Long lasting life on interstellar planets?

A short time ago I read that life might be possible on interstellar planets (i.e. planet-like objects which aren't bound to a star by gravity.) They may be insanely cold on the surface but inside they are warmer due to the radioactive decay. A planet consisting of the same materials as our earth but has $3.5$ times its mass could have liquid oceans beneath a thick sheet of ice. This ocean could stay there for about $5$ billion years. That's enough for life to evolve. It would live from chemosynthesis.

While this is already interesting, I was wondering whether longer lasting life is possible. If you imagine a planet of one Earth mass consisting of vanadium-50 (which has a half-life of $1.5*10^{17}$ years), it produces about one-fifth of the power of our Earth. At first that looks like nothing. But then, a fifty kilometre thick sheet of ice covering it can isolate it, just enough to keep a liquid ocean if the water is salty enough and the planet has some kind of atmosphere. It would stay that way something in the order of the half-life of vanadium.

This might be a little farfetched but at least in my opinion it is pretty cool to have one planet support life for $10^{17}$ years. Especially compared to the lousy $10^{10}$ years, our Earth has. However, in reality, it is unlikely to work quite as well, so I assume we need a more active and therefore shorter living isotope. (Here are a few candidates.)

So here's my question:

Is it possible that the universe generates (without help of whatever kind of sapience) such a planet?

With possible I mean to say: reasonably likely that it happens at least once during the life of our universe.

It doesn't have to be a vanadium planet, but at least one which consists for a large part of some long (meaning more than say $10^{12}$ years) living radioactive isotope and a huge ice layer on it. It should have enough of this radioactive isotope to have a liquid ocean for a long time.

I'm not asking for the specifics about life on this interstellar planet. It's almost sure bacteria-like. Also, I'm not asking whether it could really thrive under these conditions. While that might be an interesting question, I think we don't know yet enough to really answer it.

Edit: The main obstacle is whether so much radioactive material could be amassed, since these isotopes are rare in our universe. The cosmic abundance of vanadium is for example 0.0001% and most of it is stable isotopes. This is since most of the long living atoms are only generated by supernovae.

posted about 8 years ago

lurch‭

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