Implications of Tides for Life on Exoplanets

4.1. Tidal cycling and abiogenesis

About a decade ago, Lathe (2004) proposed a theoretical model that posited tides as a major player in the origin of life (abiogenesis) on Earth. The central idea was that tides facilitated the chemical reactions analogous to the polymerase chain reaction (PCR). The latter is characterized by a cyclical process oscillating between two different temperatures and driving DNA amplification in the presence of an appropriate polymerase enzyme (Mullis, 1990; Erlich et al., 1991). It was conjectured by Lathe (2004) that tides could drive cycles of flooding and drying that supplied the aforementioned temperature contrasts as well as variations in the salinity and prebiotic molecule concentrations necessary for polymerization and dissociation; more specifically, the polymerization operates during the drying/evaporation phase, while dissociation occurs during the dilution/flooding phase (Lathe, 2005).

The model relied on two central assumptions: (A) the rotation rate of Earth at the time of life's emergence was faster, leading to semidiurnal tides with a lower periodicity (≲ 6 h), and (B) a closer Earth-Moon distance, which enabled the formation of tidal areas that “extended several 100 km inland” (Lathe, 2004). Both of these assumptions were rightly critiqued by Varga et al. (2006), and Lathe revised some of his original predictions in subsequent publications (Lathe, 2005, 2006). The tidal chain reaction was further investigated by Fernando et al. (2007), who concluded that the mechanism was unlikely to be functional unless certain criteria, such as restriction ribosomes and complex (e.g., hairpin) RNA structures, were present.

In addition, several studies have suggested that Earth was composed mostly of oceans in the Hadean era (Iizuka et al., 2010; Arndt and Nisbet, 2012) and perhaps extending up to the late Archean era at 2.5 Gya (Flament et al., 2008); see, however, Harrison et al. (2008), Harrison (2009), and Hawkesworth et al. (2013). Thus, if continents emerged relatively late in Earth's history (post-abiogenesis), the role of tides in setting up wet-dry cycles would be rendered a moot point. Hence, on account of the above reasons, the tidal chain reaction is not expected to constitute a viable mechanism insofar as Earth is concerned. However, this fact ought not automatically imply that the relevance of the mechanism can be ruled out on all exoplanets in the HZ of their host stars.

We now consider (A) and (B), with the above caveats in mind. We begin by observing that condition (B) is likely to be valid in the TRAPPIST-1 system. As noted in Section 3, even accounting for the original positions of the TRAPPIST-1 planets, the tidal forces and bulges are likely to have been orders of magnitude higher than on Earth. In turn, this might result in much larger areas being subjected to cycles of flooding and evaporation. The situation regarding τ _p is trickier since we cannot estimate the rotation rates at the time of abiogenesis. However, as these planets could have rotated faster in the past, condition (A) may also be satisfied.

The above statements can be viewed as part of a broader narrative in the context of abiogenesis. The importance of dry-wet cycles (e.g., due to tides) in synthesizing prebiotic polymers has been analyzed from a thermodynamic perspective (Damer and Deamer, 2015; Ross and Deamer, 2016). Mineral surfaces have been documented to play a key role in several issues associated with the origin of life (Cleaves et al., 2012; Ruiz-Mirazo et al., 2014). They serve as a natural means of concentrating the dilute prebiotic “soup” and facilitate condensation, self-organization, and stabilization (Ferris et al., 1996; Bywater and Conde-Frieboesk, 2005; Cleaves et al., 2012). Moreover, they play an important role in separating left- and right-handed molecules (Hazen and Sholl, 2003), thereby paving the way for homochirality—a salient feature of life. Hazen and Sverjensky (2010) identified five factors of the Hadean geochemical environment that played a putative role in the origin of life: (i) chemical complexity, (ii) mineral-aqueous solution interfaces, (iii) gradients, (iv) fluxes, and (v) cycles (Eigen, 1971). Of these factors, Hazen and Sverjensky (2010) have already pointed out that tides might have played a crucial role in regulating the factors (iv) and (v).

