Prospects for Life on Temperate Planets around Brown Dwarfs

The misnomered "brown dwarfs" are substellar objects that straddle the line between hydrogen-burning stars and gas giant planets such as Jupiter. First predicted by Kumar (1962a, 1962b, 1963) and Hayashi & Nakano (1963), it would be more than three decades later before the first brown dwarf was confirmed (Rebolo et al. 1995). This brown dwarf, Teide 1, has a spectral classification of M8 (Rebolo 2014). Teide 1's designation is based upon the classification system devised by Kirkpatrick et al. (1991), which classifies M-dwarfs according to the strength of the TiO and VO bands. Thanks to the Two Micron All-Sky Survey (2MASS),³ the discovery of even cooler brown dwarfs led to the introduction of the "L" spectral class (Martin et al. 1997; Kirkpatrick et al. 1999). In this classification L-dwarf objects have fewer TiO and VO bands in their spectra, and more metallic hydrides (CrH, FeH) as well as neutral alkali metals. As surveys discovered more brown dwarfs, it became clear that objects such as Gliese 229B (Oppenheimer et al. 1995) did not belong to either the M or L class (Cushing 2014). These cooler objects show methane (CH₄) absorption in the near-infrared, and thus the "T" spectral class was introduced (Kirkpatrick et al. 1999; Burgasser et al. 2002; Geballe et al. 2002; Kirkpatrick 2005).

However, different classification schemes led to confusion within the burgeoning brown dwarf community until a unified near-infrared classification scheme for T-dwarfs was adopted (Burgasser et al. 2006), whereby the spectral sequence shows increasing H₂O and CH₄ absorption in later-type T-dwarfs (Lodders 2010). A few years later, the Wide-field Infrared Survey Explorer (WISE⁴ ) discovered seven "ultracool" brown dwarfs, which are believed to be distinct from T-dwarfs and show ammonia (NH₃) features in their spectra; thus the "Y" spectral class was created (Cushing et al. 2011; Kirkpatrick et al. 2012). Currently, the coldest known brown dwarfs have an effective temperature of ∼250 K, with one notable example being WISE J085510.83-071442.5 (Luhman 2014). However, their masses are typically ≲10 M_J, where M_J is the mass of Jupiter, and thus their classification is subject to some ambiguity (Caballero 2018).

Another way to delineate brown dwarfs is via their energy production mechanism. A main-sequence star in hydrostatic equilibrium will fuse hydrogen to helium. On the other hand, a brown dwarf will be below the threshold necessary for core hydrogen burning, yet massive enough to ignite deuterium burning (e.g., Burrows & Liebert 1993; Burrows et al. 2001; Spiegel et al. 2011; Luhman 2012; Auddy et al. 2016). This places the mass of a brown dwarf (M_BD) in the range 13 M_J ≲ M_BD ≲ 90 M_J.⁵ However, Forbes & Loeb (2019) demonstrated that it may be possible, in principle, to have brown dwarfs as massive as 0.12 M_⊙ and yet not reach core hydrogen burning. Clearly, our picture of brown dwarfs is incomplete and will doubtless evolve as we learn more. In this paper, we follow the conventional definition of a brown dwarf as an object that does not reach hydrogen burning but is massive enough for deuterium fusion.

Recent surveys suggest that there may be as many as ∼0.2–0.5 brown dwarfs per star within the Milky Way galaxy (Scholz et al. 2013; Mužić et al. 2017, 2019; Suárez et al. 2019), and this ratio might be even higher if the population of cooler Y dwarfs has been insufficiently sampled (see Kirkpatrick et al. 2019). Furthermore, the majority of brown dwarfs likely have protoplanetary disks, much the same as Sun-like stars, which can result in the formation of Earth-sized or smaller planets (Apai et al. 2005; Payne & Lodato 2007; Apai 2013; Daemgen et al. 2016). Chauvin et al. (2004) were the first to report a planetary candidate ($\sim 4{M}_{J}$) around a brown dwarf. In the ensuing years, other brown dwarfs with Jupiter-mass planets have been detected (e.g., Todorov et al. 2010; Han et al. 2013; Jung et al. 2018). Via microlensing, Udalski et al. (2015) seemingly discovered a Venus-mass planet orbiting a brown dwarf, although the data remain open to alternative interpretations that are compatible with its non-existence (Han et al. 2016).

This naturally raises the question: what are the prospects for habitable planets around brown dwarfs? Despite the importance of this question, comparatively few studies have addressed it. Before proceeding further, it is worth noting that a couple of studies have explored the prospects for life within the atmospheres of brown dwarfs, but this topic shall not be considered here (Shapley 1967; Yates et al. 2017; Lingam & Loeb 2019a). Many important aspects of planetary habitability are determined by the properties of the host brown dwarf. A classic example concerns the inner and outer limits of the habitable zone, i.e., the region where the planet can theoretically sustain liquid water on its surface (Dole 1964; Kasting et al. 1993; Kopparapu et al. 2013; Ramirez 2018). While some of the earlier models of the habitable zones around brown dwarfs did not take tidal and geological effects into consideration (Desidera 1999; Andreeshchev & Scalo 2004), this limitation was addressed by subsequent studies (Bolmont et al. 2011; Barnes & Heller 2013; Bolmont 2018).

