Context. PAMELA and, more recently, AMS-02, are ushering us into a new era of greatly reduced statistical uncertainties in experimental measurements of cosmic-ray fluxes. In particular, new ...determinations of traditional diagnostic tools such as the boron-to-carbon ratio (B/C) are expected to significantly reduce errors on cosmic-ray diffusion parameters, with important implications for astroparticle physics, ranging from inferring primary source spectra to indirect dark matter searches. Aims. It is timely to stress, however, that the conclusions obtained crucially depend on the framework in which the data are interpreted as well as on some nuclear input parameters. We aim at assessing the theoretical uncertainties affecting the outcome, with models as simple as possible while still retaining the key dependencies. Methods. We compared different semi-analytical, two-zone model descriptions of cosmic-ray transport in the Galaxy: infinite slab(1D), cylindrical symmetry (2D) with homogeneous sources, cylindrical symmetry (2D) with inhomogeneous source distribution. We tested for the effect of a primary source contamination in the boron flux by parametrically altering its flux. We also tested for nuclear cross-section uncertainties. All hypotheses were compared by χ2 minimisation techniques to preliminary results from AMS-02. Results. We find that the main theoretical bias on the determination of the diffusion coefficient index δ (up to a factor two) is represented by the assumption that no injection of boron takes place at the source. The next most important uncertainty is represented by cross-section uncertainties, which reach ± 20% in δ. As a comparison, nuclear uncertainties are more important than the shift in the best-fit when introducing a convective wind of velocity ≲30 km s-1, with respect to a pure diffusive baseline model. Perhaps surprisingly, homogeneous 1D vs. 2D performances are similar in determining diffusion parameters. An inhomogeneous source distribution marginally alters the central value of the diffusion coefficient normalisation (at the 10%, 1σ level). However, the index of the diffusion coefficient δ is basically unaltered, as well as the goodness of fit. Conclusions. Our study suggests that, differently for instance from the leptonic case, realistic modelling of the geometry of the Galaxy and of the source distribution are of minor importance to correctly reproduce B/C data at high energies and thus, to a large extent, for the extraction of diffusion parameters. The ansatz on the lack of primary injection of boron represents the most serious bias and requires multi-messenger studies to be addressed. If this uncertainty could be lifted, nuclear uncertainties would still represent a serious concern; they degrade the systematic error on the inferred parameters to the 20% level, or three times the estimated experimental sensitivity. To reduce this, a new nuclear cross-section measurement campaign might be required.
On-going measurements of the cosmic radiation (nuclear, electronic, and gamma-ray) are shedding new light on cosmic-ray physics. A comprehensive picture of these data relies on an accurate ...determination of the transport and source parameters of propagation models. A Markov Chain Monte Carlo is used to obtain these parameters in a diffusion model. From the measurement of the B/C ratio and radioactive cosmic-ray clocks, we calculate their probability density functions, with a special emphasis on the halo size L of the Galaxy and the local underdense bubble of size r_h. The analysis relies on the USINE code for propagation and on a Markov Chain Monte Carlo technique (Putze et al. 2009, paper I of this series) for the parameter determination. As found in previous studies, the B/C best-fit model favours diffusion/convection/reacceleration (Model III) over diffusion/reacceleration (Model II). A combined fit on B/C and the isotopic ratios (10Be/9Be, 26Al/27Al, 36Cl/Cl) leads to L ~ 8 kpc and r_h ~ 120 pc for the best-fit Model III. This value for r_h is consistent with direct measurements of the local interstallar medium. For Model II, L ~ 4 kpc and r_h is consistent with zero. We showed the potential and usefulness of the Markov Chain Monte Carlo technique in the analysis of cosmic-ray measurements in diffusion models. The size of the diffusive halo depends crucially on the value of the diffusion slope delta, and also on the presence/absence of the local underdensity damping effect on radioactive nuclei. More precise data from on-going experiments are expected to clarify this issue.
Primary cosmic-ray elemental spectra have been measured with the balloon-borne Cosmic Ray Energetics And Mass (CREAM) experiment since 2004. The third CREAM payload (CREAM-III) flew for 29 days ...during the 2007-2008 Antarctic season. Energies of incident particles above 1 TeV are measured with a calorimeter. Individual elements are clearly separated with a charge resolution of ∼0.12 e (in charge units) and ∼0.14 e for protons and helium nuclei, respectively, using two layers of silicon charge detectors. The measured proton and helium energy spectra at the top of the atmosphere are harder than other existing measurements at a few tens of GeV. The relative abundance of protons to helium nuclei is 9.53 0.03 for the range of 1 TeV/n to 63 TeV/n. This ratio is considerably smaller than other measurements at a few tens of GeV/n. The spectra become softer above ∼20 TeV. However, our statistical uncertainties are large at these energies and more data are needed.
