# How far could a planet be from its star and still be kept habitable by intense greenhouse gases?

Epimetheus is a planet with about three times the mass of Earth orbiting a sun-like star in the Andromeda galaxy. However, two major factors separate Epimetheus from Earth. First, it has a thick atmosphere heavy in carbon dioxide and other greenhouse gasses which formed early in its history as a planet, and second, it's much further from its star.

In the game of life, Epimetheus is far from an ideal candidate for harboring abiogenesis. A thick atmosphere may warm its surface, to some degree, but at the risk of increasing pressure too much and converting its surface water into more exotic forms of ice. Can the thick atmosphere found on Epimetheus make its surface conducive to harboring life, even if it lies outside of the generally proscribed habitable zone? How far away from its parent star could such a planet reasonably be found at and still support life?

• worldbuilding.stackexchange.com/questions/37935/… replace 1.1 with 0.53 in the first formula (on the top of the answer) Mar 14, 2016 at 17:07
• @YoustayIgo Does that account for greenhouse gas-heavy atmospheres? I don't see any mention of planetary atmosphere composition in the original source... Mar 14, 2016 at 17:25
• Habitable by what, humans? Aliens? Dogs? My grandmother? Mar 14, 2016 at 19:51
• OK. Didn't mean to rob you off of replies for your query :) I think the question is primarily opinion based, considering such complex interlinked factors such as how far it is from its star, the extent of the atmosphere, activity of mantle and core, presence (or not) of large water bodies etc. It would have been easier if you had provided with some specifics :) Mar 14, 2016 at 19:52
• I don't have time to try answering, but it depends on first having an available source of free energy for life to start with, and having enough of it to develop a better energy cycle before that energy runs out. Scientists currently believe this started on earth with the chemical pyrophosphite, right up until some enterprising critter came up with the ATP cycle. And it's thought the phosphorus for that chemical came from meteorites, as there shouldn't have been that much here. Regardless, easily accessible chemical energy is a must have, warmth isn't enough. Mar 14, 2016 at 20:48

## 2 Answers

I agree with Tim B’s assessment that this is a complicated question. However, I disagree on just why this is the case. The characteristics of the star are well defined, given that it’s a solar analog. From this, we immediately have mass, luminosity, and other characteristics. However, the reason I think that this is not a simple question is that there are a lot of conflicting models of the effects of different greenhouse gases and of the circumstellar habitable zone. I’ve tried to choose the best ones, but they’re only approximations; the exact fate of Epimetheus will require some deeper thinking.

# The Greenhouse Effect

Disclaimer: This section is mostly me muddling through a topic I’m not too familiar with.

Radiative forcing

I’ll start by assuming that the main source of atmospheric warming comes from radiative forcing because of the various greenhouse gases in the atmosphere. Radiative forcing is the difference between the amount of sunlight absorbed by a planet and the amount of sunlight emitted back into space. The difference between absorption and emission is primarily due to the atmosphere.

Radiative forcing causes a change in surface temperature, which is proportional to the radiative forcing: $$\Delta T_s=\lambda\Delta F\tag{1}$$ where $T_s$ is surface temperature, $\Delta F$ is radiative forcing, and $\lambda$ is the climate sensitivity of the planet.1 For Earth, $\lambda\approx0.8$, and without more detailed data on Epimetheus, I’ll have to assume that it’s about the same there.

Each greenhouse gas contributes differently to radiative forcing. The IPCC Second Assessment Report2, 3 gives a chart (Table 6.2) of approximations of expressions for radiative forcing contributions from several of the major greenhouse gases (CO2, CH4, N2O, CFC-11, and CFC-12): $$\begin{array}{|c|c|c|} \hline \text{Trace Gas} & \text{Simplified Expression} & \text{Constants}\\& \text{Radiative Forcing, }\Delta F \left(\text{Wm}^{-2}\right)\\ \hline \text{CO}_2 & \Delta F=\alpha\ln\left(\frac{C}{C_0}\right) & \alpha=5.35\\\text{} & \Delta F=\alpha\ln\left(\frac{C}{C_0}\right)+\beta\left(\sqrt{C}-\sqrt{C_0}\right) & \alpha=4,841,\beta=0.006\\\text{} & \Delta F=\alpha(g(C)-g(C_0) & \alpha=3.35\\ \hline \text{CH}_4 & \Delta F=\alpha(\sqrt{M}-\sqrt{M_0})-(f(M,N_0)-f(M_0,N_0)) & \alpha=0.036\\ \hline \text{N}_2\text{O} & \Delta F=\alpha(\sqrt{N}-\sqrt{N_0})-(f(M_0,N)-f(M_0,N_0)) &\alpha=0.12\\ \hline \text{CFC-11} & \alpha(X-X_0) & \alpha=0.25\\ \hline \text{CFC-12} & \alpha(X-X_0) & \alpha=0.32\\ \hline \end{array}$$ The two functions are given by $$g(C)=\ln(1+1.2C+0.005C^2+1.4\times10^{-6}C^3),$$ $$f(M,N)=0.47\ln(1+2.01\times10^{-5}(MN)^{0.75}+5.31\times10^{-15}M(MN)^{1.52})$$ $C$, $M$, $N$, and $X$ denote the concentrations of CO2, CH4, N2O, and the CFCs, respectively; the subscript $_0$ denotes a reference concentration. All gases are given in parts per billion, except CO2, which is given in parts per million.