We argue that, in planetary systems situated around low-mass stars, vigorous tides can result in a greater degree of flooding and evaporation, thereby enabling (ii), namely, interfaces, to encompass larger areas. With regard to (iii), variations in salinity and other chemical concentrations could arise through intensive tidal cycling provided that (A) and (B) are satisfied. These variations could potentially give rise to physicochemical gradients that play a crucial role in abiogenesis (Spitzer, 2013) such as, for instance, osmotic gradients that are necessary for chemiosmosis. The latter's importance stems from the fact that it plays a central role in energy metabolism and has thus been invoked as a key player in the origin of life (Lane et al., 2010; Schoepp-Cothenet et al., 2013). However, an important issue that affects planets around M dwarfs is that they may end up being either desiccated or ocean-dominated (Tian and Ida, 2015). In general, neither of these two categories will be conducive to the emergence of life via tidal flooding-drying cycles, since the latter would typically be absent on such planets.

4.2. Tides and biological rhythms

Most biological organisms on Earth have evolved internal timing mechanisms, often dubbed as biological “clocks.” These clocks are found in some Prokaryota (Dvornyk et al., 2003) and most members of Eukaryota, especially those belonging to the well-known kingdoms Plantae, Fungi, and Animalia (Sogin, 1994), thereby proving to be ubiquitous in complex organisms. Among these biological clocks, perhaps the best known are the circadian clocks that display a time period of approximately 24 h (Moore-Ede et al., 1982; Rensing et al., 2001).

The molecular bases of circadian clocks have been thoroughly explored in modern times (Dunlap, 1999; Young and Kay, 2001), with a particular emphasis on the central and peripheral mammalian circadian clocks (Reppert and Weaver, 2002; Dibner et al., 2010; Mohawk et al., 2012); the primary clock in Mammalia is located in the suprachiasmatic nuclei (SCN) that resides in the anterior hypothalamus. It has been argued that circadian clocks have originated independently at least in two instances (Bell-Pedersen et al., 2005; Rosbash, 2009). If this hypothesis proves to be correct, circadian clocks would constitute an example of evolutionary convergence (Morris, 2003). Circadian clocks play an important role in several biological contexts (Nikhil and Sharma, 2017), for example, endowing fitness advantage (Ouyang et al., 1998; Michael et al., 2003; Sharma, 2003), maintaining metabolic homeostasis (Feng and Lazar, 2012; Marcheva et al., 2013), and regulating ecologically significant processes such as reproduction and migration in animals (Morgan, 2004).

On Earth, the circadian clock of most mammals, and other organisms, is regulated by the light-dark cycle (Pittendrigh, 1993; Johnson et al., 2008; Albrecht, 2012). However, we note that the circadian clock does exist even in mammals that are incapable of visual perception (Beale et al., 2016), for example, members of the genus Spalax, and other factors such as temperature can also play a role in resetting the circadian clock (Mrosovsky, 1996; Dunlap, 1999). When we turn our attention to synchronously rotating planets around M dwarfs, we are confronted with an immediate difference, namely, the possible absence of the light-dark cycle.

This raises an important question as to how the “daily” rhythms and biological clock can be regulated on generic exoplanets in the HZ of M and K dwarfs, where the tidal forces are expected to be stronger (see Section 5.2 for further details). Here, we reiterate that these planets need not have been tidally locked in the past and may still be subject to librations in the current epoch. Moreover, asynchronous rotation may arise due to a multitude of reasons including triaxial deformation (Zanazzi and Lai, 2017), semiliquid interiors (Makarov, 2015), and the existence of a sufficiently massive atmosphere (Leconte et al., 2015). Below, we explore the hypothesis that ocean tides might play a significant role in governing the biological clocks of aquatic and semiaquatic species.