The second topic of importance is photosynthesis because it constitutes the primary source of biomass on Earth, and its emergence facilitated the transformation of Earth's geological, chemical, and biological landscapes (Knoll 2015). The only study that briefly addressed the prospects for photosynthesis on brown dwarfs was by Raven & Donnelly (2013), but the temporal evolution of brown dwarfs was not fully accounted for. Lastly, there is emerging (albeit tentative and disputed) evidence that the origin of life may have necessitated access to sufficient fluxes of UV-C radiation (Sutherland 2017; Lingam & Loeb 2019b). In this scenario, the fluxes incident on temperate planets around brown dwarfs would depend on the properties of the latter. While this issue has been investigated for planets around main-sequence stars (Guo et al. 2010; Rimmer et al. 2018), no equivalent studies have been conducted for brown dwarfs.

Thus, in this paper we examine all of these three topics—the habitable zone, photosynthesis, and UV-mediated prebiotic chemistry. The outline of the paper is as follows. We explore some properties of the habitable zone of brown dwarfs in Section 2 and describe some of the strengths and limitations of our model. In Section 3, we explore the constraints on "Earth-like" planets around brown dwarfs to sustain oxygenic photosynthesis. We follow this up in Section 4 with a study of the equivalent constraints on UV radiation to facilitate abiogenesis on these worlds. Finally, we discuss some of the potential biosignatures and their detectability along with a summary of our findings in Section 5.

The processes underlying the cooling of brown dwarfs are complex, especially during the early stages of their evolution (Burrows et al. 2001). For the purposes of our analysis, we shall employ the formulae presented in Burrows & Liebert (1993). The effective temperature (T_BD) of the brown dwarf is directly taken from Equation (2.58) of Burrows & Liebert (1993) and has the form

$$\begin{eqnarray}\begin{array}{rcl}{T}_{\mathrm{BD}} & \approx & 59\,{\rm{K}}{\left(\displaystyle \frac{{t}_{\mathrm{BD}}}{1\mathrm{Gyr}}\right)}^{-0.324}{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{0.827}\\ & & \times \,{\left(\displaystyle \frac{{\kappa }_{R}}{0.01{\mathrm{cm}}^{2}{{\rm{g}}}^{-1}}\right)}^{0.088},\end{array}\end{eqnarray} \tag{ 1 }$$

where t_BD and M_BD are the age and mass of the brown dwarf, respectively, while κ_R denotes the Rosseland mean opacity of the brown dwarf near its photosphere; recall that M_J is the mass of Jupiter. As the dependence of T_BD on κ_R is weak, we shall neglect the last term on the right of the above equation without much loss of generality. Another useful expression in our subsequent analysis is Equation (2.37) of Burrows & Liebert (1993) for the radius (R_BD) of the brown dwarf:

$$\begin{eqnarray}&&{R}_{\mathrm{BD}}\approx 35.5{R}_{\oplus }{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{-1/3}.\end{eqnarray} \tag{ 2 }$$

In order to assess the length of time that an Earth-like planet spends in the habitable zone of a brown dwarf (denoted by t_HZ), we have to take into account the cooling time and mass of the brown dwarf as well as the planet's orbital radius, a. Although we will treat a as being constant over time, it may increase by a factor of ≲2 due to outward migration driven by tidal evolution effects (Bolmont et al. 2011). We note that t_HZ has been investigated by several authors (Desidera 1999; Andreeshchev & Scalo 2004; Bolmont et al. 2011; Barnes & Heller 2013). While our model does not incorporate tidal effects, it has the advantage of being physically transparent and analytically tractable.

We shall restrict ourselves to systems that satisfy t_HZ > 10 Myr. We impose this lower bound for three reasons. First and foremost, we do so because the cooling ansatz used for brown dwarfs in (1) is not applicable at timescales ≲10 Myr (Burrows et al. 2001).⁶ Second, a timescale of ∼1–10 Myr is generally regarded as being necessary for planet formation around brown dwarfs (Bolmont et al. 2011; Apai 2013). Lastly, from an evolutionary perspective, a timescale of ∼10 Myr is smaller by ∼2 orders of magnitude than the interval required for many of the major evolutionary developments (i.e., critical steps) in Earth's history (Carter 2008; Knoll 2015; Lingam & Loeb 2019c), with the caveat that the pace of evolution on other worlds could be substantially faster or slower.

In addition, there is a crucial constraint on a that must be taken into account. At the very minimum, a must not be within the Roche limit, otherwise the planet would be subject to tidal disruption. If the secondary object is fluid-like, the Roche limit (d_RL) for the brown dwarf–planet system is given by (Murray & Dermott 1999)

$$\begin{eqnarray}&&{d}_{\mathrm{RL}}\approx 2.46{R}_{\mathrm{BD}}{\left(\displaystyle \frac{{\rho }_{\mathrm{BD}}}{{\rho }_{\mathrm{planet}}}\right)}^{1/3},\end{eqnarray} \tag{ 3 }$$

where ρ_BD and ρ_planet are the densities of the brown dwarf and the planet, respectively. After further simplification using Equation (2.38) of Burrows & Liebert (1993) for ρ_BD along with the adoption of a mean planetary density approximately equal to the Earth's density of ρ_⊕ ≈ 5.5 g cm⁻³, we obtain

$$\begin{eqnarray}&&{d}_{{\rm{RL}}}\approx 1.3\times {10}^{-3}\,{\rm{au}}\times {\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{1/3}.\end{eqnarray} \tag{ 4 }$$

Alternatively, we can reformulate (3) to arrive at

$$\begin{eqnarray}&&\displaystyle \frac{{d}_{\mathrm{RL}}}{{R}_{\mathrm{BD}}}\approx 0.86{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{2/3},\end{eqnarray} \tag{ 5 }$$

from which it is apparent that the tidal limit is very close to the surface of the brown dwarf. It should therefore be recognized that d_RL is merely a lower limit on the orbital radius. At small values of a, the insolation received can exceed the threshold associated with the inner edge of the habitable zone, as discussed later. Second, at sufficiently close-in distances, the effects of tidal heating become important and may lead to the planet entering a runaway greenhouse state. We do not explicitly tackle this factor in our calculations because the degree of heating depends on a number of parameters such as the eccentricity, inclination, and rheology of the planet, as well as the mass and composition of the brown dwarf (Barnes & Heller 2013; Bolmont 2018).

