The major effects on the habitability of exomoons orbiting this Brown Dwarf

I'll need to give some background to this question. I'm interested in the idea of a densely inhabited star system, and having large exomoons is one way that they can all orbit roughly at the same part of the habitable zone and have very high chances for lithopanspermia while not having to orbit very close to a small star and be tidally locked to it. Given the size of Jupiter's moons you would need a very large planet, more like a brown dwarf, to have Earthish exomoons, but then these planets could orbit further away from the primary star and not suffer from the huge flares and solar winds they would suffer when tightly packed around an actual red dwarf, like perhaps occurs in the Trappist-1 system. They would (probably) all be tidally locked to the brown dwarf, but have a day/night cycle with respect to the star.

Let's say that there is a star which has similar characteristics to the sun, and so the habitable zone is similar to that of Earth. At 1AU orbits a brown dwarf of 80Mj with a diameter of 200,000km; failing to be a red dwarf at the last hurdle:

It has moons that are each around half the mass of the Earth. Half the mass of the Earth seems enough to reasonably be habitable under certain conditions but not perturb each other too much gravitationally:

They are spaced varyingly, but typically between 1.5 up to 1.75 the preceding semi-major axis. The 4th moon out is at about 1,157,140km and the final moon is out at a bit over 8 million away. I don't know if the orbits are non-crossing on astronomical timeframes but it seems reasonably stable. A brown dwarf has a big hill radii in an orbit of 1AU around a sun analogue. Out beyond the 8th moon things seem to become unstable on visibly observable timeframes, so 9th and 10th moons were removed.

I realized later that the Roche Limit is the larger problem here and that the inner moons are in danger. I was told that a satellite with the density of Earth could orbit almost arbitrarily close to Jupiter because the density of Jupiter's atmosphere means the Roche radii lies within Jupiter. It would have to be in danger of interacting with the atmosphere before it was in danger of being turned into rubble.

So I winged it and placed a VERY close moon at 1 radii away. However, even assuming that information is correct, there's a BIG difference between Jupiter and an 80 Jupiter mass brown dwarf (79 Jupiters to be exact). Sadly, doing the actual calculation (Rl=2.44Rp*cube root[Pp/Ps]) for the Roche Limit, and assuming Earth density satellites, makes the limit = 4.56673413178 brown dwarf radii, which is 456,673km ish. This means that in the zoomed in picture below, the green and pink orbits are actually rings(now I'm wondering whether the other moons would make any interesting gaps):

Possibly, my brown dwarf is a little puffy at 1.4ish Jupiter radii(maybe it's spinning very quickly, or it could be very hot which would be bad), so the real point at which moons start turning into rubble is a little closer, but let's not push things too much.

EDIT:

Some questions are:

• Do Cyan and Maroonish have extreme volcanic activity like Io?
• Are ALL the moons tidally locked if the system is 4.5 billion years old or can ones at 4 million+ and 8 million+ km away avoid this fate?
• Although they have enough density, the tidal locking would prevent them having magnetic fields, so can they be protected by the magnetic field of the brown dwarf?
• Or does the magnetic field of the brown dwarf create deadly radiation bands that render them unhabitable? Would only the last few moons be okay or this not that big an issue?
• If a brown dwarf has just about failed to be a star, it's certainly fusing lithium at least... BUT it should use this up in about half a billion years, so if we wind the clock forward a billion years or so, will the temperature of the brown dwarf still be an important factor? Does it create an overlapping habitable zone that means close in moons get a double dose from both the sun and the dwarf?

More generally, what are the major issues for habitability in this system? The actual single question I'm asking to people here is; how far away do you have to go before one of these moons is habitable?

• The radiation belt question is perhaps the most important one, but also one that's pretty hard to get nice straightfoward answers for. After all, you can cheat on the tidal problems of the inner moons and make them water worlds, but surface habitability is perhaps questionable... – Starfish Prime Dec 21 '19 at 13:56
• That is rather a lot of questions for a single question – Slarty Dec 21 '19 at 15:28
• @Slarty - Those are sub-level questions that come to mind, but my main question is how habitable the system would be. Since most of those questions are to do with the inner moons, I've edited the post to condense it to a single question of where the brown dwarf habitable zone would be. – Axion Dec 21 '19 at 16:06
• Tidal locking doesn't mean it has to lack a magnetic field; Ganymede has one (albeit quite faint) and rotates synchronously. – Cadence Dec 21 '19 at 16:21

TL;DR:

The actual single question I'm asking to people here is; how far away do you have to go before one of these moons is habitable?

Your moons at 4 and 8 million km might be ok. I'm sure you can handwave that. The inner moons are more doubful due to radiation and tidal stresses, but water worlds might be habitable for aquatic species.