Context. The positron fraction in cosmic rays has recently been measured with improved accuracy up to 500 GeV, and it was found to be a steadily increasing function of energy above ~10 GeV. This ...behaviour contrasts with standard astrophysical mechanisms, in which positrons are secondary particles, produced in the interactions of primary cosmic rays during their propagation in the interstellar medium. The observed anomaly in the positron fraction triggered a lot of excitement, as it could be interpreted as an indirect signature of the presence of dark matter species in the Galaxy, the so-called weakly interacting massive particles (WIMPs). Alternatively, it could be produced by nearby sources, such as pulsars. Aims. These hypotheses are probed in light of the latest AMS-02 positron fraction measurements. As regards dark matter candidates, regions in the annihilation cross section to mass plane, which best fit the most recent data, are delineated and compared to previous measurements. The explanation of the anomaly in terms of a single nearby pulsar is also explored. Methods. The cosmic ray positron transport in the Galaxy is described using a semi-analytic two-zone model. Propagation is described with Green functions as well as with Bessel expansions. For consistency, the secondary and primary components of the positron flux are calculated together with the same propagation model. The above mentioned explanations of the positron anomaly are tested using χ2 fits. The numerical package MicrOMEGAs is used to model the positron flux generated by dark matter species. The description of the positron fraction from conventional astrophysical sources is based on the pulsar observations included in the Australia Telescope National Facility (ATNF) catalogue. Results. The masses of the favoured dark matter candidates are always larger than 500 GeV, even though the results are very sensitive to the lepton flux. The Fermi measurements point systematically to much heavier candidates than the recently released AMS-02 observations. Since the latter are more precise, they are much more constraining. A scan through the various individual annihilation channels disfavours leptons as the final state. On the contrary, the agreement is excellent for quark, gauge boson, or Higgs boson pairs, with best-fit masses in the 10 to 40 TeV range. The combination of annihilation channels that best matches the positron fraction is then determined at fixed WIMP mass. A mixture of electron and tau lepton pairs is only acceptable around 500 GeV. Adding b-quark pairs significantly improves the fit up to a mass of 40 TeV. Alternatively, a combination of the four-lepton channels provides a good fit between 0.5 and 1 TeV, with no muons in the final state. Concerning the pulsar hypothesis, the region of the distance-to-age plane that best fits the positron fraction for a single source is determined. Conclusions. The only dark matter species that fulfils the stringent gamma ray and cosmic microwave background bounds is a particle annihilating into four leptons through a light scalar or vector mediator, with a mixture of tau (75%) and electron (25%) channels, and a mass between 0.5 and 1 TeV. The positron anomaly can also be explained by a single pulsar, and a list of five pulsars from the ATNF catalogue is given. We investigate how this list could evolve when more statistics are accumulated. Those results are obtained with the cosmic ray transport parameters that best fit the B/C ratio. Uncertainties in the propagation parameters turn out to be very significant. In the WIMP annihilation cross section to mass plane for instance, they overshadow the error contours derived from the positron data.
Context. The secondary-to-primary B/C ratio is widely used for studying Galactic cosmic-ray propagation processes. The 2H/4He and 3He/4He ratios probe a different Z/A regime, which provides a test ...for the “universality” of propagation. Aims. We revisit the constraints on diffusion-model parameters set by the quartet (1H, 2H, 3He, 4He), using the most recent data as well as updated formulae for the inelastic and production cross-sections. Methods. Our analysis relies on the USINE propagation package and a Markov Chain Monte Carlo technique to estimate the probability density functions of the parameters. Simulated data were also used to validate analysis strategies. Results. The fragmentation of CNO cosmic rays (resp. NeMgSiFe) on the interstellar medium during their propagation contributes to 20% (resp. 20%) of the 2H and 15% (resp. 10%) of the 3He flux at high energy. The C to Fe elements are also responsible for up to 10% of the 4He flux measured at 1 GeV/n. The analysis of 3He/4He (and to a lesser extent 2H/4He) data shows that the transport parameters are consistent with those from the B/C analysis: the diffusion model with δ ~ 0.7 (diffusion slope), Vc ~ 20 km s-1 (galactic wind), Va ~ 40 km s-1 (reacceleration) is favoured, but the combination δ ~ 0.2, Vc ~ 0, and Va ~ 80 km s-1 is a close second. The confidence intervals on the parameters show that the constraints set by the quartet data can compete with those derived from the B/C data. These constraints are tighter when adding the 3He (or 2H) flux measurements, and the tightest when the He flux is added as well. For the latter, the analysis of simulated and real data shows an increased sensitivity to biases. Using the secondary-to-primary ratio along with a loose prior on the source parameters is recommended to obtain the most robust constraints on the transport parameters. Conclusions. Light nuclei should be systematically considered in the analysis of transport parameters. They provide independent constraints that can compete with those obtained from the B/C analysis.
