# Explaining a Low-Mass Brown Dwarf

Considering the well-established relationships between stellar mass, surface temp, and luminosity, how unusual would it be to find a star (or brown dwarf) that possesses about half the mass of an average member of its spectral category?

Follow-up questions: If such an anomaly did exist, what sort of phenomena could be responsible? Would it be relatively stable over a human lifespan? Or would it necessarily be a transient phenomenon like most variable stars?

The specific example in question is a brown dwarf with a mass ~7110 times Earth, radius ~12 times Earth's, and a spectral black-body temp of 1400K (placing it in the L8 to L9 spectral class). For a sci-fi story, I've constructed a setting with this brown dwarf, Kabina, in orbit of the star Phi2 Ceti (renamed Bahram in everyday parlance), and multiple colonized planets orbiting both the primary star and the brown dwarf.

On reviewing my notes recently and double-checking the numbers, I realized that late L-class brown dwarfs tend to have a mass 1.5 to 3 times the figure I was working with. Whereas brown dwarfs of similar mass are liable to be less than half as hot and bright.

I've calculated the orbits and surface temps of the orbiting planets based on these numbers, so if I need to fix the properties of my brown dwarf, I need to also rework the planetary orbits in order to maintain habitability. If, on the other hand, I can find a plausible explanation for the anomaly, it becomes a cool little detail of the system to add scientific curiosity, and I don't have to rewrite the calendars I've already drawn up for the colonies in orbit.

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$$\sim$$7000 Earth masses and a surface temperature of 1700 K aren't unreasonable for a brown dwarf. The lower mass limit is thought to be around 13 Jupiter masses (or 4100 Earth masses) (see e.g. Spiegel et al. 2010), and we see temperatures as low as 500 K in certain Y-class brown dwarfs. 12 Earth radii seems a bit small, but not unrealistic. To be honest, you chose decent parameters. This is certainly much too light for a red dwarf, of course; the hydrogen fusing limit is about 75-80 Jupiter masses, which is, give or take, three times as high as your choice. However, I would argue that you've chosen a fairly realistic brown dwarf.

We expect a brown dwarf - or a planet, or an M star - to cool over time, eventually reaching fairly low temperatures. A graph from Burrows et al. 2001 (taken from these slides) should emphasize that point:

A brown dwarf should reach the temperature you desire within about a few hundreds of millions of years.

Here are examples of brown dwarfs with similar properties:

The latter two are actually pretty similar to yours, in terms of mass and temperature.

If there was a brown dwarf of, say, 10 Jupiter masses, well, it might instead be classified as a rogue planet or sub-brown dwarf, rather than a brown dwarf. Cha 110913-773444 is an object like this (Luhman et al, 2005). We don't know how these bodies form; it's possible that the low mass is simply due to a dearth of material around the body early in its life.

• So tl:dr it is not an anomaly and needs no explanation? – Mołot Dec 10 '18 at 17:14
• The WISE bodies are both in the same temperature range, late-L class brown dwarves. But their masses are from 1.5 to 3.3 times my figure. COROT-3b has similar mass, but as far as I can tell is a late-T class brown dwarf with a temp of ~550K. So I have a body with the mass of a T-class dwarf, but the temp and luminosity of an L-class dwarf of twice the mass. (See additional paragraphs above for added context.) – Rich Durst Dec 10 '18 at 17:40
• The graph you shared brings up an issue that I don't think I ever accounted for: the age of the brown dwarf. If it formed with the primary star, it would be about 1.9Gy old. But if I can justify it being separately formed and then captured, I can tweak the age so as to get the temp and luminosity I want. Then again, if it's a late-captured body with its own satellites, that leads to a whole other set of orbital complications. – Rich Durst Dec 10 '18 at 17:41
• @RichDurst That's a possibility. I've also considered a scenario where the circumstellar disk from which the brown dwarf formed was fairly low-mass - which would explain an even lower mass, if you wanted it - and where perhaps the formation of the brown dwarf was delayed for a significant amount of time. Perhaps the cluster where the system formed was dominated by OB stars, and the strong winds depleted the disk? There are definitely scenarios where this could work - and yes, your capture idea is absolutely possible. – HDE 226868 Dec 10 '18 at 18:05
• @Mołot Basically, yes. The temperature and mass don't quite line up, as Rich said, but they aren't extreme, and it's not too unlikely for a brown dwarf to have both, depending on its age and initial evolution. – HDE 226868 Dec 10 '18 at 18:06