Our proposal is motivated, and partly justified, by fairly extensive empirical evidence that has clearly demonstrated the role of the tidal cycle in regulating animal behavioral patterns on Earth (Neumann, 1981; Gibson, 1992; Palmer, 2000; Barrow, 2005; Wilcockson and Zhang, 2008; Tessmar-Raible et al., 2011). It seems likely that tidal clocks had an independent origin from their circadian counterparts, based on evidence from the crustacean Eurydice pulchra (Zhang et al., 2013). We observe that the following phenomena have been observed to occur on a periodic basis: (i) variations in activity, especially in crabs belonging to the genera Uca and Carcinus, respectively (Palmer, 1973; López-Duarte and Tankersley, 2007); (ii) locomotion rhythms in aquatic animals, for example, in Limulus polyphemus and Carcinus maenas (Naylor, 1996; Chabot et al., 2004); (iii) egg-hatching and larval release activities (Neumann, 1981; Thurman, 2004); (iv) differences in oxygen consumption (Palmer, 1995); and (v) intertidal migration and selective tidal-stream transport in decapods and fishes (Gibson, 2003). In most of these cases, the rhythms recur over a period of τ _p /2 or τ _p, indicating that they are associated with semidiurnal (circatidal) or diurnal (circadian) tides, respectively.

In this context, we also observe that the earliest concrete evidence of land animals on Earth dates back to the Silurian-Ordovician period (Jeram et al., 1990; Johnson et al., 1994; Pisani et al., 2004), although arthropod tracks have been dated to the Cambrian epoch (MacNaughton et al., 2002; Rota-Stabelli et al., 2013). Most fossils from this period are from the subphyla Myriapoda (e.g., centipedes and millipedes) and Chelicerata (e.g., arachnids and horseshoe crabs) that fall under the domain of Arthropoda (Knoll and Nowak, 2017). As many aspects of the life cycle of present-day crabs, which are also arthropods, are governed by tides, we can therefore speculate that the first land-dwelling animals may also have been regulated by circatidal (and circalunar) rhythms to some degree (Naylor, 2015). If this hypothesis is correct, tides would have played an important role in the evolution of terrestrial life on Earth (Barrow, 2005), since animals play a notable role in nutrient cycling, regulating oxygen levels, and “engineering” the biosphere (Butterfield, 2011; Lyons et al., 2014; Vermeij, 2017).

As we indicate in Section 5.2, the tidal bulges for planets around M and K dwarfs are much more significant than on Earth. Hence, it stands to reason that the influence of oceanic tides on these planets (if present) on ecology and evolution would be more profound. Especially in the absence of the light-dark resetting mechanism, the tidal cycle may constitute an important biological clock and thereby regulate biological properties from the ecosystem to the cellular level. However, an important caveat worth reiterating is that the tidal cycle is likely to affect aquatic and amphibious organisms to a considerable degree, but its influence on land-based life-forms may be minimal.

4.3. Turbulent mixing in oceans

It is well known that, in the absence of turbulent mixing, oceans on Earth would become stagnant and be characterized by very weak (convective) circulation (Ferrari and Wunsch, 2009). The energy required for ocean mixing is provided primarily by tides and winds (Wunsch and Ferrari, 2004). In particular, several studies have concluded that tides provide ∼50% of the energy required for sustaining large-scale thermohaline ocean circulation (Munk and Wunsch, 1998; Egbert and Ray, 2000, 2001). The source of this energy is tidal dissipation in the ocean interior partly due to internal wave generation and breaking by interactions with topographic gradients (Jayne and St. Laurent, 2001; Garrett and Kunze, 2007). In this context, we point out that energetic internal waves can be excited at the semidiurnal tidal frequency (Ivey et al., 2008).

As noted in the work of Munk and Wunsch (1998), most of the tidal dissipation arising from the Moon (and the Sun) is dissipated in the ocean, with only a small fraction being dissipated in the atmosphere and planetary interior. We now turn our attention to (4), from which we can see that the characteristic value of tidal energy dissipation is O(10)–O(100) TW for planets around M dwarfs. This is higher than the total tidal dissipation arising from the Moon by about 1–2 orders of magnitude. Hence, if the energy budget for ocean mixing is similar to that of Earth (∼2 TW), it would appear as though tidal dissipation could play a dominant role in providing the mechanical energy for meridional overturning circulation in planets orbiting low-mass stars.

