# Tides between the TRAPPIST-1 planets

## TL;DR

This study compares tidal heating from star-planet and planet-planet interactions in the TRAPPIST-1 system, finding stellar tides dominate except under very low viscosities and specific orbital conditions.

## Contribution

It provides the first quantitative assessment of the relative importance of planet-planet versus stellar tides in the TRAPPIST-1 system.

## Key findings

- Stellar tides dominate over planet-planet tides in energy dissipation.
- Planet-planet tides can contribute up to 20% of total tidal heating for TRAPPIST-1 g.
- Orbital eccentricities must be extremely low ($10^{-3}$ to $10^{-4}$) for planet-planet tides to surpass stellar tides.

## Abstract

The TRAPPIST-1 system is sufficiently closely packed that tides raised by one planet on another are significant. We investigate whether this source of tidal heating is comparable to eccentricity tides raised by the star. Assuming a homogeneous body with a Maxwell rheology, we find that energy dissipation from stellar tides always dominates over that from planet-planet tides across a range of viscosities. TRAPPIST-1 g may experience the greatest proportion of planet-planet tidal heating, where it can account for between 2% and 20% of the total amount of tidal heating, for high ($10^{21}$ Pa s) and low viscosity ($10^{14}$ Pa s) regimes, respectively. If planet-planet tidal heating is to exceed that from stellar eccentricity tides, orbital eccentricities must be no more than e=$10^{-3}$ to $10^{-4}$ for most of the TRAPPIST-1 planets.