Habitability and Biosignatures of Hycean Worlds

We model the internal structure of Hycean planets following a conventional four-layered structure typically adopted for mini-Neptunes (see, e.g., Rogers & Seager 2010b; Nettelmann et al. 2011; Valencia et al. 2013; Madhusudhan et al. 2020). The generic model comprises an Fe inner core, a rocky (silicate) outer core, an H₂O layer, and an H₂/He-rich atmosphere. We refer to the Fe+silicate layers as the core. The mass fractions of each of the four components are free parameters in the model: x_Fe, x_silicate, ${x}_{{{\rm{H}}}_{2}{\rm{O}}}$, and x_H/He. The core mass fraction is given by x_core = x_Fe + x_silicate. Given the total mass and an interior composition, the internal structure equations are solved to determine the radius of the planet. The temperature and pressure at the outer boundary are also free parameters in the model. The temperature structure in the H₂/He-rich atmosphere is an input to the model and sets the temperature at the H₂O–H₂/He boundary (HHB). Below the HHB the temperature structure follows an adiabatic profile in the H₂O layer.

We refer the reader to Madhusudhan et al. (2012) and Madhusudhan et al. (2020) for a full description of the modeling approach. The structure equations of mass continuity and hydrostatic equilibrium are solved for the given equations of state (EOSs) in each layer using a fourth-order Runge–Kutta scheme. For the inner and outer core, we use the Birch–Murnaghan EOS (Birch 1952) for Fe (Ahrens 2000) and MgSiO₃ perovskite (Karki et al. 2000), respectively, as used by Seager et al. (2007). In this work, the core is assumed to be of Earthlike composition (32.5% Fe and 67.5% silicate). For the H₂O layer we use the temperature-dependent H₂O EOS adopted from Madhusudhan et al. (2020), which is compiled from Fei et al. (1993), Wagner & Pruß (2002), Seager et al. (2007), French et al. (2009), and Sugimura et al. (2010); see also Thomas & Madhusudhan (2016) and Nixon & Madhusudhan (2021). For the H₂/He-rich atmosphere we use the ideal gas EOS, which is accurate for the low pressures and temperatures considered here given the focus on habitable ocean surfaces under the atmosphere. The mean molecular weight (MMW) of the atmosphere is set by the atmospheric composition as discussed below.

A fiducial estimate of the possible interior composition of a planet can be obtained by considering its mass (M_p) and radius (R_p), i.e., its bulk density. The theoretical mass–radius (M–R) curves of planets with homogeneous compositions are shown in Figure 1 for 100% Fe, silicate, and H₂O (at 300 K and 1 bar surface conditions). We also show the M–R curve for Earthlike composition for reference, i.e., with 32.5% Fe and 67.5% silicate. Given the M_p and R_p for a low-mass planet the interior composition and structure cannot be uniquely determined, as a broad range of degenerate solutions can generally explain the data (e.g., Rogers & Seager 2010b; Valencia et al. 2013). However, planets with M_p and R_p above the pure silicate curve necessitate the presence of a volatile layer (e.g., H₂O and/or H₂/He) or a mineral composition less dense than silicates, e.g., carbides (Madhusudhan et al. 2012). Furthermore, for temperate planets with M_p and R_p above the 100% H₂O curve at 300 K the presence of a gaseous H₂/He-rich envelope becomes inevitable. As demonstrated in Madhusudhan et al. (2020), such a scenario still allows for a degenerate set of solutions, ranging from a rocky interior with a large H₂-rich envelope to an ocean world with an H₂-rich atmosphere. In the present work we focus on the latter set of solutions, and explore the range in the M–R plane that can be occupied by such Hycean planets. We summarize below the key model considerations made in the present work over Madhusudhan et al. (2020), aimed specifically toward modeling Hycean planets.

Zoom In Zoom Out Reset image size

Our canonical Hycean planet is composed of (a) an H₂-rich atmosphere, (b) an H₂O layer with a mass fraction between 10% and 90% and a habitable surface, and (c) an iron+rocky core with a minimum mass fraction of 10%. The temperature (T_HHB) and pressure (P_HHB) at the HHB span T_HHB ∼ 300–400 K and P_HHB = 1–1000 bar, motivated by conditions in which life is known to survive in Earth's oceans (Rothschild & Mancinelli 2001; Merino et al. 2019). We note that in our definition of a Hycean planet there is no landmass, as the entire planet would be covered by the water layer. While the mass fraction of the H₂-rich atmosphere is relatively small (≲0.1%), it contributes significantly to the planetary radius depending on the P_HHB, T_HHB, gravity, and atmospheric composition.

The MMW of the H₂-rich atmosphere can vary significantly depending on the atmospheric composition. For a solar abundance composition, which has an MMW of 2.4, the dominant chemical species in chemical equilibrium in the temperate regime (≲600 K) besides H₂ and He are H₂O, CH₄, and NH₃ at volume mixing ratios ≲0.1% (Burrows & Sharp 1999; Lodders & Fegley 2002; Madhusudhan & Seager 2011). However, for Hycean planets, with a large ocean under the atmosphere, the H₂O abundance in the atmosphere can be substantially enhanced. On the other hand, CH₄ and NH₃ can be depleted due to chemical disequilibrium in some conditions (e.g., Madhusudhan et al. 2020; Yu et al. 2021). H₂-rich atmospheres are particularly conducive to large H₂O enhancements (Koll & Cronin 2019). In the present models, we assume a 100× enhancement in the H₂O abundance compared to a solar abundance atmosphere, i.e., an H₂O volume mixing ratio of 10% and an MMW of 4.0. This nominally includes He, CH₄, and NH₃ at abundances expected for a solar elemental composition (Asplund et al. 2009). The enhanced H₂O mixing ratio is consistent with the upper end of the atmospheric H₂O abundance derived observationally for the Hycean candidate K2–18 b (Benneke et al. 2019b; Madhusudhan et al. 2020).

The radii we derive with the high MMW assumed here are expected to be conservative estimates. The observable height of the atmosphere and, hence, the radius is larger for lower MMW, as the scale height is inversely proportional to the MMW. The temperature structure in the H₂-rich atmosphere is assumed to be isothermal in the present work, motivated by the model P–T profiles derived in Section 3 and discussed further below. We set the outer boundary condition of the model to a pressure of 0.05 bar, following Madhusudhan et al. (2020), corresponding to the planetary photosphere observed in transit. This is the pressure at which the radius of the planet is defined in the interior and atmosphere models in Sections 2.2 and 3, respectively.

Zoom In Zoom Out Reset image size

We construct a Hycean M–R plane based on the minimum and maximum radii nominally expected for Hycean planets over the 1–10 M_⊕ mass range considered here. For a given mass, the factors that primarily influence the radius are x_core, ${x}_{{{\rm{H}}}_{2}{\rm{O}}}$, P_HHB, and T_HHB; the latter two parameters also influence the size of the H₂-rich atmosphere, which can contribute significantly to the radius. Since the core and H₂O layers dominate the mass content, choosing one of them naturally limits the other. Thus, the lower and upper boundaries of the Hycean M–R plane effectively correspond to the parameter combinations that lead to the lowest and highest extent, respectively, of the H₂O layer and the H₂-rich atmosphere.

The lower boundary of the Hycean M–R plane is set by the minimum H₂O mass fraction and the minimum extent of the H₂-rich atmosphere possible to sustain a liquid H₂O ocean at the HHB. Within our Hycean model considerations this is attained for ${x}_{{{\rm{H}}}_{2}{\rm{O}}}=10 \%$ and Earthlike surface conditions at the HHB, i.e., P_HHB = 1 bar and T_HHB = 300 K. From self-consistent models in Section 3, we find that the atmospheric temperature structures are nearly isothermal for most of the atmosphere. We therefore set the 1D averaged temperature profile in the H₂-rich atmosphere to be isothermal at 300 K for this case. Given the HHB pressure, the mass fraction of the H₂-rich atmosphere is ≲10⁻⁵, while the low temperature means that the scale height is also minimal. Thus, the remaining mass is occupied by the core with x_core ∼ 90%. We consider the core composition to be Earthlike, with 32.5% Fe and 67.5% in silicate (MgSiO₃) rock.

Our consideration of a minimum ${x}_{{{\rm{H}}}_{2}{\rm{O}}}$ of 10% is such that the H₂O reservoir would be able to survive photodissociation and atmospheric escape over several gigayears around the most active stellar hosts (e.g., Luger & Barnes 2015; Bolmont et al. 2017). High-energy stellar irradiation, e.g., UV activity and coronal mass ejections, can result in the photolysis of water vapor and subsequent atmospheric escape of hydrogen and oxygen. This is expected to be particularly significant for M-dwarf planets, as their host stars can be substantially more active than earlier-type stars. Through this process substantial amounts of H₂O can be lost, with estimates as high as 10 Earth oceans in some cases (Luger & Barnes 2015). We therefore conservatively set the minimum Hycean H₂O mass fraction to be 10%, i.e., equivalent to ≳100 times the Earth H₂O mass fraction. This amount allows the planet to retain a sizeable ocean over several Gyr even in the most active stellar environment. In practice, however, planets with even lower ${x}_{{{\rm{H}}}_{2}{\rm{O}}}$ than 10% could qualify as Hycean candidates. For example, even at ${x}_{{{\rm{H}}}_{2}{\rm{O}}}=1 \%$ a planet can be covered in oceans. In such cases, the lower boundary of the Hycean M–R plane will be closer to the M–R curve for Earthlike composition shown in Figure 1.

