The origin of cosmic rays in our Galaxy remains a subject of active debate. While supernova remnant shocks are often invoked as the sites of acceleration, it is now widely accepted that the difficulties of such sources in reaching PeV energies are daunting and it seems likely that only a subclass of rare remnants can satisfy the necessary conditions. Moreover the spectra of cosmic rays escaping the remnants have a complex shape that is not obviously the same as the spectra observed at the Earth. Here we investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters' winds in the interstellar medium. While the main limitation to the maximum energy in supernova remnants comes from the need for effective wave excitation upstream so as to confine particles in the near-shock region and speed up the acceleration process, at the termination shock of star clusters the confinement of particles upstream in guaranteed by the geometry of the problem. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for powerful clusters in the high end of the luminosity tail for these sources. A crucial role in this problem is played by the dissipation of energy in the wind to magnetic perturbations. Under reasonable conditions the spectrum of the accelerated particles has a power law shape with a slope $4÷4.3$, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.
Winds are ubiquitous in galaxies and often feature bubble structures. These wind bubbles are characterized by an external forward shock expanding in the surrounding medium and a wind termination shock separating the cool and fast wind from the hot shocked wind. While the forward shock could not be able to accelerate particles efficiently for a long time, at the wind termination shock the necessary conditions for efficient acceleration may be present. We develop a model for particle acceleration at the termination shock of such bubbles analysing the consequences of different possible engines po…
The interaction between the strong winds of the stars in colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration, and to produce $γ$-rays, in processes involving relativistic electrons and/or protons. We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with a test-particle approach. We use magnetohydrodynamic simulations to determine the background conditions in the wind collision region. …
We investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by winds of star clusters in the interstellar medium. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for very powerful clusters. We show how the maximum energy is limited by two different processes: the particle escape from the bubble boundary and the drop of energy gain for particles able to diffuse up to the center of the cluster. A crucial role in this problem is played by the dissipation of kinetic…
There are two distinct breaks in the cosmic ray (CR) spectrum: the so-called "knee" around $3 \times 10^{15}$ eV and the so-called "ankle" around $10^{18}$ eV. Diffusive shock acceleration (DSA) at supernova remnant (SNR) shock fronts is thought to accelerate galactic CRs to energies below the knee, while an extragalactic origin is presumed for CRs with energies beyond the ankle. CRs with energies between $3 \times 10^{15}$ and $10^{18}$ eV, which we dub the "shin," have an unknown origin. It has been proposed that DSA at galactic wind termination shocks, rather than at SNR shocks, may acceler…
We discuss the role of particle-in-cell (PIC) simulations in unveiling the origin of the emitting particles in PWNe. After describing the basics of the PIC technique, we summarize its implications for the quiescent and the flaring emission of the Crab Nebula, as a prototype of PWNe. A consensus seems to be emerging that, in addition to the standard scenario of particle acceleration via the Fermi process at the termination shock of the pulsar wind, magnetic reconnection in the wind, at the termination shock and in the Nebula plays a major role in powering the multi-wavelength signatures of PWNe…
The enhanced star forming activity, typical of starburst galaxies, powers strong galactic winds expanding on kiloparsec (kpc) scales and characterized by bubble structures. Here we discuss the possibility that particle acceleration may take place at the termination shock of such winds. We calculate the spectrum of accelerated particles and their maximum energy, that turns out to range up to a few hundred petaelectronvolt (PeV) for typical values of the parameters. Cosmic rays accelerated at the termination shock are advected towards the edge of the bubble excavated by the wind and eventually e…
