REVIEW
Massive sterile neutrinos as warm Dark Matter
High Energy Physics - Phenomenology · Submitted 7 Sep 2000 · 28 references
Pith's verdict: A careful, honest sharpening of Dodelson–Widrow: the exact Boltzmann solution and the 40 keV / 1e-11 window are worth citing, with the caveat that the normalization rests on an averaging the authors themselves call arbitrary.
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Referee report
The paper
The paper claims
Massive sterile neutrinos mixed with ordinary neutrinos can be produced in the early universe in the right abundance to be warm dark matter, with mass below about 40 keV and mixing above about $10^{-11}$.
The reading
What carries the argument
The load-bearing mechanism is matter-suppressed neutrino mixing in the early plasma. At high temperature the forward scattering of active neutrinos suppresses the effective mixing angle, so production is slow and the sterile neutrinos never reach equilibrium; as the universe cools, the suppression lifts and production peaks. The authors turn this into a quantitative tool by solving the Boltzmann equation for the sterile distribution as a function of momentum, using the temperature-dependent mixing angle and the weak collision integral, and then matching the relic density to $��_{��M}=0.3$. The output is Eq. (12), the mass-mixing relation that defines the warm-dark-matter candidate.
Extended reading notes
Core claim
The central claim is that a mostly sterile neutrino, mixed with an ordinary neutrino through a small angle $��$, is produced in the early universe by weak collisions in an amount that can equal the observed dark-matter density. The authors derive a momentum-dependent Boltzmann equation, include the finite-temperature suppression of the mixing angle, and find that the sterile distribution stays proportional to the active-neutrino distribution, with a coefficient set by mass and mixing. Requiring $��_s �� 0.3$ gives a line in the mass-mixing plane, Eq. (12), and combining it with the radiative-decay limit from the diffuse gamma-ray background leaves a viable window: $m_s �� 40$ keV and $��^2 2�� �� 10^{-11}$ for $��_��$ or $��_��$ mixing, with a slightly lower mass bound for $��_e$ mixing. The paper presents this as the simplest and oldest warm-dark-matter model, with supernova 1987A giving a weaker bound in the same low-mass region.
Load-bearing premise
The production normalization rests on a finite-temperature suppression coefficient for the mixing angle that the authors obtained by a thermal average they themselves describe as rather arbitrary, so the quoted 40 keV and $10^{-11}$ values inherit that uncertainty.
Editorial extensions
If this is right
- A sterile neutrino in the keV-to-40-keV range with $��^2 2�� �� 10^{-11}$ becomes a target for diffuse gamma-ray searches, because the radiative decay produces a line near $m_s/2$.
- If this particle is the dark matter, structure formation should be suppressed below the warm-dark-matter free-streaming scale, which can be checked against satellite-galaxy counts and other small-scale observations.
- The supernova 1987A energy-loss bound is weaker than the radiative-decay bound for masses below 40 keV, so the low-mass window survives that constraint.
- Mixing with $��_e$ rather than $��_��$ or $��_��$ shifts the allowed mass ceiling down to about 30 keV while leaving the same qualitative picture.
- The model connects a keV-scale dark-matter particle to a possible explanation of pulsar velocities, as the paper notes.
Reading between the lines
- The quoted mass ceiling is not a clean prediction: a corrected thermal averaging of $\langle E^2\rangle$ in the matter-suppression coefficient would move the Eq. (12) line and therefore the 40 keV and $10^{-11}$ numbers by a modest factor.
- A combined analysis of diffuse gamma-ray line limits and small-scale structure data would be more decisive than either alone, because the same mass-mixing line controls both the decay signal and the free-streaming length.
- The low-momentum excess produced by early production and later entropy release, which the paper mentions but does not compute in detail, could be an additional spectral signature of this scenario.
- Resonant production in a lepton-asymmetric plasma, cited by the paper as a separate route, would move the viable line to smaller mixing angles and should be treated as a distinct testable branch rather than a variation of the same calculation.
Original abstract
We show that massive sterile neutrinos mixed with the ordinary ones may be produced in the early universe in the right amount to be natural warm dark matter particles. Their mass should be below 40 keV and the corresponding mixing angles sin^2 2\theta > 10^{-11} for mixing with \nu_\mu or \nu_\tau, while mixing with \nu_e is slightly stronger bounded with mass less than 30 keV.
