Stochastic cosmic ray sources and the TeV break in the all-electron spectrum

Despite significant progress over more than 100 years, no accelerator has been unambiguously identified as the source of the locally measured flux of cosmic rays. High-energy electrons and positrons are of particular importance in the search for nearby sources as radiative energy losses constrain their propagation to distances of about 1 kpc around 1 TeV. At the highest energies, the spectrum is therefore dominated and shaped by only a few sources whose properties can be inferred from the fine structure of the spectrum at energies currently accessed by experiments like AMS-02, CALET, DAMPE, Fermi-LAT, H.E.S.S. and ISS-CREAM. We present a stochastic model of the Galactic all-electron flux and evaluate its compatibility with the measurement recently presented by the H.E.S.S. collaboration. To this end, we have MC generated a large sample of the all-electron flux from an ensemble of random distributions of sources. We confirm the non-Gaussian nature of the probability density of fluxes at individual energies previously reported in analytical computations. For the first time, we also consider the correlations between the fluxes at different energies, treating the binned spectrum as a random vector and parametrising its joint distribution with the help of a pair-copula construction. We show that the spectral break observed in the all-electron spectrum by H.E.S.S. and DAMPE is statistically compatible with a distribution of astrophysical sources like supernova remnants or pulsars, but requires a rate smaller than the canonical supernova rate. This important result provides an astrophysical interpretation of the spectrum at TeV energies and allows differentiating astrophysical source models from exotic explanations, like dark matter annihilation. We also critically assess the reliability of using catalogues of known sources to model the electron-positron flux.Comment: 30 pages, 12 figures; extended discussion; accepted for publication in JCA

Origin of Small-Scale Anisotropies in Galactic Cosmic Rays

The arrival directions of Galactic cosmic rays (CRs) are highly isotropic. This is expected from the presence of turbulent magnetic fields in our Galactic environment that repeatedly scatter charged CRs during propagation. However, various CR observatories have identified weak anisotropies of various angular sizes and with relative intensities of up to a level of 1 part in 1,000. Whereas large-scale anisotropies are generally predicted by standard diffusion models, the appearance of small-scale anisotropies down to an angular size of 10 degrees is surprising. In this review, we summarise the current experimental situation for both the large-scale and small-scale anisotropies. We address some of the issues in comparing different experimental results and remaining questions in interpreting the observed large-scale anisotropies. We then review the standard diffusive picture and its difficulty in producing the small-scale anisotropies. Having set the stage, we review the various ideas and models put forward for explaining the small-scale anisotropies.Comment: 60 pages, 16 figures; invited review for Progress in Particle and Nuclear Physics (PPNP

Breaks in interstellar spectra of positrons and electrons derived from time-dependent AMS data

Until fairly recently, it was widely accepted that local cosmic ray spectra were largely featureless power laws, containing limited information on their acceleration and transport. This viewpoint is currently being revised in the light of evidence for a variety of spectral breaks in the fluxes of cosmic ray nuclei. Here, we focus on cosmic ray electrons and positrons which at the highest energies must be of local origin due to strong radiative losses. We consider a pure diffusion model for their Galactic transport and determine its free parameters by fitting data in a wide energy range: measurements of the interstellar spectrum by Voyager at MeV energies, radio synchrotron data (sensitive to GeV electrons and positrons) and local observations by AMS up to ~ 1 TeV. For the first time, we also model the time-dependent fluxes of cosmic ray electrons and positrons at GeV energies recently presented by AMS, treating solar modulation in a simple extension of the widely used force-field approximation. We are able to reproduce all the available measurements to date. Our model of the interstellar spectrum of cosmic ray electrons and positrons requires the presence of a number of spectral breaks, both in the source spectra and the diffusion coefficients. While we remain agnostic as to the origin of these spectral breaks, their presence will inform future models of the microphysics of cosmic ray acceleration and transport.Comment: 19 pages, 9 figures; submitted to PR

A Last Look at the Microwave Haze/Bubbles with WMAP

The microwave "haze" was first discovered with the initial release of the full sky data from the Wilkinson Microwave Anisotropy Probe. It is diffuse emission towards the center of our Galaxy with spectral behavior that makes it difficult to categorize as any of the previously known emission mechanisms at those wavelengths. With now seven years of WMAP data publicly available, we have learned much about the nature of the haze, and with the release of data from the Fermi Gamma-Ray Space Telescope and the discovery of the gamma-ray haze/bubbles, we have had a spectacular confirmation of its existence at other wavelengths. As the WMAP mission winds down and the Planck mission prepares to release data, I take a last look at what WMAP has to tell us about the origin of this unique Galactic feature. Much like the gamma-rays, the microwave haze/bubbles is elongated in latitude with respect to longitude by a factor of roughly two, and at high latitudes, the microwave emission cuts off sharply above ~35 degrees (compared to ~50 degrees in the gammas). The hard spectrum of electrons required to generate the microwave synchrotron is consistent with that required to generate the gamma-ray emission via inverse Compton scattering, though it is likely that these signals result from distinct regions of the spectrum (~10 GeV for the microwaves, ~1 TeV for the gammas). While there is no evidence for significant haze polarization in the 7-year WMAP data, I demonstrate explicitly that it is unlikely such a signal would be detectable above the noise.Comment: 9 pages, 6 figures; accepted in ApJ; matches published version with significantly enhanced figure

Secondary Cosmic Ray Nuclei from Supernova Remnants and Constraints to the Propagation Parameters