The upper boundary of the canonical Hycean M–R plane is guided by the largest ${x}_{{{\rm{H}}}_{2}{\rm{O}}}$ and most extended H₂ envelope that can still provide habitable conditions at the ocean surface. We consider this limit to be ${x}_{{{\rm{H}}}_{2}{\rm{O}}}=90 \%$ and T_HHB = 400 K at P_HHB = 3 bar. This combination of T_HHB and P_HHB allows both the surface of the ocean and the atmospheric temperature to be at ∼400 K, which is the highest temperature we consider for habitability at the ocean surface. In principle, considering a deeper HHB at P_HHB = 10³ bar at the same T_HHB can also provide a similar upper limit with a more massive atmosphere. In that case the atmospheric temperatures will be significantly cooler, leading to a smaller scale height.

For T_HHB = 400 K the P_HHB of 3 bar ensures that the ocean surface is in liquid state; the vapor–liquid transition happens at 2.5 bar for this temperature. Above the HHB we assume that the atmosphere is isothermal at 400 K, motivated by the atmospheric P–T profiles derived in Section 3.2. Following Madhusudhan et al. (2020), we consider a minimum core mass fraction of x_core = 10% with Earthlike composition. We find that the Hycean upper M–R boundary leads to radii that are slightly larger, by up to ∼0.1 R_⊕, than those of 100% H₂O planets with 300 K and 1 bar surface conditions. The radius enhancement from the higher temperature and an H₂-rich atmosphere is somewhat compensated by the presence of a 10% core. We also note that assuming a lower MMW (e.g., 2.4 corresponding to 1 × solar metallicity) rather than the MMW of 4.0 assumed here (corresponding to an enhanced H₂O abundance) can lead to larger atmospheric scale heights and, hence, somewhat larger radii by up to another ∼0.1 R_⊕.

The upper boundary in the M–R plane is even higher for partially habitable Hycean worlds. We consider the possibility of "Dark Hycean" worlds where a tidally locked planet can have a habitable permanent night (dark) side even though the permanent dayside is substantially hotter. We show in Section 3.3 that such conditions can prevail on Hycean planets with equilibrium temperatures of ∼510 K or even higher, depending on the dayside albedo and the day–night energy redistribution. For such planets, the temperatures at the day–night terminator as probed by transmission spectra can be significantly higher than the ∼400 K habitable temperature limit we consider.

For the outer M–R boundary of such Dark Hycean worlds, we nominally consider the planet-wide average surface and atmospheric temperature to be 500 K. The choice of this temperature is motivated by the atmospheric models for nightsides of Dark Hycean planets discussed in Section 3.3. In particular, we find that planets with equilibrium temperatures of ∼510 K with inefficient day–night energy redistribution can lead to dayside temperatures of ∼500–600 K but nightside surface temperatures ≲400 K. Therefore, while a 510 K temperature is not considered to be habitable, it represents a planet-wide average and still allows a nonnegligible fraction of the nightside ocean surface to be at habitable surface temperatures, i.e., below 400 K. We assume a P_HHB of 30 bar, which is above the pressure of 27 bar required for the ocean surface to be in liquid state at the T_HHB of 500 K. The higher average temperature, compared to "regular" Hycean planets discussed above, both in the atmosphere and in the water layer leads to a further increase of up to ∼0.1 R_⊕ in radius across the mass range. As shown in Figure 1, such a condition allows for Dark Hycean worlds to be as large as ∼2.6 R_⊕ for M_p = 10 M_⊕.

Overall, we find that Hycean planets can occupy a wide range in the M–R plane and can be significantly larger than super-Earths, which are assumed to be predominantly rocky. The region in the mass–radius plane occupied by Hycean worlds is shown in Figure 1. We find that the uppermost M–R boundary in Figure 1 allows for Dark Hycean radii that are up to ∼0.25 R_⊕ larger than the pure H₂O curve at 300 K and 1 bar surface conditions; larger differences occur for lower masses. The differences are even larger compared to the M–R curve for Earthlike composition across the mass range. Therefore, for the same mass, Hycean and/or Dark Hycean planets can be significantly larger than super-Earths and 100% ocean worlds with habitable conditions. In the 1–10 M_⊕ mass range, the upper limit on the radius of Hycean (Dark Hycean) planets is in the range of ∼1.5–2.6 R_⊕ (∼1.7–2.6 R_⊕). We note that the Dark Hycean upper limit we consider here may be conservative considering that even hotter tidally locked planets than those with T_eq ≲ 510 K considered here may be habitable on the nightside depending on the dayside albedo and day–night redistribution, as discussed in Section 3.3.

On the lower boundary, Hycean radii are up to ∼0.2 R_⊕ larger than the M–R curve for rocky planets with Earthlike compositions, with a minimum radius of 1.1 R_⊕ at M_p = 1 M_⊕ and 2.0 R_⊕ at M_p = 10 M_⊕. Thus, between the two boundaries, Hycean planets can span a large range in masses and radii depending primarily on the mass fraction of the ocean (between 10% and 90%). The H₂-rich atmosphere, though relatively much smaller in mass fraction (<0.1%), can contribute significantly to the radius of the planet. Most notably, Hycean planets can be significantly larger than rocky super-Earths that are typically assumed to have Earthlike composition.

Recent transit surveys have led to numerous detections of mini-Neptunes orbiting late-type (M and K) stars (e.g., Dressing & Charbonneau 2015; Fulton & Petigura 2018; Hardegree-Ullman et al. 2020). Several mini-Neptunes around nearby stars are known to be conducive for atmospheric observations (e.g., Kreidberg et al. 2014; Benneke et al. 2019b; Tsiaras et al. 2019; Guo et al. 2020). While the mini-Neptune class encompasses planets with radii between ∼1.6 and 4 R_⊕ (e.g., Rogers 2015), our results above show that planets with radii between ∼1.1 and 2.6 R_⊕ can be strong candidates for Hycean worlds, depending on the mass, T_eq, and stellar host. In Figure 1 we show the masses and radii of several exoplanets with M_p < 10 M_⊕, R_p < 3 R_⊕, and T_eq < 600 K and whose host stars have J magnitudes below 13.

The identification of a Hycean candidate depends not only on its mass and radius but also on its equilibrium temperature and stellar host. In Section 3.2, we determine the ranges of equilibrium temperatures that allow for habitable surface conditions given a range of stellar hosts. Regular Hycean planets, with both dayside and nightside habitability, can have equilibrium temperatures as high as ∼210–430 K depending on the stellar host (see, e.g., Table 2). On the other hand, Dark Hycean planets can have planet-averaged equilibrium temperatures as high as ∼510 K, allowing for habitable conditions on the permanent nightside while the dayside remains uninhabitable. Therefore, all planets that lie in the Hycean M–R plane with T_eq < 510 K may be considered as candidate Hycean planets.

In Table 1, we identify several Hycean candidates with masses and radii within the nominal Hycean M–R plane that also lie within the Hycean HZ (see Figure 3). The potentially Hycean nature of K2–18 b was demonstrated recently (Madhusudhan et al. 2020), which argues for similar conditions to be possible on the other planets listed here. Of these candidates, three lie in the Dark Hycean HZ, as shown in Figure 3, namely, K2–3 b, TOI-270 c, and TOI-776 b. As discussed above in Section 2.2, in principle the lower Hycean boundary can be closer to the Earthlike M–R curve if lower H₂O mass fractions are considered. In such a scenario, other known planets may also qualify as Hycean candidates. The planet LHS 1140 b (Ment et al. 2019) with M_p = 6.98 M_⊕, R_p = 1.727 R_⊕, and T_eq = 197 K orbiting an M4.5 dwarf star is one such potential candidate.

Zoom In Zoom Out Reset image size

Table 1. Properties of Promising Hycean Candidates and Their Host Stars

Name	MP/M⊕	RP/R⊕	Teq/K	a/au	M⋆/M⊙	R⋆/R⊙	T⋆/K	J mag	V mag	Ref
K2–18 b	8.63 ± 1.35	${2.51}_{-0.18}^{+0.13}$	250	0.153	0.44	0.45	3590	9.8	13.5	1, 2
K2–3 c	${2.14}_{-1.04}^{+1.08}$	${1.74}_{-0.17}^{+0.17}$	286	0.136	0.55	0.55	3500	9.4	12.2	1, 3
TOI-1266 c	${2.2}_{-1.5}^{+2.0}$	${1.56}_{-0.13}^{+0.15}$	291	0.106	0.45	0.42	3600	9.7	12.9	4
TOI-732 c	${6.29}_{-0.61}^{+0.63}$	2.42 ± 0.10	305	0.076	0.38	0.38	3360	9.0	13.1	5
TOI-270 d	4.78 ± 0.46	2.01 ± 0.07	327	0.072	0.39	0.38	3506	9.1	12.6	6
TOI-175 d	${2.31}_{-0.45}^{+0.46}$	1.57 ± 0.14	341	0.051	0.31	0.31	3412	7.9	11.7	7, 8
TOI-776 c	5.30 ± 1.80	2.02 ± 0.14	350	0.100	0.54	0.54	3709	8.5	11.5	9
LTT 1445 A b	${2.2}_{-2.1}^{+1.7}$	${1.38}_{-0.12}^{+0.13}$	367	0.038	0.26	0.28	3337	7.3	11.2	10
K2–3 b	${6.48}_{-0.93}^{+0.99}$	${2.12}_{-0.17}^{+0.12}$	384	0.075	0.55	0.55	3500	9.4	12.2	1, 3
TOI-270 c	6.14 ± 0.38	2.33 ± 0.07	413	0.045	0.39	0.38	3506	9.1	12.6	6
TOI-776 b	4.00 ± 0.90	1.85 ± 0.13	434	0.065	0.54	0.54	3709	8.5	11.5	9

Note. The table lists properties of promising exoplanets that fall within the Hycean boundaries in Figure 1, with T_eq < 500 K, and whose host stars have J < 10. T_eq is the equilibrium temperature of the planet assuming full day–night energy redistribution and a Bond albedo of 0.5, as discussed in Section 3.1. The first five columns show the planet properties, and the following five columns show the stellar properties. M_⋆, R_⋆, and T_⋆ are the mass, radius, and effective temperature of the host star, respectively.