However, the physical reality is not quite so simple. As noted earlier, the topography plays an important role in determining the generation and breaking of internal waves. From a theoretical standpoint, this is seen from the relevance of the steepness parameter, that is, the topographic slope divided by the vertical length scale of these internal waves (St. Laurent and Garrett, 2002). Hence, it automatically follows that the existence of plate tectonics, which plays a clear role in shaping bathymetric hetereogeneity (Condie, 1989), would constitute an important factor. The factors influencing plate tectonics on exoplanets are many, and this subject has a long and much-contested history, which we will not address here. Initial studies were directed toward understanding whether plate tectonics is more likely or less likely on super-Earths (O'Neill and Lenardic, 2007; Valencia et al., 2007), although subsequent studies have pointed out the complex dependence of plate tectonics on the dynamical evolution of planetary properties (Weller and Lenardic, 2012; Stamenković and Seager, 2016).

Even if we assume that the requisite bathymetric heterogeneity exists such that it facilitates vertical transport, the strength of the mixing still remains unknown. The latter is quantified via the vertical diffusivity, which is known to depend on the depth (Bryan and Lewis, * 1979), the stratification (Gargett, 1984), the topographical roughness (Polzin et al., 1997), and several other quantities (Jayne, 2009). The mixing will also be affected by the temperature profile through the ocean (Wunsch and Ferrari, 2004). It is widely known that vertical mixing is lowest in the relatively stable thermocline and is enhanced at greater depths (Gregg, 1987). As M dwarfs on the lower end of the mass spectrum will radiate primarily in the near-infrared, the stable stratification of the upper levels can be reduced since the radiation is strongly absorbed in this range (Curcio and Petty, 1951; Kaltenegger et al., 2007) and will therefore display a lesser degree of penetration.

A potential ramification of the above point is that the stable stratification would be more pronounced on the day side than the night side, and simulations suggest that this is indeed the case (Del Genio et al., 2017), when other factors (e.g., salinity) are not included. Thus, as a consequence, it could be possible for strong mixing to occur closer to the surface on such exoplanets compared to Earth. A possible downside is that the euphotic zone would be shallower for the above reasons on planets that mostly receive near-infrared radiation. This could, however, be partly offset by the fact that tidally locked planets are typically expected to have stronger winds than Earth (Edson et al., 2011; Lingam and Loeb, 2017a). Thus, on such exoplanets, wind-driven circulation (Alford, 2001) is capable of giving rise to greater ocean mixing.

The importance of the above discussion stems from the fact that ocean mixing, which is driven primarily by tidal forces and winds, promotes the upwelling of nutrients to the euphotic zone (Sandstrom and Elliott, 1984; Holligan et al., 1985; MacKinnon and Gregg, 2003; Schafstall et al., 2010). In turn, the enhanced availability of nutrients via ocean mixing will probably have a wide array of consequences for marine ecosystems (Wolanski and Hamner, 1988; Smith et al., 2009), biogeochemistry (Sarmiento and Gruber, 2006), and climate (Dewar et al., 2006; Watson and Naveira Garabato, 2006). Naturally, it goes without saying that the availability of nutrients is a necessity for the upwelling of nutrients to take place; the former factor will depend on several aspects, such as the composition of the mantle (Seager et al., 2013), for example, whether it is predominantly ice/silicate.

4.4. Other biological implications of tides

In addition to the above processes, tides play a major role in regulating coastal erosion, sediment movement, tidal currents, tidal mixing fronts, and strength of tidal streams. ¹ All of these factors result in important biological long-term responses and give rise to regions of high biological productivity in some instances (Le Fèvre, 1987; Leigh et al., 1987). High biodiversity in these habitats, for example, in intertidal zones (Raffaelli and Hawkins, 1999; Defeo et al., 2009), is also typically accompanied by substantial environmental variability.

