Estimates of Fractional Habitability for Proxima Centauri B Using a 3D GCM

Uppsala University

Degree Project C in Physics

Astronomy

Estimates of Fractional Habitability for Proxima Centauri b using a 3D GCM

Author: Supervisor/subject reviewer: Viktor Sparrman Michael Way, Nikolai Piskunov

July 4, 2020

Abstract Exoplanet discovery has grown more quickly in recent years. However, the nature of their discovery leaves many unanswered in questions regarding exoplanetary habitability. Proxima Centauri b, an exoplanet which orbits the Sun’s closest stellar neighbour, Proxima Centauri, was recently discovered with a subzero equilibrium temperature. Although not considered habitable based on the classical definition of the liquid water range, there may be fractions of Proxima Centauri b which are habitable. A prior study simulated the climate conditions of Proxima Centauri b until equilibrium was reached, using a variety of initial conditions. In this project, various metrics for calculating the fractional habitability of Proxima Centauri b are presented and applied to the results of the prior study’s simulations. Colormaps are used to show the ice and temperature distributions that produce the calculated values of fractional habitability. The fractional habitabilities calculated show that while the value is both case and metric dependent, for the vast majority of all cases and metrics the value is nonzero implying that Proxima Centauri b is likely to have habitable regions. Sammanfattning Upptäckandet av exoplaneter har ökat i takt över de senaste åren. Samtidigt, på grund av sättet som de upptäcks finns många obesvarade frågor angående planeternas beboelighet. Proxima Centauri b är en exoplanet som kretsar kring solens närmsta granne, Proxima Centauri. Exoplaneten upptäcktes nyligen med en jämviktstemperatur under 0°C. Trots att exoplaneten inte anses beboelig enligt klassisk definition kan det finnas delar av Proxima Centauri b som är beboeliga. En tidigare studie simulerade klimatförhållandena av Proxima Centarui b till jämvikt nåddes, med varierade begynnelsetillstånd. I detta projekt beräknas andelen av Proxima Centauri b som är beboelig genom flera olika mått för "fractional habitability". Måtten jämförs med den tidigare studien och dess simuleringar. Grafiskt åsikdligörs resultaten via färgkartor över planeten för istjocklek och yttemperatur. De beräknade värdena på Proxima Centauri b’s "fractional habitability" påvisar beroende på mått och begynnelsetillstånd. Däremot, för en majoritet av både fall och mått är värdet nollskilt vilket antyder att Proxima Centauri b är delvist beboelig. Contents

1 Introduction 1

2 Background 1 2.1 Discovery and the method of radial velocity...... 1 2.2 ROCKE-3D modelling...... 2 2.3 Fractional habitability...... 2 2.4 Sea Ice...... 3

3 Methods 3 3.1 Method of Del Genio et al., (2019)...... 3 3.2 Project method...... 4 3.2.1 Surface Temperature Metric of Fractional Habitability...... 4 3.2.2 Lack of Sea Ice Metric of Fractional Habitability...... 4 3.2.3 Oceanic Volumetric Fractional Habitability...... 5

4 Results 6

5 Discussion 12

6 Outlook 13

7 Conclusions 13

8 References 14

9 Appendix 15 1 Introduction

In less than three decades the number of conﬁrmed exoplanets discovered has gone from zero to roughly 4000 as shown by the NASA Exoplanet Archive[1]. Although the number of known exoplanets has increased dra- matically exoplanet characteristics remain relatively unknown. In contrast to stars, exoplanets are generally non-luminous in visible wavelengths of light. As such, they have rarely been detected visually. Exoplanet discoveries are therefore typically indirect, being discovered through observations of the exoplanet’s parent star. The majority of exoplanet discoveries are through either transits or analysing changes in the radial velocity of the star around which the exoplanet is orbiting[1]. Unlike the solar transits of Mercury and Venus where the allowable resolution allows telescopic resolution of their disks, exoplanetary transits are observed through light curve variations of the parent star. Both transits and the radial velocity method cause a discovery bias towards large exoplanets relative to the parent star. Out of the current 937 planets with determined mass only 37 of them have masses less than three times that of Earth’s mass[1]. Additionally, exoplanets with small orbits and an orbital plane which intersects the observer are more easily discovered.