The relativistic wind of obliquely-rotating pulsars consists of toroidal stripes of opposite magnetic field polarity, separated by current sheets of hot plasma. By means of two- and three-dimensional particle-in-cell simulations, we investigate particle acceleration and magnetic field dissipation at the termination shock of a relativistic striped wind. At the shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength "lambda" or the wind magnetization "sigma" (in the regime sigma>>1 of magnetically-dominated flows), s…
The γ-ray flares from the Crab nebula observed by AGILE and Fermi-LAT reaching GeV energies and lasting several days challenge the standard models for particle acceleration in pulsar wind nebulae, because the radiating electrons have energies exceeding the classical radiation-reaction limit for synchrotron. Previous modeling has suggested that the synchrotron limit can be exceeded if the electrons experience electrostatic acceleration, but the resulting spectra do not agree very well with the data. As a result, there are still some important unanswered questions about the detailed particle acc…
We outline a model of the Crab Pulsar Wind Nebula with two different populations of synchrotron emitting particles, arising from two different acceleration mechanisms: (i) Component-I due to Fermi-I acceleration at the equatorial portion of the termination shock, with particle spectral index $p_I \approx 2.2$ above the injection break corresponding to $γ_{wind} σ_{wind} \sim 10^5$, peaking in the UV ($γ_{wind} \sim 10^2$ is the bulk Lorentz factor of the wind, $σ_{wind} \sim 10^3$ is wind magnetization); (ii) Component-II due to acceleration at reconnection layers in the bulk of the turbulent …
Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characterist…
The interaction between the strong winds in stellar colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration (DSA). We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with both a test-particle approach and a non-linear method modelling a shock locally modified by the backreaction of the accelerated protons. We use magnetohydrodynamic simulations to determine the background plasma in the WC…
Stochastic acceleration of particles under a pressure balance condition can accommodate the universal $p^{-5}$ spectra observed under many different conditions in the inner heliosphere. In this model, in order to avoid an infinite build up of particle pressure, a relationship between the momentum diffusion of particles and the adiabatic deceleration in the solar wind must exist. This constrains both the spatial and momentum diffusion coefficients and results in the $p^{-5}$ spectrum in the presence of adiabatic losses in the solar wind. However, this theory cannot explain the presence of such …
Pulsar Wind Nebulae are the astrophysical sources that host the most relativistic shocks in Nature and the only Galactic sources in which we have direct evidence of PeV particles. These facts make them very interesting from the point of view of particle acceleration physics, and their proximity and brightness make them a place where fundamental processes common to different classes of relativistic sources have a better chance to be understood. I will discuss how well we understand the physics of Pulsar Wind Nebulae, describing recent progress and highlighting the main open questions. I will be…
We consider the diffusive shock acceleration in interstellar bubbles created by powerful stellar winds of supernova progenitors. Under the moderate stellar wind magnetization the bubbles are filled by the strongly magnetized low density gas. It is shown that the maximum energy of particles accelerated in this environment can exceed the "knee" energy in the observable cosmic ray spectrum.
We present a model for the creation of non-thermal particles via diffusive shock acceleration in a colliding-wind binary. Our model accounts for the oblique nature of the global shocks bounding the wind-wind collision region and the finite velocity of the scattering centres to the gas. It also includes magnetic field amplification by the cosmic ray induced streaming instability and the dynamical back reaction of the amplified field. We assume that the injection of the ions and electrons is independent of the shock obliquity and that the scattering centres move relative to the fluid at the Alfv…
We investigate acceleration of cosmic rays by shocks and accretion flows in galaxy clusters. Numerical results for spectra of accelerated particles and nonthermal emission are presented. It is shown that the acceleration of protons and nuclei in the nearby galaxy cluster Virgo can explain the observed spectra of ultra high energy cosmic rays.