References. System properties are derived from (1) Hardegree-Ullman et al. 2020; (2) Cloutier et al. 2019b; (3) Kosiarek et al. 2019; (4) Demory et al. 2020; (5) Nowak et al. 2020; (6) Van Eylen et al. 2021; (7) Kostov et al. 2019; (8) Cloutier et al. 2019a; (9) Luque et al. 2021; (10) Winters et al. 2019.

Download table as:  ASCIITypeset image

Figure 1 also shows a few other known planets with masses and radii in the Hycean M–R plane but with T_eq > 510 K. While these planets would be too hot to be habitable given our current assumptions, the habitability of their permanent nightsides may not be entirely ruled out. As discussed in Section 3.3, the allowed equilibrium temperatures of Dark Hycean worlds can be higher than 510 K for lower day–night energy redistribution efficiencies and higher albedos than those considered in this work.

We emphasize, however, that planets in the Hycean M–R plane are only Hycean candidates. Given only the observed mass and radius of a Hycean candidate, there are significant degeneracies in establishing its internal composition and structure. A range of H₂, H₂O, and core mass fractions would be admissible by the data, as demonstrated in the case of the Hycean candidate K2–18 b (Madhusudhan et al. 2020). The scenarios include internal structures ranging from mini-Neptunes and 100% water worlds to predominantly rocky super-Earths with large H₂-rich envelopes. Nevertheless, accurately measured masses, radii, and equilibrium temperatures allow us to focus on promising Hycean candidates that, with spectroscopic observations, may lead to inferences of their atmospheric compositions, including biosignatures. The atmospheric properties of a Hycean candidate can provide further constraints on its surface conditions and habitability (e.g., Madhusudhan et al. 2020).

In what follows, we model Hycean atmospheres in order to assess their habitability across a wide range of stellar spectral types. We then discuss how spectroscopic observations can constrain the atmospheric properties, including the presence of biosignatures, in Hycean planets in Section 4.

We model the atmospheres of Hycean worlds using the GENESIS self-consistent atmospheric modeling framework (Gandhi & Madhusudhan 2017; Piette & Madhusudhan 2020). We consider an H₂-rich plane-parallel atmosphere in hydrostatic and radiative-convective equilibrium. The thermal structure is governed by radiative-convective equilibrium given the incident irradiation and internal flux and is determined following the Rybicki scheme with complete linearization (Hubeny & Mihalas 2014). The radiation field is computed using line-by-line radiative transfer following Feautrier's method (Hubeny & Mihalas 2014; Hubeny 2017) and the discontinuous finite element method (Castor et al. 1992), as described in Piette & Madhusudhan (2020).

The temperature structure of the atmosphere depends on the external and internal energy sources, the day–night energy redistribution, and the opacity and albedo of the atmosphere. The external irradiation depends on both the host star temperature, which determines the spectral distribution of incident energy, and the total energy incident upon the planet. This total energy can be represented by the irradiation temperature:

$$\begin{eqnarray}&&{T}_{\mathrm{irr}}=\displaystyle \frac{{T}_{\star }}{{2}^{1/4}}\sqrt{\displaystyle \frac{{R}_{\star }}{a}}.\end{eqnarray} \tag{ 1 }$$

T_⋆ and R_⋆ are the stellar effective temperature and radius, respectively, and a is the orbital separation. T_irr is equivalent to the dayside-average equilibrium temperature of the planet assuming no albedo or day–night redistribution. Correspondingly, the equilibrium temperature of the planet can be defined as

$$\begin{eqnarray}&&{T}_{\mathrm{eq}}{({A}_{{\rm{B}}},{f}_{{\rm{r}}})=(1-{A}_{{\rm{B}}})}^{1/4}{(1-{f}_{{\rm{r}}})}^{1/4}{T}_{\mathrm{irr}},\end{eqnarray} \tag{ 2 }$$

where A_B is the Bond albedo and f_r is the fraction of incident irradiation redistributed to the nightside.

In Section 3.2, we assume uniform day–night energy redistribution (i.e., f_r = 0.5) and A_B = 0.5, representing a limiting case for determining the inner HZ boundary. Therefore, T_eq = 0.707 T_irr. In this scenario, the equilibrium temperatures corresponding to the dayside and nightside will be equal, i.e., T_day = T_night = T_eq. In Section 3.3, we investigate models with inefficient day–night energy redistribution, i.e., f_r < 0.5. In this case, T_day = T_eq but T_night = ${[{f}_{{\rm{r}}}/(1-{f}_{{\rm{r}}})]}^{1/4}{T}_{\mathrm{eq}}$. We therefore define T_eq,av = T_eq(A_B = 0.5, f_r = 0.5) as a representative average equilibrium temperature of the planet in this scenario.

In this work, we explore both a range of stellar temperatures (from ∼2500 to 6000 K; see below) and a range of T_eq, from ∼0 to 500 K. The internal flux emanating from the planetary interior is represented by the internal temperature T_int, such that the flux input at the lower boundary is given by ${F}_{\mathrm{int}}=\sigma {T}_{\mathrm{int}}^{4}$ (see, e.g., Gandhi & Madhusudhan 2017). We explore values of T_int spanning 25–50 K, as expected for sub-Neptunian planets with ages between 1 and 10 Gyr (Valencia et al. 2013). On the nightside of a planet, day–night energy redistribution can provide a further energy source. We consider this in Section 3.3 following the methods outlined in Appendix B.

The key sources of extinction in the model atmospheres are absorption from the prominent molecules and scattering from molecular H₂, as well as hazes. For H₂-rich atmospheres in the low-temperature regime, i.e., below ∼500 K, the prominent sources of opacity in thermochemical equilibrium are typically H₂O, CH₄, and NH₃ (Burrows & Sharp 1999; Lodders & Fegley 2002; Madhusudhan & Seager 2011; Moses et al. 2013). However, CH₄ and NH₃ can be photochemically depleted depending on the ambient conditions (e.g., Madhusudhan et al. 2020; Yu et al. 2021). For all chemical species other than H₂O, which is the dominant opacity source, we nominally determine the abundances according to chemical equilibrium for the corresponding temperature structure, assuming solar elemental abundances. For a Hycean planet, H₂O may be expected to evaporate from the ocean surface, significantly increasing the atmospheric H₂O abundance compared to equilibrium values. In our models, we therefore assume a higher H₂O mixing ratio of 10%, i.e., 100 times the equilibrium abundance expected for a solar-like composition, as discussed in Section 2. The volume mixing ratios we assume for these species are therefore 0.1, 5.0 × 10⁻⁴, and 1.3 × 10⁻⁴ for H₂O, CH₄, and NH₃, respectively. We additionally assume a solar abundance for He. We further consider H₂O condensation based on the pressure–temperature (P–T) profile with respect to the H₂O saturation curve. In particular, we rain out any water vapor in excess of the H₂O vapor pressure and freeze out water vapor where it is expected to be in the ice phase.

We use the line-by-line opacities of these molecules computed from the corresponding line list (H₂O, Rothman et al. 2010; CH₄ and NH₃, Yurchenko et al. 2011; Yurchenko et al. 2013; Yurchenko & Tennyson 2014), as well as collision-induced absorption (CIA) from H₂–H₂ and H₂–He (Richard et al. 2012). The absorption cross sections are computed from the line lists following Gandhi & Madhusudhan (2017). Besides molecular absorption, we also consider Rayleigh scattering due to H₂, as well as scattering from possible hazes in the atmosphere, as described below.

In order to define the Hycean HZ, we follow the approach traditionally used for determining the HZ for terrestrial-like planets (Kasting et al. 1993; Selsis et al. 2007b; Kopparapu et al. 2013), but tailored here for Hycean conditions. It is typical in computations of terrestrial-like HZs to assume fiducial properties for the atmospheric composition and albedo. Such computations (e.g., Kasting et al. 1993; Kopparapu et al. 2013) account for scattering of incident irradiation by assuming a certain surface albedo without explicitly including the effect of clouds/hazes on the temperature profile.