The propagated fluxes of proton, helium, and heavier primary cosmic-ray species (up to Fe) are a means to indirectly access the source spectrum of cosmic rays. We check the compatibility of the ...primary fluxes with the transport parameters derived from the B/C analysis, but also if they bring further constraints. Proton data are well described in the simplest model defined by a power-law source spectrum and plain diffusion. They can also be accommodated by models with, e.g., convection and/or reacceleration. There is no need for breaks in the source spectral indices below $\sim 1$ TeV/n. Fits on the primary fluxes alone do not provide physical constraints on the transport parameters. If we let free the source spectrum $dQ/dE = q \beta^{\eta_S} {\cal R}^{-\alpha}$ and fix the diffusion coefficient $K(R)= K_0\beta^{\eta_T} {\cal R}^{\delta}$ such as to reproduce the B/C ratio, the MCMC analysis constrains the source spectral index $\alpha$ to be in the range $2.2-2.5$ for all primary species up to Fe, regardless of the value of the diffusion slope $\delta$. The $\eta_S$ low-energy shape of the source spectrum is degenerate with the low-energy shape $\eta_T$ of the diffusion coefficient: we find $\eta_S-\eta_T\approx 0$ for p and He data, but $\eta_S-\eta_T\approx 1$ for C to Fe primary species. This is consistent with the toy-model calculation in which the shape of the p/He and C/O to Fe/O data is reproduced if $\eta_S-\eta_T\approx 0-1$ (no need for different slopes $\alpha$). When plotted as a function of the kinetic energy per nucleon, the low-energy p/He ratio is shaped mostly by the modulation effect, whereas primary/O ratios are mostly shaped by their destruction rate.
Context. Two years ago, the Ams-02 collaboration released the most precise measurement of the cosmic ray positron flux. In the conventional approach, in which positrons are considered as purely ...secondary particles, the theoretical predictions fall way below the data above 10 GeV. One suggested explanation for this anomaly is the annihilation of dark matter particles, the so-called weakly interactive massive particles (WIMPs), into standard model particles. Most analyses have focused on the high-energy part of the positron spectrum, where the anomaly lies, disregarding the complicated GeV low-energy region where Galactic cosmic ray transport is more difficult to model and solar modulation comes into play. Aims. Given the high quality of the latest measurements by Ams-02, it is now possible to systematically re-examine the positron anomaly over the entire energy range, this time taking into account transport processes so far neglected, such as Galactic convection or diffusive re-acceleration. These might impact somewhat on the high-energy positron flux so that a complete and systematic estimate of the secondary component must be performed and compared to the Ams-02 measurements. The flux yielded by WIMPs also needs to be re-calculated more accurately to explore how dark matter might source the positron excess. Methods. We devise a new semi-analytical method to take into account transport processes thus far neglected, but important below a few GeV. It is essentially based on the pinching of inverse Compton and synchrotron energy losses from the magnetic halo, where they take place, inside the Galactic disc. The corresponding energy loss rate is artificially enhanced by the so-called pinching factor, which needs to be calculated at each energy. We have checked that this approach reproduces the results of the Green function method at the per mille level. This new tool is fast and allows one to carry out extensive scans over the cosmic ray propagation parameters. Results. We derive the positron flux from sub-GeV to TeV energies for both gas spallation and dark matter annihilation. We carry out a scan over the cosmic ray propagation parameters, which we strongly constrain by requiring that the secondary component does not overshoot the Ams-02 measurements. We find that only models with large diffusion coefficients are selected by this test. We then add to the secondary component the positron flux yielded by dark matter annihilation. We carry out a scan over WIMP mass to fit the annihilation cross-section and branching ratios, successively exploring the cases of a typical beyond-the-standard-model WIMP and an annihilation through light mediators. In the former case, the best fit yields a p-value of 0.4% for a WIMP mass of 264 GeV, a value that does not allow to reproduce the highest energy data points. If we require the mass to be larger than 500 GeV, the best-fit χ2 per degree of freedom always exceeds a value of 3. The case of light mediators is even worse, with a best-fit χ2 per degree of freedom always larger than 15. Conclusions. We explicitly show that the cosmic ray positron flux is a powerful and independent probe of Galactic cosmic ray propagation. It should be used as a complementary observable to other tracers such as the boron-to-carbon ratio. This analysis shows also that the pure dark matter interpretation of the positron excess is strongly disfavoured. This conclusion is based solely on the positron data, and no other observation, such as the antiproton flux or the CMB anisotropies, needs to be invoked.