The total radiative forcing is the sum of the contributions of each greenhouse gas. If the atmosphere is mostly made of carbon dioxide, then, using the first-order approximation: $$\Delta T_s=\lambda\times5.35\times\ln\left(\frac{C}{C_0}\right)\tag{2}$$ It’s easy to see from this that doubling the concentration, for example, leads to a temperature increase of about 3°C.

Different models and feedback mechanisms

Before I go further, I should address my choice of equations. Some would argue that it would be a lot simpler and much more intuitive to use the idealized greenhouse model4 (another application of radiative forcing), which can be derived from the Stefan-Boltzmann law and a few other assumptions. In fact, after exploring some of the above calculations, I began to wonder the same thing myself, because the idealized greenhouse model can be adjusted to produce different warming effects by simply changing one parameter: the emissivity, $\varepsilon$.

I eventually did decide to work with the original table from the IPCC because it allows us to play around with the specific gases a little bit. I can attack the problem quite specifically directly from concentrations, rather than having to figure out the deceptively simple $\varepsilon$. Another place where the IPCC model has have an edge is through feedback mechanisms, which is what I’ll explore next.

The runaway greenhouse effect is perhaps best known for its drastic effects on Venus, turning what was once a world similar to Earth into a hellhole beyond belief. What happened was that carbon dioxide and water vapor began warming the planet (yes, H2O is also a greenhouse gas, and an important one). The water vapor upset the balance just enough so that the oceans that once covered part of the planet began to evaporate, creating more water vapor, which intensified the problem more and more.

There are other types of feedback mechanisms at work on Earth, involving carbon dioxide, greenhouse gases being released from permafrost, changes in albedo from melting ice, and much more. However, the dominant one is still feedback from water vapor, which is actually more important than CO2. Water vapor alone can double the effects of warming, according to the IPCC and other models, and can then help start other feedback pathways that will do further damage.

The reason that we can’t just double our value of $\Delta T_s$ to compensate for this is that $\lambda$ already takes water vapor and the other feedback mechanisms into account. The reason that I said that the IPCC model has an advantage here is that all of the feedback mechanisms can be encoded into the parameter, which describes the planet as a whole. $\varepsilon$ really only describes part of the atmosphere.

Putting it all together

The above argument shows that our first-order approximation can give us a reasonable approximation of changes in temperature, given an appropriate $\lambda$. It’s true that this value will have to be adjusted; models of Earth use different $\lambda$s. However, if we assume that Epimetheus is roughly Earth-like, with the exception of the heavy concentration of CO2, then we don’t have to change much.

# The Habitable Zone

I actually think that defining where the circumstellar habitable zone is without taking the characteristics of Epimetheus into account is more challenging than modeling its atmosphere. The reason for this is that models of the inner and outer radii of the habitable zone of the Solar System differ, as a quick glance at Wikipedia shows. Inner estimates range from 0.75 AU to 0.99 AU, while outer estimates range from 1.01 AU to 3.0 AU. So which one do we use?

I’m going to instead reference Kasting et al. (1993), because, while it may be a little out of date, it bases its conclusions primarily on the effects of climate, which obviously play a major role in the situation at hand.

The authors rely on something called the carbonate-silicate cycle. The important total reaction is in their Equation 3: $$\text{CaSiO}_3+\text{CO}_2\to\text{CaCO}_3+\text{SiO}_2\tag{3}$$ In the biotic version5, organisms use CO2 to create shells, which then are buried in the seafloor; Equation 3 gives the net reaction. Eventually, carbonate metamorphism reverses the reaction, putting CO2 back into the atmosphere. This acts to keep the climate of a planet in the habitable zone in something of an equilibrium, because, as I’ve discussed before, carbon dioxide plays a major role in regulating surface temperature.

The reason that this reaction leads to equilibrium is that both the biotic and abiotic (generally involving weathering, primarily from liquid water) require liquid water. Without liquid water, carbon dioxide levels rise, melting ice and restoring liquid water levels, and with them, equilibrium.

