UV Surface Environments and Atmospheres of Earth-like Planets Orbiting White Dwarfs

We use EXO-Prime (see e.g., Kaltenegger & Sasselov 2010), a coupled 1D radiative-convective atmosphere code developed for rocky exoplanets. The code is based on iterations of a 1D climate model (Kasting & Ackerman 1986; Pavlov et al. 2000; Haqq-Misra et al. 2008) and a 1D photochemistry model (Pavlov & Kasting 2002; Segura et al. 2005, 2007), which are run to convergence (see details in Segura et al. 2005). EXO-Prime models exoplanet atmospheres and environments depending on the stellar and planetary conditions, including the UV radiation that reaches the surface and the planet's reflection, emission and transmission spectrum. We divide the atmosphere in 100 plane parallel layers for our model up to an altitude of 60 km (or a pressure of 1 mbar) using a stellar zenith angle of 60°.

Visible and near-IR shortwave fluxes are calculated with a two-stream approximation including atmospheric gas scattering (Toon et al. 1989), and longwave fluxes in the IR region are calculated with a rapid radiative transfer model. A reverse-Euler method within the photochemistry code (originally developed by Kasting et al. 1985) contains 220 reactions to solve for 55 chemical species.

First, we scale the incident WD flux at the top of the model planetary atmospheres to the total integrated flux Earth receives from the Sun (S_eff) to model how the WD's irradiance changes the planetary environment compared to Earth. We then bin the high-resolution spectra to the resolution of the wavelength grid of the climate/photochemistry models (both shown in Figure 2). We model planets with surface pressures of 0.3 bar (e.g., eroded atmosphere), 1 bar (Earth analog), and 1.5 bar and 2 bar.

In our planetary models, we keep the planetary outgassing rates constant for H₂, CH₄, CO, N₂O, and CH₃Cl and maintain the mixing ratios of O₂ at 0.21 and CO₂ at 3.55 × 10⁻⁶ to be able to compare the effect of the irradiation on the planetary atmosphere, with a varying N₂ concentration that is used as a fill gas to reach the set surface pressure of the model (following Segura et al. 2003, 2005; Rugheimer et al. 2013, 2015, 2015; Rugheimer & Kaltenegger 2018). Note that by keeping the outgassing rates constant, lower surface-pressure atmosphere models initially have slightly higher mixing ratios of chemicals with constant outgassing ratios than higher surface-pressure models.

WDs are unique stellar environments with very high surface gravities and extremely dense interiors and physical conditions. They have no internal heat source, and thus cool off over time (Figure 1). We use WD spectral energy distribution models (SED) calculated as described in Saumon et al. (2014) (Figure 2) as irradiation for the planetary models (see e.g., Bergeron et al. 1997; Kowalski & Saumon 2006; Kilic et al. 2009a, 2009b; Giammichele et al. 2012; Saumon et al. 2014 for detailed discussion on WD spectra). The WD models assume a pure H atmospheric composition with a surface gravity of log g = 8.0 in creating the models for the average mass of WD in the field (0.6 M_⊙; e.g., Kepler et al. 2016). The WD radius is then recovered by finding the intersection of the standard surface gravity formula with the WD mass–radius–(temperature) relation for C–O core WDs with thick H layers discussed by Parsons et al. (2017, see their Figure 9; also see Benvenuto & Althaus 1999; Fontaine et al. 2001; Parsons et al. 2017) extrapolated to T < 10,000 K. The radius of the WD in our model is 0.0128 ± 0.0001 R_⊙ for surface temperatures of 6000–4000 K. WD spectra are similar to black bodies with only Balmer absorption lines for surface temperatures greater than 5000 K, where hydrogen becomes neutral as shown in Figure 2. We use models from Bergeron et al. (2001) for the temperature evolution of the WD (see Figure 1).