Several colliding-wind massive binaries are known to be non-thermal emitters in the radio domain. This constitutes strong evidence for the fact that an efficient particle acceleration process is at work in these objects. The acceleration mechanism is most probably the Diffusive Shock Acceleration (DSA) process in the presence of strong hydrodynamic shocks due to the colliding-winds. In order to investigate the physics of this particle acceleration, we initiated a multiwavelength campaign covering a large part of the electromagnetic spectrum. In this context, the detailed study of the hard X-ra…
The $γ$-ray flares from the Crab nebula observed by {\it AGILE} and {\it Fermi}-LAT between 2007-2013 reached GeV photon energies and lasted several days. The strongest emission, observed during the 2011 April "super-flare," exceeded the quiescent level by more than an order of magnitude. These observations challenge the standard models for particle acceleration in pulsar wind nebulae, because the radiating electrons have energies exceeding the classical radiation-reaction limit for synchrotron. Particle-in-cell simulations have suggested that the classical synchrotron limit can be exceeded if…
The processes leading to the exceptionally hard radio spectra of pulsar-wind nebulae (PWNe) are not yet understood. Radio photon spectral indices among $29$ PWNe from the literature show an approximately normal, $α=0.2\pm0.2$ distribution. We present $\sim 3σ$ evidence for a distinct sub-population of PWNe, with a hard spectrum $α=0.01\pm0.06$ near the termination shock and significantly softer elsewhere, possibly due to a recent evacuation of the shock surroundings. Such spectra, especially in the hard sub-population, suggest a Fermi process, such as diffusive shock acceleration, at its extre…
In 2007 September, the Crab Nebula exhibited a bright gamma-ray flare in the GeV energy range that was detected by AGILE. The observed emission at >160 MeV indicates that the radiating electrons had energies above the classical synchrotron radiation-reaction limit, thus presenting a serious challenge to classical models for electron acceleration in astrophysical environments. In this paper, we apply our recently developed time-dependent self-similar analytical model describing electrostatic acceleration in the explosive reconnection region around the pulsar wind termination shock to the 2007 S…
We study the force balance and resulting acceleration of gas in general relativity basing on simulations of accretion on a stellar-mass, non-rotating black hole. We compare properties of acceleration in an optically thin, radiatively inefficient disk, and in an optically thick, super-critical disk accreting at 10 times the Eddington rate. We study both the average forces acting at given location and forces acting on a gas parcel along its trajectory. We show that the acceleration is not a continuous process - in most cases gas is accelerated only in short-lasting episodes. We find that in the …
We present a model for the non-thermal emission from a colliding-wind binary. Relativistic protons and electrons are assumed to be accelerated through diffusive shock acceleration (DSA) at the global shocks bounding the wind-wind collision region. The non-linear effects of the back-reaction due to the cosmic ray pressure on the particle acceleration process and the cooling of the non-thermal particles as they flow downstream from the shocks are included. We explore how the non-thermal particle distribution and the keV-GeV emission changes with the stellar separation and the viewing angle of th…
We perform axisymmetric relativistic magnetohydrodynamic (MHD) simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Our simulations using the PLUTO code run for 500 inner disk rotati…
We study the acceleration of electrons and positrons at an electromagnetically modified, ultra-relativistic shock in the context of pulsar wind nebulae (PWNe). We simulate the outflow produced by an obliquely rotating pulsar in proximity of its termination shock with a two-fluid code which uses a magnetic shear wave to mimic the properties of the wind. We integrate electron trajectories in the test-particle limit in the resulting background electromagnetic fields to analyse the injection mechanism. We find that the shock-precursor structure energizes and reflects a sizeable fraction of particl…
Non-thermal emission has been detected in WR-stars for many years at long wavelengths spectral range, in general attributed to synchrotron emission. Two key ingredients are needed to explain such emissions, namely magnetic fields and relativistic particles. Particles can be accelerated to relativistic speeds by Fermi processes at strong shocks. Therefore, strong synchrotron emission is usually attributed to WR binarity. The magnetic field may also be amplified at shocks, however the actual picture of the magnetic field geometry, intensity, and its role on the acceleration of particles at WR bi…
We investigate pulsar timing residuals due to the coupling effect of the pulsar transverse acceleration and the R$\rm{\ddot{o}}$mer delay. The effect is relatively small and usually negligible. Only for pulsars in globular clusters, it is possibly important. The maximum residual amplitude, which is from the pulsar near the surface of the core of the cluster, is about tens nanoseconds, and may hardly be identified for most of the globular clusters currently. However, an intermediate-mass black hole in the centre of a cluster can increase apparently the timing residual magnitudes. Particularly f…
Pulsar wind nebulae (PWNe) are outstanding accelerators in Nature, in the sense that they accelerate electrons up to the radiation reaction limit. Motivated by this observation, this paper examines the possibility that young pulsar wind nebulae can accelerate ions to ultra-high energies at the termination shock of the pulsar wind. We consider here powerful PWNe, fed by pulsars born with $\sim\,$millisecond periods. Assuming that such pulsars exist, at least during a few years after the birth of the neutron star, and that they inject ions into the wind, we find that protons could be accelerated…
Recent analytical and numerical work argue that successful relativistic Fermi acceleration requires a weak magnetization of the unshocked plasma, all the more so at high Lorentz factors. The present paper tests this conclusion by computing the afterglow of a gamma-ray burst outflow propagating in a magnetized stellar wind using "ab initio" principles regarding the microphysics of relativistic Fermi acceleration. It is shown that in magnetized environments, one expects a drop-out in the X-ray band on sub-day scales as the synchrotron emission of the shock heated electrons exits the frequency ba…
We study electron and positron acceleration at the termination shock of a striped pulsar wind. Drift motion along the shock surface keeps either electrons or positrons -but not both, close to the equatorial plane of the pulsar, where they are accelerated by the first-order Fermi process. Their energy spectrum is a power law, and both the X-ray flux and photon index of the Crab Nebula, as measured by NuSTAR, can be reproduced for sufficiently large downstream turbulence levels. The implication that one sign of charge is preferentially accelerated in pulsar wind nebulae is potentially important …
In the next years the FERMI gamma ray telescope and the Cherenkov telescopes will put very stringent constraints to models of gamma ray emission from galaxy clusters providing crucial information on relativistic particles in the inter-galactic-medium. We derive the broad band non-thermal spectrum of galaxy clusters in the context of general calculations in which relativistic particles (protons and secondary electrons due to proton-proton collisions) interact with MHD turbulence generated in the cluster volume during cluster mergers, and discuss the importance of future gamma ray observations.
