arXiv subjects

Frederic Effenberger

Publications and source records attributed to Frederic Effenberger.

At least 19 recordsLinked to original sources

arXiv2026

The impact of Solar magnetic field configurations on the production of gamma rays at the Solar disk

The Sun produces a steady signal of high-energy gamma rays through interactions of Galactic cosmic rays (GCRs) with its atmosphere. Observations with Fermi-LAT and HAWC have revealed a gamma-ray flux significantly higher than early theoretical predictions, with unexpected temporal and spectral features that suggest a crucial role of the solar magnetic field. In this work, we model GCR-induced gamma-ray emission at the solar disk using the CRPropa framework with realistic hadronic interactions, chromospheric density profiles, and several magnetic field configurations over the solar cycle. This allows us to quantify the gamma-ray emission of the entire solar disk for different phases of the solar activity cycle and we present, for the first time, maps of the production locations of gamma rays on the solar surface. We consider both mono-energetic and realistic power-law injection spectra in a simplified dipole-quadrupole current sheet model and potential-field source surface (PFSS) extrapolations for Carrington rotations during solar maximum and minimum. Our results show that magnetic mirroring and large-scale field topology strongly affect the spectral shape and spatial distribution of the emission, with slightly enhanced fluxes predicted at solar minimum. While our simulated baseline fluxes remain below observations, additional effects, such as heavier nuclei, Parker-field mirroring, and deeper atmospheric interactions, could result in further enhancements of fluxes closer to observational values. Hadronic interactions do not only produce gamma rays but also neutrinos. We estimate the expected neutrino flux from the Sun based on our gamma-ray predictions. We find that the expected flux is slightly below current upper limits from IceCube.

astro-ph.HE↗

arXiv2025

Modelling cosmic-ray transport: magnetised versus unmagnetised motion in astrophysical magnetic turbulence

Cosmic-ray transport in turbulent astrophysical environments remains a multifaceted problem and, despite decades of study, the impact of complex magnetic field geometry -- evident in simulations and observations -- has only recently received more focussed attention. To understand how ensemble-averaged transport behaviour emerges from the intricate interactions between cosmic rays and structured magnetic turbulence, we run test-particle experiments in snapshots of a strongly turbulent magnetohydrodynamics simulation. We characterise particle-turbulence interactions via the gyro radii of particles and their experienced field-line curvatures, which reveals two distinct transport modes: magnetised motion, where particles are tightly bound to strong coherent flux tubes and undergo large-scale mirroring; and unmagnetised motion, characterised by chaotic scattering through weak and highly tangled regions of the magnetic field. We formulate an effective stochastic process for each mode: compound subdiffusion with long mean free paths for magnetised motion, and a Langevin process with short mean free paths for unmagnetised motion. A combined stochastic walker that alternates between these two modes accurately reproduces the mean squared displacements observed in the test-particle data. Our results emphasise the critical role of coherent magnetic structures in comprehensively understanding cosmic-ray transport and lay a foundation for developing a theory of geometry-mediated transport.

physics.plasm-ph↗

arXiv2025

Anisotropic Cosmic Ray Transport in strong MHD Turbulence due to Magnetic Mirroring and Resonant Curvature Scattering

The transport of cosmic rays through turbulent astrophysical plasmas still constitutes an open problem. Building on recent progress, we study the combined effect of magnetic mirroring and resonant curvature scattering on parallel and perpendicular transport. We conduct test-particle simulations in snapshots of an anisotropic magnetohydrodynamics simulation with $δB/B_0\sim 1$ and record magnetic moment variation and field line curvature around pitch-angle reversals. We find for strongly magnetized particles that (i) pitch-angle reversals may occur either in coherent regions of the field with small variation of the magnetic moment via magnetic mirroring or in chaotic regions of the field with strong variation of the magnetic moment via resonant curvature scattering; (ii) parallel transport can be modeled as a Lévy walk with a truncated power-law distribution based on pitch-angle reversal times; and (iii) perpendicular transport is enhanced by resonant curvature scattering in synergy with chaotic field line separation and diminished by magnetic mirroring due to confinement in locally ordered field line bundles. While magnetic mirroring constitutes the bulk of reversal events, resonant curvature scattering additionally acts on trajectories that fall in the loss cones of typical mirroring structures and thus provides the cut-off for the reversal time distribution. Our results, which highlight the role of the magnetic field line geometry in cosmic-ray transport processes, are consistent with energy-independent diffusion coefficients. We conclude by considering how energy-dependent observations could arise from an intermittently inhomogeneous interstellar medium.

