I have a world in mind that is essentially a planet-wide underground ocean. The planet doesn't have a strong magnetic field, so radiation on the surface is too high to allow life, but what I'm thinking is that through conduction, the sun can heat the underground ocean through the ground and allow life to begin to form.

The question I have is if this is a plausible scenario. The only forms of life I know of get their energy from radiation (plants), convection (deep-sea vent extremophiles), or by eating other life forms (us). What I'm wondering if conduction is a viable energy tranference mechanism to power life.

Is there anything that makes conduction particularly difficult for life to form around? Are there any examples of life on Earth that gets its main source of energy this way?

• Can you elaborate on what the crust of your planet is made out of and how thick it is leading to your underground ocean? And are you looking for science-based or hard-science ? – James May 26 '16 at 17:52
• @James Composition and thickness of the crust is not important to me, you can assume any amount of energy that you need is making it through (as long as you can find a configuration that allows for it). And I'd say I'd appreciate both science-based and hard-science answers, provided that either one sufficiently answers the stated question. – DaaaahWhoosh May 26 '16 at 18:22
• A point for you on your setup scenario.... There's fungus in the core of the Chernobyl reactor remains that feed primarily on the "bad" forms of radiation. Genetically speaking, fungus are closer to animal than they are to plant. Further, is uses extremelly high levels of melanin to pull this off. We humans also have melanin. It's not unfeasible that you can have animals evolved to feed at least partially on solar radiation. (We actually due sort-of feed off the radiation, it helps up produce vitamin D.) – lilHar May 26 '16 at 23:19
• I believe Stephen Baxter had a story in Vacuum Diagrams about aliens on Pluto whose metabolisms were powered by temperature differentials. It was a miniscule amount of energy, so they lived incredibly slow lives by our standards, but Baxter is a legit scientist so it might be worth your attention. (Great book besides) – user3573647 Jun 9 '16 at 19:49

Thermal conduction will provide a good environment

...but it doesn't directly provide an energy source for organisms to power themselves with. From your description, there's a large underground water reservoir capped with stone to prevent solar radiation from cooking everything.

The question doesn't make any statements about orbital mechanics or distance from the local star, so we will just have to assume that the star provides enough heat near the equator to keep water moving through this underground ocean. There needs to be a thermal gradient or there won't be any circulation. If the poles are cold on this planet, like they are on Earth, then warm pole-bound currents will flow atop cooler equator-bound currents.

The stone cap isn't necessary for radiation protection since water does a really good job of absorbing the nasty wavelengths. As this below image shows, water is very good at absorbing the really dangerous wavelengths of UV, IR and other nasties.
(Source)

However, without an atmosphere, something will need to keep the ocean from boiling away and the stone cap does that.

Stone Cap Complications

• What happens when sufficient pressure builds up to blow off some of the cap? If there are undersea vents, some kind of gas is going to come out and that won't always stay in suspension.
• Does the cap reseal itself after a volcanic eruption? If so, how?
• If this environment is intended to create a space faring species, how do they make the transition from purely aquatic to living in an atmosphere?
• Are there sufficiently large & stable gas pockets that an ecosystem can evolve in them?
• I am thinking this species or at least its distant single celled and plant ancestors will have to have a specialized cellular structure that absorbs heat to create sugars (or what ever the biological power source is. – James May 26 '16 at 18:07

Awesome question. To test the feasibility of your idea, we start with the heat equation, which in our case is (from these notes) $$\frac{\partial T}{\partial t}=D_H\frac{\partial^2T}{\partial z^2}\tag{1}$$ where $T$ is temperature, $t$ is time, $D_H$ is the thermal diffusivity, and $z$ is elevation. $D_H$ can be calculated simply as $$D_H=\frac{\lambda}{c_v}$$ where $\lambda$ is the thermal conductivity and $c_v$ is the volumetric heat capacity of the soil. Exact values for $c_v$ can be calculated if the soil’s porosity, volume fraction of organic matter, and volume fraction of water are known; soils that are not homogeneous (i.e. that contain a mix of things, as is the case with most real soils) involve slightly more complicated calculations for $c_v$. Slide 10 of the notes gives values of $c_v$ for the four individual components of soil: minerals, organic matter, water, and air. $\lambda$ must also be calculated from the various values of $\lambda$ of each of its constituents.

