Shock Acceleration Model Research Articles

Investigating the Properties of the Relativistic Jet and Hot Corona in AGN with X-ray Polarimetry

X-ray polarimetry has been suggested as a prominent tool for investigating the geometrical and physical properties of the emissions from active galactic nuclei (AGN). The successful launch of the Imaging X-ray Polarimetry Explorer (IXPE) on 9 December 2021 has expanded the previously restricted scope of polarimetry into the X-ray domain, enabling X-ray polarimetric studies of AGN. Over a span of two years, IXPE has observed various AGN populations, including blazars and radio-quiet AGN. In this paper, we summarize the remarkable discoveries achieved thanks to the opening of the new window of X-ray polarimetry of AGN through IXPE observations. We will delve into two primary areas of interest: first, the magnetic field geometry and particle acceleration mechanisms in the jets of radio-loud AGN, such as blazars, where the relativistic acceleration process dominates the spectral energy distribution; and second, the geometry of the hot corona in radio-quiet AGN. Thus far, the IXPE results from blazars favor the energy-stratified shock acceleration model, and they provide evidence of helical magnetic fields inside the jet. Concerning the corona geometry, the IXPE results are consistent with a disk-originated slab-like or wedge-like shape, as could result from Comptonization around the accretion disk.

Likely Common Coronal Source of Solar Wind and 3He-enriched Energetic Particles: Uncoupled Transport from the Low Corona to 0.2 au

Parker Solar Probe (PSP) observations of a small dispersive event on 2022 February 27 and 28 indicate scatter-free propagation as the dominant transport mechanism between the low corona and greater than 35 solar radii. The event occurred during unique orbital conditions that prevailed along specific flux tubes that PSP encountered repeatedly between 25 and 35 Rs during outbound orbit 11. This segment of the PSP orbit exhibits almost stationary angular motion relative to the rotating solar surface, such that in the rotating frame, PSP’s motion is essentially radial. The time dispersion often observed in impulsive solar energetic particle (SEP) events continues in this case down to velocities including the core solar-wind ion velocities. Especially at the onset of this event, the 3He content is much larger than the usual SEP abundances seen in the energy range from ∼100 keV to several MeV for helium. Later in the event, iron is enhanced. The compositional signatures suggest this to be an example of an acceleration mechanism for generating the seed energetic particles required by shock (or compression) acceleration models in SEP events to account for the enrichment of various species above solar abundances in such events. A preliminary search of similar orbital conditions over the PSP mission has not revealed additional such events, although favorable conditions (isolated impulsive acceleration and well-ordered magnetic field connection with minimal magnetic field fluctuation) that would be required are infrequently realized, given the small fraction of the PSP trajectory that meets these observation conditions.

A Small-scale Structure Model of a Jet Based on Observations of Microvariability

We developed a multiregion radiation model for the evolution of flux and spectral index with time. In this model, each perturbation component in the jet produces an independent flare. The model can be used to study the decomposition of microvariability, the structural scale of the perturbed components, and the physical parameters of the acceleration processes. Based on the shock acceleration model for a relativistic jet, the influence of the acceleration parameters on multiband flare parameters is calculated. We present the results of multiband optical microvariability of the blazar BL Lacertae observed during 89 nights in the period from 2009 to 2021, and use them as a sample for model fitting. The results show that both the amplitude and duration of flares decomposed from the microvariability light curves conform to a log-normal distribution. The time delays between the optical bands follow a normal distribution and amount to several minutes, which corroborate with both predictions from the theoretical model and the calculation of the discrete correlation function. Using the spectral index evolution and the simultaneous fitting of the multiband variability curves, we obtain the acceleration and radiation parameters to constrain and distinguish the origins of different flares. Based on the flare decomposition, we can effectively reproduce the time-domain evolution trends of the optical variations and energy spectrum, and explain the various redder-when-brighter and bluer-when-brighter behaviors.