The effective temperature of the planet (T_P) can be readily estimated by using

$$\begin{eqnarray}&&{T}_{P}={T}_{\mathrm{BD}}\sqrt{\displaystyle \frac{{R}_{\mathrm{BD}}}{2a}}{\left(1-{A}_{P}\right)}^{1/4},\end{eqnarray} \tag{ 6 }$$

where A_P is the Bond albedo of the planet. Unless the planet has an albedo very close to unity, the last term on the right will only affect our results by a factor of ≲2. Hence, we shall set A_P ≈ 0.3 to maintain consistency with the Earth. In actuality, the albedo will depend on a number of factors such as the atmospheric and surface composition of the planet as well as the spectral type of the brown dwarf (or star). In order to determine the length of time that the planet can remain in the habitable zone, it is necessary to choose appropriate upper (T_max) and lower (T_min) bounds on T_P. We will select T_max = 270 K and T_min = 175 K in accordance with Kaltenegger & Sasselov (2011).⁷ We solve for the times at which these temperatures are obtained and take their difference to obtain t_HZ. After simplification, we end up with

$$\begin{eqnarray}&&{t}_{{\rm{HZ}}}\approx 3\times {10}^{-7}\,{\rm{Gyr}}\times {\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{2.037}{\left(\displaystyle \frac{a}{1{\rm{au}}}\right)}^{-1.543}.\end{eqnarray} \tag{ 7 }$$

Upon inverting this equation and solving for the values of a compatible with a given t_HZ, we find

$$\begin{eqnarray}&&a\approx 5.9\times {10}^{-5}\,{\rm{au}}\times {\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{1.32}{\left(\displaystyle \frac{{t}_{{\rm{HZ}}}}{1{\rm{Gyr}}}\right)}^{-0.648}.\end{eqnarray} \tag{ 8 }$$

We have plotted the compatible orbital radii for a given t_HZ in Figure 1. The regions inside the curves and above the associated red lines (Roche limits) yield the compatible values of a. First, we observe that t_HZ increases as a is lowered and vice versa. Thus, the maximum lifetime occurs when the planet is situated close to its Roche limit. Second, we see that t_HZ increases with the mass of the brown dwarf; this is along expected lines because more massive brown dwarfs have higher luminosities. These results are, for the most part, in agreement with prior analyses of this topic (Andreeshchev & Scalo 2004; Bolmont et al. 2011; Barnes & Heller 2013). For example, we find that the maximum value of t_HZ for a 70 M_J brown dwarf is ∼6 Gyr, whereas Andreeshchev & Scalo (2004) obtained 4–10 Gyr. Similarly, Bolmont et al. (2011) found that brown dwarfs with masses >50 M_J could have maximum habitable zone lifetimes of 1–10 Gyr, which happens to be consistent with our findings.

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By combining (4) and (7), as well as inspecting Figure 1, another interesting result is obtained. For ${t}_{\mathrm{HZ}}\gt 10\,\,\mathrm{Gyr}$ to be valid at the Roche limit, we would require M_BD ≳ 100 M_J (equivalent to ≳0.1 M_⊙). This limit is higher than the conventional upper bound of ∼90 M_J for brown dwarfs (Zhang et al. 2017), although it has recently been demonstrated that brown dwarfs with masses up to ∼0.12 M_⊙ are theoretically feasible (Forbes & Loeb 2019). Hence, our analysis suggests that brown dwarfs are less likely to host long-lived habitable zones than M-dwarfs because planets can remain in the habitable zones of late-type M-dwarfs for ≳100 Gyr (Rushby et al. 2013). Thus, in principle, it would appear as though planets around brown dwarfs do not constitute targets as promising as M-dwarf exoplanets. This expectation should, however, be balanced by the fact that planets around M-dwarfs might be rendered inhospitable to life via intense stellar winds, space weather events, and flares (Lingam & Loeb 2019b).

As noted earlier, most major evolutionary breakthroughs on Earth required ≳1 Gyr after its formation (Smith & Szathmary 1995; Dawkins & Wong 2016; Knoll & Nowak 2017). In habitability studies, it is generally advantageous to retain habitable conditions over timescales of gigayears. Hence, by setting t_HZ ∼ 1 Gyr, we can investigate what range of orbital radii allow for this possibility as a function of M_BD. The results are presented in Figure 2. The parameter space of interest is situated above the red curve and below the black curve. When the brown dwarf has a mass smaller than ∼20 M_J, we find that it cannot remain in the habitable zone over an interval of ∼1 Gyr. Hence, it is unlikely that such low-mass brown dwarfs host planets that remain habitable over geologically significant timescales.

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As a brown dwarf cools over time, it will emit radiation at longer wavelengths. Hence, the flux of photons received at shorter wavelengths drops dramatically (due to the exponential cutoff). Thus, the length of time for which an Earth-like planet receives sufficient photon flux for photosynthesis is constrained by this cooling. We will work out the salient details herein.