The secondary-to-primary B/C ratio is widely used to study the cosmic ray (CR) propagation processes in the Galaxy. It is usually assumed that secondary nuclei such as Li-Be-B are entirely generated by collisions of heavier CR nuclei with the interstellar medium (ISM). We study the CR propagation under a scenario where secondary nuclei can also be produced or accelerated from galactic sources. We consider the processes of hadronic interactions inside supernova remnants (SNRs) and re-acceleration of background CRs in strong shocks. Thus, we investigate their impact in the propagation parameter determination within present and future data. The spectra of Li-Be-B nuclei emitted from SNRs are harder than those due to CR collisions with the ISM. The secondary-to-primary ratios flatten significantly at ~TeV/n energies, both from spallation and re-acceleration in the sources. The two mechanisms are complementary to each other and depend on the properties of the local ISM around the expanding remnants. The secondary production in SNRs is significant for dense background media, n ~1 cm^-3, while the amount of re-accelerated CRs is relevant for SNRs expanding into rarefied media, n ~0.1 cm-3. Due to these effects, the the diffusion parameter 'delta' may be misunderstood by a factor of ~5-15%. Our estimations indicate that an experiment of the AMS-02 caliber can constrain the key propagation parameters while breaking the source-transport degeneracy, for a wide class of B/C-consistent models. Given the precision of the data expected from on-going experiments, the SNR production/acceleration of secondary nuclei should be considered, if any, to prevent a possible mis-determination of the CR transport parameters.Comment: 13 pages, 9 figures; matches the published versio

Astrophysical models for the origin of the positron "excess"

Over the last three years, several satellite and balloon observatories have suggested intriguing features in the cosmic ray lepton spectra. Most notably, the PAMELA satellite has suggested an "anomalous" rise with energy of the cosmic ray positron fraction. In this article, we summarize the global picture emerging from the data and recapitulate the main features of different types of explanations proposed. The perspectives in testing different scenarios as well as inferring some astrophysical diagnostics from current/near future experiments are also discussed.Comment: 15 pages (150 references), 2 figures: review article for a Topical Issue on Cosmic Rays, matches version appearing in Astroparticle Physic

The Fermi Gamma-Ray Haze from Dark Matter Annihilations and Anisotropic Diffusion

Recent full-sky maps of the Galaxy from the Fermi Gamma-Ray Space Telescope have revealed a diffuse component of emission towards the Galactic center and extending up to roughly +/-50 degrees in latitude. This Fermi "haze" is the inverse Compton emission generated by the same electrons which generate the microwave synchrotron haze at WMAP wavelengths. The gamma-ray haze has two distinct characteristics: the spectrum is significantly harder than emission elsewhere in the Galaxy and the morphology is elongated in latitude with respect to longitude with an axis ratio ~2. If these electrons are generated through annihilations of dark matter particles in the Galactic halo, this morphology is difficult to realize with a standard spherical halo and isotropic cosmic-ray diffusion. However, we show that anisotropic diffusion along ordered magnetic field lines towards the center of the Galaxy coupled with a prolate dark matter halo can easily yield the required morphology without making unrealistic assumptions about diffusion parameters. Furthermore, a Sommerfeld enhancement to the self annihilation cross-section of ~30 yields a good fit to the morphology, amplitude, and spectrum of both the gamma-ray and microwave haze. The model is also consistent with local cosmic-ray measurements as well as CMB constraints.Comment: 14 pages, 9 figures; submitted to Ap

Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition

In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E)\sim E^{\delta}, with $\delta=1/3$ and $\delta=0.6$ being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accounting for the spiral structure of the Galaxy. We find that the stochastic fluctuations induced by the spatial and temporal distribution of supernovae, together with the effect of spallation of nuclei, lead to mild but sensible violations of the simple, leaky-box-inspired rule that the spectrum observed at Earth is $N(E)\propto E^{-\alpha}$ with $\alpha=\gamma+\delta$, where $\gamma$ is the slope of the cosmic ray injection spectrum at the sources. Spallation of nuclei, even with the small rates appropriate for He, may account for slight differences in spectral slopes between different nuclei, providing a possible explanation for the recent CREAM observations. For $\delta=1/3$ we find that the slope of the proton and helium spectra are $\sim 2.67$ and $\sim 2.6$ respectively at energies above 1 TeV (to be compared with the measured values of $2.66\pm 0.02$ and $2.58\pm 0.02$). For $\delta=0.6$ the hardening of the He spectra is not observed. We also comment on the effect of time dependence of the escape of cosmic rays from supernova remnants, and of a possible clustering of the sources in superbubbles. In a second paper we will discuss the implications of these different scenarios for the anisotropy of cosmic rays.Comment: 28 pages, To appear in JCA

Cosmic ray electron and positron spectra at TeV energies

Observations of cosmic ray electrons have made great strides in the last decade and direct observations of the all-electron flux as well as separate electron and positron spectra are now available up to ~ 1 TeV. In this invited contribution to the 2022 edition of the Rencontres de Moriond on Very High Energy Phenomena in the Universe, we review the data on cosmic ray electron and positron spectra at TeV energies and offer general comments on their interpretation. Subsequently, we focus on the study of the stochastic fluctuations and a secondary model for the positron excess.Comment: Contribution to the 2022 Very High Energy Phenomena in the Universe (VHEPU) session of the 56th Rencontres de Moriond. 8 pages, 7 figure