Tidally Torn: Why the Most Common Stars May Lack Large, Habitable-Zone Moons

TL;DR

The study investigates whether Luna-sized exomoons can persist around Earth-like planets in the habitable zones of M-dwarfs, incorporating 3-body dynamics and tidal dissipation through N-body simulations with rebound/reboundx. It finds that large moons are generally unstable on timescales well before the ages relevant for habitability, with instability timescales < $10^7$ yr for M4, < $10^8$ yr for M2, and often < $10^9$ yr for M0 systems, though certain M0 outer-HZ configurations may sustain moons for up to ~1.5–1.6 Gyr under Earth-like tides. The work combines direct N-body integrations with secular tidal theory to extrapolate longer lifetimes and demonstrates that resonance interactions (MMRs) and planetary tides crucially regulate moon survival. These results imply a reduced prevalence of large exomoons in M-dwarf systems, potentially impacting exolife considerations and the Drake equation, and they provide guidance for future exomoon searches with upcoming observatories. Overall, the research highlights how tidal physics and multi-body dynamics shape the outer architecture of planetary systems and the prospects for habitable moons in our galaxy.

Abstract

Earth-like planets in the habitable zone (HZ) of M-dwarfs have recently been targeted in the search for exomoons. We study the stability and lifetime of large (Luna-like) moons, accounting for the effects of 3-body interactions and tidal forces using the N-body simulator rebound and its extension library reboundx. We find that those moons have a notably different likelihood of existence (and, by implication, observability). Large moons orbiting Earth-like planets in the HZs of M4 and M2 dwarfs become unstable well before $10^7$ and $10^8 \textrm{ yr}$, respectively, and in most cases, those orbiting M0-dwarfs become unstable in much less than $10^9 \textrm{ yr}$. We conclude that HZ planets orbiting M-dwarfs are unlikely to harbor large moons, thus affecting the total number of possible moons in our galaxy and the Universe at large. Since moons may help enhance the habitability of their host planet, besides being possibly habitable themselves, these results may have notable implications for exolife, and should also be considered when seeking solutions to the Drake equation and the Fermi paradox.

Figures (10)

• Figure 1: HZs and Hill Radii of M0, M2, and M4 stars. (a) Top-down and (b) edge-on views of the HZs around M0 (red), M2 (blue), and M4 (black) dwarfs along with (c) the Hill radius for a prospective 1.0 $M_\oplus$ planet at the center of its respective HZ. The overlap of the M0 and M2 HZs is noted in purple in both (a) and (b).
• Figure 2: Initial conditions for rebound simulations for M0, M2, and M4 systems.
• Figure 3: Stability simulation results for a HZ planet--moon orbiting an M2-dwarf. Logarithm of maximum moon lifetime ($\log_{10}\left[t_{\rm max}\right]$) from simulations considering a range of host planet masses (0.8 to 2 $M_\oplus$) and semi-major axis within the HZ of an M2-dwarf. (a) shows results from N-body simulations using rebound with a tidal time-lag $\tau_{\rm p}$ of 698 s, while (b-d) show outcomes from secular tidal theory Barnes_2017 with tidal dissipation timescales $\tau_{\rm p}$ of (b) 698 s, (c) 100 s, and (d) 10 s. Contour lines indicate $\log_{10}(t_{\rm max})$ values, reflecting the time of moon loss due to tidal migration. Red, yellow, green, and blue regions represent increasingly longer lifetimes while purple regions represent the longest lifetimes.
• Figure 4: Time evolution for three HZ planet--moon systems orbiting an M2-dwarf. Time evolution of the (a-c) exomoon's semi-major axis $a_{\rm m}$, (d-f) planet to moon period ratio $P_{\rm p}/P_{\rm m}$, and (g-i) exomoon's eccentricity $e_{\rm m}$ for 3 distinctive points in the parameter space (0.17 au and 2.0 $M_\oplus$, 0.34 au and 1.0 $M_\oplus$, 0.34 au and 2.0 $M_\oplus$) in the M2 case. The bottom $x$-axis, plotted on a logarithmic scale, shows time normalized by the orbital period of a planet at the inner edge of the HZ (0.17 au) while the top $x$-axis shows time (in years). The blue and red points signify rebound results while black dashed lines represent results from secular tidal theory. Black dots in the eccentricity panels represent the median value over 1 million orbits.
• Figure 5: Spin evolution for four HZ planet--moon systems orbiting an M2-dwarf. Evolution of planetary spin period for two $a_{\rm p}$ cases in the M2 parameter space (0.17 au, 0.34 au) at (a) 1.0 $M_\oplus$ and (b) 2.0 $M_\oplus$ from rebound simulations where curve lengths represent lifetimes. The bottom $x$-axis, plotted on a logarithmic scale, shows time normalized by the orbital period of a planet at the inner edge of the HZ (0.17 au) while the top $x$-axis shows time (in years).