Diluted equilibrium sterile neutrino dark matter

Amol V. Patwardhan, George M. Fuller, Chad T. Kishimoto, and Alexander Kusenko

Phys. Rev. D 92, 103509 – Published 6 November 2015

Abstract

We present a model where sterile neutrinos with rest masses in the range $\sim keV$ to $\sim MeV$ can be the dark matter and be consistent with all laboratory, cosmological, and large-scale structure, as well as x-ray constraints. These sterile neutrinos are assumed to freeze out of thermal and chemical equilibrium with matter and radiation in the very early Universe, prior to an epoch of prodigious entropy generation (“dilution”) from out-of-equilibrium decay of heavy particles. In this work, we consider heavy, entropy-producing particles in the $\sim TeV$ to $\sim EeV$ rest-mass range, possibly associated with new physics at high-energy scales. The process of dilution can give the sterile neutrinos the appropriate relic densities, but it also alters their energy spectra so that they could act like cold dark matter, despite relatively low rest masses as compared to conventional dark matter candidates. Moreover, since the model does not rely on active-sterile mixing for producing the relic density, the mixing angles can be small enough to evade current x-ray or lifetime constraints. Nevertheless, we discuss how future x-ray observations, future lepton number constraints, and future observations and sophisticated simulations of large-scale structure could, in conjunction, provide evidence for this model and/or constrain and probe its parameters.

Received 24 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.103509

Authors & Affiliations

Amol V. Patwardhan^1,*, George M. Fuller^1,†, Chad T. Kishimoto^1,2,‡, and Alexander Kusenko^3,4,§

¹Department of Physics, University of California, San Diego, La Jolla, California 92093-0319, USA
²Department of Physics, University of San Diego, San Diego, California 92110, USA
³Department of Physics and Astronomy, University of California, Los Angeles, California 90095
⁴Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8568, Japan

^*apatward@ucsd.edu
^†gfuller@ucsd.edu
^‡ckishimo@physics.ucsd.edu
^§kusenko@ucla.edu

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Vol. 92, Iss. 10 — 15 November 2015

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Images

Figure 1
Cartoon illustrating how the DESNDM model fits together with the thermal history of the Universe. So long as the diluton $D_{H}$ decays exclusively into standard model particles, and the process goes to completion before weak decoupling, the decay products can completely thermalize. In such a scenario, all standard model particle spectra remain thermal, and neither big bang nucleosynthesis nor $N_{eff}$ are affected in any way. However, since the sterile neutrinos $ν_{s}$ are already decoupled, their number densities are diluted relative to the particles still in equilibrium. The active neutrinos eventually decouple, and subsequently, the $e^{\pm}$ pairs annihilate away as the Universe cools, further diluting the active and sterile neutrino number densities relative to the photons. Scenarios with dilution built in prior to the electroweak scale, such as the one shown here, are likely better suited to meeting baryogenesis requirements.
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Figure 2
Active neutrino (solid, red) and sterile neutrino (dashed, green and dot-dashed, blue) cooling curves as a function of plasma temperature, illustrating how a combination of out-of-equilibrium particle decay and loss of statistical degrees of freedom can dilute decoupled particles relative to species still in thermal equilibrium. The curves begin to separate as the diluton starts decaying, pumping entropy into the plasma and diluting the the number density of the sterile neutrino sea. The figures are for the cases with diluton rest mass $m_{H}$ and lifetime $τ_{H}$ , and associated dilution factor $F$ , and dark matter sterile neutrino rest mass $m_{s}$ , as labeled. The sterile neutrino mass, for a given diluton mass and lifetime, is chosen to give closure fraction $Ω_{s} = 0.258$ for Hubble parameter $h = 0.6781$ (in units of $100 km s^{- 1} {Mpc}^{- 1}$ ).
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Figure 3
Figures showing contours of the sterile neutrino rest mass $m_{s}$ (in keV) which would give a current relic abundance of $Ω_{s} = 0.258$ for Hubble parameter $H_{0} = 67.81 km / s {Mpc}^{- 1}$ in the DESNDM model, plotted against a parameter space spanned by diluton rest mass $m_{H}$ and decay lifetime $τ_{H}$ .
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Figure 4
Top: total mass inside the sterile neutrino free-streaming (i.e., collisionless damping) scale, $M_{FS}$ , as a function of sterile neutrino rest mass $m_{s}$ , for $Ω_{s} h^{2} = 0.12$ . Also shown are the temperature ratio $T_{ν_{s}} / T_{γ}$ (on the $y 2$ axis) as a function of $m_{s}$ , for $Ω_{s} h^{2} = 0.12$ , and the corresponding thermally adjusted effective mass $m_{s}^{cd}$ (on the $x 2$ axis). Bottom: contours of $M_{FS}$ , in solar masses, plotted against sterile neutrino rest mass $m_{s}$ on the $x$ axis and sterile neutrino closure density parameter $Ω_{s} h^{2}$ on the $y$ axis.
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Figure 5
Curves showing the total horizon mass energy (solid, red), the Jeans mass (dashed, green), and the ratio of the energy density contributed by diluton rest mass to the total energy density in radiation (dot-dashed, blue, plotted on $y 2$ axis), as a function of plasma temperature. The Jeans mass can be seen to drop relative to the horizon mass in the matter-dominated epochs. The features (bends) in the $M_{J}$ and $M_{hor}$ curves at $T \sim 100 MeV$ are a consequence of the relatively sudden change in relativistic degrees of freedom across the QCD transition. The diluton rest mass and lifetime in this example are $m_{H} = 2.91 PeV$ and $τ_{H} = 0.7406 \times 10^{- 11} s$ , respectively.
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Figure 6
Sterile neutrino rest mass and vacuum mixing parameter space, as constrained by x-ray/ $γ$ -ray observations (constraints from Refs. [60, 61, 62, 63, 64, 65] shown here in purple), Ly- $α$ forest limits on collisionless damping (from Ref. [54], shown here in dark red), as well as the requirements that dark matter is stable (black) and does not rethermalize after dilution (gray). Also shown are the regions of allowed parameter space that can produce some observable effects on dwarf-galaxy morphology (green, cross-hatched region corresponds to $M_{FS} \sim 10^{6} - 10^{9} M_{⊙}$ in the DESNDM model), and on pulsar kicks (sky-blue, diagonally hatched region reproduced from Ref. [21]), respectively. The x-ray/ $γ$ -ray constraints shown here are premised on sterile neutrinos being all of the dark matter. The rest-mass ranges encompassed by the Ly- $α$ and dwarf galaxy regions shown here are specific to the DESNDM model. Finally, the gray solid lines are contours of sterile neutrino closure fraction produced by the Dodelson-Widrow mechanism: $Ω_{DW} = 0.26$ (right) and 0.0055 (left).
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