Here, we include the effects of hazes and parameterize their scattering as an enhanced H₂ Rayleigh scattering. The haze scattering cross section is given by ${\sigma }_{\mathrm{haze}}={n}_{\mathrm{haze}}{\sigma }_{{{\rm{H}}}_{2}\mathrm{Rayleigh}}$, where n_haze is a dimensionless free parameter and ${\sigma }_{{{\rm{H}}}_{2}\mathrm{Rayleigh}}$ is the H₂ Rayleigh scattering cross section, following Piette & Madhusudhan (2020). We refer to n_haze, the Rayleigh enhancement factor, as the haze coefficient. In Section 3.2, we calculate models with a fixed Bond albedo of A_B = 0.5 by varying n_haze until this target is met. This value is motivated by both previous studies (e.g., Selsis et al. 2007b; Yang et al. 2013) and the fact that most planets in the solar system have A_B ∼ 0.3--0.75 (de Pater & Lissauer 2010). We note that the majority of our models are too hot for H₂O clouds such as those considered in other studies (e.g., Morley et al. 2015; Piette & Madhusudhan 2020). However, a wide range of haze compositions are thought to be possible in temperate super-Earth/mini-Neptune atmospheres (e.g., Moran et al. 2020). We therefore consider haze scattering, rather than clouds, to represent the albedos across all our models for a consistent treatment.

Our conditions for habitability are motivated by the range of conditions in Earth's oceans where life is known to survive (e.g., Rothschild & Mancinelli 2001; Merino et al. 2019). We require that the ocean surface under the H₂-rich atmosphere (i.e., the HHB) is at a pressure between 1 and 1000 bar and temperature between 273 and 395 K, conditions where H₂O is in liquid phase and suitable for ocean-based life. This "habitable region" in the H₂O phase diagram is highlighted in blue in Figures 2, 4, and 5. We also note that H₂O remains in liquid form at even higher pressures and temperatures, and extraterrestrial life may acclimatize to such conditions. As such, our assumed conditions here may be considered to be conservative. We consider host stars over a wide range of spectral types spanning late M to early G, as described below. For each host star, we consider two sample planets: "planet A" with M_p = 5 M_⊕, R_p = 2.15 R_⊕, and "planet B" with M_p = 10 M_⊕, R_p = 2.60 R_⊕ (see Figure 1). For each combination of host star and planet, we consider models with a range of equilibrium temperatures. The HZ for a given star is then determined by the range in equilibrium temperature (or equivalently, orbital separation) that allows for habitable temperatures at the base of the atmosphere.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

For the host stars in our models, we use the properties of 12 exoplanet-hosting stars with effective temperatures, T_⋆, in the range 2500–6000 K. This ensures that the stellar properties used are realistic and unaffected by model choices in theoretical mass–radius–temperature grids, which have previously been used in HZ studies. These stars and their properties are listed in Table 3 (Appendix A). The planetary atmospheric models require two stellar inputs: the stellar radius and the stellar spectrum. In this work, we use Phoenix spectral models (Husser et al. 2013) for M dwarfs with T_⋆ ≤ 3500 K and Kurucz models for hotter stars (Kurucz 1979; Castelli & Kurucz 2003). For the Phoenix models, we round the stellar gravity, metallicity, and T_⋆ to the nearest value in the model grid. For the Kurucz models, we interpolate the spectra to the nominal stellar values. For all of the host stars, the stellar radius used is the empirical radius listed in Table 3.

We now discuss the different scenarios that allow for habitability on Hycean planets. In what follows, the only parameters varied are T_eq, T_int, the haze coefficient, and the host star. All other atmospheric properties are fixed to those discussed above.

We first investigate the HZ for the day sides of Hycean planets. Since close-in planets are largely expected to be tidally locked, this configuration is particularly relevant for transiting Hycean planets with observable atmospheres. We define the inner habitable boundary (IHB) as corresponding to the maximum irradiation that allows for habitable conditions at the surface of the ocean, i.e., the HHB. In this limit, the HHB occurs at the high-temperature/low-pressure corner of the "habitable region" in the H₂O phase diagram (defined in Section 3.1). Therefore, for these limiting cases, the P–T profile reaches T_HHB = 395 K at a pressure of P_HHB = 2.1 bar. Since, in this scenario, the pressure at the base of the atmosphere is 2.1 bar, we compute atmospheric models up to a maximum pressure of 2.1 bar. In this limit, the H₂O in the atmosphere near the HHB is 10% saturated on average across the day side. A case with 100% saturation, which results in a similar IHB, is shown in Appendix A. Furthermore, in this limit, T_int has a minimal value, which we consider to be 25 K for typical Hycean worlds (see Section 3.1).

For each host star, we determine the maximum T_eq, or minimum a, that achieves the conditions described above. To do this, we assume a fixed albedo of 0.5 and full day–night energy redistribution (f_r = 0.5) across all stellar types, as discussed in Section 3.1. The corresponding T_eq, a, and haze properties for each planet and host star combination are listed in Table 2. Figure 2 shows the corresponding P–T profiles for planets A and B orbiting various stellar hosts.

Table 2. Atmospheric Properties at the Inner Habitable Boundary as a Function of Host Star Properties (Effective Temperature, T_⋆, and Stellar Mass, M_⋆)

		Planet A: ${M}_{{\rm{p}}}=5\,{M}_{\oplus }$,			Planet B: ${M}_{{\rm{p}}}=10\,{M}_{\oplus }$,
		${R}_{{\rm{p}}}=2.15\,{R}_{\oplus }$			${R}_{{\rm{p}}}=2.60\,{R}_{\oplus }$
${T}_{\star }$ (K)	${M}_{\star }$ (${M}_{\odot }$)	${T}_{\mathrm{eq}}$ (K)	a (au)	${n}_{\mathrm{haze}}$	${T}_{\mathrm{eq}}$ (K)	a (au)	${n}_{\mathrm{haze}}$
2500	0.08	430	0.007	53000	431	0.006	67000
3000	0.12	427	0.011	31000	427	0.011	37000
3000	0.16	427	0.017	29000	427	0.017	35000
3300	0.26	418	0.029	17000	412	0.030	18000
3400	0.31	415	0.034	15000	411	0.035	16500
3590	0.44	410	0.057	12000	409	0.057	14000
4145	0.58	384	0.109	4800	381	0.111	5500
4430	0.69	367	0.158	2900	359	0.165	3100
4750	0.80	326	0.258	1200	325	0.261	1400
5275	0.93	286	0.487	450	286	0.487	520
5777	1.00	214	1.193	35	219	1.148	37
6025	1.18	208	1.909	30	214	1.791	33

Note. We consider a fixed Bond albedo of A_B = 0.5 and find the corresponding haze coefficient, n_haze, and irradiation at the IHB (see Section 3.2). The equilibrium temperatures quoted here assume full day–night redistribution, as well as a Bond albedo of 0.5, i.e., f_r = 0.5, A_B = 0.5 in Equation (2).

Download table as:  ASCIITypeset image

The IHB as a function of the stellar mass is shown in Figure 3. We find that the IHB typically occurs at smaller orbital distances relative to the terrestrial HZ, particularly for lower-mass stars. This is because the temperature profiles for planets orbiting these stars are more isothermal, allowing for hotter T_eq (Figure 2). The isothermal temperature profiles are a result of the relatively high haze opacity, compared to solar-like stars, required to achieve an albedo of 0.5. For cooler host stars, the incident irradiation peaks in the infrared and has less flux in the optical. Therefore, to achieve the same albedo, the optical scattering in the planetary atmosphere needs to be substantially higher compared to the case for a hotter star where the irradiation peaks in the visible.

For the coolest stars, the temperature at the base of the atmosphere can be even lower than the equilibrium temperature when A_B is fixed to 0.5. This is because a thermal inversion is caused at high altitudes when the high haze opacity intercepts the incident flux, similar to optical absorbers causing thermal inversions in planets orbiting hotter stars (Hubeny et al. 2003; Fortney et al. 2008). Therefore, for the late M host stars with T_⋆ = 2500–3300 K, we find that the IHB for an albedo of 0.5 corresponds to T_eq ≈ 410–430 K, with an orbital separation of ∼0.006–0.03 au. This result is true for both planets A and B.

For hotter stars, the IHB for Hycean atmospheres approaches that of the conventional terrestrial HZ. As shown in Figure 3, for a Sun-like star the IHB is close to that of the terrestrial case, which is expected for similar Bond albedo and host star. For the hottest host stars we consider, the temperature in the atmosphere decreases monotonically with altitude, with H₂O freezing out at higher altitudes and leading to a largely dry atmosphere. Overall, for the range of stellar hosts between T_⋆ of 2500 and 6000 K that we consider, the maximum irradiation allowing habitable conditions ranges between T_eq of ∼210 and 430 K, corresponding to orbital separations of ∼0.006–1.9 au. Again, this result is similar for planets A and B.

We also investigate the outer habitable boundary (OHB) for Hycean planets. The OHB is determined by the minimum irradiation that can still allow habitable conditions at the HHB. In this limit, the HHB occurs at the low-temperature/high-pressure corner of the "habitable region" in the H₂O phase diagram (defined in Section 3.1), i.e., T_HHB = 273 K at P_HHB ∼ 1000 bar. We find that nonirradiated, "cold" Hycean planets can satisfy this condition at the ocean surface. Therefore, the Hycean HZ extends to arbitrarily large orbital distances and is substantially wider than the terrestrial HZ. We discuss these "cold" Hycean planets further in Section 3.4.