In our subsequent analysis, we shall adopt the conservative choice of oxygenic photosynthesis that uses two coupled photosystems and operates at wavelengths of ${\lambda }_{\min }=400\,\mathrm{nm}$ and λ_max = 750 nm. While longer wavelengths are feasible in principle (Wolstencroft & Raven 2002; Kiang et al. 2007a; Lingam & Loeb 2019a), no concrete empirical evidence is available thus far to substantiate this hypothesis. At wavelengths ≲400 nm, it is likely that these photosystems would be subject to damage by UV radiation (Cockell & Airo 2002). We will also adopt an "Earth-like" atmosphere that permits the majority of photosynthetically active radiation (PAR) to reach the surface, i.e., the corresponding optical depth is smaller than unity.

With these simplifications, the PAR flux incident on the planet (Φ_PAR) is given by

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{PAR}}\approx \displaystyle \frac{{\dot{N}}_{\mathrm{BD}}}{4\pi {a}^{2}}.\end{eqnarray} \tag{ 9 }$$

Here, ${\dot{N}}_{\mathrm{BD}}$ is the photon flux emitted by the brown dwarf, which is defined as

$$\begin{eqnarray}&&{\dot{N}}_{\star }=4\pi {R}_{\mathrm{BD}}^{2}{\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}\displaystyle \frac{2c}{{\lambda }^{4}}{\left[\exp \left(\displaystyle \frac{{hc}}{\lambda {k}_{B}{T}_{\mathrm{BD}}}\right)-1\right]}^{-1}\,d\lambda ,\end{eqnarray} \tag{ 10 }$$

for a blackbody spectrum.⁸ In this equation, note that R_BD and T_BD are given by (2) and (1), respectively. Thus, we shall substitute (1), (2), and (10) into (9). After simplifying the resultant expression, we find that Φ_PAR is expressible as

$$\begin{eqnarray}\begin{array}{c}\begin{array}{rcl}{{\rm{\Phi }}}_{{\rm{PAR}}} & \approx & 9.5\times {10}^{13}\,{{\rm{m}}}^{-2}\,{{\rm{s}}}^{-1}\times {\left(\displaystyle \frac{a}{1{\rm{au}}}\right)}^{-2}\\ & & \times \,{\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{1.814}{\left(\displaystyle \frac{{t}_{{\rm{BD}}}}{1{\rm{Gyr}}}\right)}^{-0.972}{ \mathcal F }\left({t}_{{\rm{BD}}},{M}_{{\rm{BD}}}\right),\end{array}\end{array}\end{eqnarray} \tag{ 11 }$$

where the function ${ \mathcal F }\left({t}_{\mathrm{BD}},{M}_{\mathrm{BD}}\right)$ is defined to be

$$\begin{eqnarray}&&{ \mathcal F }\left({t}_{\mathrm{BD}},{M}_{\mathrm{BD}}\right)\approx {\int }_{{Y}_{1}}^{{Y}_{2}}\displaystyle \frac{y{{\prime} }^{2}\,{dy}^{\prime} }{\exp \left(y^{\prime} \right)-1},\end{eqnarray} \tag{ 12 }$$

and the two limits of integration (Y₁ and Y₂) depend on t_BD and M_BD as described below:

$$\begin{eqnarray}\begin{array}{rcl}{Y}_{1} & \approx & 610.3{\left(\displaystyle \frac{{t}_{\mathrm{BD}}}{1\mathrm{Gyr}}\right)}^{0.324}{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{-0.827},\\ {Y}_{2} & \approx & 325.5{\left(\displaystyle \frac{{t}_{\mathrm{BD}}}{1\mathrm{Gyr}}\right)}^{0.324}{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{-0.827}.\end{array}\end{eqnarray} \tag{ 13 }$$

A theoretical analysis by Raven et al. (2000) (see also Wolstencroft & Raven 2002) concluded that the minimum PAR flux necessary for photosynthesis based on biophysical constraints is Φ_c ≈ 1.2 × 10¹⁶ m⁻² s⁻¹. Thus, as the brown dwarf cools, the flux received by the planet will decline until it finally drops below Φ_c after a certain duration; here, we implicitly assume that the PAR flux immediately after planet formation is greater than Φ_c. If the interval over which Φ_PAR > Φ_c holds true is taken to be the "photosynthesis-zone lifetime" (t_PZ), we can derive a relationship between this quantity, M_BD, and a by setting Φ_PAR = Φ_c. Thus, by using (11) in conjunction with these data, we arrive at

$$\begin{eqnarray}&&a=0.09\,{\rm{au}}\times \sqrt{{ \mathcal F }({t}_{{\rm{PZ}}},{M}_{{\rm{BD}}})}{\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{0.907}{\left(\displaystyle \frac{{t}_{{\rm{PZ}}}}{1{\rm{Gyr}}}\right)}^{-0.486}.\end{eqnarray} \tag{ 14 }$$

Thus, for given values of a and M_BD, we can solve for the corresponding t_PZ. Alternatively, by choosing a range of values for t_PZ and M_BD, we can investigate what choices of a are compatible with these values. We will pursue the latter approach, whereby the permitted orbital radii (a) are estimated for different choices of t_PZ and M_BD.

