Simulating cosmic ray physics on a moving mesh

Context. Supernova remnants are known to accelerate cosmic rays on account of their nonthermal emission of radio waves, X-rays, and gamma rays. Although there are many models for the acceleration of cosmic rays in supernova remnants, the escape of cosmic rays from these sources has not yet been adequately studied. Aims. We aim to use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 100 000 years, thus covering the free-expansion, the Sedov–Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. Results. At later stages of the evolution, cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration, and feature breaks in the 10 − 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. We further find the gamma-ray luminosity to peak around an age of 4000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media generally emit more inverse-Compton radiation, matching the fact that the brightest known supernova remnants – RCW86, Vela Jr., HESS J1731−347 and RX J1713.7−3946 – are all expanding in low density environments.

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies , regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

Introduction. High-energy processes in the interstellar medium (ISM) of our Galaxy are accompanied by the acceleration of a small fraction of nuclei and electrons to ultra-relativistic velocities. Accelerated particles – cosmic rays – generate non-thermal radiation. In particular, electrons – synchrotron and inverse Compton radiation (leptonic mechanism), protons and heavier nuclei – high-energy gamma-ray emission as a result of inelastic collisions with ISM atoms, in which, in particular, pions are born and quickly decay into two gamma-photons (hadronic mechanism). Supernova remnants and pulsar-wind nebulae are potential accelerators of Galactic cosmic rays. The work simulates the gamma-ray emission of the unidentified extended gamma-ray source 4FGL J1908.6+0915e within the framework of hadronic and leptonic mechanisms working in the Supernova remnants G42.8+0.6, G043.023+0.762, G043.070+0.558 and their pulsar-wind nebulae, which positionally coincide with the source 4FGL J1908.6+0915e on the sky map. Methods. In order to model the non-thermal radiation (from the radio to the gamma-ray range) of the source 4FGL J1908.6+0915e, the observed spectrum of gamma-ray emission obtained by space-based (Fermi-LAT) and ground-based (H.E.S.S., HAWC) gamma-ray telescopes was approximated by a power-law with exponential cut-off. The NAIMA software code (Zabalza, 2016) was used for calculation the model spectra. The characteristics of potential sources of gamma-ray emission – of the Supernova remnants G42.8+0.6, G043.023+0.762 and G043.070+0.558 – were determined from the correspondence of the model spectra to the approximation of the observed spectrum. Results. It is shown that the observed gamma-ray spectral flux of the source 4FGL J1908.6+0915e can be provided by each of the Supernova remnants G42.8+0.6, G043.023+0.762 and G043.070+0.558 or as a sum of their contributions. At the same time, due to the relative proximity of these remnants to the Earth (3-5 kpc), the required energy of the explosion of these Supernovae corresponds to the typical energy of Galactic Supernovae – about 1051 ergs. Conclusions The unidentified extended source 4FGL J1908.6+0915e coincides in the sky position with the the magnetar SGR1900+14. In the work of Hnatyk et al. (2022) it is shown that it can be a manifestation of a Supernova remnant or a magnetar-wind nebula associated with a magnetar. But the necessary energies of the Supernova associated with the birth of the magnetar turn out to be extremely large – on the order of 1052 ergs due to the large distance to the magnetar – about 12.5 kpc. Such Supernovae – they are called Hypernovae – are rare phenomena in the Galaxy. In this paper, we have shown that other Supernova remnants G42.8+0.6, G043.023+0.762 and G043.070+0.558, which also coincide with the source 4FGL J1908.6+0915e on the sky map, but are at closer distances – 3-5 kpc – can provide the observed spectral flux already at typical energies of Supernova remnants – about 1051 ergs.