In order to distinguish between irradiated and nonirradiated Hycean planets, we define a boundary between the regular Hycean HZ (for irradiated planets) and the "cold" Hycean HZ (for nonirradiated planets). This boundary occurs where irradiation no longer dominates the temperature profile, i.e., where T_eq ≲ T_int and internal heat takes over as the dominant energy source in the atmosphere. The OHB for "regular" Hycean planets therefore occurs at T_eq = 25 K, since this is the minimal value of T_int that we consider for Hycean planets. This OHB corresponds to an orbital distance beyond ∼20 au for K dwarf and G dwarf stars more massive than ∼0.5 M_⊙ and is between ∼2–20 au for M dwarfs. Our findings for the OHB of Hycean planets are consistent with those suggested for rocky exoplanets with H₂-rich atmospheres in previous studies, which focused on the low irradiation regime (Stevenson 1999; Pierrehumbert & Gaidos 2011).

Overall, our results show that the HZ for Hycean planets is considerably wider than the terrestrial HZ. The Hycean IHB can be significantly closer to the host stars, i.e., with larger T_eq, depending on the albedo. The Hycean OHB is even wider, spanning orbital distances beyond ∼2–100 au across the stellar types considered. In comparison, for the terrestrial HZ investigated in previous studies, the OHB is limited by CO₂ condensation limiting the greenhouse effect. The OHB in that case (Kasting et al. 1993; Kopparapu et al. 2013) lies within ∼1.7 au for the Sun and ≲0.07 au for a late M dwarf, with HZ widths of ∼0.7 and ∼0.03 au, respectively. The terrestrial habitable zone can be somewhat wider depending on the model considerations (e.g., Selsis et al. 2007b; Yang et al. 2013; Zsom et al. 2013). The wider Hycean HZ may increase the chances that such planets host habitable conditions, as the orbital separations required are not as restrictive compared to terrestrial planets.

Here we investigate the possibility of habitable conditions on the permanent nightsides of Hycean planets that are tidally locked. With no incident irradiation from the host star, the sources of energy in the nightside atmosphere of the planet are (a) energy redistributed from the dayside through atmospheric circulation and (b) the internal energy. Depending on the efficiency of day–night energy redistribution, the nightside atmosphere may allow for habitable conditions even when the dayside may not. For planets with high equilibrium temperatures and efficient day–night energy redistribution, both the dayside and nightside may be uninhabitable (e.g., for T_eq ≳ 430 K for late M host stars). However, planets with high equilibrium temperatures and inefficient day–night energy redistribution can have significant day–night temperature contrasts, and the nightsides of such planets may be habitable. Here, we define Dark Hycean planets as those that have inefficient day–night redistribution (i.e., f_r < 0.5) such that only the nightside is habitable. On such planets, only nocturnal life would be possible.

General circulation models (GCMs) of tidally locked exo-Neptunes with H₂-rich atmospheres show that the efficiency of day–night energy redistribution is reduced for high-metallicity atmospheres (Lewis et al. 2010; Crossfield et al. 2020). This can lead to significant differences in the temperatures between the dayside and nightside atmospheres. We therefore explore models with inefficient redistribution to investigate the limiting dayside irradiation that can still allow for habitability on the nightside.

We self-consistently model the temperature structure and radiative transfer in the nightside atmosphere, accounting for energy redistributed from the dayside. Our prescription for the day–night energy redistribution is described in Appendix B. This approach was previously developed in the context of highly irradiated hot Jupiters (Burrows et al. 2008). In the present work, we test different energy redistribution profiles, including that used in Burrows et al. (2008) and a Gaussian profile, as discussed in Appendix B. In order to determine the IHB limits across the different stellar hosts, we assume a minimum redistribution efficiency of 25% (f_r = 0.25), as well as a dayside albedo of 0.5. Thus, of the total energy incident on the dayside, 12.5% is redistributed to the nightside. All other atmospheric parameters are fixed to those assumed in Section 3.2, though for simplicity we do not include haze in the nightside models. We find that including a nominal haze opacity similar to the dayside models does not have a substantial effect on the nightside given the lack of incident irradiation. To calculate the IHB for the Dark Hycean regime, we use the bulk properties of planet B, as this lies within the Dark Hycean M–R plane.

The IHB for Dark Hycean planets is somewhat closer in, i.e., at higher equilibrium temperatures, than that for regular Hycean planets across all the host stars. As described in Section 3.1, we use a planet-wide average equilibrium temperature, T_eq,av, to represent the incident irradiation. However, we highlight that the dayside and nightside of Dark Hycean planets with inefficient redistribution would have different equilibrium temperatures, allowing for a habitable nightside, while the dayside is too hot to be habitable. Figure 4 shows the nightside temperature structures of such planets with different T_eq,av and using different redistribution profiles.

Each redistribution profile deposits energy at different altitudes on the nightside, affecting the location of the IHB. We find that habitable conditions on the nightside are possible for T_eq,av as high as ∼510 K. This limit occurs when the energy deposition occurs at higher altitudes (P ≲ 0.1 bar). This limiting T_eq,av is independent of the stellar type since the energy redistributed to the nightside depends only on the total bolometric energy incident on the dayside. A T_eq,av of 510 K corresponds to an IHB as close as ∼0.005 au for late M dwarfs and within ∼0.25 au for Sun-like stars, as shown in Figure 3. When energy is deposited at lower altitudes on the nightside, up to P ∼ 1 bar, we find that the maximal T_eq,av that allows for habitable conditions is significantly lower, at ∼315 K. Therefore, we consider T_eq,av of 510 K to be an upper limit for such worlds.

We note that this Dark IHB is applicable only for Hycean planets that are tidally locked. Considering the tidal-locking limit from previous studies (Kasting et al. 1993; Selsis et al. 2007b), Dark Hycean planets may be expected to be more prevalent around low-mass stars, e.g., M dwarfs. For hotter stars the Dark Hycean IHB may be beyond the tidal-locking separation.

The upper limit on T_eq,av for the Dark Hycean IHB is conservative, because for less efficient redistribution and/or higher albedo (i.e., a lower P_n; see Appendix B) the nightside can be habitable for T_eq,av > 510 K. In the absence of constraints on redistribution efficiency and albedos for such planets, we nominally consider T_eq,av = 510 K as the upper limit. Overall, the distinguishing feature of Dark Hycean planets relative to "regular" Hyceans is that their inefficient day–night energy redistribution permits a habitable nightside while the dayside remains too hot to be habitable. On the other hand, regular Hyceans are expected to be habitable on both the dayside and nightside. The limiting planet-wide equilibrium temperature of ∼510 K for Dark Hycean planets is higher than that of the ∼430 K limit for regular Hycean planets orbiting low-mass stars. The regions in the mass–radius plane are largely similar, with the Dark Hyceans allowing for slightly larger radii, by up to ∼0.1 R_⊕ depending on the planet mass.

We also consider Hycean planets with no stellar irradiation, as would be the case for planets on very large orbital separations or for free-floating planets. We term these planets "Cold Hycean" worlds. In this scenario, the only energy source affecting the atmospheric temperature profile is internal heat. Therefore, rather than varying irradiation as in previous sections, we explore the dependence of habitability on T_int. As in Section 3.3, we use the same standard composition and bulk properties for planets A and B described above and nominally do not include hazes.

We find that Cold Hycean planets can be readily conducive to ocean life. For a T_int of ∼10 K, the P–T profile just reaches ∼270 K at 1000 bar, therefore setting the limit of the lowest T_int that allows for habitable conditions. Higher T_int then allow for habitable temperatures at shallower pressures, e.g., T_int = 30 K results in temperatures between ∼300 and 400 K at pressures between ∼100 and 300 bar. These results are true for both planets A and B, as shown in Figure 5. For planets where the HHB lies in the pressure range where T ∼ 300–400 K, a habitable ocean surface is permissible. Where the HHB is at lower pressures, the surface would be frozen but subsurface ocean life could still be possible.

As discussed in Section 3.1, we expect the T_int of Hycean planets to lie between ∼25 and 50 K (Valencia et al. 2013), thus allowing the required conditions for oceanic life on Cold Hycean planets in the far stretches of planetary systems, as well as in the interstellar medium. Our results are also consistent with those of Stevenson (1999), who considered thin H₂-rich atmospheres of rocky planetary embryos in the interstellar medium.

The atmospheric composition of a Hycean planet would depend on its specific formation mechanism and atmospheric processes. Nevertheless, one may expect a general compositional framework for such a planet. Other than H₂/He, it is natural that H₂O will be a prominent constituent in such an atmosphere. As seen in solar system ice giants, CH₄ and NH₃ could also be abundant as primary carriers of C and N, respectively (e.g., Atreya et al. 2018), but they can also be depleted due to disequilibrium processes, e.g., photochemically, in Hycean conditions (e.g., Madhusudhan et al. 2020; Yu et al. 2021). All three molecules (H₂O, CH₄, and NH₃) can be abundant in temperate H₂-rich atmospheres, even assuming solar elemental ratios, and all of them have strong spectral features (Burrows & Sharp 1999; Lodders & Fegley 2002; Madhusudhan & Seager 2011; Moses et al. 2013). We therefore consider H₂O, CH₄, and NH₃ as the dominant molecules in Hycean atmospheres providing the background opacity besides H₂/He, as discussed in Section 3.1, over which signatures from any other trace species, e.g., of biomarkers, are to be detected. We also consider a case where CH₄ and NH₃ are depleted relative to equilibrium values.