Energetic Neutral Atoms from Solar Energetic Particles due to Shocks: Inclusion of Upstream Particles

Many aspects of solar energetic particles are not well understood, including their acceleration mechanism. There has been recent interest in the potential of energetic neutral atoms (ENAs) as remote probes of solar energetic particles (SEPs) and their acceleration. The single accidental observation (in physical units) has been modeled as accelerated by a coronal mass ejection (CME)-driven shock by several authors, all of whom have assumed that the upstream component of the shock can be ignored. In this article, we relax this assumption and model the flux of ENAs at 1 au due to a CME-driven shock with an upstream component. We show the effect of varying parameters of the shock acceleration model, specifically α, the exponent of the power law in momentum of the mean free path, and η, a measure of the relative turbulence level. The main result is that including the upstream component significantly increases the flux at 1 au for typically assumed parameters in the energy range of the STEREO observation. We also derive the form of the ENA transport equation that we used in this study. These results enable a better understanding of potential observations of ENAs due to SEPs.

Insights on the Origin of Odd Radio Circles from Cosmological Simulations

We investigate shock structures driven by merger events in high-resolution simulations that result in a galaxy with a virial mass M ≈ 1012 M ⊙. We find that the sizes and morphologies of the internal shocks resemble remarkably well those of the newly detected class of odd radio circles (ORCs). This would highlight a so-far overlooked mechanism to form radio rings, shells, and even more complex structures around elliptical galaxies. Mach numbers of = 2–3 for such internal shocks are in agreement with the spectral indices of the observed ORCs. We estimate that ∼5% of galaxies could undergo merger events, which occasionally lead to such prominent structures within the galactic halo during their lifetime, explaining the low number of observed ORCs. At the time when the shock structures are matching the physical sizes of the observed ORCs, the central galaxies are typically classified as early-type galaxies, with no ongoing star formation, in agreement with observational findings. Although the energy released by such mergers could potentially power the observed radio luminosity already in Milky Way–like halos, our predicted luminosity from a simple, direct shock acceleration model is much smaller than the observed one. Considering the estimated number of candidates from our cosmological simulations and the higher observed energies, we suggest that the proposed scenario is more likely for halo masses around 1013 M ⊙ in agreement with the observed stellar masses of the galaxies at the center of ORCs. Such shocks might be detectable with next-generation X-ray instruments like the Line Emission Mapper (LEM).

Flaring activity from magnetic reconnection in BL Lacertae

ABSTRACT The evolution of the spectral energy distribution during flares constrains models of particle acceleration in blazar jets. The archetypical blazar BL Lacertae provided a unique opportunity to study spectral variations during an extended strong flaring episode from 2020 to 2021. During its brightest γ-ray state, the observed flux (0.1–300 GeV) reached up to $2.15\, \times \, 10^{-5}\, \rm {ph\, cm^{-2}\, s^{-1}}$, with sub-hour-scale variability. The synchrotron hump extended into the X-ray regime showing a minute-scale flare with an associated peak shift of inverse-Compton hump in γ-rays. In shock acceleration models, a high Doppler factor value >100 is required to explain the observed rapid variability, change of state, and γ-ray peak shift. Assuming particle acceleration in minijets produced by magnetic reconnection during flares, on the other hand, alleviates the constraint on required bulk Doppler factor. In such jet-in-jet models, observed spectral shift to higher energies (towards TeV regime) and simultaneous rapid variability arises from the accidental alignment of a magnetic plasmoid with the direction of the line of sight. We infer a magnetic field of ∼0.6 G in a reconnection region located at the edge of broad-line region (∼0.02 pc). The scenario is further supported by lognormal flux distribution arising from merging of plasmoids in reconnection region.

Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA

This is the second paper in a series of studies of the Coma cluster using the SRG/eROSITA X-ray data obtained during the calibration and performance verification phase of the mission. Here, we focus on the region adjacent to the radio source 1253+275 (radio relic, RR, hereafter). We show that the X-ray surface brightness exhibits its steepest gradient at ∼79′ (∼2.2 Mpc ≈ R200c), which is almost co-spatial to the outer edge of the RR. As in the case of several other relics, the Mach number of the shock derived from the X-ray surface brightness profile (MX ≈ 1.9) appears to be lower than needed to explain the slope of the integrated radio spectrum in the diffusive shock acceleration model (MR ≈ 3.5) if the magnetic field is uniform and the radiative losses are fast. However, the shock geometry is plausibly much more complicated than a spherical wedge centered on the cluster, given the non-trivial correlation between radio, X-ray, and SZ images. While the complicated shock geometry alone might cause a negative bias in MX, we speculate on a few other possibilities that may affect the MX − MR relation, including the shock substructure that might be modified by the presence of non-thermal filaments stretching across the shock and the propagation of relativistic electrons along the non-thermal filaments with a strong magnetic field. We also discuss the “history” of the radio galaxy NGC 4789, which is located ahead of the relic in the context of the Coma-NGC 4839 merger scenario.

Ultra High Energy Cosmic Ray Source Models: Successes, Challenges and General Predictions

Understanding the acceleration of Ultra High Energy Cosmic Rays is one of the great challenges of contemporary astrophysics. In this short review, we summarize the general observational constraints on their composition, spectrum and isotropy which indicate that nuclei heavier than single protons dominate their spectra above ˜ 5 EeV, that they are strongly suppressed above energies ˜ 50 EeV, and that the only significant departure from isotropy is a dipole. Constraints based upon photopion and photodisintegration losses allow their ranges and luminosity density to be estimated. Three general classes of source model are discussed - magnetospheric models (including neutron stars and black holes), jet models (including Gamma Ray Bursts, Active Galactic Nuclei and Tidal Disruption Events) and Diffusive Shock Acceleration models (involving large accretion shocks around rich clusters of galaxies). The value of constructing larger and more capable arrays to measure individual masses at the highest energies and probably identifying their sources is emphasized.

Diffuse radio source candidate in CIZA J1358.9−4750

AbstractWe report on results of our upgraded Giant Metrewave Radio Telescope (uGMRT) observations for an early-stage merging galaxy cluster, CIZA J1358.9−4750 (CIZA1359), in Band-3 (300–500 MHz). We achieved the image dynamic range of ∼38000 using the direction dependent calibration and found a candidate of diffuse radio emission at 4σrms significance. The flux density of the candidate at 400 MHz, 24.04 ± 2.48 mJy, is significantly positive compared to noise, where its radio power, 2.40 × 1024 W Hz−1, is consistent with those of typical diffuse radio sources of galaxy clusters. The candidate is associated with a part of the X-ray shock front at which the Mach number reaches its maximum value of $\mathcal {M}\sim 1.7$. The spectral index (Fν ∝ να) of the candidate, α = −1.22 ± 0.33, is in agreement with an expected value derived from the standard diffusive shock acceleration (DSA) model. However, such a low Mach number with a short acceleration time would require seed cosmic rays supplied from active galactic nucleus (AGN) activities of member galaxies, as suggested in some other clusters. Indeed, we found seven AGN candidates inside the diffuse source candidate. Assuming the energy equipartition between magnetic fields and cosmic rays, the magnetic field strength of the candidate was estimated to be 2.1 μG. We also find head–tail galaxies and radio phoenixes or fossils near CIZA1359.

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 Multi-Event Study of Early-Stage SEP Acceleration by CME-Driven Shocks—Sun to 1 AU

The solar corona between below 10 solar radii is an important region for early acceleration and transport of solar energetic particles (SEPs) by coronal mass ejection-driven shock waves. There, these waves propagate into a highly variable dynamic medium with steep gradients and rapidly expanding coronal magnetic fields, which modulates the particle acceleration near the shock/wave surfaces, and the way SEPs spread into the heliosphere. We present a study modeling the acceleration of SEPs in global coronal shock events in the corona, as well as their transport to 1 au, based on telescopic observations coupled with dynamic physical models. As part of the project Solar Particle Radiation Environment Analysis and Forecasting—Acceleration and Scattering Transport (SPREAdFAST), we model the interaction of observed off-limb coronal bright fronts (CBF) with the coronal plasma from synoptic magnetohydrodynamic (MHD) simulations. We then simulate the SEP acceleration in analytical diffusive shock acceleration (DSA) model. The simulated fluxes are used as time-dependent inner boundary conditions for modeling the particle transport to 1 au. Resulting flux time series are compared with 1 au observations for validation. We summarize our findings and present implications for nowcasting SEP acceleration and heliospheric connectivity.