In this paper we present a new five particle species hybrid model for calculating cosmic ray particle transport and acceleration in a dynamic heliospheric environment. In particular the effects of solar cycle related changes in the solar wind speed on the heliospheric geometry, solar wind flow and cosmic ray distribution are discussed, when a polar- ecliptic asymmetry at the inner boundary is modeled. It is shown that the disappearance of the fast solar wind over the solar poles toward solar maximum influences the geometry of the termination shock which is an important structure for cosmic ray acceleration. For solar maximum conditions, the shock radius is smaller in the polar regions and in the he- liospheric tail compared to solar minimum. These changes influence cosmic ray transport and acceleration in these re- gions, especially for the polarity cycle where positive parti- cles drift in along the heliospheric current sheet. For this po- larity cycle, and for both the anomalous and galactic cosmic ray protons, an increase in particle intensities at the shock in the heliospheric tail is computed as the shock moves in- ward toward the Sun. For the heliospheric nose, it is also shown that both the plasma speed and cosmic ray intensities are relative insensitive to changes in the latitudinal profile of the solar wind speed. Therefore toward solar maximum conditions there is a decrease in the nose-tail asymmetry of the computed cosmic ray distribution compared to solar min- imum conditions. shock fronts, the inner, the termination shock of the solar wind, and the outer, the bowshock of the interstellar ionized matter. The interstellar wind is a consequence of the rela- tive motion between the solar system and the local interstel- lar medium, while the inner solar wind results from the solar coronal outflow with asymptotically supersonic velocities. In the interface region between the two shocks a contact discon- tinuity forms, the heliopause, which separates both media by a surface which cannot penetrated by the plasmas.

RX J1713.7–3946 is a unique supernova remnant (SNR) emitting very high energy \(\gamma \)-rays and X-rays, which are likely emitted by cosmic ray particles accelerated in the SNR via diffusive shock acceleration. It has been suggested that the SNR’s shockwave interacts with the dense gas clumps around the SNR, affecting the synchrotron X-ray radiation and cosmic ray acceleration. However, to date, there has not been a quantitative study to clarify the connection among the X-rays, gas clumps, and accelerated cosmic ray electrons. In this Chapter, we show a strong connection between synchrotron X-rays and the surrounding gas distribution by comparing the spatial distribution among CO, HI, and X-rays over the entire SNR. The present work is aimed at better understanding the SNR shock interstellar gas interaction and thereby establishing the origin of the distribution of the synchrotron X-rays in the SNR RX J1713.7–3946.

It is proposed that the acceleration of cosmic rays is distributed over their propagation through interstellar space. Thus after most nuclear fragmentation reactions in the interstellar medium, cosmic rays gain about a factor of 5 in energy. This hypothesis resolves several discrepancies in composition at different energies. The present results suggest that after the principal acceleration and during their galactic confinement, cosmic rays are further accelerated by the weak shocks of widely distributed old supernova remnants.

