Dark Matter (S)pins the Planet

TL;DR

This paper develops a near-equilibrium framework linking dark matter heating in planets to rotational dynamics, showing that DM energy can be partitioned between interior heating and spin-up rather than all going into temperature. By deriving a coupled evolution with $\Omega = bT$ and applying an energy balance $\Gamma_{\text{in}} = \Gamma_{\text{out}} + I\Omega\dot\Omega$, it demonstrates that the partition emerges from planetary properties and external inputs, and that a non-equilibrium steady state can arise when DM heating dominates over radiative losses. Simulations for exoplanets and Solar System bodies reveal that previous heating-centric estimates may overstate the thermal impact, as rotational energy gains can absorb a significant fraction of DM energy, potentially pinning planetary rotation at high DM densities. The work highlights nuanced implications for planetary temperatures, rotation, and habitability, and suggests limited current ability to constrain DM parameters (via the capture fraction $f$) with Solar System data, while motivating future exoplanet observations as tests of this mechanism.

Abstract

Dark matter heating in planets has been proposed as a potential probe for dark matter detection. Assuming near-equilibrium conditions, we find that the energy input from dark matter raises planetary temperatures and accelerates rotation. The distribution of energy between heating and rotational acceleration depends on both planetary properties and external inputs, suggesting that previous studies may have overestimated the heating contribution. At high dark matter densities, planetary rotation stabilizes earlier and becomes primarily governed by dark matter effects.

Figures (4)

• Figure 1: The left and right figures respectively represent the planetary system before and after experiencing perturbation $\dot T$ due to dark matter and sun's heating. Since the perturbation is minimal, we consider the process under local dynamic thermodynamic equilibrium. The perturbations follow $\dot E_{1} + \dot E_{2} \rightarrow \dot T + \dot \Omega$, where the planetary temperature evolves as $T \rightarrow T + \dot T\mathrm{d}t$, and the planetary angular velocity changes as $\Omega\rightarrow \Omega + \dot \Omega\mathrm{d}t$.
• Figure 2: Angular velocity evolution of the planets under different dark matter densities. \ref{['sa']} shows the evolution at $\rho_{\text{local}}$, while \ref{['sb']} corresponds to $10^{4} \rho_{\text{local}}$. The time origin here is set at the current age of the star. We set the initial angular velocity of each simulated planet to that of Jupiter.
• Figure 3: \ref{['a']} shows the evolution of planetary temperature and acceleration energy ratio under the dark matter heating mechanism at a dark matter density of $\rho_{\text{local}}$. \ref{['b']} presents the evolution considering both solar and dark matter heating mechanisms at $\rho_{\text{local}}$. \ref{['c']} illustrates the evolution under the dark matter heating mechanism at a dark matter density of $10^{4} \rho_{\text{local}}$. \ref{['d']} depicts the evolution considering both solar and dark matter heating mechanisms at $10^{4} \rho_{\text{local}}$.The solid line represents temperature, while the dashed line indicates the fraction of energy used to change angular velocity.
• Figure 4: \ref{['fig:jupiter_omega_long']}, \ref{['fig:jupiter_omega_short']}, \ref{['fig:earth_omega_long']}, and \ref{['fig:earth_omega_short']} illustrate the impact of our mechanism on the rotational dynamics of Jupiter and Earth over different timescales. \ref{['fig:earth_f_onlyDM']} shows the evolution of Earth's effective temperature and rotational angular velocity under dark matter heating alone, for $f$ values of $10^{-5}, 10^{-3}$, and 1 . \ref{['fig:earth_f_sun+DM']} presents the corresponding evolution with both dark matter and solar heating included, using the same $f$ values as in \ref{['fig:earth_f_onlyDM']}.