Electron-positron Annihilation Lines and Decaying Sterile Neutrinos

If massive sterile neutrinos exist, their decays into photons and/or electron-positron pairs may give rise to observable consequences. We consider the possibility that MeV sterile neutrino decays lead to the diffuse positron annihilation line in the Milky Way center, and we thus obtain bounds on the sterile neutrino decay rate $\Gamma_e \ge 10^{-28}$ s$^{-1}$ from relevant astrophysical/cosmological data. Also, we expect a soft gamma flux of $1.2 \times 10^{-4}-9.7 \times 10^{-4}$ ph cm$^{-2}$ s$^{-1}$ from the Milky Way center which shows up as a small MeV bump in the background photon spectrum. Furthermore, we estimate the flux of active neutrinos produced by sterile neutrino decays to be $0.02-0.1$ cm$^{-2}$ s$^{-1}$ passing through the earth.

💡 Research Summary

The paper investigates whether decays of massive sterile neutrinos (νₛ) with masses in the MeV range can account for the diffuse 511 keV positron‑annihilation line observed toward the Galactic centre. Sterile neutrinos can decay through three principal channels: (i) νₛ → 3 ν (purely invisible), (ii) νₛ → ν + γ (radiative), and (iii) νₛ → ν + e⁺ + e⁻ (producing positrons). The authors write down the standard model‑derived decay rates for each channel, showing that the three‑neutrino channel scales as Γ₃ν ≈ 1.77 × 10⁻²⁰ sin²2θ (mₛ/1 keV)⁵ s⁻¹, the radiative channel as Γ_γ ≈ 1.38 × 10⁻²² sin²2θ (mₛ/1 keV)⁵ s⁻¹, and the e⁺e⁻ channel as Γₑ ≈ Γ₃ν(|V|²/2 + 1/8). Because the e⁺e⁻ channel dominates the production of observable 511 keV photons, the paper focuses on Γₑ.

Using measurements from INTEGRAL, the total positron‑annihilation rate in the Galactic bulge is (1.5 ± 0.1) × 10⁴³ s⁻¹, while the disk contributes roughly (0.3 ± 0.2) × 10⁴³ s⁻¹. The authors model the propagation of MeV positrons in the interstellar medium, accounting for ionisation losses, magnetic confinement (Larmor radius ≈10⁹ cm for a 1 MeV positron in a B ≈ 10⁻⁵ G field), and the eventual thermalisation before annihilation. The annihilation probability per positron is extremely low (≈10⁻¹⁸ s⁻¹), implying that a huge reservoir of positrons must be built up over Galactic timescales.

To connect the observed annihilation rate to sterile‑neutrino decay, the paper assumes that νₛ follows the dark‑matter density profile. Two profiles are examined: an isothermal sphere (nₛ ∝ r⁻²) and an NFW profile. The isothermal model yields a bulge‑to‑disk annihilation ratio A_bulge/A_disk ≈ 6–13, consistent with the observed ratio (≈7). The NFW model gives a much smaller ratio (1–4), disfavoured by the data. Therefore, the authors adopt the isothermal distribution for the remainder of the analysis.

From the bulge annihilation rate, they infer n₀ Γₑ ≈ 10²² m⁻¹ s⁻¹, where n₀ is the central sterile‑neutrino number density. Using the upper limit on the central mass density (ρ_c ≤ 5.5 × 10¹⁹ kg m⁻³) and assuming mₛ ≥ 1 MeV, they obtain n₀ ≤ 3 × 10⁴⁹ m⁻¹, which translates into a lower bound on the decay rate Γ ≥ 3 × 10⁻²⁸ s⁻¹ (or Γₑ ≥ 10⁻²⁸ s⁻¹). Similar calculations for the NFW profile give Γₑ ≥ 2 × 10⁻²⁷ s⁻¹. These values correspond to a mixing angle sin²2θ ≈ 10⁻²⁴, compatible with existing X‑ray background constraints.

The radiative decay channel produces mono‑energetic photons with energy E_γ = mₛ/2. The predicted photon flux along the line of sight is Φ_γ ≈ (1.2–9.7) × 10⁻⁴ ph cm⁻² s⁻¹. Most of these photons are in the 1 MeV range; a small fraction (≈1 %) scatters off interstellar electrons (Compton cross‑section) and broadens the line slightly. When added to the measured diffuse background (dF/dE ≈ 2.62 (E/0.1 MeV)⁻²·⁷⁵ MeV⁻¹ cm⁻² s⁻¹), this contribution yields a modest “MeV bump” of 2–15 % relative to the background, a feature that has historically been debated as an instrumental artifact but could have a genuine astrophysical component in this model.

Active neutrinos from the dominant νₛ → 3 ν channel also reach Earth. The integrated flux is estimated at 0.02–0.1 cm⁻² s⁻¹, corresponding to ≈10⁹ s⁻¹ passing through a detector the size of IceCube. However, their energies (≈1 MeV) are far below the detection thresholds of current high‑energy neutrino telescopes. The authors suggest that these low‑energy neutrinos could interact inside pulsar magnetospheres (σ_ν ≈ 10⁻⁴¹ (E_ν/10 MeV)² cm²), producing secondary electrons and positrons. In the strong magnetic fields of pulsars (B ≈ 10¹² G), these secondaries would emit synchrotron radiation in the X‑ray band (frequency ≈2.8 × 10¹⁸ Hz, power ≈10⁹ erg s⁻¹ per electron). Summed over the ≈10⁵ Galactic pulsars, the total synchrotron power would be ≈10²⁷ erg s⁻¹, well below the observed non‑thermal X‑ray luminosity of typical pulsars (≈10³⁰ erg s⁻¹), making this contribution difficult to detect with present instruments.

In the discussion, the authors emphasize that the derived lower bound Γ ≥ 10⁻²⁸ s⁻¹ is comfortably within broader cosmological limits (Γ ≤ 10⁻¹⁷ s⁻¹) derived from structure formation and cluster cooling flow constraints. They conclude that MeV‑scale sterile neutrinos remain viable dark‑matter candidates that can simultaneously explain the diffuse 511 keV line, produce a faint MeV γ‑ray bump, and generate a low‑energy active‑neutrino flux. Future missions with improved MeV γ‑ray spectroscopy (e.g., e‑ASTROGAM) and low‑energy neutrino detection techniques could test these predictions.