astro-ph.HE↗

arXiv2024

Exploring the Dynamics of CME-Driven Shocks by Comparing Numerical Modeling and Observations

Shocks driven by coronal mass ejections (CMEs) are primary drivers of gradual solar energetic particle (SEP) events, posing significant risks to space technology and astronauts. Concurrently, particles accelerated at these shocks may also propagate back to the Sun, potentially generating gamma-ray emissions through pion decay. We incorporated advanced modeling and multi-messenger observations to explore the role of CME-driven shocks in gamma-ray emissions and SEPs. Motivated by Fermi-LAT long-duration solar flares, we used the AWSoM MHD model to investigate the connection between the shocks and the properties of observed gamma-ray emissions. By coupling the AWSoM with iPATH model, we evaluate the impact of shock evolution complexity near the Sun on SEP intensity and spectra. Our result points to the importance of accurate background coronal and solar wind modeling, as well as detailed observations of CME source regions, in advancing our understanding of CME-driven shocks and the dynamics of associated energetic particles.

astro-ph.SR↗

arXiv2024

Superdiffusion of energetic particles at shocks: A Lévy Flight model for acceleration

In the Heliosphere, power-law particle distributions are observed e.g. upstream of interplanetary shocks, which can result from superdiffusive transport. This non-Gaussian transport regime may result from intermittent magnetic field structures. Recently, we showed that a Lévy flight model reproduces the observed features at shocks: power-law distributions upstream and enhanced intensities at the shock. We extend the Lévy flight model to study the impact of superdiffusive transport on particle acceleration at shocks. The acceleration time scale and spectral slope are compared to Gaussian diffusion and a Lévy walk model. The fractional transport equation is solved by sampling the number density with the corresponding stochastic differential equation that is driven by an alpha-stable Lévy distribution. For both Gaussian and superdiffusive transport we use a modified version of CRPropa 3.2. We obtain the number density and energy spectra for constant and energy-dependent anomalous diffusion and find, compared to the case of Gaussian diffusion, harder energy spectra at the shock as well as faster acceleration. The spectral slope is even harder than predicted for Lévy walks. Lévy flight models of superdiffusive transport lead to observed features in the Heliosphere. We further show that superdiffusive transport impacts the acceleration process by changing the probability to escape the shock. The flexibility of the Lévy flight model allows for further studies in the future, taking the shock geometry and magnetic field structure into account.

astro-ph.HE↗

arXiv2024

Towards Synthetic Magnetic Turbulence with Coherent Structures

Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic turbulence. We present a novel method, featuring coherent structures, conditional structure function scaling and fieldline curvature statistics comparable to magnetohydrodynamic turbulence. Enhanced transport of charged particles is investigated as well. This method presents significant progress towards physically faithful synthetic turbulence.

physics.space-ph↗

arXiv2023

Numerical Modeling of Time Dependent Diffusive Shock Acceleration

Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use the stochastic differential equation solver (DiffusionSDE) of the cosmic ray propagation framework CRPropa3.2 with two modifications: An importance sampling module is introduced to improve statistics at high energies in order to keep the simulation time short. An adaptive time step is implemented in the DiffusionSDE module. This ensures to efficiently meet constraints on the time and diffusion step, which is crucial to obtain the correct shock spectra. The time evolution of the spectrum at a one-dimensional planar shock is verified against the solution obtained by the grid-based solver VLUGR3 for both energy-independent and energy-dependent diffusion. We show that the injection of pre-accelerated particles can lead to a broken power law spectrum in momentum if the incoming spectrum of CRs is harder than the re-accelerated spectrum. If the injected spectrum is steeper, the shock spectrum dominates at all energies. We finally apply the developed model to the GWTS by considering a spherically symmetric shock, a spiral Galactic magnetic field, and anisotropic diffusion. The time-dependent spectrum at the shock is modeled as a basis for further studies.

