High-resolution Spectra and Biosignatures of Earth-like Planets Transiting White Dwarfs

Newly formed WDs are extremely hot (up to 100,000 K), however they gradually cool over time due to a lack of an internal heat source. An average WD has cooled to 6000 K after ∼2 Gyr, but then takes an additional ∼8 Gyr to reach 4000 K (Bergeron et al. 2001), providing planets nearly twice Earth's lifetime in the continuous WD HZ (as discussed in detail in Kozakis et al. 2018). To explore WD planet evolution throughout their host's cooling, we model the photochemistry and climates of such planets using WD spectral models described in Saumon et al. (2014) for WD hosts at 6000, 5000, and 4000 K. The models assume pure hydrogen atmospheres for the average WD mass of 0.6 M${}_{\odot }$ (Kepler et al. 2016). These WD spectra only show hydrogen lines above 5000 K, and are essentially blackbodies under 5000 K, at which point hydrogen becomes neutral (ibid).

To model planetary atmospheres and resulting spectra we use Exo-Prime (see, e.g., Kaltenegger & Sasselov 2010), which couples a 1D climate code (based on Kasting & Ackerman 1986; Pavlov et al. 2000; Haqq-Misra et al. 2008), a 1D photochemistry code (based on Pavlov & Kasting 2002; Segura et al. 2005, 2007), and a radiative transfer code (based on Traub & Stier 1976; Kaltenegger & Traub 2009). This code was designed for rocky planets and models temperature, chemical profiles, UV surface fluxes, and emergent and transmission spectra. Figure 1 and Table 1 summarize the model parameters, temperature, and chemical mixing ratios of the WD planet models described in detail in Kozakis et al. (2018).

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Using WD irradiation spectra (described above) as incoming irradiation, we divide the atmosphere into 100 parallel layers up to a pressure of 1 mbar. To model planets at the Earth-equivalent distance we scaled the integrated flux of the WD input stellar spectrum to the solar constant. After the models are run, we factor in limitations in the atmospheric depths we can probe due to refraction, which changes based on the geometry of the system. Outgoing light rays must be parallel to reach a distant observer, thus rays that are bent strongly in dense, deep regions of a planetary atmosphere will not contribute to the observed signal. Due to this effect, an Earth-analog planet's atmosphere at 1 au orbiting a Sun-sized star can only be probed down to about 12.7 km above the planetary surface (e.g., Bétrémieux & Kaltenegger 2014; Macdonald & Cowan 2019), while for a planet around a WD, the atmosphere of a planet receiving Earth-analog irradiation can be observed down to 6.5 km above the surface (Macdonald & Cowan 2019). Therefore, we cut our spectra off at the effective height equivalent to the system's lowest observable altitude.

All spectra are calculated at high-resolution 0.01 cm⁻¹ covering wavelengths from 0.4 to 20 μm and are publicly available online.¹ All transmission spectra are plotted at a resolution of λ/Δλ = 700 in the figures for clarity.

As a WD cools, its UV flux steadily decreases, causing significant changes in our model planets' atmospheric photochemistry, which is highly sensitive to the amount of incoming UV radiation (see Figure 1; as discussed in detail in Kozakis et al. 2018 and shortly summarized here). Ozone (O₃) production requires high-energy UV photons with λ < 240 nm, causing production rates to decrease for planets orbiting cooler WDs with less incident UV, and lowering the atmosphere's ability to shield the surface from UV radiation. Note that shortward of about 200 nm, absorption by atmospheric CO₂ filters out biologically harmful UV flux (see, e.g., discussion in Kozakis et al. 2018; O'Malley-James & Kaltenegger 2019).

The decrease of ozone leads to a decrease of its byproduct hydroxyl (OH), which is one of the main sinks for methane (CH₄). Methane additionally undergoes significant depletion during photolysis in high-UV environments. Cooler WDs also emit a larger percentage of their light at longer wavelengths, resulting in more efficient planetary surface heating and higher planetary surface temperatures for cooler hosts. Thus, with the evolution and cooling of the WD host, atmospheres of Earth-like planets show less ozone, more methane, higher surface temperatures, and decreasing temperature inversion in the planetary model atmospheres for similar overall incident flux from cooler WD hosts. Details of the model parameters are shown in Table 1, and temperature and chemical profiles are shown in Figure 1 for both (i) planets orbiting at the Earth-equivalent distance, and (ii) a planet on the orbit that allows the maximum time in the HZ during WD cooling.

Figure 2 shows our transmission spectra calculated using these atmospheric models from Kozakis et al. (2018), with zoomed-in biologically relevant features shown in Figure 3. A unique difference between transmission spectra of WDs versus main-sequence stars is the large difference in (R_p/R_s)², where R_p is the planet's effective radius, and R_s is the radius of the stellar host. This quantity determines the depth of the transit, with larger (R_p/R_s)² values creating a larger signal. If we were to consider an Earth-sized planet around a Sun-sized star (R_s = 1 R_⊙) versus a WD (R_s = 0.00128 R_⊙), the corresponding (R_p/R_s)² values for the planet without considering any atmospheric absorption would be 8.4 × 10⁻⁵ and 5.1 × 10⁻¹, respectively. With similar effective atmospheric heights for both cases, the contrast ratio is 4 orders of magnitudes larger for such planets orbiting WDs. In Figure 2 the Earth–Sun transmission spectra were multiplied by 1.65 × 10⁴ to show on the same contrast ratio scale as the WD planet model spectra. The transmission spectra in Figure 2 are shown at a resolution of λ/Δλ = 700 for clarity.

