Spectra of accelerated particles at supernova shocks in the presence of neutral hydrogen: the case of Tycho

The presence of neutral hydrogen in the shock proximity changes the structure of the shock and affects the spectra of particles accelerated through the first-order Fermi mechanism. This phenomenon has profound implications for the interpretation of the multifrequency spectra of radiation from supernova remnants. Neutrals that undergo charge exchange with hot ions downstream of the shock may result in fast neutrals moving towards the upstream gas, where they can suffer additional charge exchange or ionisation reactions, thereby depositing energy and momentum upstream. Here we discuss the implications of this neutral return flux, which was already predicted in our previous work on neutral mediated supernova shocks, and show how the spectra of accelerated particles turn out to be appreciably steeper than $p^{-4}$, thereby affecting the gamma ray spectra from supernova remnants in general and from Tycho specifically. The theory that describes non-linear diffusive shock acceleration in the presence of neutral hydrogen has been developed in recent years. Here we use a semi-analytical theory developed in previous work and specialise our predictions to the case of the Tycho supernova shock, where there is evidence that the spectrum of the accelerated cosmic rays is steeper than expected from the traditional theory of diffusive shock acceleration. We show that, if the fraction of neutral hydrogen in the vicinity of the Tycho supernova shock is, as suggested by observations, ~70-90, then spectra of accelerated protons steeper than $p^{-4}$ may be a natural consequence of charge exchange reactions and the associated neutral return flux. The spectral shape is affected by this phenomenon for particles with energies below ~100-1000 GeV, for which the diffusion length is less than or at most comparable to the pathlength of charge exchange and ionisation upstream of the shock.Comment: 6 pages, 3 figures. Accepted for publication by A&

On the radial distribution of Galactic cosmic rays

The spectrum and morphology of the diffuse Galactic gamma-ray emission carries valuable information on cosmic ray (CR) propagation. Recent results obtained by analyzing Fermi-LAT data accumulated over seven years of observation show a substantial variation of the CR spectrum as a function of the distance from the Galactic Center. The spatial distribution of the CR density in the outer Galaxy appears to be weakly dependent upon the galactocentric distance, as found in previous studies as well, while the density in the central region of the Galaxy was found to exceed the value measured in the outer Galaxy. At the same time, Fermi-LAT data suggest a gradual spectral softening while moving outward from the center of the Galaxy to its outskirts. These findings represent a challenge for standard calculations of CR propagation based on assuming a uniform diffusion coefficient within the Galactic volume. Here we present a model of non-linear CR propagation in which transport is due to particle scattering and advection off self-generated turbulence. We find that for a realistic distribution of CR sources following the spatial distribution of supernova remnants and the space dependence of the magnetic field on galactocentric distance, both the spatial profile of CR density and the spectral softening can easily be accounted for.Comment: 6 pages, 3 figures. Accepted for publivation to MNRAS letter

Bayesian Estimation of the Discrepancy with Misspecified Parametric Models

We study a Bayesian model where we have made specific requests about the parameter values to be estimated. The aim is to find the parameter of a parametric family which minimizes a distance to the data generating density and then to estimate the discrepancy using nonparametric methods. We illustrate how coherent updating can proceed given that the standard Bayesian posterior from an unidentifiable model is inappropriate. Our updating is performed using Markov Chain Monte Carlo methods and in particular a novel method for dealing with intractable normalizing constants is required. Illustrations using synthetic data are provided.European Research Council (ERC) through StG "N-BNP" 306406Regione PiemonteMathematic

