It is possible now with exoplanets to determine their mass, e.g. by measuring a wobble in the star’s motion due to the pull of the planet, and if the planet transits the star, you can measure its size because the light you see from the star starts to dim when the planet starts to transit, and the last of the dimming is when the other side emerges. You get a secondary measurement when it stops dimming at the bottom of the light graph, and starts brightening. You know the speed at which it crosses because you have measured its “year”, or orbital period. If you know its size and you know its mass, you can work out its density, which gives clues as to what it is made of.
Consider the following densities in g/cm cubed: Earth 5.51, Mercury 5.43, Venus 5.24, Mars, 3.93, Neptune, 1.64, Uranus, 1.27, Jupiter, 1.33, Saturn, 0.69. What we get from that is that since rocks have densities between 2.5 – 3 for felsic rocks, and 3 – 4 for basalt, and iron has a density of about 7.8, Earth, Mercury and Venus all have significant iron cores, Mars will have only a small one at best, and the other planets have a lot of gas. However, they have to have cores. The usual theory of planetary formation is that the planet starts with a core, it grows, and when it gets big enough it starts to attract gas. The cores in the outer solar system will comprise ices and silicates, while in the rocky planet zone, because the accretion disk is hotter, the ice has vaporized so we are restricted to rocks. If a rocky planet gets big enough that its gravity can hold gas, it too can become a giant. That is the theory, anyway. Our assessment of Neptune is that while the core is icy, it will also have silicates, and it took it until about 10 earth masses before it started accreting gas rapidly. Uranus would be similar, but the reason it is less dense is, at least in my interpretation, because as the disk gets denser the closer to the star, once it started accreting gas it could do so faster than Neptune could. Accordingly, since they are the same size, Neptune had to grow more core, and in my opinion, that was due to the mechanism of core formation. However, that is not relevant here. As you can see, the lowest density is Saturn, because it is full of hydrogen and helium. Jupiter is denser because, in my opinion, it accreted gas faster and the heat boiled off a lot of hydrogen and helium, which is why it has about three times the amount of gases such as nitrogen compared with hydrogen as the sun, and, of course, the stronger gravity compresses gas better. (The sun was also much hotter, but it has far more gravity.)
There is another theory of planetary formation, where the gas disk becomes unstable and collapses. This may well occur, but it usually is considered to work a long way from the star. One reason is, unless the two instabilities occur at the same time, when you get a double star, if the planetary material is orbiting the star, the closer it is to the star the orbital speeds are different at different distances and the instability would shear. Planets have to be reasonably close to the star to get a transit recorded frequently enough.
Anyway, puffy planets. If we look at Kepler 87 c, it is a planet close to a star the size of the sun and towards the end of its life in the main sequence. It is about as far away as Venus and about 6.4 times Earth’s mass, so it is not expected to be able to hold big atmospheres, yet its density is 0.152 g/cm cubed. The planet HIP 41378 f is an even worse problem. It has a mass very similar to Uranus, the star is 1.15 the size of the sun, and the planet is about 1.37 times further from the star than Earth is from the sun. Interestingly, if it had a big enough satellite, that’s satellite would be in the habitable zone. However, the planet is definitely weird: its density is approximately 0.09 g/cm cubed. That qualifies as a super-puff. There are a number of planets with densities less than 0.3 g/cm cubed, so for whatever reason, they are not freaks.
The question now is, how could a planet have such a low density? I suppose observational error cannot be entirely ruled out, but I think it should be. If there were just one, maybe we could be skeptical, but that many? The next possibility might be they are still accreting, but Kepler 87 c cannot be accommodated by that explanation because the star is so old. Further, if a giant is accreting gas, it gets very hot (we have seen these in newly forming planets) and these super-puffs are cold. Another guess might be that for some reason the atmosphere is extended far beyond what is expected. There are two reasons why this won’t be right. The first is gravity. If the planet is a giant, its gravity is strong enough to suck the gas in close. If there were more gas the planet would grab it. The second is light would get through and we would expect a spectral change during the eclipse, but we don’t see that.
So, what is the explanation? A recent proposal, and one that I think looks good, is that what we are seeing is a planet with rings, like Saturn. The rings have to be dense enough to block off quite a bit of the light passing through them, but what we are seeing is something similar to what Galileo thought Saturn was. If HIP 42378 f had rings going out to 2.6 times the planetary radius, its density would be 1.23 g/cm cubed, very similar to Uranus. Now, if we go back to the habitable moon, maybe that is not so silly after all. Why do rings form? One possibility is that some gigantic collision caused a lot of fragments, and some of them came in within the Roche limit, and fragmented. The Saturnian system is consistent with this – a lot of small moons, including some at Lagrange points of larger ones, and one anomalously very large moon. And as an aside, an alien using these sort of measurements would conclude Saturn was an exceptional super-puff.