REVIEW
Cosmic Rays below Z=30 in a diffusion model: new constraints on propagation parameters
Astrophysics · Submitted 15 Jan 2001 · 78 references
Pith's verdict: A careful, reusable scan of diffusion parameter space whose correlation structure is the real product; the 'exclusion' language on δ and on Vc=0/Va=0 outruns the error budget, though the Kolmogorov exclusion itself probably survives.
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Referee report
The paper
The paper claims
Cosmic-ray boron-to-carbon data constrain the diffusion spectral index to roughly 0.45–0.85 and exclude the Kolmogorov value 1/3.
The reading
What carries the argument
The load-bearing quantity is the secondary-to-primary ratio B/C computed from a two-zone diffusion equation. Boron is almost pure secondary and carbon is primary, so the ratio is sensitive to the grammage and to the energy dependence of diffusion. The model solves transport in a thin disk and a halo with a Bessel expansion, treats spallation as a shower from $Z=30$ downward, and uses a $��chi^2$ scan over $K_0$, $��delta$, $L$, $V_c$, and $V_a$. The new analytical solutions cover nuclei produced by radioactive decay, including decays occurring in the halo rather than only in the disk.
Extended reading notes
Core claim
The central claim is that B/C data, analysed with a semi-analytical diffusion model, exclude a Kolmogorov diffusion spectrum and constrain the transport parameters. For fixed $��delta=0.6$, good fits require $8.5 < V_c < 12$ km s$^{-1}$ and $410 < V_a/��sqrt{K_0} < 530$ in the paper's units. Across the scan, $��delta$ is restricted to about $[0.45,0.85]$, with the best $��chi^2=25.5$ at $��delta=0.70$; the Kolmogorov value $��delta=1/3$ gives $��chi^2>100$. The same scan excludes $V_c=0$ and $V_a=0$ for any combination of the other parameters. The allowed regions are strongly correlated: contours for different $��delta$ superimpose after rescaling $K_0/L$ by a function $f(��delta)$. All good B/C models are compatible with sub-Fe/Fe data, and among the tested forms only $Q(E)��propto p^{-��alpha}$ and $K(E)=K_0��beta R^��delta$ give good fits.
Load-bearing premise
The fit treats the Webber spallation cross sections and the Tripathi total inelastic cross sections as accurate enough that the shape of B/C is set by propagation; the quoted roughly 10% cross-section precision is not included in the $��chi^2$, so a systematic shift at that level could move the allowed $��delta$ band and weaken the exclusions.
Editorial extensions
If this is right
- A Kolmogorov spectrum ($��delta=1/3$) is excluded, and the diffusion index is restricted to about 0.45–0.85, with the best fit near 0.70.
- Convection-free and reacceleration-free diffusion models are excluded for the tested thin-disk, constant-wind geometry.
- The five transport parameters are correlated; fixing the halo thickness with radioactive isotopes would narrow the allowed ranges of the others.
- Good B/C fits are compatible with sub-Fe/Fe data, so the same transport parameters can be used for other secondary species.
- Among the tested forms, only a rigidity power-law source spectrum and $K(E)=K_0��beta R^��delta$ give good B/C fits.
Reading between the lines
- Because the fit uses only experimental errors, propagating the 10–20% cross-section systematics would likely widen the $��delta$ interval and could soften the exclusion of no-convection or no-reacceleration models.
- Future AMS B/C and beryllium isotope data can break the $L$–$K_0/L$ degeneracy; if the scaling $f(��delta)$ holds, a measured $L$ would translate directly into a tighter $��delta$ and $V_c$ range.
- The exclusion of $V_c=0$ and $V_a=0$ is tied to the thin-disk, constant-wind, disk-only-reacceleration setup; a more general wind profile or halo reacceleration could reopen those cases.
- For dark-matter antiproton searches, the practical consequence is that a Kolmogorov-like background is disfavoured, so any antiproton excess should be judged against a relatively hard diffusion spectrum.
Original abstract
Cosmic ray nuclei fluxes are expected to be measured with high precision in the near future. For instance, high quality data on the antiproton component could give important clues about the nature of the astronomical dark matter. A very good understanding of the different aspects of cosmic ray propagation is therefore necessary. In this paper, we use cosmic ray nuclei data to give constraints on the diffusion parameters. Propagation is studied with semi-analytical solutions of a diffusion model, and we give new analytical solutions for radioactively produced species. Our model includes convection and reacceleration as well as the standard energy losses. We perform a $\chi^2$ analysis over B/C data for a large number of configurations obtained by varying the relevant parameters of the diffusion model. A very good agreement with B/C data arises for a number of configurations, all of which are compatible with sub-Fe/Fe data. Different source spectra $Q(E)$ and diffusion coefficients $K(E)$ have been tried, but for both parameters only one form gives a good fit. Another important result is that models without convection or without reacceleration are excluded. We find that the various parameters, i.e. the diffusion coefficient normalisation $K_0$ and spectral index $\delta$, the halo thickness $L$, the Alfv\'en velocity $V_a$, and the convection velocity $V_c$ are strongly correlated. We obtain limits on the spectral index $\delta$ of thediffusion coefficient, and in particular we exclude a Kolmogorov spectrum ($\delta = 1/3$).