We restrict ourselves to those brown dwarf–planet systems wherein the length of time that the planet spends in the photosynthetic "zone" is >10 Myr for the same reasons outlined when tackling t_HZ in Section 2. We also impose the additional constraint that a must be larger than the Roche limit to avoid tidal disruption, as explained in Section 2. We have plotted the compatible orbital radii as a function of t_PZ for different choices of the brown dwarf mass in Figure 3. All values of the orbital radii lying inside the curves and upwards of the red lines (Roche limits) are permitted for a given choice of t_PZ.

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There are some general conclusions that can be drawn from Figure 3. First, as a is decreased, we find that t_PZ increases. This is along expected lines because the planet will receive higher photon fluxes for a longer period of time. Second, for a fixed a, we see that t_PZ falls off rapidly with M_BD. This is also consistent with intuition because smaller brown dwarfs possess a lower luminosity and will therefore emit sufficient PAR for a shorter duration. Lastly, we note that planets around a 10 M_J brown dwarf can never reside within the photosynthesis zone for ≳1 Gyr for reasons elucidated below.

If we set t_PZ ∼ 1 Gyr (see Section 2), we can study what ranges of a and M_BD enable this criterion to be satisfied. The result is plotted in Figure 4. The region below the black curve but above the red curve corresponds to the parameter space that permits the photosynthesis lifetime to satisfy t_PZ ≳ 1 Gyr. One of the most striking results we find is that brown dwarfs with M_BD < 30 M_J do not fulfill the requisite criterion. Hence, it is unlikely that planets around these brown dwarfs are capable of sustaining photosynthetic biospheres over timescales of gigayears.

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Before moving ahead, there are some important caveats that need to be reiterated. First, even in the context of oxygenic photosynthesis, it is theoretically feasible to extend the upper wavelength of ∼750 nm to the near- and mid-infrared by coupling together a number of photosystems in series. This would presumably lower the quantum yield and may cause (or require) a proliferation of side reactions, but such coupled multiphoton schemes are feasible (Wolstencroft & Raven 2002). It was conjectured by Kiang et al. (2007b) that the absorbance peak of photopigments might be manifested at the peak incident photon flux. The latter, in turn, depends on both the spectral properties of the brown dwarf (or star) and the atmospheric composition of the planet. As planets can vary widely in composition, it is instructive to focus on the former, specifically the peak of the brown dwarf's photon flux density. By modeling this quantity as a blackbody, we find that the peak wavelength (λ_peak) is given by

$$\begin{eqnarray}&&{\lambda }_{{\rm{peak}}}\approx 62.3\,\mu {\rm{m}}\times {\left(\displaystyle \frac{{t}_{{\rm{BD}}}}{1{\rm{Gyr}}}\right)}^{0.324}{\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{-0.827}.\end{eqnarray} \tag{ 15 }$$

In the case of the Sun, we find that λ_peak ≈ 635 nm, whereas the absorbance peak of the chlorophylls in photosystems I and II is ∼680–700 nm (Kiang et al. 2007b). It is thus evident that this simple ansatz might enable us to roughly gauge where the peak absorbance of photopigments could occur, and the approximate wavelength at which the spectral edge of photosynthetic organisms is manifested. In Figure 5, we have plotted λ_peak as a function of the brown dwarf's age for different masses. We observe that the peak shifts toward longer wavelengths for older and/or low-mass brown dwarfs. In most cases, we find that λ_peak has a range of ∼1–10 μm, thus implying that the spectral edge may shift to near- and mid-infrared wavelengths over time.

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If we move beyond oxygenic photosynthesis, there are hypothesized alternatives such as "hydrogenic" photosynthesis that might function at wavelengths as long as ∼1.5 μm (Bains et al. 2014). And last, but not least, even if photoautotrophs cannot survive, a diverse range of chemotrophs could exist on these planets. There are, in fact, a number of evolutionary features shared by chemoautotrophs and photoautotrophs, which has motivated several papers to discuss the possibility that the latter evolved from the former in appropriate geological environments (Martin et al. 2017; Onstott et al. 2019; see also Lingam & Loeb 2019e). On Earth, chemotrophs are predicted to make up ∼10% of the total biomass (Bar-On et al. 2018). Hence, it is therefore possible that planets around brown dwarfs might host thriving microbial biospheres even in the absence of sufficient PAR for photosynthesis.

The concepts of the habitable zone and photosynthesis are fairly well understood—although some unknowns do exist—and are often regarded as potentially generic features in the search for extraterrestrial life. In contrast, the origin of life remains an arguably bigger mystery, and a number of competing hypotheses exist based on geochemical, physiological, and genomic considerations, to name a few (Luisi 2016; Smith & Morowitz 2016; Walker 2017). In this part of the paper we shall focus on a particular proposal, with the express understanding that a number of other origin-of-life scenarios exist. In fact, as per recent models, even the possibility of some planets being seeded with life via galactic-scale panspermia ought not to be dismissed outright (Lingam 2016; Lingam & Loeb 2018a; Ginsburg et al. 2018).

The proposal that we deal with is sometimes referred to as "cyanosulfidic metabolism" due to its reliance on hydrogen cyanide as a core feedstock molecule for synthesizing the precursors of major biomolecular building blocks such as lipids and amino acids (Patel et al. 2015; Sutherland 2016, 2017). These pathways have been the subject of numerous sophisticated laboratory experiments and require UV radiation in the range 200 nm < λ < 280 nm. In order for the prebiotic reactions driven by UV photochemistry to function effectively, they must be more dominant than other "dark" reactions that unfold in the absence of UV radiation. In turn, this necessitates a minimum flux of UV photons in this range, whose value is 5.44 × 10¹⁶ photons m⁻² s⁻¹ (Rimmer et al. 2018; see also Lingam et al. 2019).