astro-ph.HE↗

arXiv2023

Synergies between interstellar dust and heliospheric science with an Interstellar Probe

We discuss the synergies between heliospheric and dust science, the open science questions, the technological endeavors and programmatic aspects that are important to maintain or develop in the decade to come. In particular, we illustrate how we can use interstellar dust in the solar system as a tracer for the (dynamic) heliosphere properties, and emphasize the fairly unexplored, but potentially important science question of the role of cosmic dust in heliospheric and astrospheric physics. We show that an Interstellar Probe mission with a dedicated dust suite would bring unprecedented advances to interstellar dust research, and can also contribute-through measuring dust - to heliospheric science. This can, in particular, be done well if we work in synergy with other missions inside the solar system, thereby using multiple vantage points in space to measure the dust as it `rolls' into the heliosphere. Such synergies between missions inside the solar system and far out are crucial for disentangling the spatially and temporally varying dust flow. Finally, we highlight the relevant instrumentation and its suitability for contributing to finding answers to the research questions.

astro-ph.IM↗

arXiv2023

A Comparative Study on Generative Models for High Resolution Solar Observation Imaging

Solar activity is one of the main drivers of variability in our solar system and the key source of space weather phenomena that affect Earth and near Earth space. The extensive record of high resolution extreme ultraviolet (EUV) observations from the Solar Dynamics Observatory (SDO) offers an unprecedented, very large dataset of solar images. In this work, we make use of this comprehensive dataset to investigate capabilities of current state-of-the-art generative models to accurately capture the data distribution behind the observed solar activity states. Starting from StyleGAN-based methods, we uncover severe deficits of this model family in handling fine-scale details of solar images when training on high resolution samples, contrary to training on natural face images. When switching to the diffusion based generative model family, we observe strong improvements of fine-scale detail generation. For the GAN family, we are able to achieve similar improvements in fine-scale generation when turning to ProjectedGANs, which uses multi-scale discriminators with a pre-trained frozen feature extractor. We conduct ablation studies to clarify mechanisms responsible for proper fine-scale handling. Using distributed training on supercomputers, we are able to train generative models for up to 1024x1024 resolution that produce high quality samples indistinguishable to human experts, as suggested by the evaluation we conduct. We make all code, models and workflows used in this study publicly available at \url{https://github.com/SLAMPAI/generative-models-for-highres-solar-images}.

cs.CV↗

arXiv2019

Statistical results for solar energetic electron spectra observed over 12 years with STEREO/SEPT

We present a statistical analysis of near-relativistic (NR) solar energetic electron event spectra near 1au. We use measurements of the STEREO Solar Electron and Proton Telescope (SEPT) in the energyrange of 45-425 keV and utilize the SEPT electron event list containing all electron events observed bySTEREO A and STEREO B from 2007 through 2018. We select 781 events with significant signal tonoise ratios for our analysis and fit the spectra with single or broken power law functions of energy.We find 437 (344) events showing broken (single) power laws in the energy range of SEPT. The eventswith broken power laws show a mean break energy of about 120 keV. We analyze the dependence ofthe spectral index on the rise times and peak intensities of the events as well as on the presence ofrelativistic electrons. The results show a relation between the power law spectral index and the risetimes of the events with softer spectra belonging to rather impulsive events. Long rise-time events areassociated with hard spectra as well as with the presence of higher energy (>0.7 MeV) electrons. Thisgroup of events cannot be explained by a pure flare scenario but suggests an additional accelerationmechanism, involving a prolonged acceleration and/or injection of the particles. A dependence of thespectral index on the longitudinal separation from the parent solar source region was not found. Astatistical analysis of the spectral indices during impulsively rising events (rise times<20 minutes) isalso shown.

astro-ph.SR↗

arXiv2019

Statistical analysis of interplanetary magnetic field path lengths from solar energetic electron events observed by WIND

