# Brown Dwarf Star vs Gas Giant as parent for habitable moon

I seek to build a habitable moon of a giant planet, thus I looked at the Rouche Limit Equation to figure out how to get the biggest possible Hill Sphere for my moon to exist in.

$$r_H = a(1-e)\sqrt[3]{\frac{m}{3M}}$$

$$r_H$$ = radius Hill sphere

$$a$$ = semi major axis satellite

$$e$$ = orbital eccentricity satellite

$$m$$ = mass satellite (planet)

$$M$$ = mass central object (sun)

If I interpret the formula right I want to set the secondary objects orbital eccentricity as low as possible, the mass of the star has high a possible, making the lifetime and the spectrum of the star along with the impossibility of planet formation around O and B stars due to photoevaporation the limiting factors. Since the mass of the star is related to its temperature and so to the position of the habitable zone I included this in the calculation of the optimal stellar mass.

This leaves me with the mass of the planet which should be as high as possible. For a gas giant, this would mean 13,8 Jupiter masses. However brown dwarfs offer a much higher mass of up to 0,08 Solar masses before turning into red dwarfs. Given the formula above it is obvious why it seems tempting to use a brown dwarf instead of a gas giant. I´m somewhat at a loss at classifying this system since brown dwarfs are neither planets nor proper stars, so any clarification on whether this is a binary star system or a planetary system would be appreciated.

I have come up with a number of potential benefits and issues by myself, yet I would appreciate it if someone who is more knowledgeable on the subject would check my assumptions and point out what I missed.

• Deuterium and/or Lithium burning should be over within a few million years, so it won´t mess with the system in the later stages. During the formation process, however, the radiation pressure of the active brown dwarf should create a secondary frost line around it. This isn´t necessarily a bad thing since it will make the formation of a big planet much more likely and could inhibit the formation of a radiation belt pumping Io equivalent.

• The mass of a brown dwarf will make keep the orbit of the planet/moon much more stable, as it can provide a stronger counterweight to the suns influence than any gas giant could.

• The additional heat won't be much of a problem since orbits can be adjusted to account for it.

• Some Brown Dwarfs seem to be capable of flaring, which would be bad for obvious reasons. Is this a rare occurrence or do all Brown Dwarfs flare?

• Would the magnetic field of the Brown dwarf deliver any benefits or cause any problems? I assume that a situation similar to the one with Ganymedes magnetosphere will occur.

In the end, I´m interested in whether a Brown dwarf is superior to a gas giant as the host planet for a habitable moon.

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• Would you mind sharing why you want a giant hill sphere? There might be other ways to solve whatever the underlying requirement is. – Starfish Prime May 8 at 10:53
• @Starfish Prime I want it so I can have a huge moon system along with my habitable moon. For the habitable moon scenario a captured one in an eccentric orbit seems most plausabile, yet this capture event would wreak havoc on the rest of the moon system if there is little space aka a small hill sphere. Additionally there's the astetic aspect of either having a Sudarsky Class 2 or 3 Gas Giant vs having the red glow of an L-type or the reddish purple of T-type Brown dwarf. On this front I want to know if the second set of options is even plausabile. – TheDyingOfLight May 8 at 11:43
• Ahh, moons of moons. I think they've popped up on here multiple times in the past, and they're quite problematic. Honestly, given how awesome it would look to be orbiting a gas giant, it seems almost greedy to want your own moons as well. – Starfish Prime May 8 at 11:55
• @Starfish Prime Ups I meant that differently. The habitable moon is not supposed to have any moons, but to be the biggest moon in the gas giants moon system insted of the only one. – TheDyingOfLight May 8 at 12:43