generated waves. After thoroughly testing the grid-based numerical setup with a well-known analytical solution for linear shock acceleration at a specific shock transition, we consider different nonlinear scenarios, assess the influence of various parameters, and discuss the differences of the solutions to those of the linear case. We focus on the following observable features of the acceleration process, for which we quantify the differences in the linear and nonlinear cases: (1) the shape of the momentum spectra of the accelerated particles, (2) the time evolution of the solutions, and (3) the spatial number density profiles.

Testing particle acceleration models for BL Lac jets with the Imaging X-ray Polarimetry Explorer

Mechanisms such as shock acceleration, magnetic reconnection in a kink unstable jet, and extreme turbulence in the jet flow are all expected to produce a distinctive time variability pattern of the X-ray polarization properties of high synchrotron peak blazars (HSP). To determine whether the recently launched Imaging X-ray Polarimetry Explorer (IXPE) can follow the polarization variations induced by different particle acceleration mechanisms in blazar jets, we simulated observations of an HSP blazar variable in terms of the polarization degree and angle according to theoretical predictions. We used the Monte Carlo tool ixpeobssim to create realistic IXPE data products for each model and for three values of flux (i.e., 1, 5, and 10 × 10−10 erg s−1 cm−2). We generated simulated light curves of the polarization degree and angle by time-slicing the simulated data into arbitrary short time bins. We used an χ2 test to assess the performance of the observations in detecting the time variability of the polarization properties. In all cases, even when the light curves are diluted in an individual time bin, some degree of polarization is still measurable with IXPE. A series of ~10 ks long observations permits IXPE to follow the time variability of the polarization degree in the case of the shock acceleration model. In the case of the magnetic reconnection model, the nominal injected model provides the best fit of the simulated IXPE data for time bins of ~5–10 ks, depending on the tested flux level. For the TEMZ model, shorter time slices of ~0.5 ks are needed for obtaining a formally good fit of the simulated IXPE data with the injected model. On the other hand, we find that a fit with a constant model provides a χ2 lower than the fit with the nominal injected model when using time slices of ~20 ks, ~60/70 ks, and ~5 ks for the case of the shock acceleration, magnetic reconnection, and TEMZ model, respectively. In conclusion, provided that the statistics of the observation allows for the slicing of the data in adequately short time bins, IXPE observations of an HSP blazar at a typical flux level can detect the time variability predicted by popular models for particle acceleration in jets. IXPE observations of HSP blazars are a useful tool for addressing the issue of particle acceleration in blazar jets.

A two-zone model as origin of hard TeV spectrum in extreme BL lacs

ABSTRACT The emission of the so-called extreme BL Lacs poses challenges to the particle acceleration models. The hardness of their spectrum, ≲ 2, in the high-energy band demands unusual parameters using the standard one-zone synchrotron self-Compton (SSC) model with a deficient magnetized plasma. Some authors use either two-zone or hadronic/lepto-hadronic models to relax these atypical values. In this work, we present a lepto-hadronic two-zone model to explain the multi-wavelength observations of the six best-known extreme BL Lacs. The very-high-energy gamma-ray observations are described by the photo-hadronic processes in a blob close to the AGN core and by SSC and external inverse Compton-processes in an outer blob. The photo-hadronic interactions occur when accelerated protons in the inner blob interact with annihilation line photons from a sub-relativistic pair plasma. The X-ray observations are described by synchrotron radiation from the outer blob. The parameter values found from the description of the spectral energy distribution for each object with our phenomenological model are similar to each other, and lie in the typical range reported in BL Lacs.

Observation-based modelling of the energetic storm particle event of 14 July 2012

Aims. We model the energetic storm particle (ESP) event of 14 July 2012 using the energetic particle acceleration and transport model named ‘PArticle Radiation Asset Directed at Interplanetary Space Exploration’ (PARADISE), together with the solar wind and coronal mass ejection (CME) model named ‘EUropean Heliospheric FORcasting Information Asset’ (EUHFORIA). The simulation results illustrate both the capabilities and limitations of the utilised models. We show that the models capture some essential structural features of the ESP event; however, for some aspects the simulations and observations diverge. We describe and, to some extent, assess the sources of errors in the modelling chain of EUHFORIA and PARADISE and discuss how they may be mitigated in the future. Methods. The PARADISE model computes energetic particle distributions in the heliosphere by solving the focused transport equation in a stochastic manner. This is done using a background solar wind configuration generated by the ideal magnetohydrodynamic module of EUHFORIA. The CME generating the ESP event is simulated by using the spheromak model of EUHFORIA, which approximates the CME’s flux rope as a linear force-free spheroidal magnetic field. In addition, a tool was developed to trace CME-driven shock waves in the EUHFORIA simulation domain. This tool is used in PARADISE to (i) inject 50 keV protons continuously at the CME-driven shock and (ii) include a foreshock and a sheath region, in which the energetic particle parallel mean free path, λ∥, decreases towards the shock wave. The value of λ∥ at the shock wave is estimated from in situ observations of the ESP event. Results. For energies below ∼1 MeV, the simulation results agree well with both the upstream and downstream components of the ESP event observed by the Advanced Composition Explorer. This suggests that these low-energy protons are mainly the result of interplanetary particle acceleration. In the downstream region, the sharp drop in the energetic particle intensities is reproduced at the entry into the following magnetic cloud, illustrating the importance of a magnetised CME model.

