Post-Keplerian obliquity variations and the habitability of rocky planets orbiting fast spinning, oblate late M dwarfs

Abstract

A couple of dozen Earth-like planets orbiting M dwarfs have been discovered so far. Some of them have attracted interest because of their potential long-term habitability; such a possibility is currently vigorously debated in the literature. I show that post-Keplerian (pK) orbit precessions may impact the habitability of a fictitious telluric planet orbiting an oblate late-type M dwarf of spectral class M9V with $M_{\star }=0.08M_{\odot }$ at $a=0.02\mathrm{au}$, corresponding to an orbital period $P_{\mathrm{b}}\simeq 4\mathrm{d}$, inducing long-term variations of the planetary obliquity $\epsilon$ which, under certain circumstances, may not be deemed as negligible from the point of view of life's sustainability. I resume the analytical orbit-averaged equations of the pK precessions, both classical and general relativistic, of the unit vectors $\hat{\mathbf{S}},\hat{\mathbf{h}}$ of both the planet's spin and orbital angular momenta $\mathbf{S},\mathbf{L}$ entering $\epsilon$, and numerically integrate them by producing time series of the pK changes $\Delta \epsilon (t)$ of the obliquity. For rapidly rotating M dwarfs with rotational periods of the order of $P_{\star }\simeq 0.1-1\mathrm{d}$, the planet's obliquity $\epsilon$ can undergo classical pK large variations $\Delta \epsilon (t)$ up to tens of degrees over timescales $\Delta t\simeq 20-200\mathrm{kyr}$, depending on the mutual orientations of the star's spin ${\mathbf{J}}_{\star }$, of $\mathbf{S}$, and of $\mathbf{L}$. Instead, $\Delta \epsilon (t)$ are $\lesssim 1-1.5^{\circ }$ for the planet b of the Teegarden's Star. In certain circumstances, the M dwarf's oblateness $J_2^{\star }$ should be considered as one of the key dynamical features to be taken into account in compiling budgets of the long-term habitability of rocky planets around fast spinning late M dwarfs. (Abridged)

LaTex2e, 26 pages, 6 figures, no tables. Changes suggested by an anonymous referee implemented

References in corpus (1)

• 55 Cancri (Copernicus): A Multi-Planet System with a Hot Super-Earth and a Jupiter Analogue