Knowledge of an exoplanet is limited by the nature of its discovery. For example, an exoplanet discovered through the radial velocity method has its stellar distance determined through the orbital period and star mass, but requires the orbital inclination to determine the exoplanet’s mass.

The question of exoplanetary habitability is of importance both in ﬁnding candidates for planetary coloni- sation and in the search of extraterrestrial life. With nothing known about the climate conditions of an exoplanet, the question of habitability may seem odd. However, with the mass and stellar distance alongside properties of the parent star, one can construct models for simulating these conditions.

An exoplanet known as Proxima Centauri b has been modelled with a General Circulation Model (GCM) for 18 cases with varying parameters (Del Genio et al., 2019). This project aims to create a code which reads the two-dimensional variables surface temperature and ice thickness for each case to construct measures of the fractional habitability of Proxima Centauri b. Additionally, we aim to explain case dependent diﬀerences in fractional habitability using the parameters and resulting diﬀerences in other variables.

2 Background 2.1 Discovery and the method of radial velocity Earth’s closest star, beside the Sun, is Proxima Centauri at a distance of 4.24 light-years. Therefore it is well-studied. In 2016, the exoplanet Proxima Centauri b was discovered through the method of radial velocity. By observing the light curves of Proxima Centauri peaks in radial velocity were found an average of 11.2 days apart (Anglada-Escudé et al., 2016). By knowing the orbital period one can apply Newton’s version of Kepler’s third law of planetary motion which states: " A3 = star %2 (1) 4c2 where A is the stellar distance, is the gravitational constant, "star is the stellar mass and % is the orbital period. Through the equation above the stellar distance A is obtained. For Proxima Centauri b, Anglada- Escudé et al., (2016) found the semi-major axis to be approximately 0.05 AU.

Next, by considering the center of mass reference frame and rearranging the conservation of momentum, one ﬁnds an expression for the mass of the exoplanet.

"star+star "ex = (2) +ex To use this equation the speed of the exoplanet must be determined. By using Newton’s law of gravitation and the expression for centripetal acceleration, the following equation is derived when solving for the exoplanet’s speed. p +ex = "star/A (3) Substituting A for the expression derived in equation1 yields: 2c" 1/3 + = (4) ex %

1 Before equation2 can be written only in terms of known quantities the velocity of the star must be determined from the observed Doppler amplitude, .

+ = (5) star sin 8 Here the angle 8 denotes the exoplanet’s orbital inclination deﬁned perpendicularly such that an orbit which permits observable transits would have an inclination angle of 90°. In this case, the orbital plane is said to be seen "edge on".

Combining equations2,4 and5, we ﬁnd the following expression.

% 1/3 " sin 8 = " (6) ex star 2c"

On the left hand side, the product represents the minimum mass of the exoplanet, which is the true mass if the orbital plane is seen edge on. This can be used as a bounded estimate of the true mass of the exoplanet. Anglada-Escudé et al., (2016) found the minimum mass of Proxima Centauri b to be approximately 1.3 "⊕. For this mass Anglada-Escudé et al., (2016) give three formation theories where two of them would lead to a planet with more volatiles. These are migration of an outer planet or migration of planetary embryos (Anglada-Escudé et al., 2016).

While Proxima Centauri b has a very small orbital radius compared to Earth, the lower luminosity of Proxima Centauri at 0.15% of that of the Sun compensates causing an incident stellar ﬂux approximately 65% of that of Earth’s (Anglada-Escudé et al., 2016). Such values leads Anglada-Escudé et al., (2016) to posit that the exoplanet might have liquid water on its surface.

2.2 ROCKE-3D modelling ROCKE-3D is a contemporary GCM developed at the NASA Goddard Institute for Space Studies to be used in modelling terrestrial planetary conditions (Way et al., 2017). It can model coupled interactions between the atmosphere, the surface, the ocean and sea ice. The model typically divides the atmosphere into 40 and the ocean into 13 vertical layers with 4° × 5° latitude × longitude resolutions for both ocean and atmosphere (Way et al., 2017).