Modeling of GeV-TeV gamma-ray emission of Cygnus Cocoon

OB-associations and superbubbles being energetically essential galactic powerhouses are likely to be the important acceleration sites of galactic cosmic rays (CRs). The emission profile of γ-ray sources related to superbubbles and stellar clusters indicates on continuous particle acceleration by winds of massive stars. One of the most luminous galactic γ-ray sources is Cygnus Cocoon superbubble, observed by multiple instruments, such as Fermi-LAT, ARGO, and, recently, HAWC. We discuss a model of particle acceleration and transport in a superbubble to explain GeV-TeV γ-ray spectrum of Cygnus Cocoon, which has a break at the energy of about 1 TeV. It is shown that the γ rays produced by hadronic interactions of high-energy protons accelerated by an ensemble of shocks from winds of massive stars and supernovae in the Cygnus Cocoon can explain the observations. The proton spectral shape at the highest energies depends on the MHD-fluctuation spectrum in the Cocoon. The viable solutions for Cygnus Cocoon may be applied to some other associations showing similar behaviour. We briefly discuss the similarity and differences of particle acceleration processes in extended superbubbles and compact clusters of young massive stars as represented by Westerlund 1 and 2 γ-ray sources.

Double-power-law Feature of Energetic Particles Accelerated at Coronal Shocks

Abstract Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as E B ∼ (Q/A) α , with α varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double-power-law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either a power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from the Parker Solar Probe and Solar Orbiter.

OPTICAL SYSTEM DESIGN OF THE DETECTOR FOR SOLAR TERAHERTZ EMISSION MEASUREMENTS

The objectives and scientific tasks of the planned space experiment “Solntse-Terahertz” to be performed onboard the ISS Russian Segment are briefly described in the paper. In particular, the aim of the experiment is to study uninvestigated solar electromagnetic emission in the terahertz domain, in ~ 1012 – 1013 Hz (300-30 µm) frequency range. It is expected to obtain new data on solar active region emission including solar flare emission. These data are necessary to clarify the nature of solar activity and construct physical model of charged particle acceleration in active regions during solar flares and other astrophysical objects. We focus on the telescope optical system design and evaluation of main characteristics of this system. Results of simulations and comparison with the experimental verification of obtained characteristics are presented. A close correlation of the estimations and experimental results was obtained. As a result, main parameters of the telescope optical system of experimental hardware “Solntse-Terahertz” were determined. Key words: Sun, solar flares, terahertz emission, optical system.

Self-consistent Monte Carlo model of particle acceleration by relativistic shocks

We present a self-consistent Monte Carlo model of particle acceleration by relativistic shock waves. The model includes the magnetic field amplification in the shock upstream by cosmic ray driven plasma instabilities. The parameters of the Monte Carlo model are obtained based on PIC calculations. We present the spectra of accelerated particles simulated in the frame of the model.

First Observations of Anomalous Cosmic Rays in to 36 Solar Radii

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

Monte Carlo Modeling of Nonlinear Particle Acceleration by a Collisionless Shock Wave for Different Laws of Scattering

Monte Carlo Modeling of Nonlinear Particle Acceleration by a Collisionless Shock Wave for Different Laws of Scattering

Particle acceleration in radio galaxies with flickering jets: GeV electrons to ultrahigh energy cosmic rays

ABSTRACT Variability is a general property of accretion discs and their associated jets. We introduce a semi-analytical model for particle acceleration and radio jet/lobe evolution and explore the effect of Myr time-scale jet variability on the particles accelerated by an active galactic nucleus (AGN) jet. Our work is motivated by the need for local powerful ultrahigh energy cosmic ray (UHECR) sources and evidence for variability in AGN and radio galaxies. Our main results are (i) UHECR and non-thermal radiative luminosities track the jet power but with a response set by the escape and cooling times, respectively; (ii) jet variability produces structure in the electron, synchrotron, and UHECR spectra that deviates from that produced for a constant jet power – in particular, spectral hardening features may be signatures of variability; (iii) the cutoff in the integrated cosmic ray (CR) spectrum is stretched out due to the variation in jet power (and, consequently, maximum CR energy). The resulting spectrum is the convolution of the jet power distribution and the source term. We derive an approximate form for a lognormal distribution of powers; and (iv) we introduce the idea of ${\sim}10\,$ GeV ‘proxy electrons’ that are cooling at the same rate that UHECRs of rigidity $10\,$ EV are escaping from the source, and determine the corresponding photon frequencies that probe escaping UHECRs. Our results demonstrate the link between the history of an astrophysical particle accelerator and its particle contents, non-thermal emission, and UHECR spectrum, with consequences for observations of radio galaxies and UHECR source models.