Discovery of a Double Radio Relic in ZwCl1447.2+2619: A Rare Testbed for Shock-acceleration Models with a Peculiar Surface-brightness Ratio

Abstract We report a discovery of a double radio relic in the cluster merger ZwCl1447.2+2619 (z = 0.376) with uGMRT observations at 420 MHz and 700 MHz. The linear sizes of the northern and southern relics are ∼0.3 Mpc and ∼1.2 Mpc, respectively, which is consistent with the theoretical expectation that a larger relic is produced in the less massive subcluster side. However, ZwCl1447.2+2619 is unlike other known double radio relic systems, where the larger relics are much more luminous by several factors. In this merger, the higher surface brightness of the smaller northern relic makes its total radio luminosity comparable to that of the much larger southern relic. The surface brightness ratio ∼0.1 between the two radio relics differs significantly from the relation observed in other double radio relic systems. From our radio spectral analysis, we find that both relics signify similar weak shocks with Mach numbers of 2.9 ± 0.8 and 2.0 ± 0.7 for the northern and southern relics, respectively. Moreover, the northern relic is connected to a discrete radio source with an optical counterpart, which indicates the possible presence of cosmic-ray injection and reacceleration. Therefore, we propose that this atypical surface brightness ratio can be explained with the particle acceleration efficiency precipitously dropping in the weak shock regime and/or with reacceleration of fossil cosmic rays. Our multi-wavelength analysis and numerical simulation suggest that ZwCl1447.2+2619 is a postmerger, which has experienced a near head-on collision ∼0.7 Gyr ago.

X-Ray Observations of 1ES 1959+650 in Its High-activity State in 2016–2017 with AstroSat and Swift

Abstract We present a comprehensive multifrequency study of the high-frequency-peaked BL Lac object 1ES 1959+650 using data from various facilities during the period 2016–2017, including X-ray data from AstroSat and Swift during the historically high X-ray flux state of the source observed until 2021 February. The unprecedented quality of X-ray data from high-cadence monitoring with AstroSat during 2016–2017 enables us to establish a detailed description of X-ray flares in 1ES 1959+650. The synchrotron peak shifts significantly between different flux states, in a manner consistent with a geometric (changing Doppler factor) interpretation. A time-dependent leptonic diffusive shock acceleration and radiation transfer model is used to reproduce the spectral energy distributions and X-ray light curves, to provide insight into the particle acceleration during the major activity periods observed in 2016 and 2017. The extensive data of Swift-XRT from 2015 December to 2021 February (exp. = 411.3 ks) reveals a positive correlation between flux and peak position.

Acceleration of cosmic rays by double shock waves in galaxy clusters: application to radio relics

Context. Radio relics in galaxy clusters are known to be good laboratories for verification of the applicability of the diffusive shock acceleration (DSA) model in its canonical version. The need for such verification stems from the inconsistencies in the shock properties resulting from radio observations compared to X-ray observations. Aims. In this article we aim to explore how the presence of a second shock in the vicinity of a relic modifies the spectrum of accelerated electrons and decipher which of the involved parameters can have a significant impact on their shape. Methods. We analytically studied DSA of cosmic rays in two stationary shocks aiming to investigate the change of the distribution function. The latter eventually leads to spectrum slope deviations visible in different observations and simulations that do not appear to be explained by the case wherein cosmic rays interact with a single shock wave. Results. We obtain a complex distribution function f(x, p) depending on many parameters (distance between two shocks, compression ratios, spatial diffusion coefficients, injection value, etc.). This function reveals modifications that occur because of the coupled acceleration in both shocks. Apparently, deviations in the particle spectrum from the pure power law depend on a few parameters such as Q1/Q2, κ1/κ2, r1/r2, and L. Although we do not verify this idea by taking a particular cluster as an example, we demonstrate a potential cause of spectral disturbances in radio relics. In general terms, our findings appear to correlate with results from the literature when the distance between the shocks is of the order of the width of a radio relic and κ1/κ2 ∝ 3.

