REVIEW
Unified interpretation of cosmic-ray nuclei and antiproton recent measurements
High Energy Astrophysical Phenomena · Submitted 25 Sep 2009 · 49 references
Pith's verdict: A solid, useful joint fit of nuclei and antiproton data — the physics pipeline holds up, but the combined statistic is non-standard and the quoted 95% CL ranges should be read as indicative rather than exact.
T0 · AI review
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Referee report
The paper
The paper claims
One diffusion model fits light nuclei and antiprotons at once
The reading
What carries the argument
The load-bearing device is a joint likelihood built from two independently computed $χ^2$ surfaces in the $(D_0/z_t, δ)$ plane, combined as $χ^2_{comb} = (χ^2_{B/C} + χ^2_{ap/p})/2$ for each trial Alfvén velocity. The nuclear side is handled in stages: the C/O and N/O source abundance ratios are treated as free nuisance parameters and refitted at every point so that only the B/C shape constrains transport, which matters because carbon and oxygen are themselves depleted by spallation below 100 GeV/n. The antiproton side needs no such marginalization since the He/p source ratio is fixed from the measured helium spectrum. The transport itself is solved numerically with DRAGON on a cylindrical halo, using a diffusion coefficient $D(ρ,z) = D_0 β^η (ρ/ρ_0)^δ e^{|z|/z_t}$ and momentum-space diffusion tied to it by quasi-linear theory, $D_{pp} = (4/3) δ (4-δ^2)(4-δ) v_A^2 p^2 / D$. A separate effective variant with $η = -0.4$ is introduced to extend the fit down to $0.1$ GeV/n without disturbing the high-energy constraints.
Extended reading notes
Core claim
The paper's claim is that a single diffusion-reacceleration model reproduces both the light secondary-to-primary nuclear ratios (B/C, N/O, C/O) and the antiproton-to-proton ratio within experimental errors, so that the two data sets need not be fitted by incompatible parameter choices. Working above $E_{min} = 5$ GeV/n, where solar modulation and uncertain low-energy cross sections are least troublesome, the authors map a reduced $χ^2$ over the plane of the diffusion normalization $D_0/z_t$ and the spectral index $δ$, scanning the Alfvén velocity $v_A$ as a third axis. The B/C-allowed region drifts toward lower $δ$ and higher $D_0/z_t$ as $v_A$ grows, while the antiproton-to-proton-allowed region moves the other way, so only a limited overlap survives. The reported outcome is $0.3 < δ < 0.6$ and $0.6 < D_0/z_t < 1$ at 95% confidence, with $10 < v_A < 20$ km s$^{-1}$; $v_A = 15$ km s$^{-1}$ minimizes the combined $χ^2$. Because Kraichnan-type diffusion ($δ = 0.5$) sits inside that window and Kolmogorov-type ($δ = 0.33$) sits at its edge, the authors read the result as favoring Kraichnan. A secondary result is a pair of MAX and MIN propagation models that bracket the secondary antiproton flux while still fitting the nuclear ratios at 95% confidence, giving dark-matter and exotic-source searches a conservative background envelope.
Load-bearing premise
The extraction of a single spectral index $δ$ assumes the diffusion coefficient is an unbroken power law in rigidity, and that the measured antiprotons are entirely secondary.
Editorial extensions
If this is right
- Antiproton searches for exotic sources can use the paper's MIN model as a conservative background: any claimed excess must survive the requirement that MIN plus the new component not overshoot the data.
- Kraichnan-type diffusion with $δ \approx 0.5$ is preferred over Kolmogorov, which shifts the expected secondary-to-primary ratios and the antiproton yield at high rigidity.
- The narrow allowed window for the Alfvén velocity turns reacceleration from a free knob into a constrained parameter, so models that invoke strong reacceleration to fit low-energy spectra are disfavored.
- The authors note that extrapolating $δ \approx 0.5$ to $E_k \gg 10^5$ GeV/n would overproduce cosmic-ray anisotropy, so the standard propagation picture may need modification at the highest energies.
- An effective velocity dependence $η = -0.4$ in the diffusion coefficient lets one model describe B/C, N/O, C/O, oxygen, proton and antiproton data down to $0.1$ GeV/n without changing the high-energy fit.
Reading between the lines
- The claim that Kraichnan beats Kolmogorov rests on a comparison at fixed assumptions; a reader should ask how much of the preference survives if the injection spectrum is allowed the spectral break that the paper's own Kolmogorov reference model requires at 9 GV.
- Because the quoted confidence regions use statistical errors only, and the authors cite a separate study finding cross-section systematics worth roughly 40% on $δ$ (10% for the most updated sets), the boundary between 'Kraichnan favored' and 'Kolmogorov excluded' is the softest part of the result.