The high biological productivity is a consequence of the fact that the tidal cycle maintains a continual supply of nutrients, and some of these environments (e.g., littoral zones) are also shallow enough to support photosynthesis (Pugh, 1996). As both of these elements are fairly generic, it seems plausible that similar zones, characterized by a high degree of biodiversity and productivity, could be present on exoplanets. It is worth bearing in mind that photosynthesis on planets orbiting M dwarfs, if prevalent, may produce spectral signatures in the infrared range instead of the conventional “red edge” (Kiang et al., 2007).

Another important consequence of tidal forces (due to obliquity) is their capacity to generate large-amplitude Rossby waves in the open ocean (Longuet-Higgins, 1968). On Europa, it has been suggested that the kinetic energy associated with the flow is ∼10¹⁹ J, and that it can lead to tidal dissipation and heating of the oceans (Tyler, 2008). Even if the oceanic tidal heating contribution to the overall thermal budget is subdominant (Chen et al., 2014), the generation of large-amplitude Rossby waves is an important biological result in its own right.

The importance of Rossby waves stems from the fact that they can potentially stimulate photosynthesis (Mann and Lazier, 2006; Lévy, 2008) through wave-induced upwelling (Uz et al., 2001; Sakamoto et al., 2004) via a “rototiller” mechanism that uplifts nutrients into the euphotic layer (Siegel, 2001); on the other hand, the observed chlorophyll signals have also been explained through horizontal advection by the waves against a background gradient (Killworth et al., 2004). Rossby waves may also cause the convergence of floating particles on the surface, thereby serving as a marine “hay rake” (Dandonneau et al., 2003), although the feasibility of this mechanism has been critiqued by Killworth (2004). Lastly, wave-induced action leads to evolutionary advantages and enables accelerated development, suggesting that organisms can evolve and grow more rapidly when waves are present (Tsuchiya and Ross, 2003).

Hitherto, we have discussed the effects of tides on biological processes, but it is worth emphasizing that this picture is a simplified one. In reality, a reciprocal coupling between tide-dominated environments (e.g., estuaries) and biota is likely to be prevalent (Vandenbruwaene et al., 2011; Wang and Temmerman, 2013); the situation could be quite analogous to the mutual feedback effects involved in shaping the coevolution of geomorphology and ecosystems (Corenblit et al., 2011). For instance, tidal dissipation facilitates vertical mixing in the ocean (Section 4.3), which thereby enables the delivery of nutrients to the euphotic zone, and could therefore play a beneficial role in sustaining ocean ecosystems. In turn, the marine biosphere can drive ocean mixing (and circulation) at a level that has been hypothesized to be comparable to tides and winds (Dewar et al., 2006; Katija and Dabiri, 2009), although the evidence has been debated (Visser, 2007). Such coevolution, if existent, can be viewed as a variant of the Gaia hypothesis that envisions life and the planetary environment as a coupled, coevolutionary system (Lovelock and Margulis, 1974; Lenton, 1998).

Here, it must be recalled that, as with all other hypotheses concerning biological processes, there exist a multitude of physical, geological, and biochemical factors that remain partly or wholly unknown. Hence, our conclusions concerning the role of the tides on abiogenesis, ecology, and evolution in the TRAPPIST-1 system, Proxima b, and other exoplanets must be interpreted with due caution. For instance, if the amplitudes of the tides are extremely high, they may have a detrimental effect on these phenomena. More specifically, massive tides could cause widespread habitat destruction unless they are mitigated by ecosystem resilience; mangrove forests represent a striking example of the latter since they attenuate the damage caused by tsunamis (Alongi, 2008).