Typically, exoplanets have been modelled with a GCM having a so-called thermodynamic ocean model in which the ocean is represented by only its uppermost layer. Such a model neglects horizontal and vertical ocean heat transport (Way et al., 2017). Additionally, neglecting such transports results in, for example, homogeneous salinity for the entire ocean. Such differences, which may seem small, directly affect ice coverage which in turn could affect the albedo and hence the temperature causing a feedback loop. ROCKE-3D running on 13 vertical ocean layers accounts for ocean heat transport to avoid such errors.

Estimates of the mass of Proxima Centauri b are slightly larger than that of Earth while the mean eﬀective temperature is lower (∼ 230K) (Anglada-Escudé et al., 2016). Despite the mean eﬀective temperature not being conducive to liquid water under Earth-like ocean composition, regions of Proxima Centauri b may exist where the temperature is higher. Based on the unknown origin of Proxima Centauri b, the existence of water on Proxima Centauri b in any phase is unknown (Del Genio et al., 2019). Nonetheless, Del Genio et al., (2019) chose to model Proxima Centauri b as a terrestrial aquaplanet using ROCKE-3D.

2.3 Fractional habitability To quantify the level of planetary habitability one needs a metric such as fractional habitability. The habitable range can be deﬁned in several ways typically based on surface temperature falling between 0 - 100°C (Spiegel et al., 2008). In their paper Spiegel et al., (2008) construct a habitability function dependent on latitude and time. To yield the fractional habitability the function is integrated over the respective periods of latitude and time (where the period is the orbital period). Using this metric Spiegel et al., (2008) found Earth to be 85% habitable in the year 2004.

However, surface temperature ranges may be insuﬃcient as the only metric for habitability. Given the liquid-water deﬁnition of habitability, a planet may have liquid water despite subzero temperatures if the salinity is high. Another metric for aquaplanets is the absence of sea ice, meaning that there is an open ocean.

2 If variable values are given as a time average, a habitability function based on the values will not be time dependent. Therefore, to construct the fractional habitability in this manner the habitability function needs only to be integrated or averaged with ﬁnite grid cells over the planetary area.

hab 5hab = (7) tot

Here hab is the result of the integral or ﬁnite area sum.

2.4 Sea Ice Both aforementioned metrics of fractional habitability are defined from values constrained to the surface of the exoplanet. One may challenge this definition stating that a frozen exterior of a planet does not exclude the possibility for life. Surprisingly, there are entire ecosystems living under ice sheets in Antarctica. There- fore, a volumetric fractional habitability may be defined as the volumetric fraction of liquid water in the ocean.

To ﬁnd this fraction, one needs the volume of submerged ice. On Earth, one ﬁnds that the thickness of ice above water (the freeboard) is roughly one-tenth of the total thickness. This means that the thickness of submerged ice (the draft) is roughly nine-tenths (Alexandrov et al., 2010). These proportions come from Archimedes’ principle and the density relations of ice and water. Archimedes’ principle states that the weight of the displaced water is equal to the buoyant force on the object.

1 = dF+F 6 (8)

In order to be in equilibrium, the downward force of the ice weight must be equal to the buoyant force.

d8+86 = dF+F 6 (9)

Rewriting this equation and plugging in density values we ﬁnd the following:

+F /+8 = d8/dF & 0.9 (10)

This means that slightly more than 90% of the ice is submerged. However, that is volumetric and to make the analogous thickness comparison requires the assumption that the ice has constant horizontal cross-sectional area. As an estimate, 90% works well as seen from the aforementioned empirical study (Alexandrov et al., 2010). One note about this ratio is that it is independent from the gravitational constant as can be seen from equations9 and 10. Hence, no extra concern needs to be paid to calculate the draft ratio on exoplanets with diﬀerent size and mass than Earth.

Now that the draft ratio is known, to calculate the fraction of unfrozen water one subtracts the volume of submerged ice and divides the diﬀerence by the total ocean volume.