The cosmic stories : beginning, evolution, and present days of the universe

When a star dies, it leaves a mark on its surrounding environment. The energy from the supernova explosion forms an expanding shock wave that interacts with interstellar and circumstellar material, creating what we know as a supernova remnant (SNR). If the original star has a mass that is greater than or equal to 8 solar masses, this can also lead to the formation of a rapidly rotating neutron star called a pulsar. As these objects evolve, they interact with the surrounding environment, producing non-thermal and thermal emission. For an SNR, its non-thermal emission arises from a population of relativistic particles being accelerated at the shock front of the SNR, while its thermal emission arises from the shock front heating ejecta and and swept-up interstellar medium to X-ray emitting temperatures. For pulsars, their non-thermal emission arises from relativistic particles being accelerated at the termination shock of a pulsar wind. These particles interact with surrounding magnetic fields and ambient photon fields producing synchrotron and inverse Compton emission which we observe as a pulsar wind nebula (PWN), while its thermal emission arises from the surface of the neutron star. These properties of SNRs and pulsars provide a unique window into studying the acceleration, injection, propagation and interaction of highly energetic particles called cosmic rays with the interstellar medium. In addition, they providing information about the evolution, and dynamics of these objects; properties of the shock fronts; details about the original progenitor star; and the impact that these objects have on their surroundings. The research presented here focuses on analysing the intimate connection between cosmic rays, the non-thermal emission arising from SNRs interacting with molecular clouds, and pulsar wind nebulae; as well as analysing the observational and evolutionary properties of these objects. In this thesis we model the propagation of cosmic rays through the Galaxy in an attempt to characterise a standard cosmic ray background with uncertainties, to reveal the origin of the cosmic ray electron positron anomaly. Furthermore, we analyse the gamma-ray emission from SNRs Kes 79 and MSH 11-61A, which are known to be interacting with molecular clouds, as well as the non-thermal X-ray emission arising from the PWN of PSR J1741-2054. We find that the emission from both SNRs most likely arises from the decay of neutral pions that resulted from the interaction of relativistic ions which are accelerated at the shock-front of a SNR, with ambient material. For PSR J1741-2054, we characterise the properties, minimum magnetic field and minimum energy of the particle population that produces the observed diffuse synchrotron emission that surrounds and trails the pulsar. In addition, we characterise the X-ray emission arising from Kes 79, MSH 11-61A and PSR J1741-2054, in an attempt to shed light on the origin and nature of these objects and their emission. Using X-ray data from XMM-Newton and Suzaku respectively, we probe the temperature, ionisation state, and elemental abundance of the shocked gas of each SNR. This allows us to determine their evolutionary properties, properties of the shock, and mass of the original progenitor; and constrain the density of the X-ray emitting plasma. Using Chandra, we determined the temperature of PSR J1741-2054, as well as characterised its proper motion, velocity, direction of motion, and presence of small scale structure immediately surrounding the pulsar.

Gamma-ray signatures of cosmic ray acceleration, propagation, and confinement in the era of CTA

CONTEXT: Supernova Remnants (SNRs) are considered as the primary sources of galactic cosmic rays (CRs), where CRs are assumed to be accelerated by diffusive shock acceleration (DSA) mechanism. The SNR shocks expand in the complex ambient environment, particularly in the core-collapse scenarios as those SNRs evolve inside wind-blown bubbles created by the mass-loss of massive stars. Therefore, the evolution of core-collapse SNRs, as well as CRs acceleration is expected to be considerably different from SNR evolution in a uniform environment. AIM: The aim is to observe the influence of different ambient medium of core-collapse SNR shock on the particle spectra. Furthermore, the interactions of SNR shock with fluctuations in density within the wind-blown bubble generate several transmitted and reflected shocks. So, the impact of SNR shock interactions with different discontinuities, on particle spectra, and finally the effect on emission from the remnant are also the areas of focus. Methods. The hydrodynamic structures of wind-blown bubbles at pre-supernova stages formed by $20M_{\odot}$, $35M_{\odot}$, and $60M_{\odot}$ stars have been used to create the ambient environment for SNRs. Evolution of those stars through different stages from Zero Age Main Sequence (ZAMS) to the pre-supernova stage, results into formation of structurally different wind bubbles. Then, the transport equation for cosmic rays, and hydrodynamic equations have been solved simultaneously in 1-D spherical symmetry. RESULT: The modifications in particle spectra depend on the hydrodynamics and magnetic field structure of SNR ambient medium. We have obtained softer spectra with spectra index close to 2.5 originated during SNR interaction with hot wind bubble and further, magnetic field structure effectively influences the emission morphology of SNR as it governs the transportation of particles.