We calculate the interplanetary magnetic field path lengths traveled by electrons in solar electron events detected by the WIND 3DP instrument from $1994$ to $2016$. The velocity dispersion analysis method is applied for electrons at energies of $\sim$ $27$ keV to $310$ keV. Previous velocity dispersion analyses employ the onset times, which are often affected by instrumental effects and the pre-existing background flux, leading to large uncertainties. We propose a new method here. Instead of using the peak or onset time, we apply the velocity dispersion analysis to the times that correspond to the rising phase of the fluxes that are a fraction, $η$, of the peak flux. We perform statistical analysis on selected events whose calculated path lengths have uncertainties smaller than $0.1$ AU. The mean and standard deviation, ($μ$, $σ$), of the calculated path lengths corresponding to $η=$ $3/4$, $1/2$, and $1/3$ of the peak flux is ($1.17$ AU, $0.17$ AU), ($1.11$ AU, $0.14$ AU), and ($1.06$ AU, $0.15$ AU). The distribution of the calculated path lengths is also well fitted by a Gaussian distribution for the $η=3/4$ and $1/3$ cases. These results suggest that in these electron events the interplanetary magnetic field topology is close to the nominal Parker spiral with little field line meandering. Our results have important implications for particles' perpendicular diffusion.

astro-ph.SR↗

arXiv2018

The Relation Between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares

A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the acceleration and transport mechanisms at work. This paper addresses this general problem, in particular in solar flares, where in addition to scattering by turbulence, the magnetic field convergence from the acceleration region towards its boundaries also influences the particle escape. We test an (approximate) analytic relation between escape and scattering times, and the field convergence rate, based on the work of Malyshkin and Kulsrud (2001), valid for both strong and weak diffusion limits and isotropic pitch angle distribution of the injected particles, with a numerical model of particle transport. To this end, a kinetic Fokker-Planck transport model of particles is solved with a stochastic differential equation scheme assuming different initial pitch angle distributions. This approach enables further insights into the phase-space dynamics of the transport process, which would otherwise not be accessible. We find that in general the numerical results agree well with the analytic equation for the isotropic case, however, there are significant differences weak diffusion regime for non-isotopic cases, especially for distributions beamed along the magnetic field lines. The results are important in the interpretation of observations of energetic particles in solar flares, and other similar space and astrophysical acceleration sites and for the determination of acceleration-transport coefficients, commonly used in Fokker-Planck type kinetic equations.

astro-ph.HE↗

arXiv2018

Probing the Puzzle of Behind-the-Limb $γ$-ray Flares: Data-driven Simulations of Magnetic Connectivity and CME-driven Shock Evolution

Recent detections of high-energy $γ$-rays from behind-the-limb (BTL) solar flares by the \emph{Fermi $γ$-ray Space Telescope} pose a puzzle and challenge on the particle acceleration and transport mechanisms. In such events, the $γ$-ray emission region is located away from the BTL flare site by up to tens of degrees in heliogrpahic longitude. It is thus hypothesized that particles are accelerated at the shock driven by the coronal mass ejection (CME) and then travel from the shock downstream back to the front side of the Sun to produce the observed $γ$-rays. To test this scenario, we performed data-driven, global magnetohydrodynamics simulations of the CME associated with a well-observed BTL flare on 2014 September 1. We found that part of the CME-driven shock develops magnetic connectivity with the $γ$-ray emission region, facilitating transport of particles back to the Sun. Moreover, the observed increase in $γ$-ray flux is temporally correlated with (1) the increase of the shock compression ratio and (2) the presence of a quasi-perpendicular shock over the area that is magnetically connected to the $γ$-ray emitting region, both conditions favoring the diffusive shock acceleration (DSA) of particles. These results support the above hypothesis and can help resolve another puzzle, i.e., long-duration (up to 20 hours) $γ$-rays flares. We suggest that, in addition to DSA, stochastic acceleration by plasma turbulence may also play a role, especially in the shock downstream region and during the early stage when the shock Alfvén Mach number is small.