We consider five such prominent biomarkers in Hycean atmospheres: DMS, CS₂, CH₃Cl, OCS, and N₂O. As discussed in Section 1, these species have been suggested as potential biomarkers in atmospheres of rocky habitable exoplanets in both terrestrial-like (e.g., Segura et al. 2005; Domagal-Goldman et al. 2011; Catling et al. 2018) and H₂-rich atmospheres (e.g., Seager et al. 2013b, 2016). Seager et al. (2013b) consider a rocky super-Earth of Earthlike composition (M_p = 10 M_⊕, R_p = 1.75 R_⊕) with an H₂-rich atmosphere and estimate the abundances and detectability of these biomarkers. Their estimates suggest that all these species can be present at abundances of ∼1 ppmv, and up to ∼10 ppmv for CH₃Cl, and are potentially detectable in transit spectroscopy with JWST.

Hycean atmospheres may offer even better opportunities for detecting these biomarkers than those of rocky super-earths discussed above. For a 10 M_⊕ planet, the Hycean radius range is ∼2–2.6 R_⊕, compared to the super-Earth radius of 1.75 R_⊕ considered in Seager et al. (2013b). The increased radii and lower gravities lead to larger, more easily detectable spectral signatures for Hycean planets. Second, considering that prominent sources of the above biomarkers are thought to be aquatic microorganisms, we expect them to be even more abundant on Hycean worlds compared to predominantly rocky worlds. Therefore, we adopt representative abundances from Seager et al. (2013b) as nominal values in our analyses below, assuming all five species to be present at 1 ppmv and allowing CH₃Cl abundances up to 10 ppmv, e.g., in Section 4.4.1. Finally, while Seager et al. (2013b) advocate for NH₃ as a plausible biosignature gas for rocky super-Earths with H₂-rich atmospheres, we do not make that assumption for Hycean atmospheres where NH₃ can be naturally occurring as discussed above.

We assess biosignatures of Hycean worlds that could be detectable in transmission spectra. We first investigate general characteristics of such signatures using model transmission spectra for K2–18 b, which is a candidate Hycean world. We then conduct Bayesian atmospheric retrievals of simulated spectra to assess the detectability of the biosignatures in a statistically robust manner. We model the transmission spectra using the AURA forward model (Pinhas et al. 2018). The model computes line-by-line radiative transfer in transmission geometry assuming a plane-parallel atmosphere in hydrostatic equilibrium. The temperature structure and chemical composition are free parameters in the model. The photosphere probed by transmission spectra is typically in the 0.1–100 mbar range (Welbanks & Madhusudhan 2019). As seen in Section 3, the temperature structure in the observable Hycean atmosphere is expected to be nearly isothermal in the 200–400 K range.

We calculate the line-by-line opacities of the key molecules (H₂O, CH₄, NH₃), as well as H₂–H₂ and H₂–He CIA, in the same way as described in Section 3.1. We also consider molecular absorption due to several prominent biomarker gases predicted to be possible in H₂-rich environments as discussed above (e.g., Seager et al. 2013b, 2020). These include DMS, CS₂, CH₃Cl, OCS, and N₂O. The absorption cross sections of CH₃Cl, OCS, and N₂O were derived from the corresponding line lists from the HITRAN database (Gordon et al. 2017), derived for CH₃Cl by Nikitin et al. (2016), and Bray et al. (2011); for OCS by Bouanich et al. (1986), Golebiowski et al. (2014), Müller et al. (2005), Auwera & Fayt (2006), Sung et al. (2009), Toth et al. (2010), and Régalia-Jarlot et al. (2002); and for N₂O by Daumont et al. (2001). For DMS and CS₂, we use the absorption cross sections provided directly by HITRAN (Sharpe et al. 2004; Gordon et al. 2017; Kochanov & Gordon 2019); we assume the same cross sections across all pressures owing to the limited data available. The absorption cross sections for all the species considered in the models are shown in Figure 6, for T = 300 K, P = 0.1 bar.

Zoom In Zoom Out Reset image size

As can be seen from Figure 6, all these biomarkers provide significant opacity in the NIR. Importantly, several of these species provide significant opacity in the opacity windows of the more prominent molecules that may be expected in Hycean atmospheres, such as H₂O, CH₄, and NH₃, and are equally strong. This provides motivation to investigate the detectability of biomarkers in transmission spectroscopy of Hycean atmospheres.

The atmospheric retrievals are conducted using an adaptation of the AURA retrieval code (Pinhas et al. 2018) as pursued in recent studies (e.g., Madhusudhan et al. 2020). We retrieve a total of 10 parameters: 8 corresponding to the volume mixing ratios of H₂O, CH₄, NH₃, and the 5 biomarker gases, 1 for the isotherm temperature, and 1 for the reference pressure at the fixed planet radius. For all the volume mixing ratios, we use priors that are uniform in log space, ranging from 10⁻¹² up to 10^−0.3, at which point the atmosphere can no longer be considered to be H₂-rich. For the isotherm temperature, the prior is uniform from 0 K to T_eq+200 K for the planet under consideration. Lastly, the reference pressure prior we use is log-uniform from 10² to 10⁻⁶ bar, which is the full atmospheric pressure range AURA considers in generating forward models.

We first assess the observable biosignatures of Hycean worlds using the exoplanet K2–18 b as a prototype. K2–18 b is the first mini-Neptune demonstrated to be potentially habitable (Madhusudhan et al. 2020) and hence serves as the archetypal candidate Hycean world. K2–18 b is a transiting exoplanet (Foreman-Mackey et al. 2015; Montet et al. 2015), with a mass of 8.67 ± 1 M_⊕ (Cloutier et al. 2019b), a radius of 2.61 ± 0.08 R_⊕ (Benneke et al. 2019b), and a detection of H₂O in its atmosphere (Benneke et al. 2019b; Tsiaras et al. 2019). We note that the radius has recently been revised to ${2.51}_{-0.17}^{+0.13}$ R_⊕ (Hardegree-Ullman et al. 2020), which is still consistent with the previous value within 1σ. In our atmospheric models for K2–18 b we use here a nominal radius of 2.61 R_⊕, which agrees with both estimates, to be consistent with previous retrieval studies (Madhusudhan et al. 2020).

The internal structure and atmospheric properties of the planet allow for the Hycean conditions described in Section 2. As a canonical model, we adopt representative atmospheric properties of the planet derived by Madhusudhan et al. (2020) to investigate the detectability of biosignatures in the planet's transmission spectrum. In particular, we adopt the H₂O abundance of 10 × solar, corresponding to a mixing ratio of 10⁻², which is close to the median retrieved value for K2–18 b. For CH₄ and NH₃, which were undetected in their study, we nominally assume a chemical equilibrium composition at solar elemental abundances (Asplund et al. 2009), with mixing ratios of 5 × 10⁻⁴ and 10⁻⁴, respectively. For each of the five biomarkers we use a mixing ratio of 1 ppmv, i.e., 10⁻⁶. We assume an isothermal temperature structure at 300 K for the day–night terminator region of the atmosphere probed by transmission spectra, and we assume no clouds in the observed region, consistent with the findings of Madhusudhan et al. (2020).

We find strong contributions from all five potential biomarkers in the NIR region, particularly between 1.5 and 5 μm, as shown in Figure 7. The strongest contributions in this spectral range are seen for DMS, with multiple strong absorption peaks, especially at 3.4 and 4.2 μm, where there are not many other significant peaks. While the expected abundance of DMS is lower compared to that of the prominent molecules (H₂O, CH₄, and NH₃), its strong absorption cross section in this wavelength range makes it readily detectable in transmission spectra. CS₂ and CH₃Cl also have a few comparable peaks in absorption in the 3–5 μm range. We note that most of the significant peaks from CH₃Cl coincide with regions where CH₄ also has large features. OCS and N₂O also have significant contributions to the spectrum, which enables their detectability. Their prominent absorption peaks, however, are over a narrower wavelength range, between 4 and 5 μm. We also note the strong contribution from CIA opacity in the ∼2–3 μm range that provides strong continuum opacity, capable of masking line absorption from some of the molecules considered within that range. Furthermore, the absorption cross sections of the biomarkers used here are somewhat limited to terrestrial conditions. More extensive absorption data in the future for Hycean conditions may refine the detectability estimates in this study.

Zoom In Zoom Out Reset image size

We now assess the robustness with which the biosignature molecules discussed above can be detected in Hycean atmospheres. Considering that most of the NIR spectral features of these molecules are in the 1.5–5 μm range, we consider their detectability with instruments aboard JWST that operate over this spectral range (e.g., Greene et al. 2016; Batalha et al. 2018; Kalirai 2018; Sarkar et al. 2020). Our approach here is to first generate a synthetic transmission spectrum for a planet assuming a given set of atmospheric properties. We then conduct atmospheric retrievals of the synthetic spectrum to assess which of the molecules can be confidently detected in these atmospheres and under what conditions.