Detection of Energy Cutoffs in Flare-accelerated Electrons

Abstract Energy cutoffs in electron distribution define the lower and upper limits on the energy range of energetic electrons accelerated in solar flares. They are crucial parameters for understanding particle acceleration processes and energy budgets. Their signatures have been reported in studies of flattened flare X-ray spectra, i.e., the impulsive emission of nonthermal bremsstrahlung from energetic electrons impacting ambient, thermal plasma. However, these observations have not provided unambiguous constraints on the cutoffs. Moreover, other processes may result in similar spectral features. Even the existence and necessity of cutoffs as physical parameters of energetic electrons have been under debate. Here we report a search for their signatures in flare-accelerated electrons with two approaches, i.e., in both X-ray spectra and solar energetic particle (SEP) events. These represent two different electron populations, but may contain information of the same acceleration process. By studying a special group of late impulsive flares, and a group of selected SEP events, we found evidence of cutoffs revealed in both X-ray spectra and SEP electron distributions. In particular, we found for the first time consistent low- and high-energy cutoffs in both hard X-ray-producing and escaping electrons in two events. We also showed the importance of high-energy cutoff in studies of spectral shapes. These results provide evidence of cutoffs in flare-accelerated energetic electrons and new clues for constraining electron distribution parameters and particle acceleration models.

Energy Flux Densities near the Electron Dissipation Region in Asymmetric Magnetopause Reconnection.

Magnetic reconnection is of fundamental importance to plasmas because of its role in releasing and repartitioning stored magnetic energy. Previous results suggest that this energy is predominantly released as ion enthalpy flux along the reconnection outflow. Using Magnetospheric Multiscale data we find the existence of very significant electron energy flux densities in the vicinity of the magnetopause electron dissipation region, orthogonal to the ion energy outflow. These may significantly impact models of electron transport, wave generation, and particle acceleration.

Accelerated particle beams in a 3D simulation of the quiet Sun

Context. Observational and theoretical evidence suggest that beams of accelerated particles are produced in flaring events of all sizes in the solar atmosphere, from X-class flares to nanoflares. Current models of these types of particles in flaring loops assume an isolated 1D atmosphere. Aims. A more realistic environment for modelling accelerated particles can be provided by 3D radiative magnetohydrodynamics codes. Here, we present a simple model for particle acceleration and propagation in the context of a 3D simulation of the quiet solar atmosphere, spanning from the convection zone to the corona. We then examine the additional transport of energy introduced by the particle beams. Methods. The locations of particle acceleration associated with magnetic reconnection were identified by detecting changes in magnetic topology. At each location, the parameters of the accelerated particle distribution were estimated from local conditions. The particle distributions were then propagated along the magnetic field, and the energy deposition due to Coulomb collisions with the ambient plasma was computed. Results. We find that particle beams originate in extended acceleration regions that are distributed across the corona. Upon reaching the transition region, they converge and produce strands of intense heating that penetrate the chromosphere. Within these strands, beam heating consistently dominates conductive heating below the bottom of the transition region. This indicates that particle beams qualitatively alter the energy transport even outside of active regions.

Studies of extragalactic background light with TeV BL Lacertae objects

ABSTRACT Very high energy (VHE; E ≥ 100 GeV) gamma-rays from cosmological distances are attenuated by the extragalactic background light (EBL) in the infrared to ultraviolet bands. By contrasting measured versus intrinsic emission,we can derive the EBL photon density. However, we do not know the intrinsic spectra and the EBL separately, only their combined effect. Here we first present a flexible model-dependent optical depth method to study the EBL by fitting the emission spectra of TeV BL Lacertae objects (BL Lacs) via a one-zone leptonic synchrotron self-Compton model (SSC). We have little information about electron energy distributions (EEDs) in the jet, which is critically important to build spectral energy distributions (SEDs) in the SSC scenario. Based on current particle acceleration models, we use two types of EEDs to fit the observed spectra: a power-law log-parabola (PLLP) EED and a broken power-law (BPL) EED. We find that the upper limit of the EBL density is about 30 n W m−2 sr−1, which is similar to the published measurement. Furthermore, we propose an unprecedented method to test the radiation mechanisms involved in TeV objects, by simply comparing the reduced EBL density with the limit obtained by galaxy counts. We demonstrate that for some BL Lacs, at least, the one-zone SSC model should be reconsidered.

