We may be carbon-based life forms, but carbon is actually pretty rare on Earth. If fact, only 0.03% of Earth’s crust is made of carbon, hundreds of times rarer than the foundations of the planet–silicon, aluminum, iron, and, oddly enough, oxygen. That carbon forms the building blocks of life instead of the much more common silicon says a lot about the probability of silicon-based life, but that’s another story.
Why is carbon so rare on Earth? You might guess that it’s because heavier elements like iron and silicon sank to the bottom of the Sun’s gravity well, where Earth is, while lighter elements like carbon stayed in the outer Solar System. That’s true of the very light elements, hydrogen and helium, but the most common element on Earth is oxygen, which is about the same weight as carbon. The real answer lies in chemistry.
The four most common elements in the universe, in order, are hydrogen, helium, oxygen, and carbon. Helium doesn’t react with anything, and most of the hydrogen stayed in the outer Solar System, but what’s left formed molecules when the Solar System formed. In Earth’s neighborhood, there was more oxygen than anything else, so it combined with both hydrogen and carbon to form water and carbon dioxide. It also combined with silicon to form silicate rocks, which form most of Earth.
As Earth formed, the intense light of the young Sun evaporated away most of the carbon dioxide and water, and any leftover oxygen, but not the silicates or elemental iron. That’s why Earth is made of iron, silicon, and oxygen.
We expect most rocky planets to be like Earth because there’s twice as much oxygen as carbon in most of the galaxy. But there are places–mostly regions with lots of old stars–where there is more carbon than oxygen, and that changes all of the chemistry.
With more carbon than oxygen, the atoms would combine into carbon-rich molecules like methane, oils, carbon monoxide, and silicon carbide. Carbon would also combine with titanium to form titanium carbide and with iron to form natural steel. Leftover carbon would turn into solid graphite.
We call planets made out of these chemicals “carbon planets“. The surface of a carbon planet would be made out of graphite, tar, and, just maybe, diamonds. But you wouldn’t want to go there, because the atmosphere would be mostly methane and carbon monoxide.
Some parts of the galaxy have so much carbon that they have to have carbon planets, but we don’t know any for sure that are carbon planets. We know two planets that might be carbon planets: WASP-12b, a hot Jupiter, and 55 Cancri e, a super-Earth. There is another “planet” called PSR J1719-1438 b (the PSR means it’s a pulsar planet) that we’re pretty sure is made of carbon, maybe even diamond, but it’s actually a piece of a white dwarf–a dead star that has been eaten down to planet-size by the gravity of the pulsar.
Carbon planets are special, though. They are one of the few weird types of planets that we expected to find before they were discovered. The rest of the time when you’re looking for planets, you have to expect the unexpected.