Synchrotron radiation of ultra-relativistic particles accelerated in a pulsar wind nebula may dominate its spectrum up to gamma-ray energies. Because of the short cooling time of the gamma-ray emitting electrons, the gamma-ray emission zone is in the immediate vicinity of the acceleration site. The particle acceleration likely occurs at the termination shock of the relativistic striped wind, where multiple forced magnetic field reconnections provide strong magnetic fluctuations facilitating Fermi acceleration processes. The acceleration mechanisms imply the presence of stochastic magnetic fiel…
Type IIP supernova progenitors are often surrounded by dense circumstellar media that may result from mass-loss enhancement of the progenitors shortly before their explosions. Previous light-curve studies suggest that the mass-loss rates are enhanced up to ~ 0.1 Msun/yr, assuming a constant wind velocity. However, density of circumstellar media at the immediate stellar vicinity can be much higher than previously inferred for a given mass-loss rate if wind acceleration is taken into account. We show that the wind acceleration has a huge impact when we estimate mass-loss rates from early light c…
We briefly discuss models of energetic particle acceleration by supernova shock in active starforming regions at different stages of their evolution. Strong shocks may strongly amplify magnetic fields due to cosmic ray driven instabilities. We discuss the magnetic field amplification emphasizing the role of the long-wavelength instabilities. Supernova shock propagating in the vicinity of a powerful stellar wind in a young stellar cluster is argued to increase the maximal CR energies at a given evolution stage of supernova remnant (SNR) and can convert a sizeable fraction of the kinetic energy …
We used data from the Fermi Large Area Telescope obtained during the last 7 years and spanning two passages of $η$ Carinae at periastron and compared them with the predictions of particle acceleration in hydrodynamic simulations. Two emission components can be distinguished. The low-energy component cuts off below 10 GeV and its flux, modulated by the orbital motion, varies by a factor less than 2. Short-term variability occurs at periastron. The flux of the high energy component varies by a factor 3-4 but differently during the two periastrons. The variabilities observed at low-energy, includ…
An oblique-rotating pulsar generates a relativistic striped wind in a pulsar wind nebula (PWN). The termination shock of the PWN compresses the Poynting-flux-dominated flow and drives magnetic reconnection. By carrying out particle-in-cell (PIC) simulations of the termination shock of the PWN, we study the shock structure as well as the energy conversion processes and particle acceleration mechanisms. With the recent advances in the numerical methods, we extend the simulations to the ultra-relativistic regime with bulk Lorentz factor up to γ_{0}=10^{6}. Magnetic reconnection at the termination…
We introduce the first synthetic light-curve model set of Type IIP supernovae exploded within circumstellar media in which the acceleration of the red supergiant winds is taken into account. Because wind acceleration makes the wind velocities near the progenitors low, the density of the immediate vicinity of the red supergiant supernova progenitors can be higher than that extrapolated by using a constant terminal wind velocity. Therefore, even if the mass-loss rate of the progenitor is relatively low, it can have a dense circumstellar medium at the immediate stellar vicinity and the early ligh…
The topic of this review paper is on the influence of solar wind turbulence on shock propagation and its consequence on the acceleration and transport of energetic particles at shocks. As the interplanetary shocks sweep through the turbulent solar wind, the shock surfaces fluctuate and ripple in a range of different scales. We discuss particle acceleration at rippled shocks in the presence of ambient solar-wind turbulence. This strongly affects particle acceleration and transport of energetic particles (both ions and electrons) at shock fronts. In particular, we point out that the effects of u…
