REVIEW
Sterile Neutrino Hot, Warm, and Cold Dark Matter
Astrophysics · Submitted 30 Jan 2001 · 124 references
Pith's verdict: The standard reference for keV sterile neutrino dark matter production, with a real numerical advance and a marginal adiabaticity argument at the boundary of the viable region.
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Referee report
The paper
The paper claims
The paper argues that sterile neutrinos — singlet fermions that mix weakly with ordinary neutrinos — can be produced in the early universe in just the right amount to be the dark matter, spanning hot, warm, and cold regimes depending on the
The reading
What carries the argument
The engine is a Boltzmann equation for the sterile phase-space distribution, in which the conversion rate is half the active neutrino scattering rate times a damped oscillation probability, $P_m$ roughly $Delta^2 sin^2 2theta / [Delta^2 sin^2 2theta + D^2 + (Delta cos 2theta - V_D - V_T)^2]$, where $Delta = delta m^2 / 2p$, $D$ is the quantum damping rate, and $V_D$, $V_T$ are the finite-density and finite-temperature potentials. The finite-density potential scales as $G_F T^3 L$ and grows with temperature, so an active neutrino's effective mass-squared rises, peaks, and then falls once the thermal term dominates; wherever that track crosses a sterile mass eigenvalue there is an MSW resonance, and the resonance condition $Delta cos 2theta = V_D + V_T$ sets which momenta convert at which temperature. The load-bearing check is the adiabaticity parameter $gamma$ (their Eq. 7.13), which for the mixings allowed by observation comes out small — meaning the resonances are crossed nonadiabatically, coherent transformation is negligible, and the semi-classical incoherent rate is the right tool. Everything else — the time-temperature relation through the QCD transition, dilution from annihilating degrees of freedom, enhanced scattering off muon, tau, and quark pairs — is bookkeeping layered onto that equation.
Extended reading notes
Core claim
The central claim is that incoherent scattering-induced conversion of active neutrinos into sterile neutrinos, computed with matter effects and finite-temperature corrections, yields relic abundances that match the observed dark matter density across a broad range of sterile masses and vacuum mixings. For negligible lepton asymmetry the authors give a compact fit, $O_{nu_s} h^2$ roughly $0.3 (sin^2 2theta / 10^{-10})(m_s / 100 keV)^2$, with production peaking at $T_max$ roughly $133 MeV (m_s / 1 keV)^{1/3}$. When a primordial lepton asymmetry is present, the matter potential drives mass-level crossings, and resonant conversion produces a spectrum skewed to low momenta — a nonthermal population that damps small-scale structure and can act as warm or cold dark matter even at modest mass. The authors then overlay observational limits and identify surviving islands: mixing angles below about $3$ times $10^{-10}$ for electron-flavor mixing (about $10^{-9}$ for muon or tau flavor) avoid excessive energy loss in core-collapse supernovae, while larger mixings or masses run into decay-photon, nucleosynthesis, and relativistic-energy-density bounds.
Load-bearing premise
The whole result rests on the claim that resonance crossings are nonadiabatic for the allowed mixing angles, so that coherent flavor transformation can be ignored and a semi-classical Boltzmann equation with a damping factor gives the correct relic spectra.
Editorial extensions
If this is right
- Sterile neutrinos with keV-scale masses and mixings near $10^{-10}$ become a viable dark matter candidate that is essentially undetectable in conventional weakly-interacting-massive-particle searches, since the coupling is far too small.
- Because resonant production with a lepton asymmetry gives a low-momentum, nonthermal spectrum, the same mass can behave as warm or cold dark matter, so the small-scale structure problems of cold dark matter (missing satellites, cuspy cores) get a particle-physics candidate.
- Radiative decays of these neutrinos produce a monoenergetic photon line, giving a possible x-ray signature in galaxy clusters and a route to constraint or detection.
- The relic abundance depends on the temperature of the QCD transition, because the disappearance of quark degrees of freedom changes both the scattering rate and the cooling curve during resonant conversion.
- Future cosmic microwave background measurements of the relativistic energy density at decoupling, and improved supernova neutrino modeling, would tighten or open the allowed parameter islands.
Reading between the lines
- If the adiabaticity estimate is the pivot, then the cleanest test of the whole result is a full density-matrix calculation of flavor evolution through the resonance; a finding of adiabatic crossing at the allowed mixings would shift the predicted spectra and therefore the free-streaming masses that classify the dark matter as hot, warm, or cold.
- A detected x-ray line at half the sterile mass in a nearby cluster or dwarf galaxy would convert the paper's 'interesting but unconstrained' decay region into a measurement, and the line flux would directly fix the product of mixing angle and mass.
- The same production calculation applies to any singlet fermion mixing with an active neutrino, so the allowed band functions as a generic target for hidden-sector and brane-world models rather than a prediction of one model.
- Because the lepton asymmetry is treated as a free parameter within generous bounds, the warm-dark-matter corner of the parameter space implicitly predicts a primordial asymmetry far above the baryon asymmetry, which is itself a cosmological claim that baryogenesis scenarios would have to accommodate.
Original abstract
We calculate the incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe.
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 incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. | contribution 0.78 | 0.96 | 0.03 | asserted 0.95 |
| s1 | We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. | result 1.00 | 0.96 | 0.88 | asserted 1.00 |
| s2 | The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. | method 0.58 | 0.39 | 0.09 | asserted 0.96 |
| s3 | Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. | method 0.95 | 0.92 | 0.03 | asserted 1.00 |
| s4 | We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe. | contribution 0.90 | 0.94 | 0.05 | asserted 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:astro-ph/0101524 by the authors.