astro-ph.SR↗

arXiv2017

A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

astro-ph.HE↗

arXiv2016

Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles

Flares close to the solar limb, where the footpoints are occulted, can reveal the spectrum and structure of the coronal loop-top source in X-rays. We aim at studying the properties of the corresponding energetic electrons near their acceleration site, without footpoint contamination. To this end, a statistical study of partially occulted flares observed with RHESSI is presented here, covering a large part of solar cycles 23 and 24. We perform a detailed spectra, imaging and light curve analysis for 116 flares and include contextual observations from SDO and STEREO when available, providing further insights into flare emission that was previously not accessible. We find that most spectra are fitted well with a thermal component plus a broken power-law, non-thermal component. A thin-target kappa distribution model gives satisfactory fits after the addition of a thermal component. X-rays imaging reveals small spatial separation between the thermal and non-thermal components, except for a few flares with a richer coronal source structure. A comprehensive light curve analysis shows a very good correlation between the derivative of the soft X-ray flux (from GOES) and the hard X-rays for a substantial number of flares, indicative of the Neupert effect. The results confirm that non-thermal particles are accelerated in the corona and estimated timescales support the validity of a thin-target scenario with similar magnitudes of thermal and non-thermal energy fluxes.

astro-ph.SR↗

arXiv2016

Hard X-ray morphology of the X1.3 April 25, 2014 partially occulted limb solar flare

At hard X-ray energies, the bright footpoint emission from solar flare loops often prevents a detailed analysis of the weaker loop-top source morphology due to the limited dynamic range available for X-ray imaging. Here, we study the X1.3 April 25, 2014 flare with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). This partially occulted limb flare allows the analysis of the loop-top emission in isolation. We present results on the flare light curve at different energies, the source morphology from X-ray imaging and a detailed spectral analysis of the different source components by imaging spectroscopy. The loop-top source, a likely site of particle acceleration, shows a clear composition of different emission components. The results indicate the opportunities that detailed imaging of hard X-rays can provide to learn about particle acceleration, transport and heating processes in solar flares.

astro-ph.SR↗

arXiv2016

Simulations of 3D Magnetic Merging: Resistive Scalings for Null Point and QSL Reconnection

Starting from an exact, steady-state, force-free solution of the magnetohydrodynamic (MHD) equations, we investigate how resistive current layers are induced by perturbing line-tied three-dimensional magnetic equilibria. This is achieved by the superposition of a weak perturbation field in the domain, in contrast to studies where the boundary is driven by slow motions, like those present in photospheric active regions. Our aim is to quantify how the current structures are altered by the contribution of so called quasi-separatrix layers (QSLs) as the null point is shifted outside the computational domain. Previous studies based on magneto-frictional relaxation have indicated that, despite the severe field line gradients of the QSL, the presence of a null is vital in maintaining fast reconnection. Here, we explore this notion using highly resolved simulations of the full MHD evolution. We show that for the null-point configuration, the resistive scaling of the peak current density is close to $J\simη^{-1}$, while the scaling is much weaker, i.e. $J\simη^{-0.4}$, when only the QSL connectivity gradients provide a site for the current accumulation.

astro-ph.SR↗

arXiv2015

Parameter estimation of superdiffusive motion of energetic particles upstream of heliospheric shocks

In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. In particular, a new analysis technique has permitted the study of particle transport properties from energetic particle time profiles upstream of interplanetary shocks. Indeed, the time/spatial power laws of the differential intensity upstream of several shocks are indicative of superdiffusion. A complete determination of the key parameters of superdiffusive transport comprises the power-law index, the superdiffusion coefficient, the related transition scale at which the energetic particle profiles turn to decay as power laws, and the energy spectral index of the shock accelerated particles. Assuming large-scale spatial homogeneity of the background plasma, the power-law behaviour can been derived from both a (microscopic) propagator formalism and a (macroscopic) fractional transport equation. We compare the two approaches and find a relation between the diffusion coefficients used in the two formalisms. Based on the assumption of superdiffusive transport, we quantitatively derive these parameters by studying energetic particle profiles observed by the Ulysses and Voyager 2 spacecraft upstream of shocks in the heliosphere, for which a superdiffusive particle transport has previously been observed. Further, we have jointly studied the electron energy spectra, comparing the values of the spectral indices observed with those predicted by the standard diffusive shock acceleration theory and by a model based on superdiffusive transport. For a number of interplanetary shocks and for the solar wind termination shock, for the first time we obtain the anomalous diffusion constants and the scale at which the probability of particle free paths changes to a power-law...

astro-ph.SR↗