Cosmic Ray propagation in sub-Alfvenic magnetohydrodynamic turbulence

This work has the main objective to provide a detailed investigation of cosmic ray propagation in magnetohydrodynamic turbulent fields generated by forcing the fluid velocity field at large scales. It provides a derivation of the particle mean free path dependences in terms of the turbulence level described by the Alfv\'enic Mach number and in terms of the particle rigidity. We use an upgrade version of the magnetohydrodynamic code {\tt RAMSES} which includes a forcing module and a kinetic module and solve the Lorentz equation for each particle. The simulations are performed using a 3 dimension periodical box in the test-particle and magnetostatic limits. The forcing module is implemented using an Ornstein-Uhlenbeck process. An ensemble average over a large number of particle trajectories is applied to reconstruct the particle mean free paths. We derive the cosmic ray mean free paths in terms of the Alfv\'enic Mach numbers and particle reduced rigidities in different turbulence forcing geometries. The reduced particle rigidity is $\rho=r_L/L$ where $r_L$ is the particle Larmor radius and $L$ is the simulation box length related to the turbulence coherence or injection scale $L_{inj}$ by $L \sim 5 L_{inj}$. We have investigated with a special attention compressible and solenoidal forcing geometries. We find that compressible forcing solutions are compatible with the quasi-linear theory or more advanced non-linear theories which predict a rigidity dependence as $\rho^{1/2}$ or $\rho^{1/3}$. Solenoidal forcing solutions at least at low or moderate Alfv\'enic numbers are not compatible with the above theoretical expectations and require more refined arguments to be interpreted. It appears especially for Alfv\'enic Mach numbers close to one that the wandering of field lines controls perpendicular mean free path solutions whatever the forcing geometry.Comment: 15 pages, 18 figures. Accepted for publication in section 2. Astrophysical processes of Astronomy and Astrophysic

MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration

We present a new code aimed at the simulation of diffusive shock acceleration (DSA), and discuss various test cases which demonstrate its ability to study DSA in its full time-dependent and non-linear developments. We present the numerical methods implemented, coupling the hydrodynamical evolution of a parallel shock (in one space dimension) and the kinetic transport of the cosmic-rays (CR) distribution function (in one momentum dimension), as first done by Falle. Following Kang and Jones and collaborators, we show how the adaptive mesh refinement technique (AMR) greatly helps accommodating the extremely demanding numerical resolution requirements of realistic (Bohm-like) CR diffusion coefficients. We also present the paral lelization of the code, which allows us to run many successive shocks at the cost of a single shock, and thus to present the first direct numerical simulations of linear and non-linear multiple DSA, a mechanism of interest in various astrophysical environments such as superbubbles, galaxy clusters and early cosmological flows.Comment: accepted for publication in MNRAS by the Royal Astronomical Society and Blackwell Publishin

Cosmic-ray acceleration in young protostars

The main signature of the interaction between cosmic rays and molecular clouds is the high ionisation degree. This decreases towards the densest parts of a cloud, where star formation is expected, because of energy losses and magnetic effects. However recent observations hint to high levels of ionisation in protostellar systems, therefore leading to an apparent contradiction that could be explained by the presence of energetic particles accelerated within young protostars. Our modelling consists of a set of conditions that has to be satisfied in order to have an efficient particle acceleration through the diffusive shock acceleration mechanism. We find that jet shocks can be strong accelerators of protons which can be boosted up to relativistic energies. Another possibly efficient acceleration site is located at protostellar surfaces, where shocks caused by impacting material during the collapse phase are strong enough to accelerate protons. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as an argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact on the star and planet formation process as well as on the formation of pre-biotic molecules.Comment: Accepted by Astronomy and Astrophysic

Shape and evolution of wind-blown bubbles of massive stars: on the effect of the interstellar magnetic field