For given planetary parameters, we generate a synthetic transmission spectrum in the 0.5–5.5 μm range. The canonical model spectrum assumes the molecular abundances (volume mixing ratios) given in Section 4.3, namely, ${X}_{{{\rm{H}}}_{2}{\rm{O}}}={10}^{-2}$, ${X}_{{\mathrm{CH}}_{4}}=5\times {10}^{-4}$, ${X}_{{\mathrm{NH}}_{3}}={10}^{-4}$, and all five biomarkers at 1 ppmv, i.e., 10⁻⁶ each. The temperature structure is assumed to be isothermal at 300 K, and the atmosphere is assumed to be cloud-free in the observable atmosphere. Beyond this canonical model, we also investigate other conditions in cases discussed below.

We generate synthetic data using the Pandexo software package (Batalha et al. 2017), which allows for simulation of JWST observations. We provide a high-resolution forward model to Pandexo, which then yields the appropriate wavelength bins and corresponding uncertainties for the particular planet under consideration and chosen instrument settings. We then bin a high-resolution forward model to the Pandexo-provided bins, accounting for each instrument's spectral point-spread function and overall transmission function. We lastly introduce noise to the synthetic data by adding an offset to each data point, drawn from a Gaussian distribution with standard deviation equal to the Pandexo uncertainty in that bin.

We simulate observations with NIRISS Order 1 (Doyon et al. 2012) and NIRSpec G395M (Ferruit et al. 2012; Birkmann et al. 2014), achieving a wavelength coverage between 1 and 5.1 μm. We consider a baseline configuration requiring only modest observing time with JWST: one transit with NIRISS and three transits with NIRSpec. For NIRISS we simulate one observed transit using the GR700XD grism, subarray SUBSTRIP96, and the NISRAPID readout mode. For NIRSpec G395M, we simulate three observed transits using the F290LP filter, NRSRAPID readout mode, and the SUB2048 subarray for maximal wavelength coverage. Binned to R = 100, our simulated NIRISS and NIRSpec G395M observations have average uncertainties of ∼40 and ∼30 ppm, respectively, for the case of K2–18 b. Similar uncertainties at lower resolution can be achieved in the NIR (1.1–1.7 μm) with the HST WFC3 spectrograph for super-Earths and mini-Neptunes (e.g., Kreidberg et al. 2014; Benneke et al. 2019b; Guo et al. 2020). We note that the amount of JWST observing time needed for such observations corresponds to a Small or Medium General Observer Proposal, depending on specific system parameters and overheads, while even more precise observations than these are possible by dedicating more JWST observing time.

4.4.1. Case Study: K2–18 b

We first consider the case of the Hycean candidate planet K2–18 b. We explore the detectability of biomarkers under different assumptions for their abundances relative to those of the dominant molecules in the atmosphere. We start with a synthetic model spectrum based on the canonical abundances described above, i.e., the dominant molecules at ${X}_{{{\rm{H}}}_{2}{\rm{O}}}={10}^{-2}$, ${X}_{{\mathrm{CH}}_{4}}=5\times {10}^{-4}$, ${X}_{{\mathrm{NH}}_{3}}={10}^{-4}$, and all five biomarkers at 1 ppmv, i.e., 10⁻⁶ each. We then investigate deviations from this canonical model and its effect on the detectability of the biomarkers. In each case, we create synthetic data based on the assumed model composition as described above and then retrieve it to assess the accuracy and precision with which the biomarkers can be retrieved. The retrieved posterior distributions for three different compositions are shown in Figure 8. We find that for the canonical model the dominant molecules H₂O, CH₄, and NH₃ are retrieved accurately, with the true values lying within the 1σ uncertainties of ∼0.6 dex for H₂O and ∼0.5 dex for CH₄ and NH₃. Additionally, two of the five biomarkers, DMS and N₂O, are also retrieved accurately at their trace values of 1 ppmv with uncertainties of ∼0.5 and ∼0.9 dex, respectively. Two more biomarkers, CS₂ and OCS, also have posterior distributions showing significant peaks near the correct mixing ratios, but with larger uncertainties. However, we do not constrain CH₃Cl at this abundance, instead finding only an upper limit (99% confidence) of ∼10⁻⁵.

Zoom In Zoom Out Reset image size

The nondetection of CH₃Cl at 1 ppmv is due to the fact that its strongest absorption feature, lying between 3 and 3.5 μm, is masked by stronger absorption at the same wavelengths by the more abundant CH₄, as well as equally abundant DMS, besides minor contributions from other species, as seen in Figure 7. Similarly, its absorption peak between 4 and 4.5 μm also overlaps with stronger contributions from other molecules. However, we are able to better constrain CH₃Cl if in the synthetic model we either (a) increase its abundance by 1 dex (to 10 ppmv) or (b) decrease the abundance of CH₄ by 1 dex to 0.1 × solar or 5 × 10⁻⁵. Both these scenarios are plausible in K2–18 b; the lower CH₄ abundance is consistent with its nondetection in previous studies (Benneke et al. 2019b; Tsiaras et al. 2019; Madhusudhan et al. 2020), and the 10 ppmv CH₃Cl abundance is plausible based on the biomass estimates of Seager et al. (2013b), discussed in Section 4.1. While reducing the abundance of CH₄ alone is enough to constrain CH₃Cl, previous atmospheric retrievals of K2–18 b have also resulted in nondetections of NH₃. In subsequent retrievals, we therefore vary the abundances of CH₄ and NH₃ together to maintain the solar C/N ratio and also because both of them can be depleted due to disequilibrium processes. In the case where the abundance of CH₃Cl is increased to 10 ppmv it becomes better constrained, albeit still with a large uncertainty, as shown in Figure 8. Similar results are obtained when the abundances of CH₄ and NH₃ are instead decreased to 0.1 × solar.

The last scenario we consider involves both decreasing the abundances of CH₄ and NH₃ to 0.1 × solar and also increasing the CH₃Cl abundance to 10 ppmv. The posterior distributions of this retrieval are shown in Figures 8 and 9. We obtain a precise and accurate estimate of the CH₃Cl abundance at $\mathrm{log}({X}_{{\mathrm{CH}}_{3}\mathrm{Cl}})=-{5.00}_{-0.55}^{+0.46}$. This brings the CH₃Cl estimate in line with those obtained for the other biomarkers, except CS₂, as shown in Figure 8. The retrieved spectrum and the simulated data for this case are shown in Figure 11.

Zoom In Zoom Out Reset image size

We find that all five biomarkers in this scenario are detectable in K2–18 b with a reasonable amount of JWST time. With our baseline configuration of one transit of K2–18 b with NIRISS and three transits with NIRSpec G395M, we find that DMS and OCS are detected at ∼4σ, while the remaining three biomarkers are detected at ∼2σ–3σ. Even with a total of only two transits, one each with NIRISS and NIRSpec G395M, we still detect DMS at 4σ confidence. This is possible owing to NIRSpec G395M achieving the highest precision in the region where DMS has its strongest absorption peak, as can be seen in Figure 11. We have also considered a case including one transit with NIRISS and five transits with NIRSpec G395M, which is similar to observations that have been approved with these instruments in JWST Cycle 1 programs. For this configuration, we find that DMS is detected at over 6σ and the remaining four biomarkers are all detected at over 3σ. We therefore find that biomarkers are readily detectable in K2–18 b with JWST, although their detectability relies strongly on the abundances of the biomarkers and dominant species present, as well as the quality of observations. We predict that the approved Cycle 1 JWST observations of K2–18 b will be able to detect these biomarkers if present at the quantities considered here.

As seen in Figure 10, we find that both NIRISS and NIRSpec G395M are necessary to obtain tight constraints on the abundances of both the dominant molecules and the trace biomarkers. We find that using only NIRISS data, thereby limiting the wavelength range to ∼1–2.8 μm, only yields constraints on the abundances of the dominant molecules. Conversely, using only NIRSpec G395M observations does not meaningfully constrain the abundances of the dominant molecules, while offering less precise constraints on the abundances of the five biomarkers compared to using both instruments together. Similarly, an underabundance of the biomarkers, below 1 ppmv, or overabundance of the prominent molecules CH₄ and NH₃ can affect the detectability of some biomarkers, particularly the ones with weaker or limited spectral features such as CH₃Cl and OCS. On the other hand, DMS is the most promising of all the biomarkers owing to its multiple strong features across the 1–5 μm range, making it readily detectable even with only two JWST transits, i.e., one each with NIRISS and NIRSpec G395M, as noted above. Furthermore, we find that the 2.9–5.1 μm range probed by NIRSpec G395M is necessary (but not sufficient) to constrain the abundances of all five biomarkers, due to both their multiple absorption bands in this range and the relative lack of strong features of the prominent molecules. To obtain the tightest constraints on biomarker abundances, we find it necessary to combine NIRSpec G395M observations with NIRISS, which will also constrain the abundances of the prominent molecules.