From the standpoint of abiogenesis, however, large tides ought not to prove to be a major problem. Planets around low-mass stars (like the TRAPPIST-1 system) may have formed at greater distances and migrated inward (Winn and Fabrycky, 2015). Thus, it is conceivable that the tides, at the time of abiogenesis, were a factor of ∼10–100 lower than their final value, as seen from the discussion regarding TRAPPIST-1 in Section 3. A corollary of this fact is that the tidal elevation would be O(1)–O(10) m; although this range is on the higher side, we note that waves of this amplitude have been documented on Earth even in the Anthropocene (Dysthe et al., 2008; Bryant, 2014).

Furthermore, the time of abiogenesis is not properly constrained on Earth due to a scarcity of paleontological evidence (Knoll et al., 2016), and it is known that the Earth-Moon distance was initially ∼4 R _⊕ (Canup, 2012), compared to the current distance of ∼60 R _⊕. Thus, from (7) the lunar tidal forces could have been stronger (when life originated) by a factor of ≲10 if the corresponding lunar distance was about half its present-day value. Taken collectively, the discrepancy between tides on Earth and those on planets orbiting low-mass stars might be reduced at the time of abiogenesis, implying that the latter is only about an order of magnitude higher than the former.

Lastly, we can draw some insights from the studies of tsunamis, while being cognizant of the fact that they are not simple oceanic tides. Nonetheless, if one supposes that they can be modeled via a solitary wave approach (Carrier et al., 2003)—see, however, Constantin and Johnson (2006)—a few interesting conclusions can be drawn. For values of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${\cal H/D}$$ \end{document}  ≲ 0.2, where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${\cal H}$$ \end{document} is the wave height and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${\cal D}$$ \end{document} is the depth of the water, it was found that wave breaking and dissipation of energy occurred before the shoreline was reached (Li and Raichlen, 2002; Madsen et al., 2008); in some cases, large tsunamis bypassed islands and collided behind them (Liu et al., 1995).

Empirical evidence from the 2009 South Pacific tsunami (with a height of 14 m) was inundated ∼250 m onshore (Apotsos et al., 2011). The height is comparable to tides on M dwarf exoplanets provided that abiogenesis occurred when they were migrating inward; it is also equal to the tidal amplitudes for exoplanets orbiting K dwarfs. Even if the tides had a higher amplitude than O(10) m, abiogenesis could still be initiated inland, close to the point of inundation, where the level of sediment deposition is not so great; that is, the dry-wet cycles would operate in a habitat (e.g., hydrothermal pools) not situated near the coast (Damer and Deamer, 2015).

Thus, taken collectively, all of these results appear to suggest that large-amplitude oceanic tides might not pose as much of a threat as one would expect for the origin of life.

5.1. Tides caused by the TRAPPIST-1 planets

Hitherto, when discussing the TRAPPIST-1 system, we have restricted ourselves to the tidal force exerted by the host star, as it constitutes the most dominant source. Now, we turn our attention to the additional forces exerted by one planet on another; we do not consider tidal effects due to (large) exomoons in the TRAPPIST-1 system since they are unlikely to survive dynamically (Kane, 2017).

Suppose that we consider the tidal force exerted by planet II (with mass M ₂) on planet I (with mass M ₁ and radius R ₁), and the two planets are separated by a distance d ₁₂; for the sake of simplicity, we assume that the two planets are nearest neighbors. Along the lines of our treatment in Section 3, we can express the tidal elevation (7) in terms of the Earth-Sun value: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \frac { { H_ { 12 } } } { { H_ { \rm { E } } } } } \approx 3 { \left( { { \frac { { R_1 } } { { R_ \oplus } } } } \right) ^4 } \left( { { \frac { { M_2 } } { { M_1 } } } } \right) { \left( { { \frac { { d_ { 12 } } } { 0.01 \ { \rm { AU } } } } } \right) ^ { - 3 } } \tag { 9 } \end{align*} \end{document}

where we have normalized d ₁₂ in terms of the characteristic distance of closest approach between the two neighboring planets of the TRAPPIST-1 system.