With this new critical flux, it is fairly straightforward to analyze the brown dwarf–planet system along the lines of Section 3. By doing so, we can determine the relationship between a, M_BD, and the length of time in the "abiogenesis zone" (t_AZ); the latter quantifies the time during which the planet receives enough photons to permit the synthesis of biomolecular building blocks (and thence biopolymers) via UV-mediated reactions. As the steps are quite similar, we provide the final expression for the compatible values of a. The analog of (14) is therefore given by

$$\begin{eqnarray}&&a=0.04\,{\rm{au}}\times \sqrt{{ \mathcal G }({t}_{{\rm{AZ}}},{M}_{{\rm{BD}}})}{\left(\displaystyle \frac{{M}_{{\rm{BD}}}}{{M}_{J}}\right)}^{0.907}{\left(\displaystyle \frac{{t}_{{\rm{AZ}}}}{1{\rm{Gyr}}}\right)}^{-0.486},\end{eqnarray} \tag{ 16 }$$

where ${ \mathcal G }({t}_{\mathrm{AZ}},{M}_{\mathrm{BD}})$ is defined as

$$\begin{eqnarray}&&{ \mathcal G }\left({t}_{\mathrm{AZ}},{M}_{\mathrm{BD}}\right)\approx {\int }_{{Z}_{1}}^{{Z}_{2}}\displaystyle \frac{z{{\prime} }^{2}\,{dz}^{\prime} }{\exp \left(z^{\prime} \right)-1},\end{eqnarray} \tag{ 17 }$$

where the upper and lower limits of integration are

$$\begin{eqnarray}\begin{array}{rcl}{Z}_{1} & \approx & 1220.5{\left(\displaystyle \frac{{t}_{\mathrm{AZ}}}{1\mathrm{Gyr}}\right)}^{0.324}{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{-0.827},\\ {Z}_{2} & \approx & 871.8{\left(\displaystyle \frac{{t}_{\mathrm{AZ}}}{1\mathrm{Gyr}}\right)}^{0.324}{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{-0.827}.\end{array}\end{eqnarray} \tag{ 18 }$$

In deriving these relations, we have implicitly assumed that the young planet in question is optically thin to UV radiation within the specified range; at the minimum, this requires the planet to resemble Hadean–Archean Earth in not having a sizable ozone layer.

From this equation, we can determine the values of a compatible with a given t_AZ. We also impose the dual constraints of t_AZ > 10 Myr and a > d_RL (where d_RL is the Roche limit) for reasons explicated previously. The final result is depicted in Figure 6. Note that we have plotted the curve for a 20 M_J brown dwarf instead of its 10 M_J counterpart because the latter does not fulfill the above two inequalities. From the plot, we see that t_HZ is longer when the orbital radius is smaller and when the brown dwarf mass is higher, both of which are consistent with expectations. For all brown dwarfs within the mass range considered in the paper, we discover that the two conditions t_AZ > 1 Gyr and a > d_RL are not simultaneously realizable.

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We do not have a precise estimate for the time taken for life to originate on Earth. There is also the added complication that the abiogenesis timescale is not necessarily the same on other worlds (Spiegel & Turner 2012). For the sake of further quantitative analysis, we will suppose that the transition from pre-life to life on other worlds occurs on a timescale comparable to that required on Earth. While the earliest definitive evidence for life on Earth dates from ∼3.7 Ga, a combination of genomic and fossil analyses as well as theoretical arguments suggest that the timescale for life's emergence on Earth ranged between ${ \mathcal O }\left({10}^{7}\right)$ and ${ \mathcal O }\left({10}^{8}\right)$ yr at the most (Lazcano & Miller 1994; Dodd et al. 2017; Betts et al. 2018).

Thus, by erring on the side of caution, we shall specify t_AZ ∼ 100 Myr. By substituting this number into (16), we can determine what values of a are compatible with this timescale as a function of M_BD. In Figure 7, the zone of interest is depicted and it lies amid the black and red curves. By inspecting the plot, we find that the two curves intersect at ∼40 M_J. Hence, as per our analysis, it is relatively unlikely for planets around brown dwarfs with masses <40 M_J to support UV-mediated prebiotic reactions over a significant timespan (≳100 Myr).

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At this stage, it is worth reiterating that a dearth of UV radiation ought not be regarded as a death knell insofar as abiogenesis is concerned. As noted earlier, there are numerous hypotheses for the origin of life, of which one of the most well known posits that life originated at alkaline hydrothermal vents on the seafloor (Baross & Hoffman 1985; Martin et al. 2008; Sojo et al. 2016). Clearly, in this scenario, the access to substantial fluxes of UV photons is unlikely to be a limiting factor. On account of this reason, we recommend that the results herein should be viewed with due caution.

It is unknown exactly how many brown dwarfs reside within the Milky Way. However, recent surveys indicate that the corresponding number is potentially comparable to the number of stars (Mužić et al. 2019). Thus, in the most optimal circumstances, brown dwarfs might sustain as much life (on terrestrial planets) as stars.

To this end, we have studied how the habitability of Earth-like planets is affected by the brown dwarfs they orbit. We focused our attention on three different concepts of central importance in astrobiology: the habitable zone, photosynthesis, and prebiotic chemistry leading to abiogenesis. To keep our analysis as conservative as possible, we restricted our attention to biochemical pathways and mechanisms found on Earth and to planets where the habitability intervals associated with each of these processes are comparable to those present on Earth. We took a number of parameters, such as the planet's orbital radius and the brown dwarf's mass and age, into account to develop the appropriate models.

