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TRAPPIST-1 is described as "Jupiter-sized" (comparable radius), although at 8% of the Sun's mass, must be on the order of 100x greater (Jupiter : Sun is about 1 : 1000). This seems paradoxical and raises several questions.

Since Jupiter is thought to be mostly hydrogen and other light gasses, and as a star, TRAPPIST-1 must be mostly hydrogen (it is fusing hydrogen into helium, isn't it?), how can it be so much hotter and denser at the same time? Shouldn't the high temperature keep the density down?

Jupiter has been described as a "failed star" - too small to produce the conditions necessary for nuclear fusion to occur. Does TRAPPIST-1 offer any useful insight as to where that threshold lies - how big is big enough to get the process started? Just how close is Jupiter to that threshold, anyway?

Could it just be that some of the facts are wrong, and when corrected, there is really no paradox at all?

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  • $\begingroup$ Possibly belongs on a different site? $\endgroup$
    – Russell Borogove
    Feb 23, 2017 at 4:52
  • $\begingroup$ @RussellBorogove take a look at DavidHammon's answer, this NASA item, and this Nature news item about Juno's investigation of what's inside Jupiter. Jupiter's funky center is certainly on topic and it will probably continue to be a reference point for TRAPPIST-1 discussions. This is not only a question about brown dwarf stars in general, it's about our next-door neighbor, and it's similarity to 'our' Jupiter. $\endgroup$
    – uhoh
    Feb 23, 2017 at 7:48
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    $\begingroup$ @RussellBorogove so suggesting it belongs on a different site sort-of sounds like it does not belong here. I sometimes suggest a question might receive a better answer somewhere else, or vote it off-topic. But the belongs somewhere else concept casts a dim light, which might attract the occasional drive-by close vote. $\endgroup$
    – uhoh
    Feb 23, 2017 at 8:15
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    $\begingroup$ TRAPPIST-1 now has its own web site: trappist.one It says "Presenting Humanity with Many Opportunities to Study Terrestrial Worlds Beyond our Solar System" which sounds like Space Exploration to me. I vote to re-open the question. I think SXSE should include a few nearest neighbor systems. It now even has a travel agency as well! $\endgroup$
    – uhoh
    Feb 23, 2017 at 16:03
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    $\begingroup$ @uhoh That reason is a little contrived, but planetary science is on topic here and this definitely involves planetary science. $\endgroup$
    – called2voyage ♦
    Feb 23, 2017 at 17:20

1 Answer 1

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Jupiter is about as large as a planet can get, physically. Suppose we slowly add hydrogen and helium to Jupiter, so slowly so as to keep it at more or less its current temperature. Surprisingly, it would get smaller. Jupiter is about as large as a planet can get. (There are exoplanets that are larger than Jupiter, but that's because they orbit so close to their star that they are very hot.)

A very large brown dwarf that is just below the edge of being able to fuse hydrogen and that is as cool as is Jupiter would be smaller in diameter than is Jupiter, despite being about 65 or so times more massive than is Jupiter. A star that is just above the edge of being able to fuse hydrogen would be larger than its just under the edge cousin, but not by that much. The star in question is about 83 times more massive than is Jupiter, which makes it warm enough to be larger than Jupiter.

The reason for this seemingly paradox is the nature of degenerate matter. Jupiter's core is very slightly degenerate. Adding mass would increase the degeneracy. This is the root of the solution to the paradox. Adding mass to a degenerate object makes the object get smaller.

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  • $\begingroup$ So if you add mass to such a gas giant, the distribution of that mass is changing (mass is "transferred" into the degenerated core which takes up less volume, so we end up with less mass in the "shell"), which makes it shrink. Is that correct? $\endgroup$
    – DarkDust
    Feb 23, 2017 at 9:20
  • $\begingroup$ Are you implying that a normal star's (or even Jupiter's!) core contains degenerate matter? What I (as a complete layman) find with a quick google search seems to suggest that only star remnants or white dwarfs have degenerate cores, see e.g. faculty.wcas.northwestern.edu/~infocom/The%20Website/…. The shrinking with increasing mass of a massive planet/brown dwarf is a simple result of a classical gas under gravitational pressure, and the (counter-)pressure of a normal stellar core is classic pressure of a heated gas. $\endgroup$
    – Peter - Reinstate Monica
    Feb 23, 2017 at 10:21
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    $\begingroup$ @PeterA.Schneider Well metallic hydrogen is more or less degenerate matter, just not in the sense of a white dwarf etc. Metallic hydrogen is so densly packed, that electrons can move freely around their protons that hydrogen becomes conductive. This form of hydrogen exists in the core of gas giants. But there is nothing "transfered" anywhere. It's just a form of forces in equilibrium - if you add more mass, the equilibrium shifts to more metallic hydrogen and less gaseous thus slightly reducing the overall volume of the planet while its mass increases. $\endgroup$
    – Adwaenyth
    Feb 23, 2017 at 10:37
  • $\begingroup$ @Adwaenyth I didn't think about that until your comment. Hydrogen has only one electron. So when all the electrons have moved from valence to conduction bands, all you've got is bare protons and an electron gas. What really strange stuff! So is the difference between liquid metal hydrogen and solid metal hydrogen the protons 'freezing' into a lattice? $\endgroup$
    – uhoh
    Feb 23, 2017 at 17:50
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    $\begingroup$ @uhoh yes that is exactly the case that I meant. And it is just one step away from becoming a fusion reaction if the pressure rises even further - which is what we would expect to happen when we add more mass. $\endgroup$
    – Adwaenyth
    Feb 24, 2017 at 6:25

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