Frozen Stars - Alternate sources of electricity

Question

As in my previous question, I was talking about survival, when the parent star of a planet, Eridanus, froze due to some unknown cause. So the residents of this planet Taurus, the Villagers, have done everything possible to ensure their survival, and for a later time, generate enough heat to warm up the surface to prevent the atmosphere from freezing over and creating a second "Pail of Air" scenario. It was basically a rudimentary "nuclear" reactor, or, simply just 10 million tonnes of Uranium-238 thrown together into a cave and left to warm up from radioactive decay and create HTHP steam for powering turbines for electrical generation.

However, as pointed out by someone in the comments, it would take a hell lot of time for the reactors to be operational. 4 years for it to get hot enough to atleast boil water, and 20 years for it to generate HTHP steam. The Villagers have nothing to do for the first 20 years, so they have to search for an alternate solution of electricity. The Villagers have temporarily ruled out these sources of electricity, for the following reasons:

• Wind energy - Sounds promising, because the sudden cooling of the atmosphere irregularly would lead to catastrophic turbulence, which could be used to spin wind turbines, but considering the fact that the atmosphere is about to freeze over in like, a few months, the atmosphere is going to be a near vacuum, and thus is ruled out.
• Solar Stellar energy - Do I need to explain myself
• Fusion energy - Trying to harvest deuterium from frozen-over oceans is like trying to ask an ant to lift the Burj Khalifa. No guarantee if you get more output energy or not. Furthermore, Villager Fusion tech is just similar to what we currently have now. (large energy wasting tokamaks and other bunkum)
• Fossil Fuels - They do have plenty of barrels of petroleum left (~11 trillion barrels of petroleum reserves). But considering the fact that they they have to heat up the atmosphere next, that feat is impossible. The atmospheric pressure pre-freezing was about 1 bar, but the surface area of the planet is much bigger, which would mean that the amount of frozen air to be boiled into gas, would be tremendous (I cannot calculate how much energy would be required to warm up the atmosphere, however, based on my estimates, it would take nearly a whooping 10 quadrillion oil barrels to heat up the atmosphere enough to make it remain gaseous).
• Geothermal Energy - This is like the most viable option, something that the Villagers can construct easily, as they have sufficient oil for drilling out and manufacturing mining bits. However, as the goals of the Villagers are huge (heating up the atmosphere and keeping it gaseous), it would require a ton of geothermal wells to be created. And based on this EAS scenario about a similar thing, building a ton of GT-wells caused a ton of earthquakes and tectonic shenanigans.

Note that this does not mean that these energy sources are forbidden forever, it just means that the Villagers will look for alternate energy sources, but if they failed they will have to use either of the energy sources mentioned above. But for now, they have to exclude them from the list and look for other sources of energy.

What alternate energy source should the Villagers use for their survival and heating up their atmosphere?

EDIT

• The Villagers are not attempting to reignite their parent star, Eridanus. They know that they have limited energy resources, and they just have 2 goals in mind - That of remaining alive and keeping plants alive, and warming up the atmosphere to atleast keep it gaseous.
• The Star is not frozen forever. As I mentioned in a previous question, Eridanus is only frozen for like 10,000 years, which slowly causes it to compress and heat up, and again reignite into a star again. However, as the star is really small, it takes about nearly 10,000 years for the compression to finally heat up and become a star. So the Villagers look for alternate electricity sources.

Answer 1

Trying to harvest deuterium from frozen-over oceans is like trying to ask an ant to lift the Burj Khalifa

Oceans are deep, they freeze from the top, ice is not a particularly great conductor of heat and water has a pretty high specific heat capacity. That means that the deep parts of the ocean will remain liquid for a very long time indeed.

If your peeps can manage both fusion power and apparently feel that smelting a few million tonnes of uranium is a reasonable thing to do, then a combination of fission and fusion reactors seems like an obvious first step.

However, as the goals of the Villagers are huge (heating up the atmosphere and keeping it gaseous),

Woah there. This isn't just huge, but astronomical.

Using the very lazy approximation that Earth is a black body radiator with an average surface temperature of 0 degrees C or ~273 K and an emissivity of ~0.95, it will radiate away about 1.6x10¹⁷ W (which is fairly close to the amount of power the Sun provides, so it'll do as a good approximation). Keeping the CO₂ gaseous means a minimum average temperature of ~195 K quarters the power demand to ~4x10¹⁶ W. If you don't mind all the carbon dioxide snowing out, you can drop the average surface temperature to ~90 K which is enough to keep oxygen and argon gasous, giving a power demand of 1.8x10¹⁵ W. Earth itself would provide ~47x10¹² W from its primordial heat and radionuclide decay but that's basically a rounding error on the amount of power you'd need. Clearly geothermal is never going to solve your problem.