Our basic conclusion is that planets around brown dwarfs with masses smaller than ∼20 M_J, ∼30 M_J, and ∼40 M_J have a low likelihood of sustaining long-term temperate climates (i.e., remaining in the habitable zone), photosynthesis, and UV-mediated abiogenesis, respectively. Even when these limits are exceeded, the prospects for long-term habitability are determined by the orbital radius at which the planet is situated. Planets that are too far out (≳0.1 au) are not guaranteed to receive sufficient fluxes of electromagnetic radiation in the appropriate range, whereas overly close-in planets (≲10⁻³ au) are susceptible to tidal heating, desiccation, and tidal disruption. Another crucial point that emerged from our analysis is that brown dwarfs have temporally limited habitable zones (≲10 Gyr) with respect to M-dwarfs; all other factors held equal, one would therefore not expect brown dwarfs to host habitable planets when their ages exceed ∼10 Gyr.⁹

Recent statistical studies indicate that the number of brown dwarfs with M_BD > 30 M_J is potentially as high as ∼10¹¹ because the ratio of main-sequence stars to brown dwarfs is apparently ∼2–5 (Scholz et al. 2013; Mužić et al. 2017, 2019; Suárez et al. 2019); note that the number of stars in the Milky Way is ≳10¹¹. However, it is not possible to estimate the number of Earth-sized planets in the habitable zones of brown dwarfs (η_⊕) at this stage due to the paucity of available statistics; in fact, even for stars, the uncertainty in the range of values for η_⊕ approaches an order of magnitude (Kaltenegger 2017). However, in the event that η_⊕ for brown dwarfs is comparable to that for stars, we see that the number of potentially habitable planets around brown dwarfs in the Milky Way might be similar to the number of such planets orbiting main-sequence stars.

This raises the question of what types of biosignatures can be produced. To answer this question, recall that oxygenic photosynthesis may be feasible over timescales of gigayears provided that M_BD > 30 M_J. Thus, planets around these brown dwarfs might evolve oxygenic photosynthesis. The real issue, however, is that the net primary productivity on these worlds will be photon-limited in addition to other constraints imposed by access to nutrients and water.¹⁰ Drawing an analogy with M-dwarf exoplanets (Lehmer et al. 2018; Lingam & Loeb 2019d), it is possible that planets around brown dwarfs could likewise possess anoxic atmospheres (with negligible ozone layers) despite the presence of biospheres, and could thereby give rise to "false negatives" during searches for biological O₂ and O₃.

Oxygenic photosynthesis not only gives rise to O₂ but also to the "vegetation red edge" at ∼0.7 μm (Seager et al. 2005), which may be discernible in principle by means of photometric observations provided that a sufficient fraction of the surface is covered by vegetation. On the other hand, if photosynthesis in the infrared is feasible, it is theoretically conceivable that the peak absorbance of photopigments might evolve over time in accordance with (15). Thus, once a brown dwarf's mass and age are known, we can use (15) to determine the approximate wavelength at which the spectral edge might exist. There are a number of other atmospheric and surface biosignatures arising from autotrophs and heterotrophs; a comprehensive review of this subject can be found in Schwieterman et al. (2018).

The next question that arises has to do with the relative ease of detecting biosignatures. We will draw upon the scaling relations presented in Fujii et al. (2018) for our purpose. For starters, we note that the transit depth and transit probability for Earth-like planets around brown dwarfs are of the order of 1%, both of which are higher than (or similar to) the estimates for planets around main-sequence stars. If we opt to carry out transmission spectroscopy for an Earth-analog using the James Webb Space Telescope (JWST),¹¹ the resultant signal-to-noise ratio (S/N), after invoking Fujii et al. (2018), is expressible as

$$\begin{eqnarray}\begin{array}{rcl}{\rm{S}}/{\rm{N}} & \sim & 3{\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{1/3}{\left(\displaystyle \frac{d}{10\mathrm{pc}}\right)}^{-1}{\left(\displaystyle \frac{{\rm{\Delta }}t}{30\mathrm{hr}}\right)}^{1/2}\\ & & \times \,{\left(\displaystyle \frac{\dot{n}\left(\lambda ;{T}_{\mathrm{BD}}\right)}{\dot{n}(3\mu {\rm{m}};2500{\rm{K}})}\right)}^{1/2},\end{array}\end{eqnarray} \tag{ 19 }$$

where Δt is the integration time, d is the distance to the brown dwarf from Earth, and $\dot{n}\left(\lambda ;{T}_{\mathrm{BD}}\right)$ is the photon flux density for a blackbody at temperature T_BD and measured at wavelength λ; it equals the integrand present in (10). If we desire an S/N of ∼5, we can invert the above equation to solve for Δt as a function of the brown dwarf's age and mass. The resultant integration time is plotted in Figure 8. By inspecting this figure, we see that an integration time of ${ \mathcal O }(10)$ hr is achievable only for comparatively young (∼0.1–1 Gyr) and massive (M_BD ≳ 40 M_J) brown dwarfs.