Zoom In Zoom Out Reset image size

4.4.2. Case Studies: TOI-270 d and TOI-732 c

We investigate the potential for biomarker detection in two other Hycean planet candidates: TOI-270 d (Günther et al. 2019) and TOI-732 c (Cloutier et al. 2020; Nowak et al. 2020). TOI-270 d has a radius of 2.01 R_⊕ and a mass of 4.78 M_⊕ (Van Eylen et al. 2021). It orbits its host star, an M3V-type star, at a distance of 0.0722au, giving it an equilibrium temperature of T_eq = 327 K. TOI-732 c has a radius of 2.42 R_⊕ and a mass of 6.29 M_⊕ (Nowak et al. 2020). It orbits its M3.5V-type host at a semimajor axis of 0.0762 au and an eccentricity of 0.12, giving it a T_eq of 288 and 324 K at its apocenter and pericenter, respectively. Table 1 lists the full properties of the two planetary systems. With stellar masses in the range 0.38–0.39 M_⊙ and T_eq values well below ∼400 K, both planets are well within the Hycean HZ (see Table 2). The equilibrium temperatures can be higher for Bond albedos below the 0.5 value assumed here.

For each of these two planets we generate a synthetic transmission spectrum using a nominal isothermal terminator temperature structure, set to 350 K for both TOI-270 d and TOI-732 c for illustration purposes. Following our results for K2–18 b above, we simulate the model atmospheres with the same abundances that yielded good constraints for all five biomarkers, i.e., ${X}_{{{\rm{H}}}_{2}{\rm{O}}}={10}^{-2}$, ${X}_{{\mathrm{CH}}_{4}}=5\times {10}^{-5}$, ${X}_{{\mathrm{NH}}_{3}}={10}^{-5}$, 10 ppmv for CH₃Cl, and 1 ppmv for the other four biomarkers. We use the same instrument configurations as for K2–18 b described at the start of Section 4.4, allocating one transit for NIRISS observations and three transits for NIRSpec G395M. The resulting synthetic data for both planets, as well as the corresponding retrieved spectral fits, are shown in Figure 11.

Zoom In Zoom Out Reset image size

As shown in Figure 12, all five biomarkers are accurately constrained for both TOI-270 d and TOI-732 c, with CS₂ now also being precisely retrieved. For TOI-270 d, the retrieval yields biomarker estimates that are more precise than those for K2–18 b, with uncertainties of ∼0.3 dex for DMS, CS₂, and CH₃Cl and ∼0.5 dex for OCS. N₂O is retrieved with 0.6 and 1 dex upper and lower 1σ uncertainties, respectively. The three dominant molecules are retrieved to within 0.3 dex, the only exception being the lower 1σ uncertainty for NH₃ at 0.7 dex. In the case of TOI-732 c, the biomarker abundance values are again retrieved precisely, with even smaller uncertainties of ∼0.25 dex for DMS, CS₂, and CH₃Cl and ∼0.4 dex for OCS and N₂O. The three dominant molecules are all constrained to ∼0.3 dex or better. This is a consequence of their host stars being brighter than K2–18, leading to a higher spectroscopic precision. Additionally, their higher atmospheric temperatures yield larger scale heights and hence a larger signal-to-noise ratio compared to K2–18 b as seen in the synthetic spectra and corresponding retrieved spectra shown in Figure 11.

Zoom In Zoom Out Reset image size

For both planets, all five biomarkers are retrieved at better precision and detected at greater significance compared to those for K2–18 b discussed above. For the same baseline instrument configuration for both planets (i.e., one transit with NIRISS and three transits with NIRSpec G395M), all five biomarkers are detected with a significance ≳4σ–5σ, with the exception of N₂O in TOI-270 d, which is detected at >2σ. We further find that despite the favorable conditions for such planets, reverting to canonical abundances yields a nondetection for CH₃Cl, as is the case with K2–18 b. However, the remaining four biomarkers are retrieved with precision comparable to or better than that of K2–18 b.

Overall, our results show that the detection of all five biomarkers is possible under these conditions for a range of Hycean planets. Given that such detections are achievable for the Hycean planets shown here, we expect that biomarker detection is also possible for Dark Hycean planets, whose somewhat higher temperatures and, hence, larger scale heights can facilitate even more precise abundance estimates. However, if biomarker abundances are below 1 ppmv or there is a higher abundance of CH₄ and NH₃, we expect the detectability of biomarkers to vary on a case-by-case basis.

Following many previous studies, we have defined the HZ based on the requirement of liquid water at the planetary surface (e.g., Kasting et al. 1993; Kasting & Catling 2003; Selsis et al. 2008; Forget 2013; Kaltenegger 2017; Kopparapu 2018; Meadows & Barnes 2018), with the additional requirement of surface temperatures known to be habitable on Earth (Rothschild & Mancinelli 2001; Merino et al. 2019). However, other physical factors are also involved in determining habitability. One such factor is the role of geochemical cycling in regulating atmospheric composition and surface temperature, e.g., the carbonate–silicate cycle on Earth (e.g., Walker et al. 1981; Kasting et al. 1993; Franck et al. 2000; Lammer et al. 2010). While this has been widely studied in the context of Earth and terrestrial planets, such cycles would evidently be very different for Hycean planets. Future work will be needed to establish how such processes work.

Another significant factor affecting habitability is stellar activity and stellar winds (e.g., Khodachenko et al. 2007; Lammer et al. 2007; Rodríguez-Mozos & Moya 2019). This is especially relevant for M-dwarf planets, as these stars are known to be more active than hotter stars (e.g., Shields et al. 2016). UV flux, coronal mass ejections, and stellar winds can gradually erode planetary atmospheres and potentially damage life existing on the surface (but see, e.g., O'Malley-James & Kaltenegger 2017, 2019). However, more massive planets may be more robust to stellar activity owing to factors such as higher gravity, stronger magnetic moments, and thicker atmospheres (e.g., Lammer et al. 2007; Kopparapu et al. 2014). Planets with thicker atmospheres could also plausibly limit the UV flux reaching their surfaces, thereby protecting any existing life. In the context of stellar activity, Hycean planets orbiting M-dwarf hosts may therefore provide better chances for habitability compared to terrestrial planets in similar conditions.

Habitability also requires the maintenance of liquid surface water for a significant period of time such that life can be initiated and subsequently sustained. In the case of terrestrial-like planets, water loss at the inner edge of the HZ can preclude life by quickly removing the planetary water reservoir, especially around active stars (e.g., Luger & Barnes 2015; Wolf & Toon 2015; Ribas et al. 2016; Bolmont et al. 2017; Kopparapu et al. 2017; Wordsworth et al. 2018). However, for Hycean planets, the planetary water reservoir is very large (over 10% by mass), and water is unlikely to be exhausted by atmospheric escape. This also allows for higher temperatures at the ocean surface, up to 400 K or higher, without the risk of total runaway loss of the ocean. A further consideration for the maintenance of liquid water is orbital dynamics. For example, a highly eccentric or otherwise perturbed orbit may change the irradiation incident on the planet on fairly short timescales and may therefore preclude the stability of liquid surface water (e.g., Dvorak et al. 2010; Kopparapu & Barnes 2010; Bolmont et al. 2016; Palubski et al. 2020).

Some of the challenges underlying the characterization of habitable rocky exoplanets are also common to Hycean planets. First, while mass and radius are imperative to establish whether a certain planet is a Hycean candidate (see, e.g., Figure 1), they are not sufficient to confirm a unique interior composition due to natural compositional degeneracies (e.g., Rogers & Seager 2010b; Madhusudhan et al. 2020). Second, even if a candidate Hycean planet is in the Hycean HZ, it may not necessarily have the right conditions for habitability, e.g., the internal structure and atmospheric properties may be such that the ocean surface pressure and/or temperature is too high. Finally, the detection of H₂O in the atmosphere does not guarantee the presence of an ocean on the planet, as H₂O can be naturally occurring in H₂-rich atmospheres as the prominent oxygen-bearing species. Conversely, the nondetection of H₂O does not preclude the presence of an ocean, since at low atmospheric temperatures H₂O can rain out and not be detectable in the atmosphere. Nevertheless, in all these aspects Hycean candidates offer better prospects for establishing their habitability compared to habitable rocky exoplanets, which are inherently harder to characterize.

Observationally, Hycean planets provide a promising avenue in the search for habitable exoplanets and their biosignatures. Demographics of exoplanetary systems discovered by transit surveys (e.g., Fulton & Petigura 2018; Hardegree-Ullman et al. 2020) show that the known exoplanet radius distribution peaks in the Hycean range between ∼1 and 2.6 R_⊕. Thus, Hycean worlds could potentially be ubiquitous in nature. Hycean planets are also optimal targets for atmospheric spectroscopy of habitable planets using current and future facilities. Habitable rocky exoplanets with heavy molecular atmospheres (e.g., of H₂O, CO₂, N₂, or O₂) are expected to have small scale heights, making them challenging for atmospheric spectroscopy. For example, detection of biomarkers on rocky exoplanets such as TRAPPIST-1 d could require tens of transits with JWST (Barstow & Irwin 2016; Lustig-Yaeger et al. 2019). On the other hand, H₂-rich atmospheres with larger scale heights are more favorable for atmospheric characterization. The potential for biosignature detection in H₂-rich atmospheres of rocky exoplanets has already been suggested (e.g., Seager et al. 2013b). The prospects of such biomarker detections are even more favorable for a Hycean planet, which has not only an H₂-rich atmosphere but also a substantial H₂O ocean underneath, potentially providing a large biosphere. The combination of large radii and large atmospheric scale heights makes Hycean planets optimal targets for atmospheric spectroscopy.

We hope our study provides impetus in expanding the search for habitable planets and biosignatures beyond the conventional boundaries of rocky exoplanets. Such an effort could bring the search for biosignatures within the reach of upcoming facilities in the near future.