Is this Solar System Stable for Long-Term Evolution of Intelligent Life?

[dysfunction]

Aspiring hard-scifi writer here. I try to make sure details in my fiction are consistent with known science or reasonable extrapolations thereof, unless absolutely demanded by the plot (and even then I try to offer some justification). I'm wondering if the solar system I'm setting a short story in would be stable over several billion years, long enough for intelligent life to evolve:

Primary is a red dwarf star of around one quarter solar mass. Orbiting it is a brown dwarf of 25-40 Jupiter masses at a distance of say 50-100 million kilometers, and orbiting that is a planet (according to the IAU it's still a planet even though it's orbiting a failed star) of around a tenth Earth's mass with around a third the volume, say two million kilometers out- far enough out, from my sloppy estimation, to be quite cold on the surface, but close enough to have become tidally locked relatively early in its history and for those tidal forces to heat a subsurface ocean. Achieving a Europa-like effect, essentially, in a very different system. Does this work?

 

[SpiffyKavu]

The small planet would be able to orbit around the brown dwarf in your system. The sun is about 1,000 Jupiter masses, so a 40 Jupiter mass brown dwarf is not much smaller than your red dwarf. See the wikipedia for "Hill sphere" for a small discussion on this.

And it seems reasonable to assume your planet will be tidally locked to the brown dwarf, but there would likely not be any more tidal heat generated. Tides will lock one face of the planet to the brown dwarf, and then circularize the orbit. The tides will generate heat only when there is a change in tides, which changes the shape of the planet. With a circular orbit, the tidal forces will not change, so your heat source will disappear.

Europa is kept warm because it is forced into an elliptic orbit. It is in an orbital resonance with Io; Europa orbits Jupiter once each time Io orbits twice. This situation gives a constructive gravitational kick (see: resonances), which keeps the orbit of Europa from becoming a circle.

By the way, your planet is similar in mass to Mars. However, your quoted volume is much larger than Mars, so it would be a rather fluffy planet. It is also worth noting it's similarity to Mars because Mars is geologically inactive. Granted, Mars has been around for over 4.5 billion years. My point is that a planet the size of Mars will cool down pretty quickly, so the planet would require another source of heat to maintain a subsurface ocean if your star system is pretty old.

 

[dysfunction]

Thanks for the helpful reply! I made an oopsie- I said the planet had a third Earth's volume, when I meant a third Earth's radius, which would actually make it considerably denser than Mars. I'm not wedded to most of these figures, though.

Hmm. I suppose there could be another planet orbiting the brown dwarf in resonance with the first, though I hadn't thought about that. Alternatively, I suppose I could move the planet in a bit closer to the brown dwarf, such that its heat warms the planet's core enough to keep the sub-surface ocean liquid, but the surface stays cold enough to remain solid ice. Not sure if that would work, though.

EDIT: Did the Hill sphere calculation, and if I did it right, even if the primary had one solar mass, the brown dwarf the minimum (~13 Jupiters) mass to qualify for that designation, and it orbited at less than 50 million km, the Hill sphere would have a radius over 7 million km, so there's plenty of room to play with in distances and masses where the system would remain stable.

EDIT 2: Also did a very rough estimation of the brown dwarf's Roche limit for this planet, getting around 800,000 km, so I can't move the planet too far in.