# The upper limit to a planet

Contributed by
Sep 7, 2006
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See that little dot next to the bright one? Here's an interesting puzzle: is it a planet, or a star? If you're thinking "Here we go again!" then you're not too far off the mark.

With all the Pluto nonsense going on, the meaning of the word "planet" is under fire. Mostly, the definition has been causing grief due to how it applies to objects at the small end of the scale. But what about the upper end?

Take Jupiter. It's the biggest planet in the solar system. What happens if you dump mass into it? Let's throw Saturn, Uranus, Neptune into it. Of course, Jupiter will get more massive. Oddly, it won't get much bigger: more mass means more gravity, and since Jupiter is mostly gas, it compresses. That extra compression will pretty much balance out the extra volume being added, and the size stays the same. Weird, huh? Weirder yet is that Jupiter is right at the lower end of the size to do that. Saturn will get bigger as you add mass, but once you get to something about Jupiter's mass, the size stays pretty much the same even if you dump ten times as much stuff onto it!

But as you compress a gas, it heats up (do a web search on Boyle's Law). So at the center, it gets hot. As the mass increases, it gets very hot. At some point, the mass will be enough that the core temperature will reach the point where hydrogen atoms will fuse together, forming helium (actually, it's a lot more complicated than that, but this is the main process). This releases a lot of energy, heating things up more. The core expands, and this means the star expands too. As it does, it cools (Boyle's Law again, but in reverse this time). Eventually, a balance is reached such that the heat generated expands the gas, while the gravity compresses it, and the two balance. Literally, a star is born.

The magic mass for this is around 0.08 times the Sun's mass. Anything with this mass or more is a full fledged star. If it has a smaller mass, it isn't a star. It's called a brown dwarf.

So brown dwarfs have an upper mass limit. But what is the lower limit? Where is the borderline between what we call a planet and a brown dwarf?

Jupiter has a mass about 1/1000th of the Sun. You might sometimes hear that Jupiter is a failed star, but that's Bad Astronomy: it would need to be more than 80 times more massive to become a star! So if it's a failed star, it's a really failed one. But if we dump mass into it, when does it become a brown dwarf?

The answer is most likely never. Why? Well, we get into dumb, arbitrary planet definitions again! Most astronomers think of BDs as forming like stars: collapsing under their own gravity from a cloud of gas and dust. Planets, however, form from the disk of material circling a star. That's not a gravitational collapse process, but more of fragmentation and accretion. However, this distinction is a bit silly: you could have two objects, both of which look exactly the same, but one formed from gravitational collapse, and one formed from disk fragmentation. Yet one would be a brown dwarf, and the other a planet. That's dumb.

But what would you use as a mass limit? There really isn't anything that distinguishes between, say, something that has 10 times Jupiter's mass and something that has 20. One's more massive, but other than that they're pretty much the same. So a mass cutoff between planet and BD is arbitrary, and you know how I feel about that. Arbitrary rules do not a definition make.

So astronomers fudge, and just say that something more than about 13 times Jupiter's mass is a BD. Why?

Well, theoretically, this is about the upper limit to the mass of an object that will form from fragmentation. Not terribly satisfying, is it? It isn't to me, but there you go. Nature doesn't always provide us with a line in the sand, labeled "That be planets, here be brown dwarfs". It's around this mass that deuterium, an isotope of hydrogen, will fuse. The problem here is that this is not a sustainable source of energy; a BD fusing deuterium can only keep it up for a few million years or so before running out. What is it then? And the mass limit is not rock solid: other factors come into play (elemental abundances, convection, etc.) that can change things such that a lower mass object can fuse deuterium. So while there is a physical change around 13 Jupiter masses -- fusing deuterium versus not fusing it -- it's still a fuzzy border.

Which brings us, finally, to the object in the picture above. The bright object is a star, named CHXR 73. It's actually really faint, a low-mass red M-type dwarf. But the fainter object is CXHR 73b, its companion. This is a newly-released Hubble image of the pair, and astronomers say that the mass of 73b is about 12 times that of Jupiter. So what is it? A planet, or a brown dwarf?

The mass indicates it's a planet. But, and this is a big but, it's really far from its parent star: about 31 billion kilometers (19.5 billion miles). That's about 200 times the distance of Earth from the Sun, and according to all theories that's too far out for a planet to form. The original disk of junk circling the star would never reach that far out, especially around a dinky star like CXHR 73. So most likely 73b formed from gravitational collapse out of the original gas cloud that the primary star formed from. That makes it a brown dwarf.

I think this is all very silly. We may never know for sure how 73b formed, and I absolutely guarantee we'll find objects that'll be even closer to the line than this, causing even more confusion. Worse, if we label it one way, it may cloud our judgement. If I think of it as a planet, I might overlook some star-like qualities of it, and vice-verse. That's why labelling things can not only be silly, but outright damaging to science. You have to tread very carefully.