- The MAX/MIN envelope is a genuinely reusable product: it converts a propagation fit into a statement about how large an exotic antiproton component could hide, which is the form most useful to dark-matter analyses.
- The $η = -0.4$ device is presented as an effective stand-in for wave damping by streaming cosmic rays; if that interpretation is right, the same physics should leave a detectable imprint on the low-energy spectra of heavier secondaries, which would be a cleaner test than the antiproton fit alone.
Original abstract
We use our numerical code, DRAGON, to study the implications of recent data on our knowledge of the propagation properties of cosmic ray nuclei in the Galaxy. We show that B/C (as well as N/O and C/O) data, including those recently taken by CREAM, and ${\bar p}/p$ data, especially including recent PAMELA results, can consistently be fitted within a unique diffusion-reacceleration model. The requirement that light nuclei and $\bar p$ data are consistently reproduced within experimental uncertainties places significant limits on the main propagation parameters. In particular, we find the allowed range of the diffusion coefficient spectral index to be $0.3 < \delta < 0.6$ at 95% confidence level and that Kraichnan type diffusion is favored with respect to Kolmogorov. While some amount of reacceleration is required, only a limited range of the Alfv\'en velocity value ($10 \simleq v_A \simleq 20 \km \s^{-1}$) is allowed by a combined analysis of nuclear and antiproton data, which we perform here for the first time. If antiproton data are not used to constrain the propagation parameters, a larger set of models is allowed. In this case, we determine which combinations of the relevant parameters maximize and minimize the antiproton flux under the condition of still fitting light nuclei data at 95% C.L. These models may then be used to constrain a possible extra antiproton component arising from astrophysical or exotic sources (e.g. dark matter annihilation or decay).
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We use our numerical code, DRAGON, to study the implications of recent data on our knowledge of the propagation properties of cosmic ray nuclei in the Galaxy. We show that B/C (as well as N/O and C/O) data, including those recently taken by CREAM, and ${\bar p}/p$ data, especially including recent PAMELA results, can consistently be fitted within a unique diffusion-reacceleration model. The requirement that light nuclei and $\bar p$ data are consistently reproduced within experimental uncertainties places significant limits on the main propagation parameters. In particular, we find the allowed range of the diffusion coefficient spectral index to be $0.3 < \delta < 0.6$ at 95% confidence level and that Kraichnan type diffusion is favored with respect to Kolmogorov. While some amount of reacceleration is required, only a limited range of the Alfv\'en velocity value ($10 \simleq v_A \simleq 20 \km \s^{-1}$) is allowed by a combined analysis of nuclear and antiproton data, which we perform here for the first time. If antiproton data are not used to constrain the propagation parameters, a larger set of models is allowed. In this case, we determine which combinations of the relevant parameters maximize and minimize the antiproton flux under the condition of still fitting light nuclei data at 95% C.L. These models may then be used to constrain a possible extra antiproton component arising from astrophysical or exotic sources (e.g. dark matter annihilation or decay).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use our numerical code, DRAGON, to study the implications of recent data on our knowledge of the propagation properties of cosmic ray nuclei in the Galaxy. | method 0.56 | 0.87 | 0.03 | asserted 0.89 |
| s1 | We show that B/C (as well as N/O and C/O) data, including those recently taken by CREAM, and ${\bar p}/p$ data, especially including recent PAMELA results, can consistently be fitted within a unique diffusion-reacceleration model. | result 0.93 | 0.87 | 0.61 | asserted 0.99 |
| s2 | The requirement that light nuclei and $\bar p$ data are consistently reproduced within experimental uncertainties places significant limits on the main propagation parameters. | result 0.70 | 0.72 | 0.29 | asserted 0.99 |
| s3 | In particular, we find the allowed range of the diffusion coefficient spectral index to be $0.3 < \delta < 0.6$ at 95% confidence level and that Kraichnan type diffusion is favored with respect to Kolmogorov. | result 1.00 | 0.96 | 0.28 | asserted 1.00 |
| s4 | While some amount of reacceleration is required, only a limited range of the Alfv\'en velocity value ($10 \simleq v_A \simleq 20 \km \s^{-1}$) is allowed by a combined analysis of nuclear and antiproton data, which we perform here for the first time. | result 0.99 | 0.94 | 0.19 | asserted 1.00 |
| s5 | If antiproton data are not used to constrain the propagation parameters, a larger set of models is allowed. | result 0.83 | 0.64 | 0.06 | asserted 0.89 |
| s6 | In this case, we determine which combinations of the relevant parameters maximize and minimize the antiproton flux under the condition of still fitting light nuclei data at 95% C.L. | method 0.57 | 0.93 | 0.05 | asserted 0.98 |
| s7 | These models may then be used to constrain a possible extra antiproton component arising from astrophysical or exotic sources (e.g. dark matter annihilation or decay). | interpretation 0.74 | 0.47 | 0.08 | hedged possibility 1.00 |
What was examined, and what was not
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- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
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Figures
Figures reproduced from arXiv:0909.4548 by the authors.