+tot − +sub 5hab,V = (11) +tot

This deﬁnes the oceanic volumetric fractional habitability, 5hab,V.

3 Methods 3.1 Method of Del Genio et al., (2019) Del Genio et al., (2019) used ROCKE-3D to simulate the 18 cases. Simulations were run with 40 vertical atmospheric layers and an atmospheric resolution of 4 × 5 latitude × longitude. Due to the unknown conditions of Proxima Centauri b, simulations were run for 18 cases. Since Proxima Centauri b is close to its star with a short orbital period, for 16 of the cases it was assumed that the exoplanet is tidally locked. In two of the 18 cases the exoplanet is assumed to be in 3:2 spin orbit resonance like that of the planet Mercury. The rotational period of Proxima Centauri b is then 7.5 days with the cases having eccentricities of 0 and 0.30 respectively (Del Genio et al., 2019). The higher eccentricity lies just below the upper bound of 0.35 calculated by Anglada-Escudé et al., (2016). For climatic composition, the 18 cases use the ﬁrst case "Control" as a baseline which has Earth-like atmospheric initial conditions. In "Control" the atmosphere

3 has the same surface pressure as Earth (0.984 bar) and is primarily composed of molecular nitrogen with 376 part per million by volume carbon dioxide. Ocean depth is assumed to be 900 meters globally. The incident stellar ﬂux of 881.7 W/m2 matches that calculated by Anglada-Escudé et al., (2016) (Del Genio et al., 2019). From "Control" the cases branch out by varying one parameter at a time. For example, cases with higher or lower atmospheric pressure, deeper or shallower ocean, and higher or lower salinity are simulated. Two special cases in which the planet has Earth’s continents are also simulated with diﬀerent substellar points (Del Genio et al., 2019). All cases are simulated until radiative equilibrium is reached after which variables are taken from averages of the last 100 orbits in a given simulation. Below is an image of the case descriptions.

Figure 1: Image of case description table from Del Genio et al., (2019). The table details the model parameters used in each simulation.

The results of these simulations are in the form of NetCDF ﬁles[2] which contain variables deﬁned on the 2D surface of Proxima Centauri b.

3.2 Project method This project is based on the resulting NetCDF files of Del Genio et al., (2019). For this project, MATLAB code for analysing the aforementioned NetCDF files was created. Other than using the NetCDF results for further calculations, the files were also examined using the software Panoply[3] to give a colormap representation of the variables.

3.2.1 Surface Temperature Metric of Fractional Habitability The NetCDF ﬁles of all 18 cases were loaded into MATLAB. A 19th case which was a simulated 10 year average of Earth was also loaded. To calculate the fractional habitability the total area of Proxima Centauri b is needed. Since each case has the same areas of each grid cell the areas were read once and summed. Next, for each grid cell "tsurf" corresponding to the surface air temperature of each grid cell was read. If the value of "tsurf" was between 0 - 100°C the area of the corresponding grid cell was added to the habitable area. When checking grid cells one must be careful in that there is only one grid cell on the poles which has its variable values duplicated for each longitude. Once the surface temperature of each grid cell was checked, the fractional habitability was calculated according to equation7. This was done for all 19 cases.

3.2.2 Lack of Sea Ice Metric of Fractional Habitability Once more the NetCDF ﬁles of all 18 cases and the Earth comparison case were loaded into MATLAB, and the areas were read from one of the cases. For each grid cell the value of "ZSI" corresponding to ice

4 thickness was checked. Given no sea ice in a grid cell, reading "ZSI" yields an arbitrary negative number. As such, grid cells for which "ZSI" was negative were added to the habitable area. Like the surface temperature metric, the fractional habitability was then calculated according to equation7 for all 19 cases.