Some atmospheric species exhibit noticeable features in our planet's spectrum as a result directly or indirectly from biological activity. The main ones are oxygen (O₂), ozone (O₃), methane (CH₄), nitrous oxide (N₂O), and methyl chloride (CH₃Cl) (see e.g., Demarais et al. 2012; Kaltenegger 2017). We summarize the most important reactions that influence these species in Earth's atmosphere here. Many reactions in Earth's atmosphere are driven by the Sun's UV flux. Ozone and O₂ are created with UV photons through the Chapman reactions (Chapman 1930),

$$\begin{eqnarray}&&{{\rm{O}}}_{2}+{\rm{h}}\nu \to {\rm{O}}+{\rm{O}}(\lambda \lt 240\,\,\mathrm{nm}),\\ &&{\rm{O}}+{{\rm{O}}}_{2}+M\to {{\rm{O}}}_{3}+M,\\ &&{{\rm{O}}}_{3}+{\rm{h}}\nu \to {{\rm{O}}}_{2}+{\rm{O}}\ (\lambda \lt 320\,\,\mathrm{nm}),\\ &&{{\rm{O}}}_{3}+{\rm{O}}\to 2{{\rm{O}}}_{2},\end{eqnarray} \tag{ 1 }$$

where M is a background molecule such as N₂. These reactions are primarily responsible for ozone production on present-day Earth. A higher UV flux additionally increases the primary source reactions of tropospheric hydroxyl (OH) for 300 < λ < 320 nm in the troposphere,

$$\begin{eqnarray}{{\rm{O}}}_{3}+{\rm{h}}\nu & \to & {\rm{O}}{(}^{1}{{\rm{D)}}{\rm{+}}{\rm{O}}}_{2},\\ {\rm{O}}{(}^{1}{{\rm{D)}}{\rm{+}}{\rm{H}}}_{2}{\rm{O}} & \to & {\rm{OH}}\,{\rm{+}}\,{\rm{OH}},\end{eqnarray} \tag{ 2 }$$

reducing O₃ and H₂O. Increased OH is the primary sink for H₂, CH₄, CH3Cl, and CO abundances.

Methane (CH₄) is a reducing gas that has a lifetime of 10–12 years in present-day Earth's atmosphere (Houghton et al. 1994) due to reactions with oxidizing species. It has both natural (termites, wetlands) and anthropogenic sources (rice agriculture, natural gas). It is oxidized via

$$\begin{eqnarray}&&{\mathrm{CH}}_{4}+2{{\rm{O}}}_{2}\to {\mathrm{CO}}_{2}+2{{\rm{H}}}_{2}{\rm{O}},\end{eqnarray} \tag{ 3 }$$

creating H₂O and H₂ via photolysis,

$$\begin{eqnarray}&&{\mathrm{CH}}_{4}+{\rm{h}}\nu \to {\mathrm{CH}}_{2}+{{\rm{H}}}_{2}.\end{eqnarray} \tag{ 4 }$$

Its main sink is due to the reaction,

$$\begin{eqnarray}&&{\rm{OH}}+{{\rm{CH}}}_{4}\ \to \ {{\rm{CH}}}_{3}+{{\rm{H}}}_{2}{\rm{O}},\end{eqnarray} \tag{ 5 }$$

in the troposphere, and photolysis in the stratosphere. This reaction also creates H₂O in the stratosphere, above where it is shielded by the ozone layer.

On Earth, both nitrous oxide (N₂O) and methyl chloride (CH₃Cl) are primarily produced by life, and are depleted by higher amounts of UV. N₂O is a greenhouse gas that is extremely effective when trapping heat. It is produced naturally in soil through nitrification and denitrification, and its anthropogenic source is from agriculture. Photolysis of N₂O occurs for λ < 220 nm, and is its main sink on present-day Earth. Increased O₃, e.g., due to UV irradition, is also a sink of N₂O,

$$\begin{eqnarray}&&{{\rm{N}}}_{2}{\rm{O}}+{\rm{O}}{(}^{1}{\rm{D}})\to 2\mathrm{NO},\end{eqnarray} \tag{ 6 }$$

creating NO. It depletes ozone via

$$\begin{eqnarray}&&\mathrm{NO}+{{\rm{O}}}_{3}\to {\mathrm{NO}}_{2}+{{\rm{O}}}_{2}.\end{eqnarray} \tag{ 7 }$$