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Alternatively, one can analyze the thermal emission of the planet by computing the spectra of the system during secondary eclipses and taking the difference. For this procedure, the S/N for an Earth-analog using the parameters of the JWST is (Fujii et al. 2018)

$$\begin{eqnarray}\begin{array}{rcl}{\rm{S}}/{\rm{N}} & \sim & 0.5\zeta {\left(\displaystyle \frac{{M}_{\mathrm{BD}}}{{M}_{J}}\right)}^{1/3}{\left(\displaystyle \frac{d}{10\mathrm{pc}}\right)}^{-1}{\left(\displaystyle \frac{{\rm{\Delta }}t}{30\mathrm{hr}}\right)}^{1/2}\\ & & \times \,{\left(\displaystyle \frac{\dot{n}\left(\lambda ;{T}_{\mathrm{BD}}\right)}{\dot{n}(10\mu {\rm{m}};2500{\rm{K}})}\right)}^{-1/2},\end{array}\end{eqnarray} \tag{ 20 }$$

where ζ represents the normalized depth of the spectral features generated by putative biosignatures. Note that the photon flux density of the brown dwarf is raised to a negative power, implying that older (and therefore cooler) and smaller brown dwarfs ought to be favored by this method. This intuition is borne out by Figure 9, from which we find that thermal emission spectroscopy yields an integration time of ${ \mathcal O }(10)$ hr for low-mass (M_BD ∼ 10 M_J) brown dwarfs that have ages of ≳1 Gyr.

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Lastly, when it comes to direct imaging via scattered light, it is feasible to achieve contrast ratios of the order of ∼10⁻⁶ for Earth-analogs because the contrast between the planet and the substellar object in the visible and near-infrared (${ \mathcal C }$) is expressible as

$$\begin{eqnarray}&&{ \mathcal C }\sim {10}^{-10}{\left(\displaystyle \frac{a}{1\mathrm{au}}\right)}^{-2}.\end{eqnarray} \tag{ 21 }$$

The primary obstacle, however, is that the small orbital radius of the planet, which increases the contrast as seen above, also leads to an angular separation between the planet and star that is lower than the inner working angle of current coronagraphs and starshades as well as charge injection devices (Batcheldor et al. 2016).

Finally, we wish to highlight some other crucial issues that merit further study. First, it is necessary to determine the typical composition of Earth-sized planets around brown dwarfs. There is tentative evidence suggesting that these planets might be water-poor and carbon-rich (Pascucci et al. 2013); if correct, the former factor is detrimental to habitability insofar as life-as-we-know-it is concerned. Observations also indicate that the abundance of certain feedstock molecules—such as HCN, whose importance was described in Section 4—could be much lower in protoplanetary disks around brown dwarfs (Pascucci et al. 2009). If prebiotic chemistry is dependent on the exogenous delivery of these compounds, it is plausible that exoplanets orbiting brown dwarfs would be hampered in this regard.

Second, a sizable fraction of brown dwarfs are binaries, either in conjunction with other brown dwarfs or with stellar companions (see Reggiani et al. 2016; Fontanive et al. 2018 and references therein). Although planets around binaries appear to possess some intrinsic advantages (Shevchenko 2017), they are also potentially susceptible to other issues such as formation of terrestrial planets, orbital destabilization over geological timescales, and rapid (∼10³ yr) fluctuations in climate (Cuntz 2014; Jaime et al. 2014; Forgan 2016; Pilat-Lohinger et al. 2019); however, some of the issues alleged to suppress the habitability of certain circumbinary exoplanets may be overstated (Popp & Eggl 2017). Third, accurate dynamical treatments are necessary to determine whether lithopanspermia in multiplanet systems around brown dwarfs is several orders of magnitude more likely from a dynamical perspective than the Earth-to-Mars transfer of rocky ejecta, as argued in Lingam & Loeb (2017).

Last and not least, the issues of atmospheric escape and ocean desiccation merit thorough scrutiny. While some studies have addressed these topics from the standpoint of X-rays and UV radiation (Barnes & Heller 2013; Bolmont 2018), it is being increasingly appreciated that stellar winds and coronal mass ejections (CMEs) may contribute significantly in both respects (Dong et al. 2017b, 2018a, 2019; Airapetian et al. 2019). It is therefore necessary to synthesize observational limits on brown dwarf magnetic fields (Kao et al. 2019), theoretical models and observational constraints for stellar winds and CMEs, and multifluid magnetohydrodynamic simulations to determine the rates of atmospheric escape and water depletion (Dong et al. 2017a, 2018b). If theoretical models of M-dwarf exoplanets are anything to go by (Lingam & Loeb 2018b, 2019b), it is conceivable that exoplanets around brown dwarfs might be likewise depleted of ≲10 bar atmospheres in timescales less than 1 Gyr. However, it is necessary to utilize models of volatile delivery by means of impactors in tandem (Mulders et al. 2015; Tian et al. 2018; Brunini & López 2018), because they can serve to replenish the water reservoirs of brown dwarf exoplanets.

In summary, we investigated the prospects for long-term habitability of exoplanets around brown dwarfs by studying their habitable zones and prospects for photosynthesis and UV-mediated abiogenesis. We found that planets around brown dwarfs with masses ≲30 M_J are comparatively unlikely to be habitable (or inhabited) over timescales of gigayears. We also briefly explored the potential number of such brown dwarfs in our Galaxy, and the prospects for detecting biosignatures on temperate planets orbiting them. Our analysis suggests that there may be nearly as many astrobiological targets around brown dwarfs as around main-sequence stars under the most optimal circumstances, thereby highlighting the need for in-depth theoretical, experimental, and observational studies in the future.

We thank Adam Burrows for helpful clarifications concerning the paper. We also thank the reviewer for the insightful report that helped improve the quality of the paper. This work was supported in part by the Breakthrough Prize Foundation, Harvard University, and the Institute for Theory and Computation.