References
How later papers used it
55 later papers cite it
2 later papers by other authors are listed below: 1 used its method or tool and 1 cited it as support.
Uses its method or tool 1 of 9 papers with this label
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Illustrated the effect of solar modulation using the simple recipe of this paper.
Cosmic ray driven winds in the Galactic environment and the cosmic ray spectrum (2017) · 1.00 · paraphrased: the licence does not allow quoting
Cites it as support 1 of 3 papers with this label
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Said that its scenario is also consistent with antiproton data, citing this paper.
Testing universality of cosmic-ray acceleration with proton/helium data from AMS and Voyager-1 (2016) · 0.97 · paraphrased: the licence does not allow quoting
How the literature uses it
48 arXiv papers cite this in 62 sentences
Papers citing it · 42 sentences without a confident label
Uses its method or tool 7 papers
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In the present work, we study high energy CR propagation in our Galaxy, by solving the transport equation numerically, using publicly available code DRAGON[The 3D version of the DRAGON code is available at https://github.com/cosmicrays/DRAGON for download.] (Diffusion of cosmic RAys in Galaxy modelizatiON) [ref] .
Positron Excess from Cosmic Ray Interactions in Galactic Molecular Clouds · Model setup · 1.00
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To simulate the propagation of electrons in the GC and Inner Galaxy regions, we make use of the publicly available numerical codes [ref] and [ref] .
The Galactic Center GeV Excess from a Series of Leptonic Cosmic-Ray Outbursts · Numerical simulations of outburst events · 1.00
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Notice that the spectrum has been corrected for the solar modulation using the widely used force-free approximation as in [ref] .
Impact of transport modelling on the $^{60}$Fe abundance inside Galactic cosmic ray sources · Transport model · 0.98
Uses its data or values 1 paper
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In addition, it has been noted that data from the PAMELA experiment [ref] exhibit a 40% excess of antiprotons in the 1-3 GeV energy range over expectations from cosmic ray propagation models [ref] .
Galactic Centre GeV Photons from Dark Technicolor · Introduction · 0.83
Compares with it 3 papers
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This precision is much greater than that obtained with present (pre-AMS-02) data; see Refs. [ref] .
Pinpointing Cosmic Ray Propagation With The AMS-02 Experiment · Constraining propagation models · 0.87
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It is worth noting here that the $δ$ required by the new high-energy measurements is in perfect agreement with the best-fit value obtained in our earlier statistical analysis [ref] , based on the available high-energy measurements preceding PAMELA and AMS-02 releases.
Secondary antiprotons as a Galactic Dark Matter probe · Discussion on AMS-02 data · 0.83
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We notice that the KRA model in [ref] , though similar to its homologous in this paper, reproduced the positron fraction measured by PAMELA down to $1$ rather than that of AMS-01.
Cosmic Ray Electrons, Positrons and the Synchrotron emission of the Galaxy: consistent analysis and implications · Back to the $e^+$ and $e^-$ observed spectra · 0.99
Cites it as support 2 papers
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Here we suggest that at least part of the low energy positron fraction anomaly could be related to other issues encountered by strong reacceleration propagation setups: 1) as we mentioned, those models do not provide a satisfactory description of the antiproton spectrum measured by PAMELA and other experiments [ref] ; 2) they reproduce the observed proton spectrum only by introducing a break ad hoc in the source spectrum; 3) strong reacceleration rise similar problems with the electron spectrum in the GeV region [ref] ; 4) they are incompatible with the observed spectrum of the synchrotron emission of the Galaxy [ref] .
Cosmic ray models compared to Fermi-LAT positron and electron separate spectra · The case of moderate reacceleration · 0.96
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This change is partly motivated by recent studies [ref] which observed a substantial improvement in the fit to secondary nuclear cosmic rays within the diffusion model with free $η$.
Dark matter or correlated errors: Systematics of the AMS-02 antiproton excess · Cosmic-ray production and propagation · 1.00
Cites it as background 7 papers
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If data are interpreted assuming a low convection wind (i.e., null or linearly increasing in the vertical direction), ratios of secondaries to primaries can be typically well-fitted by diffusion (plus reacceleration) models with Kolmogorov ($γ=1/3$) [ref] or Kraichnan ($γ=1/2$) [ref] spectrum of turbulence.