Solving this gives us $$T(z,t)=T_0+(T_s-T_0)\text{ erfc}\left[\frac{z}{\sqrt{4D_Ht}}\right]\tag{2}$$ where $$T_0=T(z,0)=T(\infty,t),\quad T_s=T(0,t)$$ and $\text{erfc}(x)$ is the complementary error function.

The example given in the notes finds a $D_H\approx8.907\times10^{-7}$ m2s-1; if we take the initial temperature at the top of the underground ocean to be that of deep-ocean water (around 32-38 °F, or 0-3 °C, or 273-276 K), and assume that the crust is around 100 meters thick (I’m just taking a random value of this), with the planet having an effective temperature $T_s$ of about that of Earth, at 252 K as per the equation), then we get $$T(\text{top of ocean},t)=252\text{ erfc}\left[\frac{100}{\sqrt{4\times8.907\times10^{-7}\cdot t}}\right]=252\text{ erfc}\left[52979t^{-1/2}\right]$$ Notice that as $t\to\infty$, $T(\text{top of ocean},t)=T_0$, so the heat will eventually reach the water. The big problem, though, is that it’s going to take a long time for changes in temperature to propagate, because of the large depth of the crust. As we can see by taking the derivative of $T(x,t)$ with respect to $t$, heat will move relatively slowly.

This is made worse because the surface of the ocean will cool. I assumed this value of $T_0$ to be true at the start of the heat conduction (i.e. at the very beginning of the planet), so the ocean will slowly start to heat up. It might have been better to study the change in temperature $\Delta T$, $T-T_0$. Other things I’ve ignored include the actual effective temperature of the planet, which may be nothing like that of Earth, and circulation of water from the depths of the ocean, however thick it is.

Here’s the big problem when you’re trying to help life survive: The energy source isn’t too good. You’ll of course have the equivalent of a geothermal gradient (see also here), but in reverse (i.e. heat traveling downwards from the surface). The geothermal gradient is the change in temperature over the change in depth, or $$\text{Geothermal gradient}=\frac{\partial T}{\partial z}=-252\frac{2}{\sqrt{\pi}}\frac{1}{\sqrt{4D_Ht}}\exp\left[-\frac{z^2}{4D_Ht}\right]\tag{3}$$ After about one year, I find a $\frac{\partial T}{\partial z}$ of about 5.96$\times$10-35 K/km - a tiny, tiny, tiny fraction of the geothermal gradient at Earth’s surface (roughly 25 K/km). This means that geothermal energy is not good, if the surface reaches thermal equilibrium.

So where’s the energy source? That’s the real problem. There will be a larger gradient between the top of the ocean and the far depths, but most organisms likely won’t move that far. I feel like the eventual lack of a change in temperature will be an enormous problem.

One thing I don’t know about is whether or not the crust - a shell, really - will transfer heat into the ocean via radiation. If we treat it as a black body, then it it should emit a power of $$P=4\pi\sigma(R_\text{planet}-100)^2T_s^4\tag{4}$$ as per the Stefan-Boltzmann law; the power per unit area comes out to about 229 W/m2, less than the amount recieved on Earth’s surface (which, by comparison, is about 340 W/m2). However, I’m a little shaky on whether or not all of that radiation will actually be emitted by the crust and absorbed by the water.

Hi: I've included an Ocean thermal energy conversion theory link here, with some examples to support your scenario. I'm not sure about the radiation factor, but thermal oceanic energy supporting life seems plausible, yes. https://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion

• Welcome to the site Erin. Could you extract the relevant information out of the article. SE frowns upon answers that are dependent upon links. Links should be used for "additional information" or "background info". If you have questions, check out the help center and feel free to ask about the site in Worldbuilding Chat – James May 26 '16 at 17:51
• HI: I'm sorry you frowned upon my response. It's important to me to give credit to those who have spent time with the material and questions asked, and in this instance, it wasn't me. I would have preferred to post a comment rather than an answer, but because I am new, that's not permitted. – Erin McLeod May 28 '16 at 1:00
• Not a problem. Attribution is good and you should certainly do so, we just need the content itself here on the site rather than solely in a link. – James May 28 '16 at 15:49