On Earth, CH₃Cl is naturally produced in oceans via light interacting with sea foam chlorine and biomass and in small amounts by phytoplankton. CH₃Cl reacts with OH creating Cl, a component of chlorofluorocarbons which damage the ozone layer. It is converted into chlorine via the reactions

$$\begin{eqnarray}{\mathrm{CH}}_{3}\mathrm{Cl}+\mathrm{OH} & \to & \mathrm{Cl}+{{\rm{H}}}_{2}{\rm{O}},\\ \mathrm{CHCl}+{\rm{h}}\nu & \to & \mathrm{CH}+\mathrm{Cl},\\ {\mathrm{CH}}_{3}\mathrm{Cl}+\mathrm{Cl} & \to & {\rm{HCl}}\,{\rm{+}}\,{\rm{Cl}}.\end{eqnarray} \tag{ 8 }$$

During the cooling process of a WD, its surface temperature, as well as its overall luminosity, decreases. This, in turn, influences the orbital distance of its HZ. The HZ is the circular region around one or multiple stars in which standing bodies of liquid water could exist on a rocky planet's surface (e.g., Kasting et al. 1993; Kaltenegger & Haghighipour 2013; Haghighipour & Kaltenegger 2013; Kopparapu et al. 2013, 2014; Ramirez & Kaltenegger 2017) and facilitate the detection of possible atmospheric biosignatures (see e.g., Kaltenegger 2017). The classical, conservative N₂–CO₂–H₂O HZ is defined by the greenhouse effect of two gases: CO₂ and H₂O vapor. The inner edge corresponds to the distance where the mean surface temperatures exceed the critical point of water (∼647 K, 220 bar), triggering a runaway greenhouse that leads to rapid water loss to space on very short timescales (see Kasting et al. 1993 for details). Toward the outer edge of the classical HZ, weathering rates decrease, allowing atmospheric CO₂ concentrations to increase as stellar insolation decreases. At the outer edge, condensation and scattering by CO₂ outstrips its greenhouse capacity, the so-called maximum greenhouse limit of CO₂.

The cooling of a WD translates into an inward shift of the orbital distances of the WD HZ (Figure 3(a)). In addition to the decrease in overall irradiance (S_eff) as the WD cools, some of the change in the HZ orbital distance is also caused by the shift of the peak wavelength of emission of the WD SED to redder wavelengths, which heat the surface of the planet more efficiently than bluer light (e.g., Kasting et al. 1993). A 0.6 M_⊙WD spends about 7 Gyr cooling from 6000 to 4000 K, providing a phase during which its luminosity does not rapidly change, thus it could provide temperate conditions for an orbiting planet. The size of the WD HZ is shown in Figure 3(a), as well as the corresponding irradiance of a planet, normalized to the value for Earth (S_eff) shown in Figure 3(b). Because of the small size of a WD compared to the Sun, the WD HZ is a factor of ∼100 to ∼1000 times closer to the WD than Earth is to the Sun.

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An alternative HZ limit that is not based on atmospheric models (like the classical HZ), but rather on empirical observations of our solar system, is also shown in Figure 3 for comparison. The inner edge of the empirical HZ is defined by the stellar flux received by Venus when we can exclude the possibility that it had standing water on the surface (about 1 Gyr ago), equivalent to a stellar flux of S_eff = 1.77, corresponding to a distance of 0.75 au for Earth's current Solar flux (Kasting et al. 1993). The "early Mars" limit is based on observations suggesting that the Martian surface may have supported standing bodies of water  ∼3.8 Gyr ago, when the Sun was only 75% as bright as today. For our solar system, S_eff = 0.32 for this limit, corresponding to a distance of ∼1.77 au (e.g., Kasting et al. 1993).