Radial Profiles of Non-thermal Emission from Supernova Remnant RX J1713.7-3946

Abstract Supernova remnant RX J1713.7-3946 has exhibited the largest surface brightness and a detailed spectral and shell-type morphology, and is one of the brightest TeV sources. The recent H.E.S.S. observation of RX J1713.7-3946 revealed a broken power-law GeV–TeV gamma-ray and a more extended gamma-ray spatial radial profile than in the X-ray band. Based on the diffusion shock acceleration model, we solve spherically symmetric hydrodynamic equations and particle transport equations, and investigate the multi-band non-thermal emission of RX J1713.7-3946 and radial profiles of its surface brightness for two selected zones in the leptonic scenario for gamma-ray emission. We found (1) the diffusion coefficient has a weak energy dependence, and the Kolmogorov type is favored; (2) the magnetic field strength can vary linearly or nonlinearly with radius for different surrounding environments because of possible turbulence in the shock downstream region, and compressional amplification is likely to exist at the shock front; (3) the non-thermal photons from radio to X-ray bands are dominated by synchrotron emission from relativistic electrons if the GeV–TeV gamma-rays are produced by inverse Compton scattering from these electrons interacting with the background photons; then the X-ray and gamma-ray radial profiles can be reproduced except for the more extended gamma-ray emission.

An explanation for 13 consecutive day activities of Mrk 421

It is surprising to find an instance of migration in the peak positions of synchrotron spectral energy distribution components during the activity epochs of Markarian 421 (Mrk 421), accompanying an orphan flare at the X-ray and GeV-TeV γ-ray bands. A geometric interpretation and standard shock or stochastic acceleration models of blazar emission have difficulty reproducing these observed behaviors. The present paper introduces a linear acceleration by integrating the reconnection electric field into the particle transport model for the observed behaviors of Mrk 421. We note that strong evidence for evolution in characteristic of multi-wavelength spectral energy distribution including shifting the peak frequency, accompanying an orphan flare at the X-ray and GeV-TeV γ-ray bands provides an important electrostatic acceleration diagnostic in a blazar jet. Assuming suitable model parameters, we apply the results of the simulation to the 13-day flaring event in March 2010 of Mrk 421, concentrating on the evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency. It is clear that the ratio of the electric field and magnetic field strength plays an important role in temporal evolution of the peak frequency of synchrotron spectral energy distribution component. We suggest it is reasonable that the electrostatic acceleration is responsible for the evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency. Based on the model results, we assert that the peak frequency of the synchrotron spectral energy distribution component may signify a temporary characteristic of blazars, rather than a permanent one.

Non-linear diffusive shock acceleration: A recipe for injection of electrons

Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In particle-in-cell simulations of quasi-parallel magnetized collisionless shocks, we analyse the evolution of particle spectra. We find that in the later stages of shock evolution, the initially strong suprathermal part in the ion spectra fades, thus leaving the spectra composed of a Maxwellian and a power law. Once the electron and ion spectra flatten and become parallel, we find that the amounts of cosmic ray ions and electrons become similar. We make the step towards relating the micro and macro-scale physics by applying this injection rule to Blasi’s semi-analytical model of non-linear diffusive shock acceleration, in order to obtain the particle spectra and electron-to-proton ratio Kep at high energies. By using shock jump conditions that include the electron heating, we find Kep as a function of Mach number. For Mach number ∼ 100, our model finely reproduce the typically observed ratio for Galactic cosmic-rays Kep∼ 1:100 in the test particle regime.