Galactic Magnetic Turbulence from Radio data · Results and Discussion · 0.89
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These include both semi-analytic [ref] as well as fully numerical treatments [ref] .
Antiproton Flux in Cosmic Ray Propagation Models with Anisotropic Diffusion · Introduction · 0.85
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The INJ.BRK (injection break) model has been explored extensively in literature [ref] .
Fast and accurate AMS-02 antiproton likelihoods for global dark matter fits · Choice of models · 0.97
What it cites · 36 sentences without a confident label
Uses the method or tool of 2 papers
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In this work we use DRAGON [ref] to constrain the main diffusion parameters against updated experimental data in the energy range $1 ≲E ≲10^3 /n$.
Cosmic-Ray Nuclei, Antiprotons and Gamma-rays in the Galaxy: a New Diffusion Model · Introduction · 1.00
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Inelastic scattering, annihilation and tertiary $p̅$ (antiprotons which have been inelastically scattered) are treated as in [ref] .
Secondary antiprotons and propagation of cosmic rays in the Galaxy and heliosphere · Nuclear cross sections · 1.00
Uses data or values from 3 papers
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Besides CR nuclear measurements, valuable complementary data were recently provided by the PAMELA satellite experiment which measured the antiproton to proton ratio up to $∼100$ with unprecedented accuracy [ref] .
A new measurement of the antiproton-to-proton flux ratio up to 100 GeV in the cosmic radiation · Introduction · 0.90
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For protons and antiprotons we use a potential which allows to match BESS98 [ref] , AMS-01 [ref] and PAMELA [ref] proton data even well below 1 GeV/n (see Fig. [ref]).
Precise Measurement of Cosmic-Ray Proton and Helium Spectra with the BESS Spectrometer · Solar modulation · 0.96
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Following [ref] we take the He/H numerical fraction in the ISM to be 0.11.
The solar chemical composition · Target gas · 1.00
Compares with 6 papers
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In order to clarify the reasons of such a discrepancy, in Fig. [ref] and [ref] we compare the predictions of our reference diffusion-reacceleration model $(δ, D_0/z_t, v_A, η) = (0.5, 0.7, 15, - 0.4)$, which for brevity we call Kraichnan model, with those obtained using the propagation parameters (and source distribution) of the Kolmogorov model discussed in [ref] , namely $(δ, D_0(4 GV)/z_t, v_A, η) = (0.33,1.45, 30, 1)$ [In [ref] a spatially uniform diffusion coefficient ($z_t=z_max = 4$) was assumed.
Diffuse Galactic continuum gamma rays. A model compatible with EGRET data and cosmic-ray measurements · Discussion and comparison with previous results · 0.98
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In spite of these differences, and that CREAM and PAMELA data were not included in those analyses for chronological reasons, it is comforting that for low values of the convective velocity $v_c ≃0$ the preferred value of $δ$ estimated in [ref] is in remarkably good agreement with that found in this work: $δ≃0.45$.
Cosmic Rays below Z=30 in a diffusion model: new constraints on propagation parameters · Discussion and comparison with previous results · 1.00
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In spite of these differences, and that CREAM and PAMELA data were not included in those analyses for chronological reasons, it is comforting that for low values of the convective velocity $v_c ≃0$ the preferred value of $δ$ estimated in [ref] is in remarkably good agreement with that found in this work: $δ≃0.45$.
New results on source and diffusion spectral features of Galactic cosmic rays: I- B/C ratio · Discussion and comparison with previous results · 1.00
Cites as support 1 paper
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As shown in [ref] , a vertically growing $D$ is physically more realistic than a uniform one and allows to get a more regular behavior of the CR density at the vertical boundaries of the propagation halo with respect to the case of uniform diffusion.
Cosmic-Ray Nuclei, Antiprotons and Gamma-rays in the Galaxy: a New Diffusion Model · Spatial diffusion coefficient · 0.97
Cites as background 14 papers
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Well known realizations of these two approaches are respectively the two-zone model (see e.g. [ref] ) and the GALPROP package [ref] .
Cosmic-ray propagation and interactions in the Galaxy · Introduction · 0.90
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Well known realizations of these two approaches are respectively the two-zone model (see e.g. [ref] ) and the GALPROP package [ref] .
Cosmic Rays below Z=30 in a diffusion model: new constraints on propagation parameters · Introduction · 0.90
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Well known realizations of these two approaches are respectively the two-zone model (see e.g. [ref] ) and the GALPROP package [ref] .
New results on source and diffusion spectral features of Galactic cosmic rays: I- B/C ratio · Introduction · 0.90
Discussion
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