This cycle determines the outer edge of the habitable zone because at low enough temperatures, CO2 can condense, forming clouds. The clouds then alter the planet’s albedo by reflecting substantial amounts of solar radiation, drastically cooling the planet. Additionally, the latent heat amplifies the greenhouse effect even more. The authors use this to estimate a conservative outer limit of approximately 1.77 AU, assuming non-negligible amounts of greenhouse gases.

The authors then created a more complicated and detailed climate model using different planetary masses. They found that the greenhouse effect could let the habitable zone extend to about 1.67 AU for a planet of one Earth mass, and to about 1.64 AU for a planet ten times that mass. These outer boundaries take versions of radiative forcing into account, but are limited by the formation of CO2 clouds. The authors’ calculations indicate that Epimetheus should reside somewhere in that vicinity, at maximum.

Some things to note: - The authors’ models ignore the formation and effects of clouds, as they say. - The drastically high levels of CO2 on Epimetheus will result in different partial pressures, meaning that the outer edge will be affected. - CO2 levels may be affected by the amount stored in the crust.

That said, newer models have replicated the results of Kasting et al. Kopparapu (2013) came up with a nearly identical result for the outer edge, also assuming greenhouse effects, and with models partially based on the older ones.

# Conclusion

We can make some basic approximations of temperature changes if we choose the correct values for several constants and use simple models of radiative forcing, primarily of CO2, but with feedback from water vapor taken into account. We can actually do this with any greenhouse gas, but these two are the primary culprits.

Carbon dioxide actually turns out to also be a good indicator of the outer edge of the habitable zone, because lower temperatures cause CO2 condensation, even accounting for the greenhouse effect. We can place an outer limit on Epimetheus’ orbit somewhere around 1.67 AU, assuming an atmosphere similar to the ones investigated by Kasting et al.

1 Note that this is not the same as the equilibrium climate sensitivity (ECS), which is currently thought to lie around 3°C on Earth.
2 The linked section is on radiative forcing; all IPCC reports (including the second, from 2001) can be found here. The equations are taken from or derived from Hansen et al. (1988), IPCC (1990), Shi (1992), and IPCC (1999).
3 The first equation for CO2 is the first-order approximation of a Taylor series; see Lam (2007), referenced here.
4 You can read more about it here.
5 There is, of course, an abiotic version, which plays a bigger role in planets without life or without life that can carry out these processes.

• dang. I hadn't considered that there would be crustal influences on the atmosphere like that. This is an excellent excellent answer. Apr 14, 2016 at 23:59

There is no simple answer to this, as distance from the star will depend upon the brightness of the star. You can orbit a hot star much further away than a cool one and still be in the habitable zone.

It will also depend on factors like the wavelength of the incoming and outgoing radiation and other sources of heat such as internal volcanic activity of the planet or even tidal heating if it's close enough to another massive body.

So all we can say for sure if that yes, greenhouse gasses will allow you to place a planet further from the sun and still have liquid water on the surface.

The Circumstellar Habitable Zone is the term for the area where that is true. In particular see this part of the article where it says:

Given the large spread in the masses of planets within a circumstellar habitable zone, coupled with the discovery of super-Earth planets which can sustain thicker atmospheres and stronger magnetic fields than Earth, circumstellar habitable zones are now split into two separate regions—a "conservative habitable zone" in which lower-mass planets like Earth or Venus can remain habitable, complemented by a larger "extended habitable zone" in which super-Earth planets, with stronger greenhouse effects, can have the right temperature for liquid water to exist at the surface.

Searching for "extended habitable zone theory" will find more information on the subject as well. In particular this article looks very relevant:

http://www.astrobio.net/news-exclusive/greenhouse-effect-could-extend-habitable-zone/

The distant region beyond Saturn is too cold for liquid water, a necessity for life as we know it. But new research indicates that rocky planets far from their parent star could generate enough heat to keep water flowing – if their atmospheres were made up primarily of hydrogen.

[snip]

But according to Pierrehumbert’s research, , a rocky planet with a hydrogen atmosphere could have a habitable zone extending as far as 1.5 AUs for M-stars and 15 AUs for G-stars.

This means that for stars similar to the Sun, rocky planets beyond the reach of Saturn could contain oceans of water.

• An Earth sized planet at Saturn's distance should have no trouble holding onto hydrogen and helium, the real issue is forming rocky planets at such distances. Besides hydrogen isn't a greenhouse gas, significant amounts of methane could warm up a large Earth sized planet at such distances. Mar 17, 2016 at 21:29
• @Stephanie According to that report hydrogen can act as a greenhouse gas at that distance. Mar 17, 2016 at 21:33
• Oh I did not see that part lol, the only way I can see that working is if the hydrogen works as an insulator preventing heat from escaping on a planet with a lot of volcanoes. Neptune has a very hot interior but it's too hot to be an example of a planet like the type we're talking about Mar 17, 2016 at 21:50