General relativistic spin precessions and the habitability of rocky planets of fast spinning late M dwarfs
Lorenzo Iorio
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. I show that the General Theory of Relativity (GTR) predicts spin precessions which, to the post-Newtonian (pN) order, may impact the habitability of a fictitious telluric planet orbiting a late M dwarf with M⋆=0.08M⊙ at a=0.02au, corresponding to an orbital period Pb≃4d, inducing long-term variations of the obliquity ε of its spin S which, under certain circumstances, may not be deemed as negligible from the point of view of life’s sustainability. I analytically derive the orbit-averaged equations of the pN precessions of the polar angles θ,α of Ŝ and of the orbital inclination I and node Ω entering ε, and numerically integrate them by producing time series of the pN changes Δε(t) of the obliquity. For rapidly rotating M dwarfs with rotational periods of the order of P⋆≃0.1−1d, the planet’s obliquity ε can undergo pN large variations Δε(t) up to tens of degrees over timescales Δt≃20−200kyr, depending on the mutual orientations of the star’s spin J⋆, of S, and of the orbital angular momentum L. Instead, Δε(t) are ≲1−1.5∘ for the planet b of the Teegarden’s Star. GTR should be considered one of the key factors to be taken into account in compiling budgets of the long-term habitability of rocky planets around fast spinning late M dwarfs. My approach can be extended also to other astronomical scenarios where features of the target bodies other than their habitability are of interest.
Comments: LaTex2e, 24 pages, 5 figures, no tables
Subjects: General Relativity and Quantum Cosmology (gr-qc); Earth and Planetary Astrophysics (astro-ph.EP); Space Physics (physics.space-ph)
Cite as: arXiv:2102.07815 [gr-qc] (or arXiv:2102.07815v1 [gr-qc] for this version)
Submission history
From: Lorenzo Iorio
[v1] Mon, 15 Feb 2021 19:48:07 UTC (1,114 KB)