Do Cyan and Maroonish have extreme volcanic activity like Io?

Tidal effects are Hella Complex. We can simplify things quite a lot though simply by looking at the definition of the tidal force, minus some of the extraneous bits: $$F_T \propto {M \over d^3}$$, or, the strength of the tidal force is proportional to the mass of the primary and inverse proportional to the cube of the separation of the satellite from the primary. You've increased your primary's mass by a factor of 80, so you'd need to increase the separation by a factor of 4.3 to keep the magnitude of the tidal force in the same ballpark... the Io-equivalent orbital radius is ~1.8 million kilometres which would encompass both Cyan and Maroonish.

As I said, tidal effects are complicated, so it isn't by any means guaranteed that these will be Io-type worlds. Consider also that a water world could exist at those orbits... the habitability of such a world would be a difficult thing to establish but, y'know, you have supreme authorial power there.

Are ALL the moons tidally locked if the system is 4.5 billion years old or can ones at 4 million+ and 8 million+ km away avoid this fate?

Time-to-tidal-lock is something that isn't at all well understood. Depending on the approximations you use, you might get locking times of under a billion years or over ten billion. I suspect you could handwave the outermost moon as unlocked without any major issues (especially if it had a submoon, but that's a separate subject). The 4-million km moon seems less likely, though, but there's enough wiggle room for you to handwave something in here, I suspect.

Although they have enough density, the tidal locking would prevent them having magnetic fields, so can they be protected by the magnetic field of the brown dwarf?

Jupiter's magnetosphere stretches out to 100 Jovian radii... a bit over 7 million kilometres. Your brown dwarf should be denser and hotter and more energetic than Jupiter, and so might reasonably be expected to have a larger magnetosphere. Even if its magnetosphere was simply scaled up to 100 of its own radii, it would encompass your outer worlds.

Or does the magnetic field of the brown dwarf create deadly radiation bands that render them unhabitable? Would only the last few moons be okay or this not that big an issue?

This is a biggun, and very difficult to answer well. If I had to hazard a guess, I'd say your inner worlds would have very hostile surfaces if they had no atmospheres, but your outermost world is probably OK even if it had no atmosphere. There's a huge amount of wiggle-room here, and I'd like to offer a bit more clarity but I'm coming up short.

You could a) have hostile surfaces but more benign oceans on your inner worlds and b) in a suitably advanced scifi setting, use giant electrostatic tethers to discharge any radiation belts. That won't help if you want intelligent surface live to arise on all your worlds, but everyone likes a good superadvanced precursor species who built nice things and vanished like an unreliable parent.

If a brown dwarf has just about failed to be a star, it's certainly fusing lithium at least... BUT it should use this up in about half a billion years, so if we wind the clock forward a billion years or so, will the temperature of the brown dwarf still be an important factor? Does it create an overlapping habitable zone that means close in moons get a double dose from both the sun and the dwarf?

It'll be warm, certainly... a lot warmer than Jupiter. You might have to nudge the whole thing a little bit further away from the sun, but I'll leave that to you to work out, as computing the contribution of the glowing embers of your brown dwarf to the heating of your moons requires all sorts of bits of information you haven't shared.

• Thanks. What details do you need to know to compute the brown dwarf heating contribution? If it formed a certain amount of time ago, and it has a certain mass, doesn't its cooling rate broadly depend on how long it's been since then? – Axion Dec 22 '19 at 20:19
• @Axion working out its temperature seems likely to be complex... it'll probably be 300K < T< 1000K given its age, but that doesn't take into account heating by the local star which seems like it will be non-trivial, given how close it is. After that it comes down to atmospheric compositions of the moons. I suspect you'll need to move a brown dwarf that size a bit further away from the primary to keep your moon surface temperatures down. Mostly it just seems too much like hard work to figure it out ;-) – Starfish Prime Dec 22 '19 at 21:14

There are many previous questions with answers about possible habitable moons of gas giant planets (or sometimes brown dwarfs) in the habitable zones of stars.

Here is a link to apparently 667 posts on that topic:

And I think that someone interested in the habitability of exomoons, moons of planets in other star systems, should check out:

"Exomoon Habitability Constrained by Illumination and Tidal heating" by Rene Heller and Roy Barnes, Astrobiology, January 2013.

And someone interested in creating a fictional solar system with many habitable worlds should check out the PlanetPlanet blog, especially the posts in the Ultimate Solar System section.

Note that the most extreme solar systems there are described as engineered solar systems, since they are so improbable that they would have to be built by highly advanced civilizations instead of forming naturally.