Towards Closing the Window on Strongly Interacting Dark Matter: Far-Reaching Constraints from Earth's Heat Flow

TL;DR

This work derives a new, largely model-independent upper bound on the DM–nucleon cross section by requiring that DM captured by Earth and subsequently annihilating in the core would not heat Earth beyond the observed internal heat flow. By combining a physically motivated capture model, annihilation in the core, and Earth’s measured heat (~44 TW with a conservative 20 TW allowance for exotic sources), they show that efficient capture plus annihilation would generate heat on the order of thousands of terawatts, thereby excluding a wide range of $\sigma_{\chi N}$ for $m_\chi$ between ~1 GeV and up to ~10^{10} GeV. This Earth-heat constraint fills the gap between indirect astrophysical limits at large cross sections and underground direct-detection limits at small cross sections, effectively closing the window for strongly interacting DM and reinforcing that DM–nucleon interactions must be genuinely weak. The results are robustly grounded in Earth’s well-measured heat flow and standard DM capture/annihilation formalism, with implications that direct detection experiments are probing the correct cross-section range for typical DM candidates.

Abstract

We point out a new and largely model-independent constraint on the dark matter scattering cross section with nucleons, applying when this quantity is larger than for typical weakly interacting dark matter candidates. When the dark matter capture rate in Earth is efficient, the rate of energy deposition by dark matter self-annihilation products would grossly exceed the measured heat flow of Earth. This improves the spin-independent cross section constraints by many orders of magnitude, and closes the window between astrophysical constraints (at very large cross sections) and underground detector constraints (at small cross sections). In the applicable mass range, from about 1 to about 10^{10} GeV, the scattering cross section of dark matter with nucleons is then bounded from above by the latter constraints, and hence must be truly weak, as usually assumed.

Figures (2)

• Figure 1: Excluded regions in the $\sigma_{\chi N}$--$m_\chi$ plane, not yet including the results of this paper. From top to bottom, these come from astrophysical constraints (dark-shaded) Starkman:1990njNatarajan:2002cwChen:2002yhCyburt:2002uw, re-analyses of high-altitude detectors (medium-shaded) Rich:1987stStarkman:1990njWandeltErickcek:2007jv, and underground direct dark matter detectors (light-shaded) Akerib:2006riAlbuquerque:2003eiSanglard:2005weBernabei:1999ui. The dark matter number density scales as 1/$m_\chi$, and the scattering rates as $\sigma_{\chi N}$/$m_\chi$; for a fixed scattering rate, the required cross section then scales as $m_\chi$. We will develop a constraint from Earth heating by dark matter annihilation to more definitively exclude the window between the astrophysical and underground constraints.
• Figure 2: Inside the heavily-shaded region, dark matter annihilations would overheat Earth. Below the top edge of this region, dark matter can drift to Earth's core in a satisfactory time. Above the bottom edge, the capture rate in Earth is nearly fully efficient, leading to a heating rate of 3260 TW (above the dashed line, capture is only efficient enough to lead to a heating rate of $\gtrsim$ 20 TW). The mass ranges are described in the text, and the light-shaded regions are as in Fig. \ref{['regions']}.