3.2.3 Oceanic Volumetric Fractional Habitability As before, all 19 case ﬁles are loaded into MATLAB. However, for volumetric fractional habitability the total ocean volume is needed. Unlike the area, this varies between cases since the ocean depth does. To calculate the ocean volume, the grid cell areas were read for one case. Afterwards, for each case the total volume was calculated by adding the product of the cell area and the ocean depth. This ocean depth (variable name "zocean") was read from the ocean topography ﬁle corresponding to the given case. As seen from equation 11, to calculate the volumetric fractional habitability the volume of submerged ice is also needed. For each grid cell the value of "ZSI" was read. The volume of submerged ice was then calculated from "ZSI" and the grid cell areas using the aforementioned draft ratio of 0.9. Once the submerged ice volume of each grid cell was calculated the volumetric fractional habitability was calculated according to equation 11.

5 4 Results

Table 1 shows calculated values for the various metrics of fractional habitability for each case. As a metric, the surface temperature based fractional habitability seems most restrictive due to it having the lowest average. It is also the only metric that has cases with no fractional habitability. The fractional habitability based on lack of sea ice has a non-zero value for case 16, 3:2e0, although low enough to be essentially zero. An- other diﬀerence in values of fractional habitability based on our metrics is apparent in case 14, High Salinity. While the temperature based fractional habitability is zero ∼55% of the ocean contains zero sea ice. This means High Salinity is instead one of the cases with highest fractional habitability based on the lack of sea ice.

As can be seen from the volumetric column, all fractional habitabilities are essentially one, indicating that the vast majority of the planetary water is unfrozen. Even in case 2 with the shallow thermodynamic ocean only ∼5% of its water frozen. This implies that the ocean depth, which Del Genio et al., (2019) sets mainly for computational convenience, is not essential for high values of volumetric fractional habitability. Instead checking the differences in fractional habitability for lack of sea ice between case 1, case 11 and case 12 we find a noteworthy difference. In both the shallow ocean and deep ocean case the fractional habitability is nearly half that of the control case.

Table 1: Calculated values for fractional habitability for each of the metrics. Earth used as comparison case. Third column taken from results of Del Genio et al., (2019). Case speciﬁcations can be found in ﬁgure1 Case (#) \ fhab metric Surf. Temp. Lack of Sea Ice Del Genio et al., 2019 Volumetric 1. Control 0.19 0.18 0.42 0.9980 2. Thermo 0.19 0.19 0.20 0.9458 3. Control-High 0.40 0.32 0.55 0.9985 4. Control-Thin 0.08 0.07 0.23 0.9968 5. Control-Thick 0.53 0.50 0.65 0.9989 6. Archean Low 0.25 0.38 0.50 0.9980 7. Archean Med 0.24 0.17 0.38 0.9979 8. Archean Med NoCH4 0.20 0.24 0.45 0.9982 9. Archean High 0.42 0.33 0.56 0.9984 . 10. Pure CO2 1.00 1.00 1.00 1.0000 11. Control-Shallow 0.25 0.10 0.38 0.9809 12. Control-Deep 0.15 0.09 0.38 0.9990 13. Zero Salinity 0.27 0.25 0.32 0.9965 14. High Salinity 0 0.55 0.87 0.9973 15. 3:2e0 0 0.00 0.21 0.9971 16. 3:2e 30 0.24 0.35 0.51 0.9985 17. Day-Ocean 0.33 0.60 0.44 0.9905 18. Day-Land 0.24 0.45 0.38 0.9853 19. Earth Comparison 0.83 0.79 N/A 0.9998 Average 0.3058 0.3454 0.4683 0.9934

While case 1 and 2 seem similar based on the fractional habitability they differ greatly in their temperature distribution, as can be seen in figure 2. The lack of heat transfer due to currents can be seen in Thermo (2) where the temperature is almost symmetrically distributed around the exoplanet’s substellar point. The heat transport in Control (1) causes the temperature of peripheral areas of the planet to be higher than in the same areas for Thermo (2). However, it also means that the temperature around the substellar point is lower. This is most visually apparent in the bottom half of figure 2. The pattern which arises from the inclusion of heat transport seen in the bottom left is called a "lobster" pattern, as opposed to the "eyeball" pattern seen in thermo (2).

Figure 3 shows the surface air temperature distribution for Shallow (case 11) and Deep (case 12). Like in ﬁgure 2 the "lobster" pattern can be seen in the deeper ocean. For Shallow (11) which lies between Control (1) and Thermo (2) in terms of ocean depth, the pattern seems to be somewhere in between the "lobster" pattern and the "eyeball" pattern. Shallow (11) has high temperatures at the poles as can be seen from the upper left of ﬁgure 3.

