REVIEW
Dark matter in the solar system II: WIMP annihilation rates in the Sun
High Energy Astrophysical Phenomena · Submitted 9 Feb 2009 · 53 references
Pith's verdict: The qualitative claim holds — finite thermalization and Jupiter torques do suppress the solar annihilation rate — but the headline 10 TeV spin-dependent number is an extrapolation the paper never validates.
T0 · AI review
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Referee report
The paper
The paper claims
WIMPs captured by the Sun may not sink to its core as fast as standard calculations assume, and Jupiter can throw some of them out of the solar system entirely, so the annihilation rate that neutrino telescopes are meant to detect can be up
The reading
What carries the argument
The argument turns on the semi-major axis of a captured WIMP's orbit, which plays the role of a clock on thermalization. A single scatter off a nucleus of mass $m_A$ deposits energy of order $m_A v_esc^2$, which corresponds to a characteristic semi-major axis $a_q  (m_χ/m_A) R_⊙$; iterating this gives a differential equation $da/dt = -τ a^{1/2}/(a + a_q)$ whose solution yields the number of scatters $X$ needed to fall from an initial orbit to the core. Combined with the median semi-major axis of freshly captured WIMPs, $a_m  (m_χ/m_A) R_⊙/10$, this fixes which regions of $(m_χ, σ_p)$ parameter space thermalize within $t_⊙$, which lose only the Jupiter-crossing fraction $f_{Jupiter}$, and which lose the long-lived fraction $f_{ll}$ as well. The paper then classifies parameter space into regimes (a1, a2 with sub-cases a21 and a22, a3, b) and solves the population equation $̇N = C - C_a N^2$ in each, with a time-dependent capture rate in the transition case where the long-lived population arrives late.
Extended reading notes
Core claim
The paper's claim is that the instantaneous thermalization model, which treats every captured WIMP as instantly available for annihilation at the solar center, systematically overestimates the annihilation rate $ ½ C$ once the particle mass is high or the elastic scattering cross section is low. Two mechanisms drive the suppression. First, the optical depth of the Sun is small: a WIMP on a bound orbit rescatters only once per $P_χ/τ$, and the number of such scatters needed to shrink the orbit to the core grows with $m_χ/m_A$, so for sufficiently high mass or low cross section the thermalization time exceeds $t_⊙$ and the particles never annihilate. Second, for orbits with semi-major axis between roughly $1.5$ and $2.6$ AU, mean-motion and secular resonances with Jupiter pull perihelia out of the Sun for long stretches, lengthening the rescattering time by about two orders of magnitude, while WIMPs on Jupiter-crossing orbits ($a > 2.6$ AU) are usually ejected from the solar system before they can rescatter. The suppression is stronger for spin-dependent scattering, because hydrogen is the only appreciable spin-dependent target in the Sun and the optical depth for a given proton cross section is roughly a hundred times smaller than in the spin-independent case. The concrete payoff is a revised mapping from neutrino-telescope event rates to WIMP mass and cross section: $100$ GeV sensitivity is essentially as previously advertised, but $10$ TeV sensitivity may be an order of magnitude worse.
Load-bearing premise
The quantitative suppression factors rest on treating every captured WIMP population by a single median thermalization time rather than the full spread of times, so the numbers in the suppression figures are representative rather than exact.
Editorial extensions
If this is right
- IceCube-scale limits on the spin-dependent WIMP-proton cross section should be weakened by a factor of order $(1-f_{Jupiter})^{-1}$ above roughly $1$ TeV, rather than scaled naively from Super-Kamiokande by detector area.
- Model forecasts that place a WIMP at $10$ TeV with a spin-dependent cross section near $10^{-42}$ cm$^2$ should predict a solar neutrino flux well below what the equilibrium formula gives, because the number of Sun-bound WIMPs has not yet reached its steady state.
- For Kaluza-Klein dark matter in universal extra dimensions, the allowed region straddles the boundary where Jupiter-crossing WIMPs fail to thermalize, so detecting it would need at least an order of magnitude more sensitivity than a kilometer-scale detector.
- For Little Higgs dark matter with a modest mass splitting, the annihilation rate can collapse to nearly nothing, so a null solar neutrino search in that region would not by itself exclude the model.
