Escape of cosmic rays from the Galaxy and effects on the circumgalactic medium

The escape of cosmic rays from the Galaxy is expected to shape their spectrum inside the Galaxy. Yet, this phenomenon is very poorly understood and, in the absence of a physical description, it is usually modelled as free escape from a given boundary, typically located at a few kpc distance from the Galactic disc. We show that the assumption of free escape leads to the conclusion that the cosmic ray current propagating in the circumgalactic medium is responsible for a non resonant cosmic ray induced instability that in turn leads to the generation of a magnetic field of strength $\sim 2\times 10^{-8}$ Gauss on a scale $\sim 10$ kpc around our Galaxy. The self-generated diffusion produces large gradients in the particle pressure that induce a displacement of the intergalactic medium with velocity $\sim 10-100$ km/s. Cosmic rays are then carried away by advection. If the overdensity of the intergalactic gas in a region of size $\sim 10$ kpc around our Galaxy is $\gtrsim 100$ with respect to the cosmological baryon density $\Omega_{b}\rho_{cr}$, then the flux of high energy neutrinos as due to pion production becomes comparable with the flux of astrophysical neutrinos recently measured by IceCube.Comment: Accepted for publication in Phys. Rev. Letter

High energy cosmic ray self-confinement close to extragalactic sources

The ultra-high energy cosmic rays observed at the Earth are most likely accelerated in extra-galactic sources. For the typical luminosities invoked for such sources, the electric current associated to the flux of cosmic rays that leave them is large. The associated plasma instabilities create magnetic fluctuations that can efficiently scatter particles. We argue that this phenomenon forces cosmic rays to be self-confined in the source proximity for energies $E<E_{\rm cut}$, where $E_{\rm cut}\approx 10^{7} L_{44}^{2/3}$ GeV for low background magnetic fields ($B_{0}\ll nG$). For larger values of $B_{0}$, cosmic rays are confined close to their sources for energies $E<E_{\rm cut}\approx 2\times 10^{8} \lambda_{10} L_{44}^{1/4} B_{-10}^{1/2}$ GeV, where $B_{-10}$ is the field in units of $0.1$ nG, $\lambda_{10}$ is its coherence lengths in units of 10 Mpc and $L_{44}$ is the source luminosity in units of $10^{44}$ erg/s.Comment: To Appear in Physical Review Letter

Non-linear diffusive shock acceleration with free escape boundary

We present here a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream. This solution, besides allowing us to determine the spectrum of particles accelerated at the shock front, including the shape of the cutoff at some maximum momentum, also allows us to determine the spectrum of particles escaping the system from upstream. This latter aspect of the problem is crucial for establishing a connection between the accelerated particles in astrophysical sources, such as supernova remnants, and the cosmic rays observed at the Earth. An excellent approximate solution, which leads to a computationally fast calculation of the structure of shocks with an arbitrary level of cosmic ray modification, is also obtained.Comment: 11 pages, 2 figures, Accepted for publication in APh

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles, $p_{max}$, decreases with time, as is the case for the Sedov-Taylor phase of expansion of a shell Supernova Remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time $t$, particles with momenta larger than $p_{max}(t)$ leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at Earth. In this paper we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov-Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at Earth.Comment: Version accepted for publication in MNRA

The contribution of supernova remnants to the galactic cosmic ray spectrum

The supernova paradigm for the origin of galactic cosmic rays has been deeply affected by the development of the non-linear theory of particle acceleration at shock waves. Here we discuss the implications of applying such theory to the calculation of the spectrum of cosmic rays at Earth as accelerated in supernova remnants and propagating in the Galaxy. The spectrum is calculated taking into account the dynamical reaction of the accelerated particles on the shock, the generation of magnetic turbulence which enhances the scattering near the shock, and the dynamical reaction of the amplified field on the plasma. Most important, the spectrum of cosmic rays at Earth is calculated taking into account the flux of particles escaping from upstream during the Sedov-Taylor phase and the adiabatically decompressed particles confined in the expanding shell and escaping at later times. We show how the spectrum obtained in this way is well described by a power law in momentum with spectral index close to -4, despite the concave shape of the instantaneous spectra of accelerated particles. On the other hand we also show how the shape of the spectrum is sensible to details of the acceleration process and environment which are and will probably remain very poorly known.Comment: 19 pages, 8 figures, published version (references updated

Contribution to diffuse gamma-ray emission coming from self-confined CRs around their Galactic sources

Recent observations of the diffuse Galactic gamma-ray emission by the Fermi-LAT satellite have shown significant deviations from models which assume the same diffusion properties for cosmic rays (CR) throughout the Galaxy. We explore the possibility that a fraction of this diffuse Galactic emission could be due to hadronic interactions of CRs self-confined in the region around their sources. In fact, freshly accelerated CRs that diffuse away from the acceleration region can trigger the streaming instability able to amplify magnetic disturbance and to reduce the particle diffusion. When this happen, CRs are trapped in the near source region for a time longer than expected and an extended gamma-ray halo is produces around each source. Here we calculate the contribution to the diffuse gamma-ray background due to the overlap along lines of sight of several of these extended halos. We find that if the density of neutrals is low, the halos can account for a substantial fraction of the diffuse emission observed by Fermi-LAT, depending on the orientation of the line of sight with respect to the direction of the galactic center.Comment: 8 pages, 2 figs. Proceeding the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Kore

Cosmic Ray acceleration and Balmer emission from SNR 0509-67.5

Context: Observation of Balmer lines from the region around the forward shock of supernova remnants may provide precious information on the shock dynamics and on the efficiency of particle acceleration at the shock. Aims: We calculate the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR 0509-67.5, as a function of the cosmic ray acceleration efficiency and of the level of thermal equilibration between electrons and protons behind the shock. This calculation aims at using the width of the broad Balmer line emission to infer the cosmic ray acceleration efficiency in this remnant. Methods: We use the recently developed non-linear theory of diffusive shock acceleration in the presence of neutrals. The semi-analytical approach that we developed includes a description of magnetic field amplification as due to resonant streaming instability, the dynamical reaction of both accelerated particles and turbulent magnetic field on the shock, and all channels of interaction between neutral atoms and background plasma that change the shock dynamics. Results: We achieve a quantitative assessment of the CR acceleration efficiency in SNR 0509-67.5 as a function of the shock velocity and different levels of electron-proton thermalization in the shock region. If the shock moves faster than ~4500 km/s, one can conclude that particle acceleration must be taking place with efficiency of several tens of percent. For lower shock velocity the evidence for particle acceleration becomes less clear because of the uncertainty in the electron-ion equilibration downstream. We also discuss the role of future measurements of the narrow Balmer line.Comment: 7 pages, 5 figure. Accepted for publication in Astronomy & Astrophysic