Since the tides caused by the Moon (on Earth) are about twice as large as those caused by the Sun, we are led to the following conclusion: the tidal forces exerted by a nearest neighbor pair of TRAPPIST-1 planets on each other are approximately equal to that exerted by the Moon on Earth. As the magnitudes of the tidal bulges are similar to those present on Earth, most of our preceding discussion concerning terrestrial oceanic tides and their biological consequences may also prove to be applicable here.

In addition, we note that the existence of mean-motion resonances (Luger et al., 2017) in the TRAPPIST-1 system could enhance tidal effects by causing the respective amplitudes to “add” up, or be subject to modulation. A somewhat analogous situation is also seen on Earth when the Moon and Sun are collinear with Earth, have zero declination, and at simultaneous perihelion (with respect to Earth)—this scenario results in maximum semidiurnal tides (Pugh, 1996). Recently, Balbus (2014) proposed that tidal modulation was responsible for the formation of a complex network of shallow pools on Earth, which led to the development of chiridian limbs in tetrapodomorphs (enabling efficient motor control) during the Devonian period (Daeschler et al., 2006).

As there will be six planets exerting tidal forces on the seventh, and given the existence of Laplace resonances, it seems reasonable to conclude that the tidal forces could be amplified (by a factor of a few) in certain instances. Generally speaking, we anticipate that the rich dynamical behavior of the TRAPPIST-1 system (Luger et al., 2017; Tamayo et al., 2017) will translate to equally diverse tidal modulations (with multiple periods) that may have interesting consequences for abiogenesis and the evolution of life on these planets in a manner similar to that of Earth.

5.2. Looking beyond the TRAPPIST-1 system

We now interpret the results from Sections 2 and 3 in a more general setting. We hold the mass, radius, orbital eccentricity, and effective temperature of the planet to be fixed (equaling that of Earth), since we are interested in determining how the properties of the host star influence the tidal forces; the planet can thus be interpreted as an Earth analogue, albeit in a superficial sense.

Along the lines of Lingam and Loeb (2018a), we choose L _★ ∝  \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$M_ \star ^3$$ \end{document} as an approximate mass-luminosity relationship. For fixed values of the planetary parameters, it is easy to show that d ∝ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$L_ \star ^{1 / 2}$$ \end{document} , thereby leading us to d ∝ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$M_ \star ^{3 / 2}$$ \end{document} . Thus, we are led to the relations: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \dot E \propto {n^5} \propto M_ \star ^{ - 35 / 4} \tag{10} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} a \propto { \frac { { M_ \star } } { { d^3 } } } \\ \propto M_ \star ^ { - 7 / 2 } \tag { 11 } \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} H \propto { \frac { { M_ \star } } { { d^3 } } } \propto M_ \star ^ { - 7 / 2 } \tag { 12 } \end{align*} \end{document}

Hence, it is clear that the tidal heating, force, and elevation experienced by the Earth-analogue display a strong dependence on the mass of the host star. For instance, if we choose a host star that is one-half the solar mass, it will result in tidal heating that is ∼400 times higher than Earth. Moreover, the tidal force (per unit mass) and bulge experienced by this Earth analogue will be an order of magnitude higher than the Earth-Sun system.

Thus, it is clear that most of our preceding discussion concerning the biological implications of tides is also applicable in general to planets in the HZ of M and K dwarfs. Even though the tidal forces are stronger on M dwarfs, it does not necessarily mean that such stars are more suited for life to originate and evolve; there are a host of other factors that must be taken into consideration, for example, atmospheric losses and ultraviolet radiation (Shields et al., 2016; Lingam and Loeb, 2017c, 2018b, 2018a), which can lower the prospects of life inhabiting M dwarf planetary systems.

Based on the above scalings, we argue that the role of tides is likely to be important when the primary object has a mass lower than the Sun provided that the eccentricity is not too low. Hence, our results are also applicable to planets around brown dwarfs and Mars/Earth-sized moons orbiting jovian planets. We observe that physical, but not biological, tidal effects in both these systems have been quite extensively investigated in recent times (Barnes and Heller, 2013; Heller and Barnes, 2013; Dobos and Turner, 2015; Dobos et al., 2017).