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
Cosmic ray nuclei fluxes are expected to be measured with high precision in the near future. For instance, high quality data on the antiproton component could give important clues about the nature of the astronomical dark matter. A very good understanding of the different aspects of cosmic ray propagation is therefore necessary. In this paper, we use cosmic ray nuclei data to give constraints on the diffusion parameters. Propagation is studied with semi-analytical solutions of a diffusion model, and we give new analytical solutions for radioactively produced species. Our model includes convection and reacceleration as well as the standard energy losses. We perform a $\chi^2$ analysis over B/C data for a large number of configurations obtained by varying the relevant parameters of the diffusion model. A very good agreement with B/C data arises for a number of configurations, all of which are compatible with sub-Fe/Fe data. Different source spectra $Q(E)$ and diffusion coefficients $K(E)$ have been tried, but for both parameters only one form gives a good fit. Another important result is that models without convection or without reacceleration are excluded. We find that the various parameters, i.e. the diffusion coefficient normalisation $K_0$ and spectral index $\delta$, the halo thickness $L$, the Alfv\'en velocity $V_a$, and the convection velocity $V_c$ are strongly correlated. We obtain limits on the spectral index $\delta$ of thediffusion coefficient, and in particular we exclude a Kolmogorov spectrum ($\delta = 1/3$).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Cosmic ray nuclei fluxes are expected to be measured with high precision in the near future. | background 0.99 | 0.04 | 0.02 | hedged possibility 0.90 |
| s1 | For instance, high quality data on the antiproton component could give important clues about the nature of the astronomical dark matter. | background 0.99 | 0.04 | 0.02 | hedged possibility 1.00 |
| s2 | A very good understanding of the different aspects of cosmic ray propagation is therefore necessary. | background 0.97 | 0.05 | 0.02 | asserted 0.95 |
| s3 | In this paper, we use cosmic ray nuclei data to give constraints on the diffusion parameters. | contribution 0.97 | 0.92 | 0.08 | asserted 0.99 |
| s4 | Propagation is studied with semi-analytical solutions of a diffusion model, and we give new analytical solutions for radioactively produced species. | method 0.78 | 0.94 | 0.06 | asserted 1.00 |
| s5 | Our model includes convection and reacceleration as well as the standard energy losses. | method 0.98 | 0.59 | 0.03 | asserted 1.00 |
| s6 | We perform a $\chi^2$ analysis over B/C data for a large number of configurations obtained by varying the relevant parameters of the diffusion model. | method 0.99 | 0.97 | 0.05 | asserted 0.98 |
| s7 | A very good agreement with B/C data arises for a number of configurations, all of which are compatible with sub-Fe/Fe data. | result 1.00 | 0.93 | 0.18 | asserted 0.98 |
| s8 | Different source spectra $Q(E)$ and diffusion coefficients $K(E)$ have been tried, but for both parameters only one form gives a good fit. | result 0.98 | 0.95 | 0.12 | asserted 1.00 |
| s9 | Another important result is that models without convection or without reacceleration are excluded. | result 1.00 | 0.91 | 0.24 | asserted 1.00 |
| s10 | We find that the various parameters, i.e. the diffusion coefficient normalisation $K_0$ and spectral index $\delta$, the halo thickness $L$, the Alfv\'en velocity $V_a$, and the convection velocity $V_c$ are strongly correlated. | result 1.00 | 0.96 | 0.17 | asserted 1.00 |
| s11 | We obtain limits on the spectral index $\delta$ of thediffusion coefficient, and in particular we exclude a Kolmogorov spectrum ($\delta = 1/3$). | result 1.00 | 0.96 | 0.34 | asserted 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:astro-ph/0101231 by the authors.
References
How later papers used it
112 later papers cite it
3 later papers by other authors are listed below: 2 used its method or tool and 1 used its data or values. 2 more papers by the same authors are listed: 1 used its method or tool and 1 used its data or values.
Uses its method or tool 3 of 23 papers with this label · 1 by the same authors
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Solved the transport equation following the semianalytical method introduced in this paper.
Voyager 1 $e^\pm$ Further Constrain Primordial Black Holes as Dark Matter (2018) · 0.82 · paraphrased: the licence does not allow quoting
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Made use of the WNEWTR code to compute the contribution of intermediate lived parent nuclei as in this paper.
Cosmic-ray propagation with DRAGON2: II. Nuclear interactions with the interstellar gas (2017) · 0.99 · paraphrased: the licence does not allow quoting
By the same authors
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Used the semianalytic method proposed in this paper to solve the transport equation.