References
How later papers used it
195 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 2 of 14 papers with this label · 1 by the same authors
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In order to compare with the DM abundance, we adopt the approximated form of the production of the sterile neutrino [ref] , [equation] where the active-sterile mixing angle is defined by $sin^2 2θ= ∑_i=e,μ,τ|Θ_i 1|^2$.
Seesaw mechanism in the R-parity violating supersymmetric standard model with the gauged flavor $\mathrm{U}(1)_X$ symmetry (2021) · $keV$-scale sterile neutrino dark matter · 0.94
By the same authors
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Followed this paper's detailed resonant production calculations, as specified for quark-hadron transition properties in another work.
Resonantly-Produced 7 keV Sterile Neutrino Dark Matter Models and the Properties of Milky Way Satellites (2014) (same authors) · 0.97 · paraphrased: the licence does not allow quoting
How the literature uses it
161 arXiv papers cite this in 308 sentences
Papers citing it · 197 sentences without a confident label
Uses its method or tool 14 papers
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Production Calculations — To calculate the resonant production of the sterile neutrino, I follow the detailed resonant production calculations first performed in Ref. [ref] and specified for properties of the quark-hadron transition in Ref. [ref] .
Resonantly-Produced 7 keV Sterile Neutrino Dark Matter Models and the Properties of Milky Way Satellites · Introduction · 0.97
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An accurate calculation of sterile neutrino production requires solving the evolution equation in the matrix density formalism, while in the collision-dominated period (which it's indeed the case of the production peak of sterile neutrino, i.e. $T∼0.1$), the quasi-classical Boltzmann equation is a good approximation [ref] , [equation] here $f_ν_s$ and $f_ν_α$ stand for the distribution functions of sterile neutrino and SM neutrino, $Γ_α$ is the reaction rate where SM neutrino takes part in. $⟨P_m ⟩$ is the averaged converting probability between sterile neutrino and SM neutrino, expressed as [ref] [equation] with $Δ= m_s^2/2p$, the effective potential is shown as $V$, which characterizes the effects of SM neutrinos passing through the thermal background.
Axion-assisted Resonance Oscillation Rescues the Dodelson-Widrow Mechanism · Production of sterile neutrino · 0.92
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The time evolution of the sterile neutrino phase-space distribution, $f_ν_s$, can be described by the classical Boltzmann equation [ref] : [equation] where: $f_ν_α$ is the active neutrino phase-space distribution, $H(t)$ is the Hubble expansion rate and $Γ(ν_α →ν_s)$ is the sterile neutrino effective production rate: [equation] where $Γ_ν_α$ is the collision rate: [equation]
Subdominant Dark Matter sterile neutrino resonant production in the light of Planck · Phase-space distributions · 0.92
Uses its data or values 5 papers
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[equation] We substitute Eqs. [ref] and [ref] into Eq. [ref] and solve for the relation between the scale factor and temperature [equation] Substituting Eq. [ref], we obtain the time-temperature relation[We note that we correct here an error introduced in Ref. [ref] .] [equation] Defining the number of SM relativistic degrees of freedom for the energy and entropy densities via [equation] we have the final form of the time-temperature relation [equation] We use numbers of relativistic degrees of freedom $g_*$ and $g_*,s$ from Ref. [ref] in our numerical implementation.
Sterile neutrino dark matter: A tale of weak interactions in the strong coupling epoch · Time-temperature relation · 0.90
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The Dodelson-Widrow production has a peak at $T≃133 (m_s/keV)^1/3$ MeV [ref] .
Prospects for Finding Sterile Neutrino Dark Matter at KATRIN · Production through Dodelson-Widrow Mechanism · 0.89
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Here we follow Ref.s [ref] and [ref] and take the rate for this process as [equation]
Heavy sterile neutrinos, entropy and relativistic energy production, and the relic neutrino background · $ν_s →ν+γ$ · 0.81
Compares with it 4 papers
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If one replaces the right-handed coupling $𝒢_R$ in Eq.([ref]) by active-sterile mixing angle $θ_Nν$, the only deviation from the radiative decay rate obtained in the context of seesaw model [ref] , is the appearance of $m_ℓ^2M_N^3$ instead of $M_N^5$.
Shedding New Light on Sterile Neutrinos from XENON1T Experiment · Sterile Neutrino DM and Coupling Constraints · 0.93
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Two common mechanisms that rely on the active-sterile neutrino mixing provide a warmer spectrum: near thermal distribution for non-resonant production with $y_DW=3.15$ [ref] , and resonant production in presence of lepton asymmetries can lead to average momenta as low as $y_SF=1.8/𝒮^1/3$ [ref] .
Induced resonance makes light sterile neutrino Dark Matter cool · Spectrum with narrow resonance · 0.89
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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
Cites it as support 1 paper
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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 62 papers
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The DM sterile neutrinos with rest mass $m_s ≥$ 1 keV are produced through neutrino oscillations at temperatures close to the QCD phase transition [ref] .
Subdominant Dark Matter sterile neutrino resonant production in the light of Planck · Sterile neutrino resonant production calculations · 0.86
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We refer the reader to Refs. [ref] for more details.
Sterile neutrino dark matter: A tale of weak interactions in the strong coupling epoch · Overview of resonant sterile neutrino production · 0.99
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As discussed in Ref. [ref] , as the Universe expands and cools with time, for a given $δm^2$, the resonance will sweep through the $ν_α$ energy distribution function from low to high neutrino spectral parameter $ϵ$.
Resonantly-Produced 7 keV Sterile Neutrino Dark Matter Models and the Properties of Milky Way Satellites · Introduction · 0.91
Discussion
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