Cosmic ray driven Galactic winds

The escape of cosmic rays from the Galaxy leads to a gradient in the cosmic ray pressure that acts as a force on the background plasma, in the direction opposite to the gravitational pull. If this force is large enough to win against gravity, a wind can be launched that removes gas from the Galaxy, thereby regulating several physical processes, including star formation. The dynamics of these cosmic ray driven winds is intrinsically non-linear in that the spectrum of cosmic rays determines the characteristics of the wind (velocity, pressure, magnetic field) and in turn the wind dynamics affects the cosmic ray spectrum. Moreover, the gradient of the cosmic ray distribution function causes excitation of Alfven waves, that in turn determine the scattering properties of cosmic rays, namely their diffusive transport. These effects all feed into each other so that what we see at the Earth is the result of these non-linear effects. Here we investigate the launch and evolution of such winds, and we determine the implications for the spectrum of cosmic rays by solving together the hydrodynamical equations for the wind and the transport equation for cosmic rays under the action of self-generated diffusion and advection with the wind and the self-excited Alfven waves.Comment: 14 pages, 15 figures. Accepted for publication to MNRAS main journa

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

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

Broad Balmer line emission and cosmic ray acceleration efficiency in supernova remnant shocks

Balmer emission may be a powerful diagnostic tool to test the paradigm of cosmic ray (CR) acceleration in young supernova remnant (SNR) shocks. The width of the broad Balmer line is a direct indicator of the downstream plasma temperature. In case of efficient particle acceleration an appreciable fraction of the total kinetic energy of the plasma is channeled into CRs, therefore the downstream temperature decreases and so does the broad Balmer line width. This width also depends on the level of thermal equilibration between ions and neutral hydrogen atoms in the downstream. Since in general in young SNR shocks only a few charge exchange (CE) reactions occur before ionization, equilibration between ions and neutrals is not reached, and a kinetic description of the neutrals is required in order to properly compute Balmer emission. We provide a method for the calculation of Balmer emission using a self-consistent description of the shock structure in the presence of neutrals and CRs. We use a recently developed semi-analytical approach, where neutral particles, ionized plasma, accelerated particles and magnetic fields are all coupled together through the mass, momentum and energy flux conservation equations. The distribution of neutrals is obtained from the full Boltzmann equation in velocity space, coupled to Maxwellian ions through ionization and CE processes. The computation is also improved with respect to previous work thanks to a better approximation for the atomic interaction rates. We find that for shock speeds >2500km/s the distribution of broad neutrals never approaches a Maxwellian and its moments differ from those of the ionized component. These differences reflect into a smaller FWHM than predicted in previous calculations, where thermalization was assumed. The method presented here provides a realistic estimate of particle acceleration efficiency in Balmer dominated shocks.Comment: 6 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic

Cosmic Ray acceleration and Balmer emission from RCW 86 (G315.4-2.3)

Context. Observation of Balmer lines from the region around the forward shock of supernova remnants (SNR) may provide valuable information on the shock dynamics and the efficiency of particle acceleration at the shock. Aims. We calculated the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR RCW 86 (G315.4-2.3) as a function of the cosmic-ray (CR) 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 CR acceleration efficiency in this remnant. Methods. We used the recently developed nonlinear theory of diffusive shock-acceleration in the presence of neutrals. The semianalytical approach we developed includes a description of magnetic field amplification as due to resonant streaming instability, the dynamical reaction of accelerated particles and the turbulent magnetic field on the shock, and all channels of interaction between neutral hydrogen atoms and background ions that are relevant for the shock dynamics. Results. We derive the CR acceleration efficiency in the SNR RCW 86 from the Balmer emission. Since our calculation used recent measurements of the shock proper motion, the results depend on the assumed distance to Earth. For a distance of 2 kpc the measured width of the broad Balmer line is compatible with the absence of CR acceleration. For a distance of 2.5 kpc, which is a widely used value in current literature, a CR acceleration efficiency of 5-30% is obtained, depending upon the electron-ion equilibration and the ionization fraction upstream of the shock. By combining information on Balmer emission with the measured value of the downstream electron temperature, we constrain the CR acceleration efficiency to be ~20%.Comment: 7 pages, 6 figures. Accepted for publication in A&A (minor changes to match the published version