The application of the adiabatic compression scenario to the radio relic in the galaxy cluster Abell 3411−3412

ABSTRACT Although radio relics are understood to originate in intracluster shock waves resulting from merger shocks, the most widely used model for describing this (re-)acceleration process at shock fronts, the diffusive shock acceleration (DSA) model, has several challenges, including the fact that it is inefficient at low shock Mach numbers. In light of these challenges, it is worthwhile to consider alternative mechanisms. One possibility is the adiabatic compression by a shock wave of a residual fossil electron population which has been left over from a radio galaxy jet. This paper applies this model to the relic hosted in the merging galaxy cluster Abell 3411−3412, where a radio bridge between the relic and a radio galaxy has been observed, with the aim to reproduce the spatial structure of the spectral index of the relic. Four scenarios are presented, in which different effects are investigated, such as effects behind the shock front and different shock strengths. The results show that the adiabatic compression model can reproduce the observed spectral indices across the relic for a shock Mach number that is lower than the value required by the DSA-type modelling of this relic and is in accordance with the values derived from X-ray observations, if other mechanisms, such as an expansion phase or post-shock turbulence, are effective behind the shock front.

Gamma-Ray and Neutrino Emissions due to Cosmic-Ray Protons Accelerated at Intracluster Shocks in Galaxy Clusters

Abstract We examine the cosmic-ray protons (CRp) accelerated at collisionless shocks in galaxy clusters using cosmological structure formation simulations. We find that in the intracluster medium (ICM) within the virial radius of simulated clusters, only ∼7% of shock kinetic energy flux is dissipated by the shocks that are expected to accelerate CRp—that is, supercritical, quasi-parallel (Q ∥) shocks with sonic Mach number M s ≥ 2.25. The rest is dissipated at subcritical shocks and quasi-perpendicular shocks, both of which may not accelerate CRp. Adopting the diffusive shock acceleration (DSA) model recently presented in Ryu et al., we quantify the DSA of CRp in simulated clusters. The average fraction of the shock kinetic energy transferred to CRp via DSA is assessed at ∼(1–2) × 10−4. We also examine the energization of CRp through reacceleration using a model based on the test-particle solution. Assuming that the ICM plasma passes through shocks three times on average through the history of the universe and that CRp are reaccelerated only at supercritical Q ∥-shocks, the CRp spectrum flattens by ∼0.05–0.1 in slope and the total amount of CRp energy increases by ∼40%–80% from reacceleration. We then estimate diffuse γ-ray and neutrino emissions, resulting from inelastic collisions between CRp and thermal protons. The predicted γ-ray emissions from simulated clusters lie mostly below the upper limits set by Fermi-LAT for observed clusters. The neutrino fluxes toward nearby clusters would be ≲10−4 of the IceCube flux at E ν = 1 PeV and ≲10−6 of the atmospheric neutrino flux in the energy range of E ν ≤ 1 TeV.

Evidence for a Coronal Shock Wave Origin for Relativistic Protons Producing Solar Gamma-Rays and Observed by Neutron Monitors at Earth

Abstract We study the solar eruptive event on 2017 September 10 that produced long-lasting >100 MeV γ-ray emission and a ground level enhancement (GLE72). The origin of the high-energy ions producing late-phase gamma-ray emission (LPGRE) is still an open question, but a possible explanation is proton acceleration at coronal shocks produced by coronal mass ejections. We examine a common shock acceleration origin for both the LPGRE and GLE72. The γ-ray emission observed by the Fermi-Large Area Telescope exhibits a weak impulsive phase, consistent with that observed in hard X-and γ-ray line flare emissions, and what appear to be two distinct stages of LPGRE. From a detailed modeling of the shock wave, we derive the 3D distribution and temporal evolution of the shock parameters, and we examine the shock wave magnetic connection with the visible solar disk. The evolution of shock parameters on field lines returning to the visible disk mirrors the two stages of LPGRE. We find good agreement between the time history of >100 MeV γ-rays and one produced by a basic shock acceleration model. The time history of shock parameters magnetically mapped to Earth agrees with the rates observed by the Fort Smith neutron monitor during the first hour of GLE72 if we include a 30% contribution of flare-accelerated protons during the first 10 minutes, having a release time following the time history of nuclear γ-rays. Our analysis provides compelling evidence for a common shock origin for protons producing the LPGRE and most of the particles observed in GLE72.