Dark matter sterile neutrinos in stellar collapse: alteration of energy/lepton number transport and a mechanism for supernova explosion enhancement

TL;DR

The paper investigates whether keV-scale sterile neutrinos that mix with electron neutrinos can modify energy and lepton-number transport during stellar collapse. Using a single-zone in-fall calculation, it demonstrates that active-sterile MSW conversion can substantially reduce the electron fraction $Y_e$, shrinking the homologous core and the initial shock energy, while outlining a post-bounce mechanism in which high-energy sterile neutrinos enhance energy transport to the neutrino sphere. This dual effect can both hinder and potentially promote explosions, depending on the parameter region and subsequent transport dynamics. It maps current astrophysical and cosmological constraints on sterile neutrinos and identifies parameter space where such neutrinos could still play a consequential role in core-collapse outcomes and neutrino signals. The work underscores the sensitivity of core-collapse dynamics to lepton-number-violating neutrino physics and motivates more realistic time-dependent simulations and multi-messenger constraints.

Abstract

We investigate matter-enhanced Mikheyev-Smirnov-Wolfenstein (MSW) active-sterile neutrino conversion in the $ν_e \rightleftharpoons ν_s$ channel in the collapse of the iron core of a pre-supernova star. For values of sterile neutrino rest mass $m_s$ and vacuum mixing angle $θ$ (specifically, $0.5 {\rm keV}< m_s<10 {\rm keV}$ and $\sin^22θ> 5\times{10}^{-12}$) which include those required for viable sterile neutrino dark matter, our one-zone in-fall phase collapse calculations show a significant reduction in core lepton fraction. This would result in a smaller homologous core and therefore a smaller initial shock energy, disfavoring successful shock re-heating and the prospects for an explosion. However, these calculations also suggest that the MSW resonance energy can exhibit a minimum located between the center and surface of the core. In turn, this suggests a post-core-bounce mechanism to enhance neutrino transport and neutrino luminosities at the core surface and thereby augment shock re-heating: (1) scattering-induced or coherent MSW $ν_e\toν_s$ conversion occurs deep in the core, at the first MSW resonance, where $ν_e$ energies are large ($\sim 150$ MeV); (2) the high energy $ν_s$ stream outward at near light speed; (3) they deposit their energy when they encounter the second MSW resonance $ν_s\toν_e$ just below the proto-neutron star surface.

Figures (9)

• Figure 1: The solid curve shows the effective potential scale height $\mathcal{H}$ (left vertical axis) in the radial direction as a function of radius $r$. Also shown is the adiabaticity parameter $\gamma$ (right vertical axis) as a function of $r$ for $\nu_e\rightleftharpoons\nu_s$ with $\sin^22\theta={10}^{-9}$ and with sterile neutrino rest mass $m_s = 3\,{\rm keV}$ and energy $E_\nu = 10\,{\rm MeV}$ (long-dashed curve) and $E_\nu = 100\,{\rm MeV}$ (short-dashed curve), and for sterile neutrinos with rest mass $m_s = 10\,{\rm keV}$ and energy $E_\nu = 10\,{\rm MeV}$ (long dash-dot curve) and $E_\nu = 100\,{\rm MeV}$ (short dash-dot curve).
• Figure 2: The resonance energy $E_{\rm res}$ sweeps from higher toward lower energy through the $\nu_e$ distribution function (shown as a function of energy $E_{\nu_e}$), at any instant converting the $\nu_e$'s contained in energy interval $E_{\rm res}-\Delta E$ to $E_{\rm res}+\Delta E$ (where $\Delta E = E_{\rm res}\,\tan2\theta$) to sterile neutrinos $\nu_s$. The number of $\nu_e$'s converted at this instant is $\Delta N$.
• Figure 3: One-zone calculations of $\nu_e\rightleftharpoons\nu_s$ resonance energy $E_{\rm res}$ in MeV (left vertical axis, solid line) and $\nu_e$ forward scattering potential $V$ in units of ${10}^{-8}\,{\rm MeV}$ (right vertical axis, dashed line) are shown as a function of density (in ${\rm g}\,{\rm cm}^{-3}$). This calculation employs $m_s= 3\,{\rm kev}$ and $\sin^22\theta={10}^{-9}$
• Figure 4: Same one-zone calculation as in Figure \ref{['fig 3']}: resonance energy $E_{\rm res}$ (solid line), electron fraction $Y_e$ (dashed line), and $\nu_e$ Fermi energy $\mu_{\nu_e}$ (dotted line) are shown as functions of density.
• Figure 5: The one-zone calculation evolutionary track (solid line) with $m_s=3\,{\rm keV}$ and $\sin^22\theta={10}^{-9}$ is shown in the resonance energy $E_{\rm res}$, density $\rho$ (${\rm g}\,{\rm cm}^{-3}$) plane. The conditions $T_{\rm osc}/\delta t_{\rm res}=1$, $T_{\rm osc}/T_{\rm coll}=1$ , and $\delta t_{\rm res}/T_{\rm coll}=1$ obtain along the dashed, dotted, and dot-dashed contours, respectively. Values of these ratios are $< 1$ everywhere below these contours.