We first explore the range of conditions for Earth-like planets orbiting WDs of different temperatures seen at one point in time (see Sections 3.2 and 3.3). Then we model two case studies, A and B, as shown in Figure 3, which explore the environment of a planet in the HZ of a WD as it cools (see Section 3.4).

The lack of chromospheric activity for a WD at different stages in its evolution causes photochemical differences in the atmospheres of planets orbiting it compared with Earth. We modeled planets with different surface pressures, which receive an equivalent total irradiance as Earth from the Sun (S_eff) from a WD at three different stages in its evolution: for WD surface temperatures of 6000, 5000, and 4000 K. We model planets with surface pressures ranging from 2 to 0.3 bar. Table 1 summarizes the model planet surface temperature and integrated overall ozone column depth (ozone column depth) for the different planetary models, as well as our Earth model for comparison. Figure 4 shows the changes in temperature as well as the mixing ratio for O₃, CH₄, H₂O, CH₃Cl, and N₂O for the different models, compared with Earth.

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Figure 4 shows that in the model atmospheres, H₂O photolysis increases with higher UV levels in the upper atmosphere where H₂O is not shielded from incoming photons below the ozone layer. N₂O is depleted by photolysis, with a decreasing mixing ratio toward the top of the atmosphere, but remains well mixed beneath the ozone layer, where it is shielded. All higher surface-pressure models show increased amounts of CH₄, N₂O, and CH₃Cl in the upper atmosphere. Atmospheric H₂O increases with higher surface temperatures.

The WD cooling process provides a changing luminosity, as well as UV environment at a set orbital distance, as seen in Figure 1. The decrease in UV incident flux leads to an overall decrease in the ozone level. Compared with present-day Earth's integrated overall ozone column depth, a higher surface-pressure atmosphere receiving similar UV irradiance has a higher ozone column depth, as seen in the values for our planet models with surface pressures above 1 bar orbiting a WD with a surface temperature of 6000 K. Table 1 shows the absolute values for our models as well as present-day Earth's.

3.2.1. WD Photochemistry: Earth-analog: 1 bar Surface-pressure Models

3.2.2. WD Photochemistry Eroded Atmospheres: 0.3 bar Surface-pressure Models

3.2.3. WD Photochemistry: Higher Surface-pressure Planets: 1.5 and 2.0 bar Surface-pressure Models

The WD cooling process provides a changing luminosity, as well as UV environment at a set orbital distance, as seen in Figure 2. The UV surface environment for our planetary models from eroded atmospheres to dense atmospheres with increased surface pressure is shown in Figure 5, with integrated fluxes for UVA (315–400 nm), UVB (280–315 nm), and UVC (121.6–280 nm) are shown in Table 2, with comparisons with the Earth–Sun system's integrated fluxes in Table 3. Note that this model does not take scattering or clouds into account, and thus overestimates the amount of UV that reaches the surface. However, the comparison between the values and models for the UV environment on present-day Earth gives a clearer picture of the level of UV radiation that reaches the ground, compared with our own planet. High energetic UV is capable of causing harm to biological molecules, like DNA (e.g., Voet et al. 1963; Diffey 1991; Matsunaga et al. 1991; Tevini 1994; Cockell 1998; Kerwin & Remmele 2007). Present-day Earth surface life is protected by the ozone layer, which shields the surface from the most biologically dangerous radiation (UVC).

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3.3.1. Surface UV Environments: Earth 1 bar Surface-pressure Models

3.3.2. WD Surface UV Environments: Earth-analog: 1 bar Surface-pressure Models

3.3.3. WD Surface UV Environments: Eroded Atmospheres: 0.3 bar Surface-pressure Models

3.3.4. WD Surface UV Environments: Higher Surface-pressure Planets: 1.5 bar and 2 bar Surface-pressure Models

We model two case studies, A and B, as shown in Figure 3, which explore the environment of a planet with a 1 bar surface pressure (i.e., an Earth analog) in the HZ of a WD during its evolution. Case A shows the maximum time a planet can stay in the HZ of the WD, as the WD cools from 6000 to 4000 K. This amounts to ∼6 Gyr for the classical (conservative) HZ and ∼8.5 Gyr for the empirical HZ. Case B focuses on a planet that initially receives the same irradiance as Earth around a WD with a surface temperature of 5000 K. As the WD cools from 6000 to 4000 K the planet spends ∼4 Gyr in the conservative HZ and ∼7 Gyr in the empirical HZ. Model parameters and results are shown in Tables 4 and 5, with comparisons with Earth in Table 6 for both cases. UV environments are shown in Figure 6 for Case A and Figure 7 for Case B, and photochemistry is shown in Figure 8.