- Any conversion of an observed solar neutrino flux into a scattering cross section must account for the thermalization history, not just the capture rate.
Reading between the lines
- The suppression is a threshold effect tied to orbital period rather than a smooth correction, so the boundary between the regimes in Fig. 2 is where a modest improvement in detector sensitivity buys the most information about WIMP mass.
- Because the suppression depends on the ratio $m_χ/m_A$ and the target species differ between spin-dependent and spin-independent capture, a solar neutrino detection combined with a direct-detection signal could in principle separate the two couplings through the shape of the suppression.
- The same orbital-resonance argument should apply to the Earth, but with the Moon or the giant planets playing Jupiter's role; the paper's companion analysis finds Earth rates far below threshold, which suggests the resonance channel is not worth pursuing there.
- A full Monte Carlo carrying the distribution of thermalization times, rather than the median per population, would be the natural next step and would give a quantitative error bar on Fig. 4.
Original abstract
We calculate the annihilation rate of weakly interacting massive particles (WIMPs) in the Sun as a function of their mass and elastic scattering cross section. One byproduct of the annihilation, muon neutrinos, may be observed by the next generation of neutrino telescopes. Previous estimates of the annihilation rate assumed that any WIMPs from the Galactic dark halo that are captured in the Sun by elastic scattering off solar nuclei quickly reach thermal equilibrium in the Sun. We show that the optical depth of the Sun to WIMPs and the gravitational forces from planets both serve to decrease the annihilation rate below these estimates. While we find that the sensitivity of upcoming km^3-scale neutrino telescopes to ~100 GeV WIMPs is virtually unchanged from previous estimates, the sensitivity of these experiments to ~10 TeV WIMPs may be an order of magnitude less than the standard calculations would suggest. The new estimates of the annihilation rates should guide future experiment design and improve the mapping from neutrino event rates to WIMP parameter space.
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 calculate the annihilation rate of weakly interacting massive particles (WIMPs) in the Sun as a function of their mass and elastic scattering cross section. One byproduct of the annihilation, muon neutrinos, may be observed by the next generation of neutrino telescopes. Previous estimates of the annihilation rate assumed that any WIMPs from the Galactic dark halo that are captured in the Sun by elastic scattering off solar nuclei quickly reach thermal equilibrium in the Sun. We show that the optical depth of the Sun to WIMPs and the gravitational forces from planets both serve to decrease the annihilation rate below these estimates. While we find that the sensitivity of upcoming km^3-scale neutrino telescopes to ~100 GeV WIMPs is virtually unchanged from previous estimates, the sensitivity of these experiments to ~10 TeV WIMPs may be an order of magnitude less than the standard calculations would suggest. The new estimates of the annihilation rates should guide future experiment design and improve the mapping from neutrino event rates to WIMP parameter space.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the annihilation rate of weakly interacting massive particles (WIMPs) in the Sun as a function of their mass and elastic scattering cross section. | contribution 0.99 | 0.96 | 0.08 | asserted 0.99 |
| s1 | One byproduct of the annihilation, muon neutrinos, may be observed by the next generation of neutrino telescopes. | background 0.46 | 0.11 | 0.03 | hedged possibility 1.00 |
| s2 | Previous estimates of the annihilation rate assumed that any WIMPs from the Galactic dark halo that are captured in the Sun by elastic scattering off solar nuclei quickly reach thermal equilibrium in the Sun. | background 0.98 | 0.03 | 0.04 | asserted 0.99 |
| s3 | We show that the optical depth of the Sun to WIMPs and the gravitational forces from planets both serve to decrease the annihilation rate below these estimates. | result 0.99 | 0.90 | 0.63 | asserted 1.00 |
| s4 | While we find that the sensitivity of upcoming km^3-scale neutrino telescopes to ~100 GeV WIMPs is virtually unchanged from previous estimates, the sensitivity of these experiments to ~10 TeV WIMPs may be an order of magnitude less than the standard calculations would suggest. | result 0.78 | 0.95 | 0.49 | hedged possibility 0.60 |
| s5 | The new estimates of the annihilation rates should guide future experiment design and improve the mapping from neutrino event rates to WIMP parameter space. | future work 0.52 | 0.33 | 0.19 | asserted 0.70 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
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Figures
Figures reproduced from arXiv:0902.1347 by the authors.