The winds of massive stars create large (>10 pc) bubbles around their progenitors. As these bubbles expand they encounter the interstellar coherent magnetic field which, depending on its strength, can influence the shape of the bubble. We wish to investigate if, and how much, the interstellar magnetic field can contribute to the shape of an expanding circumstellar bubble around a massive star. We use the MPI-AMRVAC code to make magneto-hydrodynamical simulations of bubbles, using a single star model, combined with several different field strengths: B = 5, 10, and 20 muG for the interstellar magnetic field. This covers the typical field strengths of the interstellar magnetic fields found in the galactic disk and bulge. Furthermore, we present two simulations that include both a 5 muG interstellar magnetic field and a 10,000 K interstellar medium and two different ISM densities to demonstrate how the magnetic field can combine with other external factors to influence the morphology of the circumstellar bubbles. Our results show that low magnetic fields, as found in the galactic disk, inhibit the growth of the circumstellar bubbles in the direction perpendicular to the field. As a result, the bubbles become ovoid, rather than spherical. Strong interstellar fields, such as observed for the galactic bulge, can completely stop the expansion of the bubble in the direction perpendicular to the field, leading to the formation of a tube-like bubble. When combined with a warm, high-density ISM the bubble is greatly reduced in size, causing a dramatic change in the evolution of temporary features inside the bubble. The magnetic field of the interstellar medium can affect the shape of circumstellar bubbles. This effect may have consequences for the shape and evolution of circumstellar nebulae and supernova remnants, which are formed within the main wind-blown bubble.Comment: Proposed for acceptance for publication in Astronomy & Astrophysics. The published version will contain animations of each simulatio

Embedded star clusters as sources of high-energy cosmic rays: Modelling and constraints

Massive stars are mainly found in stellar associations. These massive star clusters occur in the heart of giant molecular clouds. The strong stellar wind activity in these objects generates large bubbles and induces collective effects that could accelerate particles up to high energy and produce gamma rays. The best way to input an acceleration origin to the stellar wind interaction in massive stellar cluster is to observe young massive star clusters in which no supernova explosion has occurred yet. This work aims to constrain the part of stellar wind mechanical energy that is converted into energetic particles using the sensitivity of the ongoing Fermi/LAT instrument. This work further provides detailed predictions of expected gamma-ray fluxes in the view of the on-set of the next generation of imaging atmospheric Cherenkov telescopes. A one-zone model where energetic particles are accelerated by repeated interactions with strong supersonic shocks occurring in massive star clusters was developed. The particle escape from the star cluster and subsequent interaction with the surrounding dense material and magnetic fields of the HII region was computed. We applied this model to a selection of eight embedded star clusters constricted by existing observations. We evaluated the gamma-ray signal from each object, combining both leptonic and hadronic contributions. We searched for these emissions in the Fermi/LAT observations in the energy range from 3 to 300 GeV and compared them to the sensitivity of the Cherenkov Telescope Array. No significant gamma-ray emission from these star clusters has been found. Less than 10% of stellar wind luminosities are supplied to the relativistic particles. Some clusters even show acceleration efficiency of less than 1%. The CTA would be able to detect gamma-ray emission from several clusters in the case of an acceleration efficiency of close to 1%.Comment: accepted for publication in Astronomy&Astrophysic

Non-linear diffusion of cosmic rays escaping from supernova remnants - I. The effect of neutrals

Supernova remnants are believed to be the main sources of galactic Cosmic Rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disc volume, where most supernovae explode, and are characterised by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that streaming instability affects the propagation of CRs even in the presence of ion-neutral friction. The diffusion coefficient can be suppressed by more than a factor of $\sim 2$ over a region of few tens of pc around the remnant. The suppression increases for smaller distances. The propagation of $\approx 10$ GeV particles is affected for several tens of kiloyears after escape, while $\approx 1$ TeV particles are affected for few kiloyears. This might have a great impact on the interpretation of gamma-ray observations of molecular clouds located in the vicinity of supernova remnants.Comment: Revised to match the version published in MNRA

Non-linear Cosmic Ray propagation close to the acceleration site

Recent advances on gamma-ray observations from SuperNova Remnants and Molecular Clouds offer the possibility to study in detail the properties of the propagation of escaping Cosmic Rays (CR). However, a complete theory for CR transport outside the acceleration site has not been developed yet. Two physical processes are thought to be relevant to regulate the transport: the growth of waves caused by streaming instability, and possible wave damping mechanisms that reduce the growth of the turbulence. Only a few attempts have been made so far to incorporate these mechanisms in the theory of CR diffusion. In this work we present recent advances in this subject. In particular, we show results obtained by solving the coupled equations for the diffusion of CRs and the evolution of Alfven waves. We discuss the importance of streaming instabilities and wave damping in different ISM phases.Comment: Contribution to the Proceedings of the 34th International Cosmic Ray Conference (ICRC 2015), The Hague, The Netherland