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Such a planet could have orbited in the HZ of a cool WD for longer than the Earth has existed. Single-celled life likely emerged on Earth less than 1 Gyr after its formation, with multicellular life following 2.7 Gyr later.

3.4.1. Case A

3.4.2. Case B

The mechanisms required for a WD planetary system to form as secondary generation objects from a disk or to survive post-main-sequence evolution are not well understood. During the post-main-sequence evolution of the host into a WD, inner rocky planets (within 1–2 au) would likely be destroyed (e.g., Kunitomo et al. 2011; Villaver et al. 2012; Mustill & Villaver 2012; Villaver et al. 2014), while stellar mass loss would cause semimajor axis expansion for outer planets (e.g., Ramirez & Kaltenegger 2016; Veras 2016). Exomoons of outer planets could potentially migrate inward (Ramirez & Kaltenegger 2016; Veras 2016), although the estimated occurrence rate would not explain the rate of polluted WDs (Van Eylen et al. 2017; van Sluijs & Van Eylen 2017). Second-generation planets could even form from fall-back of debris initially expelled during the post-main-sequence evolution of the host star (Veras 2016). An interesting system is WD1145+017, a WD orbited by a rocky minor planet undergoing tidal disintegration at the system's Roche limit (Vanderburg et al. 2015).

With no stellar mass loss during the WD phase (and assuming rapid tidal circularization of its orbit), a planet should remain at the same orbital distance during a WD's evolution. Due to the extreme change in luminosity early in a WD's evolution (Figure 1), a temperate planet around a cool WD would have thus experienced an extremely high luminosity and corresponding surface temperature early in its history. This would initiate a runaway greenhouse process and extreme water loss on such planets early in their history. Similarly, for planets orbiting pre-main-sequence M-type stars, which also are more luminous initially and should be able to initiate a runaway greenhouse phase and water loss on a temperate planet that can be found in the main-sequence HZ later on (see Ramirez & Kaltenegger 2014; Barnes et al. 2015), there may be methods of late water delivery occurring in a WD system after to the WD has cooled to a surface temperature that maintains a slower changing luminosity (e.g., Jura & Xu 2010; Farihi et al. 2013; Malamud & Perets 2016, 2017a, 2017b).

Any Earth-like planet that is orbiting too close to the WD would remain in a runaway greenhouse stage for a certain time until it entered the WD HZ. Whether such planets would have lost all their water at that point would depend strongly on the initial water reservoir, and whether it can be replenished. Thus, whether a WD planet can host water and an Earth-like atmosphere, is an open question and will depend on its evolution as well as when the WD planet is formed, from what materials it is made of and whether the possibility of a continuous water delivery exists in WD planetary systems.

A planet orbiting a WD will receive decreasing overall energy from its host during the WD's cooling process. Its evolution is very different from that of a planet orbiting a main-sequence star, whose luminosity increases with time, pushing the HZ to wider separations. For a planet around a main-sequence star, the increase in greenhouse gases at the inner edge of the HZ coupled with the increasing luminosity of the host star limit the time it can remain habitable. If a cycle similar to the carbonate-silicate cycle could also operate on WD planets, planets on the inner edge of a WD could build up substantial greenhouse gas amounts in their atmospheres as well; however, due to the decreasing luminosity of their WD host, such buildup of greenhouse gases could help to maintain warm surface temperature as the WD flux decreases, possibly extending the length of time life could survive on WD planets.