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 show that massive sterile neutrinos mixed with the ordinary ones may be produced in the early universe in the right amount to be natural warm dark matter particles. Their mass should be below 40 keV and the corresponding mixing angles sin^2 2\theta > 10^{-11} for mixing with \nu_\mu or \nu_\tau, while mixing with \nu_e is slightly stronger bounded with mass less than 30 keV.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that massive sterile neutrinos mixed with the ordinary ones may be produced in the early universe in the right amount to be natural warm dark matter particles. | result 0.73 | 0.90 | 0.90 | asserted 0.63 |
| s1 | Their mass should be below 40 keV and the corresponding mixing angles sin^2 2\theta > 10^{-11} for mixing with \nu_\mu or \nu_\tau, while mixing with \nu_e is slightly stronger bounded with mass less than 30 keV. | result 0.99 | 0.59 | 0.15 | asserted 0.95 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/0009083 by the authors.
References
How later papers used it
107 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 paper
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Used this paper's Boltzmann equation for ν_R1, with its collision term and oscillation probability, in its own treatment.
Sterile neutrino dark matter from right-handed neutrino oscillations (2017) · 0.82 · paraphrased: the licence does not allow quoting
How the literature uses it
92 arXiv papers cite this in 121 sentences
Papers citing it · 73 sentences without a confident label
Compares with it 3 papers
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We see that the DM momentum distribution ([ref]) has a unique form and differs from both non-resonantly [ref] and resonantly produced sterile neutrinos [ref] .
Einstein-Cartan Portal to Dark Matter · Introduction · 1.00
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The additional suppression factor which we have bounded to be $ζ0.01$ is consistent with the estimates obtained in 4D sterile neutrino models; see e.g. [ref] .
Cosmological Constraints on Dark Neutrino Towers · Conclusions · 0.90
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The final form of the quantum kinetic equation ([ref]) is similar to that used in [ref] , although in these articles the mixing angle only includes the index of refraction (real part), valid in the temperature regime of interest in those articles.
Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures · Comparison to other results · 0.90
Cites it as support 2 papers
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However, it is interesting to note that both the annihilation and the coannihilation into active neutrinos depends on the active-sterile mixing angles (to the fourth power), which are suppressed at high temperature (i.e. at $T ≳200$ MeV) due to over dominating thermal masses of the active neutrinos [ref] , and therefore these channels are subdominant.
Gauged Inverse Seesaw from Dark Matter · Scalar dark matter · 0.96
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Massive neutral fermions which are long lived enough compared to the age of the universe and have mass in the range $2keV ≲m_N_k ≲5keV$ [ref] are good warm dark matter candidates [ref] .
Light Majorana Neutrinos in (Semi)invisible Meson Decays · Introduction · 0.96
Cites it as background 37 papers
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Dodelson and Widrow [ref] (see also Refs. [ref] ) provided the first analytical calculation of the production of sterile neutrinos lighter than 100 keV in the early Universe, under the assumption (which we maintain here) of a negligible primordial lepton asymmetry.
MeV sterile neutrinos in low reheating temperature cosmological scenarios · Introduction · 0.80
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The spectrum and the number density of produced particles depends essentially on three parameters: the mixing angle with ordinary neutrino, the sterile neutrino mass and the lepton asymmetry of the Universe ($ΔL$) at the production time (for a recent analysis, see [ref] ; earlier considerations can be found in [ref] ).
Resonant production of the sterile neutrino dark matter and fine-tunings in the [nu]MSM · Introduction · 0.81
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Sterile neutrinos may also play the role of the dark matter, e.g., [ref] and affect a host of interesting cosmological and astrophysical processes, including the production of baryon [ref] and lepton [ref] asymmetries, Big Bang Nucleosynthesis [ref] , the evolution of the matter power spectrum [ref] , reionization [ref] , neutrino oscillations [ref] , pulsar kicks [ref] , and supernovae [ref] .
Constraining Sterile Neutrino Warm Dark Matter with Chandra Observations of the Andromeda Galaxy · Introduction · 0.95
Discussion
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