The Influence of Tidal Heating on the Habitability of Planets Orbiting White Dwarfs

TL;DR

This work investigates whether planets orbiting cooling white dwarfs can sustain habitable conditions by jointly considering radiative heating from the WD and tidal heating from orbital dissipation. It develops a coupled model in which surface temperature follows $ \sigma T^4 = \frac{(1-A)L_*}{16 \beta \epsilon \pi a^2} + \eta \frac{dE_p}{dt}{4 \pi r_p^2}$ with tidal power $\frac{dE_p}{dt} = \frac{21}{2} \frac{k_2}{Q_p} G^{3/2} M_*^{5/2} r_p^{5} a^{-15/2} e^2 (1-e^2)^{-15/2} (1 + 15 e^2/4 + 15 e^4/8 + 5 e^6/64)$, and couples this to orbital evolution via $da/dt$ and $de/dt$ with a circularization timescale $t_{circ}$. By applying the model to Earth-like and TRAPPIST-1 e–like planets, the authors identify an island of habitability where tidal heating sustains $T \sim 273-373$ K for multi-Gyr timescales, extending habitability beyond the radiative HZ that shrinks as the WD cools. The results show that interior planetary properties (e.g., $Q_p$, $k_2$, $r_p$) modulate the location and extent of this island, indicating that tidal heating can critically widen the population of plausibly habitable WD planets. Observationally, the work argues for expanded WD-target surveys (e.g., JWST, LSST) and transmission spectroscopy as viable pathways to detect and characterize such worlds and their biosignatures.

Abstract

In recent years, there have been a growing number of observations indicating the presence of rocky material in short-period orbits around white dwarfs. In this Letter, we revisit the prospects for habitability around these post-main-sequence star systems. In addition to the typically considered radiative input luminosity, potentially habitable planets around white dwarfs are also subjected to significant tidal heating. The combination of these two heating sources can, for a narrow range of planetary properties and orbital parameters, continuously maintain surface temperatures amenable for habitability for planets around white dwarfs over time scales up to 10 Gyr. We show that for a specific locus of orbital parameter space, tidal heating can substantially extend the timescale of continuous habitability for a planet around a white dwarf.

Figures (5)

• Figure 1: The semi-major axis spanned by the habitable zone for two white dwarfs with masses of 1.1$M_\odot$ (dashed yellow lines) and $0.54 M_\odot$ (solid red lines), neglecting tidal heating within the planet. As the white dwarf luminosity decreases over time, the location of the habitable zone moves inward and shrinks. The white dwarf cooling curves used to compute the location of the habitable zone are from Salaris2022 and use the opacity models of Cassisi2007.
• Figure 2: The total power received via tidal heating as a function of the orbital semi-major axis and eccentricity for a planet with an Earth-like composition and tidal parameters. This power is computed using Equation (\ref{['eq:tidalheating']}). Contours for the orbital locations where the planet receives Io- and Earth-like levels of tidal heating are marked.
• Figure 3: Evolution of the habitable zone (HZ) for planets around a white dwarf with contributions to total planetary heating (dashed) from tidal heating (blue) and incident stellar radiation (red). Each panel shows a different mode of evolution with a different selection of initial physical and orbital parameters. In the top panel, we show the evolution of an Earth-analog with initial semi-major axis of $a = 0.2$ and eccentricity of $e=0.7$. This planet initially resides within the tidal habitable zone. The subsequent semi-major axis evolution caused by tidal circularization does not follow the location of the habitable zone at late times. In the bottom panel, we show the evolution of a TRAPPIST-1 e-analog with initial semi-major axis of $a = 0.2$ and eccentricity of $e=0.8$. Its semi-major axis evolution traces the location of the habitable zone for the first $10Gyr$ of the white dwarf phase. The physical parameters of each planet are presented in Table \ref{['tab:planetparams']}.
• Figure 4: (Top panel) The computed amount of time that a planet like TRAPPIST-1 e (with physical parameters given in Table 1) around a white dwarf maintains habitable surface temperatures when both tidal heating and radiative heating are considered. (Bottom panel) The difference between the time that the same planet remains in the habitable zone while including tidal heating as compared to when ignoring tidal heating. Both quantities are shown for a range of initial semi-major axis and eccentricity values for the orbiting planet. In both plots, the solid black line denotes the threshold eccentricity above which planets will be tidally disrupted; the parameter space where planets may be habitable is safely below this limit. The habitable lifetime of a planet increases when including tidal heating for all but a very narrow range of parameter space.
• Figure 5: For the two objects under consideration (Earth and TRAPPIST-1 e), we show the section of parameter space where the habitable time during the white dwarf phase due to tidal heating is greater than 3 Gyr, 6 Gyr, and 9 Gyr. For comparison, the Earth has a habitable lifetime of 6.3-7.8 Gyr around the main sequence sun Rushby2013. Planets with physical parameters outside the range considered in this work will occupy slightly different locations in parameter space.