Population synthesis of pulsar wind nebulae and pulsar halos in the Milky Way -- Predicted contributions to the very-high-energy sky

The discovery of extended gamma-ray emission toward a number of middle-aged pulsars suggests the possibility of long-lived particle confinement beyond the classical pulsar wind nebula (PWN) stage. How this emerging source class can be extrapolated to a Galactic population remains unclear. We aim to evaluate how pulsar halos fit in existing TeV observations, under the assumption that all middle-aged pulsars develop halos similar to those observed toward the J0633+1746 or B0656+14 pulsars. We modeled the populations of supernova remnants, PWNe, and pulsar halos in the Milky Way. The PWN-halo evolutionary sequence is described in a simple yet coherent framework, and both kinds of objects are assumed to share the same particle injection properties. We then assessed the contribution of the different source classes to the very-high-energy emission from the Galaxy. The synthetic population can be made consistent with the flux distribution of all known objects, including unidentified objects, for a reasonable set of parameters. The fraction of the populations predicted to be detectable in surveys of the Galactic plane with HESS. and HAWC is then found to be in good agreement with their actual outcome, with a number of detectable halos ranging from 30 to 80% of the number of detectable PWNe. Prospects for CTA involve the detection of 250-300 sources in the Galactic Plane Survey, including 170 PWNe and up to 100 halos. The extent of diffusion suppression in halos has a limited impact on such prospects but its magnitude has a strong influence. The level of diffuse emission from unresolved populations in each survey is found to be dominated by halos and comparable to large-scale interstellar radiation powered by cosmic rays above 0.1-1TeV. Pulsar halos are shown to be viable counterparts to a fraction of the currently unidentified sources if they develop around most middle-aged pulsars (abridged).Comment: 16 pages, 22 figures, accepted for publication in A&

Young star clusters as gamma ray emitters and their detection with Cherenkov Telescopes

Young massive star clusters as sites of strong stellar winds and supernova explosions may accelerate charged particles at high energies and produce gamma-rays. These sources may also contribute to the production of cosmic rays in our galaxy. At TeV energies several candidates have already been detected: Cygnus OB2, Westerlund 1 \& 2, W43, Pismis 22 and W49A. Our study addresses the issue of very young star clusters where no supernova has occurred yet. During the lifetime of a massive star (M$> 20 M_{\odot}$), supersonic stellar winds do indeed release as much energy as a supernova explosion. As supernova remnants are already known as gamma-ray emitters our purpose is to avoid any ambiguity on the origin of a possible gamma ray emission and to fully assume a stellar wind contribution. In this work we first present a catalogue of potential gamma-ray emitting clusters and discuss the criteria used to built the catalogue. We hence model the expected energetic particle spectrum including escapes and losses. We deduce gamma-ray luminosities produced by Inverse Compton and pion decay emission of each cluster and their associated HII regions. We finally compare these gamma-ray luminosities with HESS-II and CTA Cherenkov telescopes sensitivities

Using PIC and PIC-MHD to investigate cosmic ray acceleration in mildly relativistic shocks

Astrophysical shocks create cosmic rays by accelerating charged particles to relativistic speeds. However, the relative contribution of various types of shocks to the cosmic ray spectrum is still the subject of ongoing debate. Numerical studies have shown that in the non-relativistic regime, oblique shocks are capable of accelerating cosmic rays, depending on the Alfv\'enic Mach number of the shock. We now seek to extend this study into the mildly relativistic regime. In this case, dependence of the ion reflection rate on the shock obliquity is different compared to the nonrelativistic regime. Faster relativistic shocks are perpendicular for the majority of shock obliquity angles therefore their ability to initialize efficient DSA is limited. We define the ion injection rate using fully kinetic PIC simulation where we follow the formation of the shock and determine the fraction of ions that gets involved into formation of the shock precursor in the mildly relativistic regime covering a Lorentz factor range from 1 to 3. Then, with this result, we use a combined PIC-MHD method to model the large-scale evolution of the shock with the ion injection recipe dependent on the local shock obliquity. This methodology accounts for the influence of the self-generated or pre-existing upstream turbulence on the shock obliquity which allows study substantially larger and longer simulations compared to classical hybrid techniques.Comment: 38th International Cosmic Ray Conference, Proceedings of Science (ICRC2023) 54