Inspired by this question and my comment on one of the answers.

If the earth were to be flung out of the solar system, it would rapidly become far too cold for any unprotected life to survive on the surface, especially once the atmosphere began condensing and eventually freezing. Any remaining humans would have to live in pressurized domes. However, if the earth was ejected from the solar system on a shallow enough trajectory, it's possible that governments or groups could put together such domes before the temperature dropped too severely. However, such domes need to be kept heated, oxygen needs to be provided, and food needs to be grown for long-term survival. Therefore, I nominate Iceland as the candidate most likely to support a long-term surviving colony. The reason for this is Iceland's reliance on geothermal power, just about the only power source likely to remain viable over the long-term as the earth drifts away from the sun. According to Wikipidia, Iceland used 79.7PJ of geothermal power in 2004, which, if my math is right, gives them about 2.5GW. (If anyone manages to find more recent numbers, please comment and I'll add them).

Given these facts, how likely is it that Iceland could maintain a colony of this type indefinitely, and how large is the maximum colony size that could be maintained?

Iceland can hold out indefinitely

• It would take 2-3 months before the average temperature on the surface to be below zero (the reason for this is that the ocean has tremendous heat capacity, inland regions will fall much faster). That gives them a reasonable amount of time to prepare a living space. Iceland would have slightly more time due to the natural heating due to geothermal and their proximity to the ocean.


• Due to it's molten core, the earth's surface will stabilize at an average temperature of -160 C on the surface. David Stevenson, Caltech professor of planetary science This is not cold enough for the atmosphere to condense, so the need for pressurized domes is incorrect.


• It would take approximately two years to get down to this steady state temperature. And -160 C is not impossible for a human with appropriate equipment to survive and work on the surface.


• The best option for the Icelanders is to tunnel beneath the surface to maximize the benefits of the geothermal heating (without having to turn it into electricity). That way, they can use the electricity they produce for cultivating crops.


• As for how large this colony can be, it probably depends more on their digging speed (to produce adequate farmland area) than it does on actual energy constraints. Just because it produces that much geothermal energy doesn't mean that that is all the geothermal available to it as it expands.


• Food stockpiles will obviously give them more time to increase their living spaces before they have to depend on their own farming to sustain them. Additionally if they have a submarine, then they will be able to operate limited fishing operations (and later mining for frozen fish), as the frozen surface of the ocean will insulate the water, keeping it liquid for many years.

Given these facts, how likely is it that Iceland could maintain a
colony of this type indefinitely, and how large is the maximum colony
size that could be maintained?

Ok, given time to erect an airtight and thermaly insulated environment or series of them.

For sure heating is going to be your bigest problem as the outside temperatures approach single digits Kelvin, but we'll assume with "Perfect thermal insulation":

The energy requirements for lighting sufficient to provide plant growth for food and for Krebbs cycle for oxygen for one person comes out to about 10 Kw. (Figure extrapolated from Bios3 data, exchanging the xenon arc lamps for more efficient LEDs) For the non vegans, gastropods, fish, insects could be cultivated with a modest increase of that budget to say 15 Kw per person.

Doing the simple maths gives you the energy budget for 160,000 people.
The more energy used for recycling water, air circulation, creating materials for repair, and leaving a safety margin - 100,000 people is not unreasonable in a perfect (if artificial) world.