6 Figure 2: Surface air temperature for control (case 1) and thermo (case 2) with two diﬀerent scales. (a) and (b) scaled to include all values (-90 to 20 °C). (c) and (d) scaled to show temperatures 0 to 20 °C. Images rendered by Panoply.

Figure 3: Surface air temperature for shallow (case 11) and deep (case 12) with two diﬀerent scales. (a) and (b) scaled to include all values (-62 to 8 °C). (c) and (d) scaled to show temperatures 0 to 8 °C. Images rendered by Panoply.

7 Figure 4: Surface air temperature for Earth continent cases with two diﬀerent scales. Center is on substellar point. (a) and (b) scaled to include all values (-93 to 31 °C). (c) and (d) scaled to show temperatures 0 to 31 °C. Images rendered by Panoply.

Figure 5: Surface air temperature for cases in 3:2 spin orbit resonance. (a) and (b) scaled to include all values (-68 to 1.5 °C). (c) and (d) scaled to show temperatures 0 to 1.5 °C. Images rendered by Panoply.

Figure 4 shows surface temperature distributions for the two cases with Earth’s continents. In these cases

8 ocean current transport is blocked by the shape of the continents, which shapes the temperature-based habitable area. Note the higher maximum value of surface temperature in case 18 where the substellar point is centered on Africa. Figure 5 shows the temparature distribution for the two cases in 3:2 spin orbit resonance. Since 3:2e0 (case 15) has only subzero values, the colormap scaled with a minimal value of 0°C is entirely blue. Without tidal locking or eccentricity the surface temperature pattern which arises appears only dependent on latitude. Note the similarity to the Earth comparison (ﬁgure 6) which also isn’t tidally locked. With an eccentricity of 0.3 and no tidal lock, a pattern with three "bulbs" emerges.

Figure 6: Surface air temperature for Earth comparison case (19) with two diﬀerent scales. (a) scaled to include all values (-68 to 35 °C). (b) scaled to show temperatures 0 to 35 °C. Images rendered by Panoply.

Figure 7 compares the surface temperature and sea ice thickness for case 14 (High Salinity). In no grid cell does the surface temperature exceed subzero temperatures. Shape and size of area with no sea ice most aligns with colder scale minimum mappings. Despite being alike Control in all respects but salinity, this case shows no "lobster" pattern in surface temperature distribution.

Figure 7: First three images show surface temperature of High Salinity case with colormap scale minima set to −10°C, −5°C and −2°C. Last image shows ocean ice thickness, where grey indicates lack of ice. Images rendered by Panoply.

9 Figure 8 and ﬁgure 9 show a graphical representation of the results from table1. From here, the tendency for higher values of fractional habitability from Del Genio et al., as compared to the other two areal metrics is visible.

Figure 8: Plot of fractional habitability for each metric and case. Case numbers 1-18 deﬁned in ﬁgure 1. Case 19 is the Earth comparison.

Figure 9: Plot of average value of fractional habitability for each metric.

10 Figure 8 does not show a clear tendency for larger values of fractional habitability as based on lack of sea ice rather than temperature. Some cases have higher temperature fractional habitability, for example the Shallow case (11).

Figure 10: Plot of diﬀerence between lack of sea ice 5hab and surf. temp. 5hab. Positive values imply lower temperature fractional habitability than based on ice coverage.

Figure 10 shows the difference between temperature fractional habitability and lack of ice fractional habitability. For six of the cases the difference is distinctly positive, most notably so for case 14 (High Salinity) and the Earth continent cases (17 & 18, Earth comparison case excluded). For the Earth continent cases this may be explained due to how ice thickness is limited inland as can be seen in figure 11.

Figure 11: Ice thickness for Earth continent cases (17 & 18). Grey areas indicate lack of ice. Substellar point centered.

