Capture of Inelastic Dark Matter in the Sun

TL;DR

The paper investigates how inelastic dark matter (iDM) can be captured by the Sun via inelastic WIMP–nucleus scattering and how this influences the neutrino flux from WIMP annihilations. It develops a modular framework to separately treat capture and annihilation, analyzes the approach to equilibrium, and computes the capture rate across WIMP masses and inelastic thresholds while accounting for solar composition and form-factor effects. The key result is that for a fiducial cross-section of sigma_n ≈ 1e-40 cm^2, the solar WIMP population can reach equilibrium, allowing current neutrino bounds (notably from Super-K) to strongly constrain annihilation channels into heavy SM states (WW, ZZ, tau tau, ttbar, nu nu), with lighter channels (bbbar, ccbar) subjected to weaker limits. The findings have important implications for iDM model building and indirect detection, including PAMELA-motivated scenarios with light mediators, and they emphasize the role of the inelastic threshold and iron as a dominant solar capture target.

Abstract

We consider the capture of dark matter in the Sun by inelastic scattering against nuclei as in the inelastic dark matter scenario. We show that, assuming a WIMP-nucleon cross-section of σ_n = 10^{-40}\cm^2 the resulting capture rate and density are sufficiently high so that current bounds on the muon neutrino flux from the Sun rule out any appreciable annihilation branching ratio of WIMPs into W^+W^-, Z^0Z^0, τ^+τ^-, t\bar{t} and neutrinos. Slightly weaker bounds are also available for annihilations into b\bar{b} and c\bar{c}. Annihilations into lighter particles that may produce neutrinos, such as μ^+μ^-, pions and kaons are unconstrained since those stop in the Sun before decaying. Interestingly enough, this is consistent with some recent proposals motivated by the PAMELA results for the annihilation of WIMPs into light bosons which subsequently decay predominantly into light leptons and pions.

Figures (7)

• Figure 1: On the left pane we show the WIMP's density (normalized to unity) against the distance from the Sun's center for $m_{ \chi} = 100~\mathrm{GeV}$ and $\delta = 100~\mathrm{keV}$ (solid-black), $\delta = 150~\mathrm{keV}$ (dashed-blue), and $\delta=200~\mathrm{keV}$ (dotdashed-red). On the right pane we depict the ratio $t_{\odot}/\tau_{ {\rm eq}}$ as a function of the WIMP's mass for $\delta=100~\mathrm{keV}$ (black-solid) and $\delta=150~\mathrm{keV}$ for $\langle\sigma_A v \rangle = 3\times 10^{-26}~\mathrm{cm}^3\rm{~sec^{-1}}$ and $C = 10^{25}\rm{~sec^{-1}}$ as in Eq. (\ref{['eqn:eqbratio']}).
• Figure 2: The kinetic energy in the WIMP-nucleus center of mass frame as a function of the mass $m$ (in units of $M_{\odot}$) enclosed in a given shell. The velocity at infinity was taken to be $u = 220~{\rm km/s}$ as explained in the text. The curves correspond to scattering against iron, oxygen, and carbon from top to bottom. The WIMP mass was fixed at $100~\mathrm{GeV}$ ($500~\mathrm{GeV}$) on the left (right) pane. Carbon is the lightest element present in the Sun against which the WIMP can scatter inelastically.
• Figure 3: On the left pane we plot the capture rate against the WIMP mass. The solid curve correspond to an inelastic model with $\delta =125~\mathrm{keV}$ and $v_\odot = 220~{\rm km/s}$ whereas the dotted curve to $v_\odot = 254~{\rm km/s}$. In both cases we take $\sigma_n=10^{-40}~\mathrm{cm}^2$. On the right pane we depict the growth of the capture rate as a function of the inelasticity for $v_\odot = 220{\rm km/s}$ (solid) and $v_\odot = 254{\rm km/s}$ (dashed). The upper two curves correspond to $m_{ \chi} = 200~\mathrm{GeV}$ (blue) and the lower two curves to $m_{ \chi} = 400~\mathrm{GeV}$ (purple).
• Figure 4: On the left is a plot of the muon yield in the inelastic case ($\delta=125~\mathrm{keV}$, $\sigma_n =10^{-40}~\mathrm{cm}^2$) for different annihilation channels from top to bottom on the left: $\nu_\mu\nu_\mu$, $\tau^+\tau^-$, $Z^0Z^0$, $W^+W^-$, $t\bar{t}$, $b\bar{b}$, and $c\bar{c}$. The area above the thick (violet) curve is excluded by Super-K. On the right pane we plot the corresponding bound on the annihilation branching ratio for the respective channels against the WIMP's mass.
• Figure 5: Same as Fig. \ref{['fig:currentLimits']}, but with $v_\odot = 254~{\rm km/s}$.