Wednesday , October 28 2020

How big can a planet be?

Jupiter is the largest planet in the solar system. In mass terms, Jupiter rises above the other planets. If you gathered all the other planets into one mass, Jupiter would still be 2.5 times more massive. It's hard to underestimate how big Jupiter is. But, as we have discovered thousands of exoplanets in recent decades, this raises an interesting question about how Jupiter compares. In other words, how big can a planet be? The answer is more subtle than you might think.

The simple answer is that a big planet is too small to be a star. The usual definition for a star is that it should be large enough to fuse helium hydrogen into its nucleus. A star in the main sequence is one in which the heat and pressure generated by the fusion are balanced by the gravitational weight of the star.

Stars are made mostly of hydrogen and helium, and it is safe to assume that the largest planets would have a similar composition. The sun is made up of about 75% hydrogen and 24% helium, with the other 1% heavier elements. Jupiter is approximately 71% hydrogen, 24% helium and 5% others. So let's find out that any big planet has 3 parts hydrogen to 1 part

As long as there is no fusion, a large planet will be in a hydrostatic equilibrium state. This means that the weight of all this collapsing gas is balanced by the pressure of the gas that does not want to be squeezed. The more mass you have, the more the inside will be squeezed and the hotter it will get. With enough mass, the interior becomes hot enough for hydrogen to begin to fuse with helium. This critical mass is about 80 Jupiter. Anything with more mass than this must be a star.

But this is not the best upper bound, because there are objects in the universe known as brown dwarfs. These objects look like stars because they are not in hydrostatic equilibrium. Their interiors generate heat like a star and may even fuse hydrogen into deuterium but not helium. On the other hand, the smaller brown dwarfs have cold, cloudy surfaces and look like a planet. The lower mass limit for a brown dwarf is about 13 Jupiter masses.

In terms of mass, 13 Jupiter masses are a good upper bound. But when it comes to large planets, the most massive ones are not the largest in size.

Estimated planet size in mass compared to observed exoplanets. Credit: Chen and Kipping

Unlike solids, which do not compress much under pressure, gases can compress significantly. Thus, as you add mass to a gaseous planet, its volume does not increase by the same amount. For example, Jupiter is three times the mass of Saturn, but it is less than 20% larger in volume. Returning to our hydrostatic equilibrium model, the most massive planets are actually smaller than Jupiter's size.

A few years ago, Jingjing Chen and David Kipping analyzed how the size of the planets can vary depending on their mass.[^1] They found that there is a transition point between the Neptune-type worlds, where more mass tends to increase its size and the Jupiter-type worlds, where more mass tends to simply compress more gas. This critical point is about half the mass of Jupiter, so the largest planets should have around this mass. This agrees with the observation. The largest confirmed exoplanet is WASP-17b. It is approximately twice the size of Jupiter, but only 49% of Jupiter's mass.

Some of the largest exoplanets compared. Credit: NASA / ESA / Hubble

Obviously, there are other factors that come into play, such as composition and temperature. The largest known exoplanets tend to be hot Jupiter orbiting near their star. This means that they are much warmer and less dense than a cold Jovian planet like Jupiter. Jupiter also has a dense rock core, which means it is smaller than it would be if it were made only of hydrogen and helium.

But even taking these factors into account, the Jovian planets are clearly the largest and most massive in existence. Jupiter is not the largest planet in the universe, but it is one of the giants.

Source: Probabilistic prediction of masses and rays of other worlds, by Chen, Jingjing and David Kipping.

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