11 5 Discussion

The fractional habitability of Proxima Centauri b is highly dependent on both the choice of metric and the assumed case parameters. Both areal metrics constructed have fractional habitabilities at both extremes, zero and one. This can be seen in Table1 implying strong parameter dependence. Additionally, for certain cases the difference between metrics of areal fractional habitability may be large, going from 0% to 55% in the case of High Salinity (14). In this case Proxima Centauri b is considered "non-habitable" according to one metric and "partially habitable" according to another. Such a difference is significant. If the volumetric fractional habitability is to be included, there is an even greater dependence on metric.

Due to the climate conditions of Proxima Centauri b being unknown, a dependence on choice of case parameters may seem demoralizing. However, while the values of fractional habitability may change from case to case for the vast majority of cases the fractional habitability is non-zero for both areal metrics. This implies that at an absolute minimum of one 4° × 5° latitude × longitude grid cell is habitable. Also, as previously mentioned, no value for the volumetric fractional habitability goes below ∼ 95%. If the exoplanet were less aqueous lower volumetric fractional habitability would be possible. For the cases considered the shal- lowest ocean was 100 m deep in Thermo. However, even in that case the maximum ice thickness is less than 20 m deep. Unless such an ocean depth is considered, the volumetric fractional habitability will be non-zero.

Validation of the calculations of different fractional habitability metrics were done by examining the simulations in Panoply. For example, Control has a temperature fractional habitability of ∼ 20%. When viewing the surface air temperature of Control in Figure 2 (which has Equal Earth projection) the light blue area is also roughly ∼ 20% of the total area. Similarly, from figure 3 it is visible that the habitable area in Shallow is larger than that of Control while the habitable area in Deep is smaller than that of Control. This matches the calculated values of their fractional habitability. Additionally, the values of volumetric fractional habitability are easily verified by colormaps of the ice thickness whose values rarely supersede 20 meters in oceans several hundred meters deep homogeneously.

An unexpected results is that both the shallow and the deep ocean cases have almost half the fractional habitability based on lack of sea ice. These results do not match either the surface temperature metric or the one used by Del Genio et al., (2019). If instead of "ZSI" one looks at the ocean ice fraction "oicefr" there is no large areal discrepancy between Control and either Shallow or Deep. The diﬀerence in ocean ice fraction and lack of sea ice as metrics stems from grid cells in which the ocean surface is partially covered in ice. For the lack of sea ice metric grid cells which contain a small amount of ice would nonetheless be neglected fully, whereas using ocean ice fraction results in a percentage of the grid cell area being added to the habitable area. One possible explanation for the discrepancy may be that both Shallow and Deep have more grid cells which are partially covered in sea ice than Control. Shallow may have more grid cells with partial sea ice coverage due to smaller ocean heat content. Deep, on the other hand, may have more partial sea ice coverage due to horizontal transport of sea ice which, as previously mentioned, increases with ocean depth.

An additional metric for fractional habitability based on sea surface temperature, distinct from the air surface temperature, was planned. However, the variable gave values for the uppermost ocean layer regard- less of existence of sea ice coverage. As such, any value of sea surface temperature was in the habitable range according to the deﬁnition of liquid water due to the temperature being that of liquid water. This obstacle was attempted to be surpassed by reading the values of sea surface salinity. However, due to both sea ice transport and brine rejection resulting in a lower ice salinity there may be sea ice on top of water whose temperature and salinity are not close to freezing. As such, the sea surface temperature metric was rejected for the lack of ice metric.

Evaluating the habitability of exoplanets is done with two intentions in mind. One may see a habitable exoplanet candidate as a possibility for colonization or as a possibility for ﬁnding extra-terrestrial life. Depending on what the intent is the value of the diﬀerent metrics of fractional habitability changes. For example, if the intent is for future human colonization one may be less interested in the oceanic volumetric fractional habitability. However, if the intent is to discover extra-terrestrial life the habitability of the ocean may be interesting even if it’s covered in thick ice. For either intent, the choice of Proxima Centauri b as a future candidate for further study is aided by its close proximity.