1.8 PW for 10000 years is 5.7x10²⁶ J. You could get that if you fused 6 million tonnes of deuterium and tritium, though refining that much hydrogen into deuterium will be tricky and tritium breeding is itself non-trivial. If you used the neutrons provided by the fusion to do fast fission of natural uranium you could significantly reduce the amount of hard-to-come-by fusibles you'd need.

All that, and you'd still be living on a lethally cold, snowball world. It'd take a hundred times more power to keep the surface above freezing on average, but then maybe you could run enough fusion-powered grow-lamp space-heaters to keep plants alive on the surface, too. Snowball earth wasn't melted in a day though, so by the time you've got a suitable industrial base up and running, everything on the surface is going to be dead, dead, dead. So why not give yourself realistic goals and build city-scale habitats with nuclear and/or geothermal heat and light, and wait out the dark times until the star lights up again? Iceland looks nice this epoch...

Answer 2

The Villagers are dead, and it's all your fault...

Only a few hundred survivors are able to delay their death in subterranean bunkers, and up to a few thousand more aboard nuclear submarines.

Civilization cannot be sustained without solar energy within the limits of modern and currently foreseeable (end of 21st century) technology.

• Without solar radiation, the surface will freeze very quickly. Temperatures will drop below freezing in a day. It's not gradual, it's instant night that's getting colder by the hour. In the first days, you lose cars, trains, planes - there's no infrastructure for reheating frozen fuel.

• Wind energy comes from the unevenness of insolation as the planet spins. You will get some bursts of winds while the planet's cooling down, but the turbines might not be strong enough to handle them.

• In a week, the phytoplankton is dead, all the surface plants and animals are dead, the fish still have some time, but losing the plankton breaks their food chain too. There's no new food supply for humans.

• Starfish has correctly calculated that you will never reheat the planet, neither the atmosphere nor the surface. Not enough energy for that anywhere except a star. Surface will settle at 30-40 kelvin for the continents, somewhat warmer over the oceans.

• While oceans are still warm, they can only extend the atmosphere's life for months, since ice acts as an insulator. Air is constantly radiating energy into the outer space. First it turns into a liquid over the continents, some of which flows down to the oceans and evaporates over them. In a couple months, it freezes the surface enough to start turning solid, and then you can only expect a thin Mars-like atmosphere, measured in millibars.

• In a year, the planet is covered in a thin crust of solid oxygen and nitrogen, like Triton. Without air, fossil fuels are useless. Surface-based nuclear powerplants are trapped in frozen nitrogen. It's a rock in space.

• The rudimentary reactor produces some heat, but little electricity, since it's not producing superheated steam. Heat is easily available underground, by simply digging deep enough - the reactor isn't necessary. However, any bunkers that aren't airtight - normally they are only NBC sealed, relying on positive pressure - are losing air to the vacuum outside. A

If you had a lot of years to prepare, you could have built air-tight, nuclear-powered, subterranean bunkers, that are able to function as closed ecosystems for a while. Geothermal heat will keep them warm for millennia. But they are useless long-term, as there's no surface to repopulate, and nowhere to get the resources to expand their underground habitat. The stored resources will gradually dwindle away. At least the Villages can sleep safely, knowing the government's still there, and so are the taxes.

Nuclear submarines are sealed, so they have all it takes, except for the food. For years, thanks to ocean's thermal inertia, their crews can find some pockets of relatively warm land - island towns surrounded by deep water, which aren't covered in frozen air, and thus possible to raid for supplies, wearing emergency escape suits converted into spacesuits. Eventually the reactor's core will run out its life, too, and there's no facilities to replace it.

Your civilization's only hope of survival is a Hollywood save - a hot new star coming along and rebooting the franchise.

...For not equipping them with Kardashev Type I technology.

Replacing solar radiation reaching the planet corresponds to level 1 on the Kardashev scale. A lot of that article is fiction, but it's science fiction.

(Science for Types 0 to 3. Everything trying to extend Kardashev's already beyond-extreme scale, begins at space opera and gradually slides into high fantasy).

Early 21st century Earth is around 0.7 on the scale. It took us 60 years to get here from early space travel, 80 from early atomic power, 200 years from experimental and 150 from commercial electric lighting.

The earliest estimate for reaching 1.0 would be 150-200 years from now, but the gap from 0.9 to 1.0 is huge, since it enters the second half of the S-curve. So most optimistically you might manage what you want with 23th century technology, but more realistically 24th-25th, if we don't slide back due to a war or an environmental crisis.