General Relativity Can Prevent a Runaway Greenhouse on Potentially Habitable Planets Orbiting White Dwarfs

TL;DR

This paper investigates whether general relativistic apsidal precession can protect a potentially habitable planet in the white dwarf habitable zone from tidal heating-induced runaway greenhouse effects driven by perturbations from exterior planets. Using a secular Laplace-Lagrange framework augmented with GR terms and a parameter sweep implemented in the celmech integrator, the authors quantify how GR alters eccentricity pumping from outer companions. They find that GR often suppresses forced eccentricity, substantially widening the stable, habitable parameter space, though very massive or closely spaced outer planets can still trigger runaway conditions. The results indicate GR should be included in habitability assessments for white dwarf systems and have implications for target prioritization in biosignature searches with JWST and related instruments.

Abstract

Planets orbiting in the habitable zones of white dwarfs have recently been proposed as promising targets for biosignature searches. However, since the white dwarf habitable zone resides at 0.01 - 0.1 AU, planets residing there are subject to tidal heating if they have any orbital eccentricity. Previous work (Barnes & Heller 2013) identified nearby planetary companions as potential roadblocks to habitability of planets around white dwarfs, as such companions could induce secular oscillations in eccentricity for the potentially habitable planet, which could in turn heat a surface ocean and induce a runaway greenhouse for even very low values ($e \sim 10^{-4}$) of the eccentricity of the potentially habitable planet. In this work, we examine the potential for general relativistic orbital precession to protect habitable planets orbiting white dwarfs from such a runaway greenhouse, and demonstrate that for some system architectures, general relativity can be protective for planetary habitability.

Figures (7)

• Figure 1: The plot shows the precession rate for an inner planet $a_1$ perturbed by an exterior companion planet with mass $m_2 = 10 M_{\oplus}$ at a orbital distance of $a_2 = 0.1$ AU. The red curve represents the precession rate due to GR, while the dashed black curve represents the precession rate due to perturbations from the exterior companion. The shaded green region highlights the range corresponding to the Continuous Habitable Zone (CHZ) identified in Agol_2011.
• Figure 2: Parameter space showing the effect of GR on eccentricity oscillations due to an exterior planetary companion for a variety of combinations of the mass ratio $m_2/m_1$ and semi-major axis ratio $a_2/a_1$. The interior planet was assumed to be a 1 $M_{\oplus}$ planet at 0.01 AU. When $\xi < 1$ (bottom-left, red), GR amplifies eccentricity oscillations; when $\xi > 1$ (top-right, black), GR suppresses them. The dashed line marks the transition as derived in Adams2006.
• Figure 3: Example integrations of the inner planet's eccentricity $e_1$ for two values of the outer planet's semi-major axis $a_2$, with all other system parameters identical. In each panel, the pink curve shows the solution without GR and the green curve includes GR. The top panel corresponds to $a_2 = 0.05\,\mathrm{AU}$ and the bottom to $a_2 = 0.25\,\mathrm{AU}$. The outer planet mass is set at a value of 20 $M_\oplus$. The eccentricity oscillations are larger for the closer outer planet, and in both cases the inclusion of GR suppresses their amplitude.
• Figure 4: Example integrations of the inner planet’s eccentricity $e_1$ for two values of the outer planet’s mass $m_2$ (top panel: $m_2 = 5\,M_\oplus$; bottom panel: $m_2 = 150\,M_\oplus$), with all other system parameters identical and the outer planet semi-major axis set at a value of 0.15 AU. Larger outer planet masses lead to higher-frequency eccentricity oscillations. In both cases, the inclusion of GR strongly suppresses the oscillation amplitude, more strongly for smaller masses of the outer planet.
• Figure 5: Parameter sweep over outer planet mass ($m_2$) and semi-major axis ($a_2$), testing whether a $1\,M_\oplus$ inner planet at $a_1=0.01$ AU orbiting a $0.5\,M_\odot$ white dwarf undergoes a tidal-driven runaway greenhouse, if the runaway greenhouse will onset at the level of tidal heating caused by a orbital eccentricity of $e\approx10^{-4}$. Left panel: A parameter sweep which includes GR apsidal precession. Right panel: an identical parameter sweep but without GR. GR enlarges the stable region (where the inner potentially habitable planet avoids the runaway greenhouse) by suppressing secularly forced eccentricity, whereas without GR nearly all configurations with $a_2 \lesssim 0.18$ AU trigger a runaway greenhouse. All runs assume $e_2=0.05$ and are integrated for $3\times10^{5}$ yr.