A model of cosmic ray propagation is proposed to explain the knee of the cosmic ray energy spectrum in the energy range E ∼ 10 14 −10 17 eV. The numerous stellar winds (SW), ionized hydrogen regions (H-II) and supernova remnants (SNR) in the Galaxy are taken into account in this model. The gas density and the magnetic field in these regions are different from the interstellar gas density and the interstellar magnetic field. Therefore they act as scattering centres and magnetic traps for cosmic rays. It is shown that these regions influence cosmic ray propagation in the Galaxy. Our results show that the collision time between cosmic rays and the SNR, SW, and H-II regions is much less than the cosmic ray lifetime in standard models (Berezinskii et al. 1984; Ginzburg & Syrovatskii 1963), in which only the nuclear interaction of the particles with interstellar gas is taken into account. Cosmic ray energies, and thus the cosmic ray spectrum, change due to interactions with these regions. Cosmic ray energy losses in these regions due to adiabatic cooling are comparable to the losses due to nuclear interaction with interstellar gas. It is therefore necessary to take these into account in galactic cosmic ray propagation models.

It is largely accepted that Galactic cosmic rays, which pervade the interstellar medium, originate by means of shock waves in supernova remnants. Cosmic rays activate the rich chemistry that is observed in a molecular cloud and they also regulate its collapse timescale, determining the efficiency of star and planet formation, but they cannot penetrate up to the densest part of a molecular cloud, where the formation of stars is expected, because of energy loss processes and magnetic field deflections. Recently, observations towards young protostellar systems showed a surprisingly high value of the ionisation rate, the main indicator of the presence of cosmic rays in molecular cloud. Synchrotron emission, the typical feature of relativistic electrons, has been also detected towards the bow shock of a T Tauri star. Nevertheless, the origin of these signatures peculiar to accelerated particles is still puzzling. Here we show that particle acceleration can be driven by shock waves occurring in protostars through the diffusive shock acceleration mechanism. We find that shocks in protostellar jets and on the protostellar surface can be strong accelerators of thermal particles, which can be easily boosted up to relativistic energies. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as the argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact over the stellar and planet formation process as well as on the formation of pre-biotic molecules. Finally, I will discuss the challenges for current and future telescopes such as ALMA, SKA, and CTA.

There are cosmic rays in the current universe. They play various important roles in the current universe. However, we do not understand when, where, how cosmic rays are first accelerated since the Big Bang. We show that supernova remnants of first stars can accelerate the first cosmic rays at z~20. Shock waves of the first supernova remnants are nonrelativistic Weibel mediated shock, so that the coherent length scale of magnetic field fluctuations is much smaller than the gyroradius of the accelerated particles. Therefore, the maximum energy of the first CRs becomes much smaller than that in the current universe, which is about 100 MeV. Furthermore, we discuss cosmic-ray acceleration by accretion shocks due to the cosmological structure formation at z~20. Since the accretion shocks at z~20 propagate not an ionized medium but a neutral medium, they cannot accelerate the first cosmic rays.

The hypothesis that supernova remnants are key sources of Galactic cosmic rays gains support from evidence that HESS J1731-347 one of the few Galactic objects capable of accelerating hadronic cosmic rays to TeV energies may harbor an exotic strange quark star rather than a conventional neutron star. This conclusion stems from its unusually low mass and compact radius, which challenge standard neutron star models. If confirmed, such a quark star could generate cosmic rays through the transition from the two-flavor color-superconducting (2SC) phase to the color-flavor-locked (CFL) phase, potentially releasing strangelets, hypothetical strange quark matter (SQM) particles. Detecting these strangelets in cosmic rays would provide groundbreaking evidence for quark matter. The future Cherenkov Telescope Array (CTA), with its unmatched sensitivity and spectral resolution in the very-high-energy (VHE) gamma-ray regime, is uniquely positioned to search for their annihilation or decay signatures. We analyze theoretical predictions for these gamma-ray signals and evaluate CTA’s potential to detect or constrain them. Additionally, we present an in-depth assessment of CTA observations of HESS J1731-347, focusing on spectral features that could confirm strangelet production. A positive detection would not only validate the existence of strange quark stars but also establish a direct link between quark matter and cosmic-ray acceleration, reshaping our understanding of compact objects and high-energy astrophysics.

The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.