References
How the literature uses it
43 arXiv papers cite this in 71 sentences
Papers citing it · 48 sentences without a confident label
Contests it 1 paper
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The studies of [ref] still found these effects important since they only looked at diffusion in one direction, neglecting the reverse process.
WIMP diffusion in the solar system including solar WIMP-nucleon scattering · Introduction · contest 0.84
Uses its method or tool 1 paper
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We calculate this following the method presented in Ref. [ref] .[In some regions of this parameter space, the DM capture rate would not be in equilibrium for typical annihilation rates, thus we use the full solution [ref] to obtain the DM induced neutrino flux.] The dashed and dot-dashed lines correspond to two different models of SA$ν$.
Neutrinos from the Sun can discover dark matter-electron scattering · Results and Discussion · 1.00
Compares with it 1 paper
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The equilibrium time scales presented agree with the computation in Refs. [ref] , which is performed for $m_χ= 100$GeV.
A tale of dark matter capture, sub-dominant WIMPs, and neutrino observatories · Are capture processes in equilibrium? · 0.98
Cites it as support 2 papers
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However, it was shown previously that the combined effects of gravitational diffusion from solar system bodies such as the Sun, Jupiter, Mercury, and Venus, as well as elastic scattering from these bodies, leads to about the same DM phase-space distribution as the scenario where the celestial-body is not placed deep in the gravitational well of the solar system; see Ref. [ref] as well as the earlier Refs. [ref] .
Dark Matter Capture in Celestial Objects: Treatment Across Kinematic and Interaction Regimes · Capture for Benchmark Objects · 0.97
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It has been shown [ref] that the changes of the velocity distribution at the Earth from WIMP capture in neighboring massive bodies such as other planets or the Sun (cf. [ref] ) is negligible.
A tale of dark matter capture, sub-dominant WIMPs, and neutrino observatories · Velocity distribution · 0.99
Cites it as background 14 papers
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We defer the topic of annihilation of WIMPs in the Sun to Paper II [ref] , and the simulations of gravitationally captured WIMPs to Paper III [ref] .
Dark matter in the solar system I: The distribution function of WIMPs at the Earth from solar capture · This Work · 0.80
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The calculation of the capture and annihilation of DM in the Sun is well established [ref] .
Solar Gamma Ray Constraints on Dark Matter Annihilation to Secluded Mediators · Capture in general · 0.96
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The Sun is an alternate probe, as it can gravitationally capture DM [ref] , after DM loses energy through scattering with solar nucleons.
Powerful Solar Signatures of Long-Lived Dark Mediators · Introduction · 0.85
What it cites · 22 sentences without a confident label
Uses the method or tool of 2 papers
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We followed the orbits using a symplectic integrator with an adaptive time step [ref] , with passages through the Sun, close encounters with the planets, and nearly unbound orbits treated as special cases.
astro-ph/9906322 · The Simulations · 1.00
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Our principal tool will be a large set of numerical simulations of the evolution of WIMPs captured in the Sun, including the gravitational influence of the planets and rescattering by solar nucleons [ref] .
Dark matter in the solar system I: The distribution function of WIMPs at the Earth from solar capture · Introduction · 0.90
Uses data or values from 1 paper
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The most stringent limit on the cross section came for $m_χ∼100 GeV$, $≲10^-39 cm^2$ [ref] .
Search for Dark Matter WIMPs using Upward Through-going Muons in Super-Kamiokande · Discussion · 0.84
Cites as background 14 papers
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There has recently been significant progress in understanding ingredient (ii) [ref] .
High energy neutrinos from neutralino annihilations in the Sun · Introduction · 0.96
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There has recently been significant progress in understanding ingredient (ii) [ref] .
Spectra of neutrinos from dark matter annihilations · Introduction · 0.96
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Many experiments (most obviously Fermi, but see also [ref] ) are searching for annihilation products from the Galactic center, the Milky Way halo, or Local Group satellite galaxies—the latter sites are promising because they are predicted to have high dark matter densities, and the annihilation rate goes as the square of the density.
Study of TeV Neutrinos with Upward Showering Muons in Super-Kamiokande · Introduction · 0.83
Discussion
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