Novel cosmic-ray electron and positron constraints on MeV dark matter particles (2016) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Uses its data or values 2 of 16 papers with this label · 1 by the same authors
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Utilized the best-fit model found in this paper for the transport parameters.
Cosmic-ray antiproton constraints on light singlino-like dark matter candidates (2011) · 0.84 · paraphrased: the licence does not allow quoting
By the same authors
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Computed secondary antiproton spectra with the set of about 1,600 propagation models found in this paper to pass the B/C test.
Dark Matter Indirect Signatures (2012) (same authors) · 0.89 · paraphrased: the licence does not allow quoting
How the literature uses it
98 arXiv papers cite this in 161 sentences
Papers citing it · 103 sentences without a confident label
Uses its method or tool 22 papers
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To generate these maps, we apply the propagation scheme introduced by [ref] , modified according to [ref] for primary electrons.
Can the morphology of gamma-ray emission distinguish annihilating from decaying dark matter? · Producing gamma-ray maps · 0.99
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Neglecting energy gain and loss terms, using cylindrical coordinates and Bessel-expanding \(𝒩(r,z,T)\) and \(Q^prim(r,z,T)\) [equation] where \(ξ_i\) is the ith zero of \(J_0(x)\), the equation to solve in the halo is [ref] [equation] Imposing the boundary condition \(N_i(z=L)=0\) and ensuring continuity with the solution in the disk, where the equation to solve is [equation] (there are no sources in the thin disk, but there is annihilation on the ISM, described by \(Γ^ann(T)\)), one gets the solution[With [equation] 0.5 [equation] 0.495 [equation] ] [equation] Finally, for the flux \(Φ(r,z,T)=v/4π𝒩(r,z,T)\) near the Earth one therefore gets [equation] where $B$ is the boost factor.
Anti-deuterons from heavy Dark Matter · Propagation · 0.99
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The transport equation is solved following the semianalytical method introduced in Ref. [ref] and extended for sub-10 GeV $e^±$ while accounting for all propagation processes by the pinching method [ref] .
Voyager 1 $e^\pm$ Further Constrain Primordial Black Holes as Dark Matter · Introduction · 0.82
Uses its data or values 15 papers
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Model A is the model MAX of Refs. [ref] , where $L = 15$ kpc, $K_0=0.0765$ kpc$^2$/Myr, $δ=0.46$, $V_a=117.6$ km/s, and $V_c=5$ km/s, derived from HEAO-3 (High Energy Astrophysical Observatory) boron/carbon (B/C) data [ref] .
Voyager 1 $e^\pm$ Further Constrain Primordial Black Holes as Dark Matter · Introduction · 0.95
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For the transport parameters, we have utilized the best-fit model found in [ref] and still in excellent agreement with more recent analyses ( [ref] ).
Cosmic-ray antiproton constraints on light singlino-like dark matter candidates · Antiproton transport and flux at the Earth · 0.84
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Regarding the propagation parameters $L$, $K_0$ and $α$, we take their values from the commonly used MIN, MAX and MED models [ref] (see Table [ref]), which correspond to the minimal, maximal and median primary positron fluxes over some energy range that are compatible with the B/C data [ref] .
Constraining Dark Matter Properties with Gamma-Rays from the Galactic Center with Fermi-LAT · Gamma–Rays from Inverse Compton Scattering · 0.92
Compares with it 2 papers
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We report on the same plots the B/C constraints obtained in Ref. [ref] , in the form of bands corresponding to different slices in $δ$.
Direct constraints on diffusion models from cosmic-ray positron data: Excluding the Minimal model for dark matter searches · Results and discussion · 0.88
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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: $δ≃0.45$.
Unified interpretation of cosmic-ray nuclei and antiproton recent measurements · Discussion and comparison with previous results · 1.00
Cites it as background 13 papers
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The standard secondary-to-primary ratio to constrain diffusion is B/C [ref] , but also Li/C, Be/C, Li/O, Be/O, B/O, N/O, $^3$He/$^4$He as well as $p̅ / p$ have been considered [ref] .
Cosmic-ray antiprotons in the AMS-02 era: A sensitive probe of dark matter · Constraining propagation · 0.85
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We are not interested in performing a full scan of the propagation parameters space and estimating the corresponding uncertainties in the CR spectra (see, e.g., Refs. [ref] ); rather, we want to investigate how different scalings along the $z$-direction due to different propagation models can affect the predictions for the signal to background ratio.
Testing the Dark Matter Interpretation of the PAMELA Excess through Measurements of the Galactic Diffuse Emission · Cosmic-ray propagation in the Galaxy · 0.90
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The most widely used ratio is B/C [ref] , although other ratios like $^2$He/$^1$H and $^3$He/$^4$He are equally powerful [ref] .
Direct constraints on diffusion models from cosmic-ray positron data: Excluding the Minimal model for dark matter searches · Introduction · 0.84
Discussion
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