The formation of a large-scale current sheet is a generic feature of pulsar magnetospheres. If the magnetic axis is misaligned with the star rotation axis, the current sheet is an oscillatory structure filling an equatorial wedge determined by the inclination angle, known as the striped wind. Relativistic reconnection could lead to significant dissipation of magnetic energy and particle acceleration although the efficiency of this process is debated in this context. In this study, we aim at reconciling global models of pulsar wind dynamics and reconnection in the stripes within the same numeri…
Cosmic-ray acceleration has been a long-standing mystery and despite more than a century of study, we still do not have a complete census of acceleration mechanisms. The collision of strong stellar winds in massive binary systems creates powerful shocks, which have been expected to produce high-energy cosmic-rays through Fermi acceleration at the shock interface. The accelerated particles should collide with stellar photons or ambient material, producing non-thermal emission observable in X-rays and gamma-rays. The supermassive binary star eta Carinae drives the strongest colliding wind shock …
Giant radio halos in galaxy clusters probe mechanisms of particle acceleration connected with cluster merger events. Shocks and turbulence are driven in the inter-galactic-medium (IGM) during clusters mergers and may have a deep impact on the non-thermal properties of galaxy clusters. Models of turbulent (re)acceleration of relativistic particles allow good correspondence with present observations, from radio halos to gamma-ray upper limits, although several aspects of this complex scenario remain still poorly understood. After providing basic motivations for turbulent acceleration in galaxy c…
We study the acceleration of cosmic rays by collisionless structure formation shocks with ENZO grid simulations. Data from the FERMI satellite enable the use of galaxy clusters as a testbed for particle acceleration models. Based on advanced cosmological simulations that include different prescriptions for gas and cosmic rays physics, we use the predicted γ-ray emission to constrain the shock acceleration efficiency. We infer that the efficiency must be on average <0.1% for cosmic shocks, particularly for the 2<M<5 merger shocks that are mostly responsible for the thermalisation of the intracl…
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. In this work, we study the role played by the large-scale anisotropy of the transverse magnetic field profile on the shock dynamics. We performed large two-dimensional particle-in-cell simulations for a wide range of upstream plasma magnetizations. A large-scale vel…
An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just…
Recently, gas entropy at the outskirts of galaxy clusters attracts much attention. We propose that the entropy profiles could be used to study cosmic-ray (CR) acceleration around the clusters. If the CRs are effectively accelerated at the formation of clusters, the kinetic energy of infalling gas is consumed by the acceleration and the gas entropy should decrease. As a result, the entropy profiles become flat at the outskirts. If the acceleration is not efficient, the entropy should continue to increase outwards. By comparing model predictions with X-ray observations with Suzaku, which show fl…
We use multi-frequency radiation hydrodynamics (rad-HD) to simulate radiative acceleration of a spherically symmetric stellar wind. We demonstrate the rad-HD capabilities of Athena++ for a series of test problems with multi-group radiation transfer. We then model the radiative transfer of a single spectral line through a spherically symmetric, isothermal, "CAK"-type line driven wind. We find that correctly accounting for the Doppler shift of the absorbed radiation, the force is well described by the analytic Sobolev line transfer in the supersonic parts of the solution where the flow is statio…
Acceleration of cosmic-ray electrons (CRe) in the intra-cluster-medium (ICM) is probed by radio observations that detect diffuse, Mpc-scale, synchrotron sources in a fraction of galaxy clusters. Giant radio halos are the most spectacular manifestations of non-thermal activity in the ICM and are currently explained assuming that turbulence driven during massive cluster-cluster mergers reaccelerates CRe at several GeV. This scenario implies a hierarchy of complex mechanisms in the ICM that drain energy from large-scales into electromagnetic fluctuations in the plasma and collisionless mechanisms…