12 6 Outlook

For further study, I would recommend expanding the project by including more cases and more metrics for fractional habitability. One case type of interest are cases with increasingly shallow ocean to determine if there is a limit with an entirely frozen ocean. Additionally, a planet with separated bodies of water would be interesting to study for various depths due to limited transport. A difference between that and the homogeneous ocean depth of most of our cases would question the validity of the simplification. Having separated bodies of water is almost covered in the Earth continent cases (17 & 18). However, Earth has a deeper ocean than the other cases (in case 17 & 18 simulated as 1360 m deep on non-land grid cells) and there may be different results for shallow separated bodies of water.

A new type of metric for fractional habitability that could be added is a metric based on the incoming light from the parent star. While the volumetric fractional habitability states that there is liquid water far underneath sea ice, that may be of little use to a life form which relies on photosynthesis. Although it may not be a problem for lifeforms which sustain themselves on the energy of hydrothermal vents. As a measure of habitability for photosynthesising lifeforms I propose a metric which checks if there is liquid water in a grid cell within reach of a speciﬁc percentage of the parent star’s light. The percentage could be varied to construct diﬀerent metrics. This metric would be distinct from the lack of sea ice metric where a grid cell is neglected even if the sea ice thickness is small. This light metric could also be volumetric by reaching further down in grid cells with low or no ice coverage. Additionally, the metric could be varied in terms of which wavelength of light is considered as the ice opacity may be wavelength dependent. For example, one may consider the spectral range for which phytoplankton absorb light. However, this range may be the product of evolution. Therefore, another option would be to consider the wavelength corresponding to the spectral peak of Proxima Centauri.

7 Conclusions

The fractional habitability of Proxima Centauri b, and any other similar exoplanet may strongly depend on both the metric used and the assumed case parameters. There is a slight tendency for higher fractional habitability based on temperature range than lack of ice. Volumetric fractional habitability is essentially one for all of the considered cases. For the vast majority of cases, the fractional habitability in all metrics is non-zero implying existence of partial habitability on Proxima Centauri b.

13 8 References

1. NASA Exoplanet Archive. Exoplanet and Candidate Statistics, exoplanetarchive.ipac. caltech.edu/docs/counts_detail.html [accessed 2020-02-27, last update 2020-02-19] 2. NASA/GISS. Panoply netCDF, HDF and GRIB Data Viewer, giss.nasa.gov/tools/panoply/ [accessed 2020-05-21]. 3. UCAR/Unidata. Network Common Data Form (NetCDF), unidata.ucar.edu/software/ netcdf/ [accessed 2020-05-21]. 4. M. J. Way, I. Aleinov, David S. Amundsen, et al. Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics (ROCKE-3D) 1.0: A General Circulation Model for Simulating the Climates of Rocky Planets. The Astrophysical Journal Supplement Series 231:12, 2017. 5. Anglada-Escudé, G., Amado, P., Barnes, J. et al. A terrestrial planet candidate in a temperate orbit around Proxima Centauri. Nature 536, 437–440 (2016). 6. Anthony D. Del Genio, Michael J. Way, David S. Amundsen, et. al. Habitable Climate Scenarios for Proxima Centauri b with a Dynamic Ocean Astrobiology. Volume 19, Number 2 (2019). 7. Spiegel, D., Menou, K. and Scharf, C. Habitable Climates The Astrophysical Journal 681:1609, 2008. 8. Alexandrov, V., Sandven, S., Wahlin, J. and Johannessen, O. M. The relation between sea ice thickness and freeboard in the Arctic The Cryosphere, 4:373, 2010.

14 9 Appendix

Figure 12: Sea surface salinity for Control (1) and Thermo (2). Shows lack of ocean current transport in Thermo.

Figure 13: Sea ice thickness for Control (1) and Thermo (2). Scale set with maximal ice thickness at 20 m.

Figure 14: Ocean depth for the (a) Earth continent cases and (b) the Earth comparison case. (a) scaled between 0 and 1360 m. (b) scaled between 0 and 5967 m.

15 Figure 15: Ocean ice fraction for Control, Shallow and Deep cases. Dark blue and dark red correspond to 0 and 100% ocean ice respectively.