# 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.

• Would you mind sharing why you want a giant hill sphere? There might be other ways to solve whatever the underlying requirement is. May 8, 2019 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. May 8, 2019 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. May 8, 2019 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. May 8, 2019 at 12:43