Context. The source spectrum of cosmic rays is not well determined by diffusive shock acceleration models. The propagated fluxes of proton, helium, and heavier primary cosmic-ray species (up to Fe) ...are a means to indirectly access it. But how robust are the constraints, and how degenerate are the source and transport parameters? Aims. We check the compatibility of the primary fluxes with the transport parameters derived from the B/C analysis, but also ask whether they add further constraints. We study whether the spectral shapes of these fluxes and their ratios are mostly driven by source or propagation effects. We then derive the source parameters (slope, abundance, and low-energy shape). Methods. Simple analytical formulae are used to address the issue of degeneracies between source/transport parameters, and to understand the shape of the p/He and C/O to Fe/O data. The full analysis relies on the USINE propagation package, the MINUIT minimisation routines (χ2 analysis) and a Markov Chain Monte Carlo (MCMC) technique. Results. Proton data are well described in the simplest model defined by a power-law source spectrum and plain diffusion. They can also be accommodated by models with, e.g., convection and/or reacceleration. There is no need for breaks in the source spectral indices below ~1 TeV/n. Fits to the primary fluxes alone do not provide physical constraints on the transport parameters. If we leave the source spectrum free, parametrised by the form dQ/dE = qβηSℛ−α, and fix the diffusion coefficient K(R) = K0βηTℛδ so as to reproduce the B/C ratio, the MCMC analysis constrains the source spectral index α to be in the range 2.2−2.5 for all primary species up to Fe, regardless of the value of the diffusion slope δ. The values of the parameter ηS describing the low-energy shape of the source spectrum are degenerate with the parameter ηT describing the low-energy shape of the diffusion coefficient: we find ηS − ηT ≈ 0 for p and He data, but ηS − ηT ≈ 1 for C to Fe primary species. This is consistent with the toy-model calculation in which the shape of the p/He and C/O to Fe/O data is reproduced if ηS − ηT ≈ 0−1 (no need for different slopes α). When plotted as a function of the kinetic energy per nucleon, the low-energy p/He ratio is determined mostly by the modulation effect, whereas primary/O ratios are mostly determined by their destruction rate. Conclusions. Models based on fitting B/C are compatible with primary fluxes. The different spectral indices for the propagated primary fluxes up to a few TeV/n can be naturally ascribed to transport effects only, implying universality of elemental source spectra.
The B/C ratio is used in cosmic-ray physics to constrain the transport parameters. However, from the same set of data, the various published values show a puzzling large scatter of these parameters. ...We investigate the impact of using different inputs (gas density and hydrogen fraction in the Galactic disc, source spectral shape, low-energy dependence of the diffusion coefficient, and nuclear fragmentation cross-sections) on the best-fit values of the transport parameters. We quantify the systematics produced when varying these inputs, and compare them to statistical uncertainties. We discuss the consequences for the slope of the diffusion coefficient delta. The analysis relies on the propagation code USINE interfaced with the Minuit minimisation routines. We find the typical systematic uncertainties to be larger than the statistical ones. The several published values of delta (from 0.3 to 0.8) can be recovered when varying the low-energy shape of the diffusion coefficient and the convective wind strength. Models including a convective wind are characterised by delta > 0.6, which cannot be reconcile with the expected theoretical values (1/3 and 1/2). However, from a statistical point of view (chi^2 analysis), models with both reacceleration and convection-hence large delta-are favoured. The next favoured models in line yield delta that can be accommodated with 1/3 and 1/2, but require a strong upturn of the diffusion coefficient at low energy (and no convection). To date, using the best statistical tools, the transport parameter determination is still plagued by many unknowns at low energy (~ GeV/n). To disentangle between all these configurations, measurements of the B/C ratio at TeV/n energies and/or combination with other secondary-to-primary ratios is necessary.
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