A time-dependent particle acceleration and emission model: understanding particle spectral evolution and blazar flares

ABSTRACT The jets of blazars are renowned for their multiwavelength flares and rapid extreme variability; however, there are still some important unanswered questions about the physical processes responsible for these spectral and temporal changes in emission properties. In this article, we develop a time-dependent particle evolution model for the time-varying emission spectrum of blazars. In the model, we introduce time-dependent electric and magnetic fields, which consistently include the variability of relevant physical quantities in the transport equation. The evolution of the electron distribution is solved numerically from a generalized transport equation that contains terms describing the electrostatic, first- and second-order Fermi acceleration, escape of particles due to both advection and spatial diffusion, and also energy losses due to synchrotron emission and inverse-Compton scattering of both synchrotron and external ambient photon fields. We find that the light-curve profiles of blazars are consistent with the particle spectral evolution resulting from time-dependent electric and magnetic fields, rather than the effects of acceleration or cooling processes. The proposed model is able to account simultaneously for the variability of both the energy spectrum and the light-curve profile of the BL Lac object Mrk 421, with reasonable assumptions about the physical parameters. The results indicate strongly that the magnetic field evolution in the dissipated region of a blazar jet can account for the variabilities.

Forward Modeling of Particle Acceleration and Transport in an Individual Solar Flare

Abstract The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modeling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on 2017 September 8, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-center approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the “thin-target” approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally driven modeling of individual solar flares, including manifestations of energetic particles in the corona, as well as the inner heliosphere.

A global model of particle acceleration at pulsar wind termination shocks

Context. Pulsar wind nebulae are efficient particle accelerators, and yet the processes at work remain elusive. Self-generated, microturbulence is too weak in relativistic magnetized shocks to accelerate particles over a wide energy range, suggesting that the global dynamics of the nebula may be involved in the acceleration process instead. Aims. In this work, we study the role played by the large-scale anisotropy of the transverse magnetic field profile on the shock dynamics. Methods. We performed large two-dimensional particle-in-cell simulations for a wide range of upstream plasma magnetizations, from weakly magnetized to strongly magnetized pulsar winds. Results. The magnetic field anisotropy leads to a dramatically different structure of the shock front and downstream flow. A large-scale velocity shear and current sheets form in the equatorial regions and at the poles, where they drive strong plasma turbulence via Kelvin-Helmholtz vortices and kinks. The mixing of current sheets in the downstream flow leads to efficient nonthermal particle acceleration. The power-law spectrum hardens with increasing magnetization, akin to those found in relativistic reconnection and kinetic turbulence studies. The high end of the spectrum is composed of particles surfing on the wake produced by elongated spearhead-shaped cavities forming at the shock front and piercing through the upstream flow. These particles are efficiently accelerated via the shear-flow acceleration mechanism near the Bohm limit. Conclusions. Magnetized relativistic shocks are very efficient particle accelerators. Capturing the global dynamics of the downstream flow is crucial to understanding them, and therefore local plane parallel studies may not be appropriate for pulsar wind nebulae and possibly other astrophysical relativistic magnetized shocks. A natural outcome of such shocks is a variable and Doppler-boosted synchrotron emission at the high end of the spectrum originating from the shock-front cavities, reminiscent of the mysterious Crab Nebula gamma-ray flares.

Cosmic-Ray Acceleration in Radio-jet Shear Flows: Scattering Inside and Outside the Jet

Abstract A steady-state, analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity is explored, including particle scattering both into and out of the shear flow acceleration region. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The spectrum of the accelerated particles is harder than the free-escape case from the edge of the jet. The flow velocity u = u(r) e z is along the axis of jet (the z-axis). u is independent of distance z along the jet axis, and u(r) is a monotonically decreasing function of cylindrical radius r from the jet axis. The scattering time where p is the particle momentum in the fluid frame in the shear flow region 0 < r < r 2, and outside the jet (r > r 2). Green’s functions are obtained for monoenergetic injection of particles with momentum p = p 0 at radius r = r 1 (0 < r 1 < r 2). The Green’s function and Green’s formula are used to determine solutions for a general spectrum of particles at . Solutions are obtained corresponding to a monoenergetic spectrum at infinity. We discuss the implications of these results for the acceleration of ultra-high-energy cosmic-rays in active galactic nucleus jet sources. Leaky box models of particle acceleration in shear flows, including synchrotron losses and particle escape, are used to describe the momentum spectrum of accelerated particles. The use of the relativistic telegrapher transport equation model is discussed.