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H₂O: although the higher surface temperatures for the cooler WD hosts result in increased water abundance in the upper atmosphere than for hotter WD hosts, the spectral features are dominated by the lower atmosphere, thus water features are stronger for planet models orbiting hotter WDs, because larger amounts of ozone protect the water from depletion via photolysis (see Figure 1). The strongest H₂O transmission spectra absorption features can be seen in Figure 2 at 0.9, 1.4, 1.9, 5, and 20 μm.

O₂: the strongest O₂ features in the transmission spectra models in the modeled wavelength range from 0.4 to 20 μm are at 0.76 μm (see Figure 3 for a detailed view). All model atmospheres assume a O₂ mixing ratios of 0.21, leading to similar strength of the oxygen absorption line. The differences are due to overlapping features.

O₃: the two strongest O₃ spectral features in our transmission spectra models are at 0.6 and 9.6 μm (seen in Figure 3). The spectral features increase for hotter WD hosts due to higher production rates of ozone.

CH₄: the strongest CH₄ absorption features in transmission are at 1.7 and 7.6 μm (seen in Figure 3). CH₄ absorption features are stronger in the atmosphere for the coolest WD case, where its concentration increases because of the lower-UV environment causing less depletion via photolysis as well as fewer reactions with OH, a byproduct of ozone, which is also reduced in the atmosphere for cool WDs.

CO₂: the strongest CO₂ absorption features in transmission are at 2.0, 2.7, and 15 μm. CO₂ is set to a fixed mixing ratio of modern-Earth concentration for all models, and the absorption features show comparable strength for all model planets.

N₂O: the strongest N₂O absorption features in transmission are at 4.4, 8, and 17 μm (see Figure 3 for details on the 17 μm feature). N₂O is depleted similarly to CH₄ around hotter WD hosts due to increased photolysis and reactions via OH.

The most prominent spectral features of potential biosignatures in the visible to NIR in transmission are O₃ at 0.6 μm, CH₄ at 1.7 μm, and O₂ at 0.76 μm, and in the IR O₃ at 9.6 μm, CH₄ at 7.6 μm, and N₂O at 17 μm. These spectral features are shown in detail in Figure 3 (top: visible to NIR 0.4–3 μm, bottom: IR 3–20 μm) for planets orbiting at the Earth-equivalent distance.

An average WD takes about ∼8 Gyr to cool from 6000 to 4000 K (Bergeron et al. 2001), providing a stable, continuous WD HZ during that time (discussed in detail in Kozakis et al. 2018). A planet orbiting at a semimajor axis 3.9 times the Roche limit from its WD host would spend ∼6 Gyr in the conservative WD HZ, and ∼8.5 Gyr in the empirical WD HZ (ibid) using empirical HZ limits based on early Mars and recent Venus irradiation (Kasting et al. 1993). Such a planet would initially (evolution stage 1) receive 134% of modern Earth's flux from its 6000 K WD host, which reduces to 64% for a WD that cooled to 5000 K (evolution stage 2), and 26% of modern Earth's flux when the WD cools to 4000 K (evolution stage 3). This change in irradiation is similar to a planet at an orbital distance between Venus and modern Earth, to a Mars orbit in our solar system.

During this WD cooling process the amount of incident UV flux upon the planet steadily decreases, changing the planet's atmospheric chemistry as well as its UV surface environment. Details of the model parameters from Kozakis et al. (2018) are shown in Table 1, and temperature and mixing ratio profiles are shown in the bottom row of Figure 1. We summarize the results here to link them to the spectral features shown in Figure 2, with specific biologically relevant features shown in Figure 4.

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At the first stage in the modeled evolution of such a WD planet, for a 6000 K WD host such a planet receives high-UV flux, causing large ozone production as well as high rates of photolysis in the model atmospheres. O₃, CH₄, and N₂O are significantly depleted via photolysis. The high total incident flux causes high surface temperatures and thus a high amount of water vapor throughout the atmosphere.

At the second stage of the modeled evolution, for a 5000 K WD, with a decreasing incident UV and overall flux the planet shows a substantial ozone layer because of reduced O₃ depletion via photolysis. The concentration of CH₄ and N₂O also increases compared to the first stage because of reduced depletion via photolysis.

At the third stage, for a 4000 K WD host, the reduced incident flux causes cold surface temperatures and very low photolysis rates. Only a small amount of ozone is produced in our models and there is very little depletion via photolysis for all chemical species. Due to the low surface temperature, water concentration is also lower. Note that we did not consider in our models that a similar geological cycle to Earths carbonate–silicate cycle could increase the CO₂ concentration in the atmosphere of such colder planets, maintaining warmer surface temperatures than shown in our models (see Kozakis et al. 2018).  

Most notable in Figure 2 are the differences in H₂O absorption, caused by the decrease of H₂O for a cooling WD host. High ozone production rates in the first evolution stage for the 6000 K WD produce stronger ozone features in evolution stage 1. Methane shows stronger absorption features for the later evolution stages 2 and 3, the two cooler WD cases, where photolysis rates are low.

The most prominent spectral features of potential biosignatures in the visible to NIR in transmission are O₃ at 0.6 μm, CH₄ at 1.7 μm, and O₂ at 0.76 μm and in the IR O₃ at 9.6 μm, CH₄ at 7.6 μm, and N₂O at 17 μm. These spectral features are shown in detail in Figure 4 (top: visible to NIR 0.4 to 3 μm, bottom: IR 3 to 20 μm) for the planetary evolution models for a cooling WD host.