Is there any planet bigger than a star?

Question

Or a star smaller than a planet?

Which star and planet would be an example of this?

Answer 1

The answer depends on whether you mean is any planet bigger than any star (Case 1), or whether the planet and star have to be in the same system and have been discovered/measured (Case 2), rather than just that they could exist in principle. There is also now a Case 3 which would be planets orbiting compact objects like neutron stars and white dwarfs.

The answer to Case 1 is yes - planets can be demonstrably bigger than stars. The answer to Case 2 is that whilst such systems may exist in principle, they are probably rare and there are not yet (in late 2024) any reported examples. The answer to Case 3 is yes; there are now several planets known orbiting both neutron stars and white dwarfs that are almost certainly bigger than the compact star.

Case 1

There are a few known planets with measured radii that are bigger than the lowest mass stars. Here is a plot from Chabrier et al. (2008) (and plenty more data will have been added since), which shows the basic picture. This is the mass-radius plot for both stars and exoplanets.

It turns out that there are some hot Jupiters that have radii about twice that of Jupiter in our Solar System. You can find examples at exoplanets.org, such as HAT P-67b and XO-6b. These planets are bigger than theory suggests for a "cold" exoplanet, probably because of "insolation" (heating by their parent star) - e.g. Enoch et al. (2012).

On the other hand, the smallest stars, those just above the brown dwarf limit of $\sim 0.075M_\odot$, that are predicted to have radii (at least once they are a billion years old and have reached the main sequence), of about 1.3 times that of Jupiter. At older ages they can become even smaller - about the size of Saturn (black dashed line).

In terms of measurements, there are low-mass objects in eclipsing binaries and also a handful of very low-mass stars that have interferometric radii. For example Proxima Cen (the nearest star to the Sun) is reported to have an interferometric radius of $(0.145 \pm 0.011)R_\odot$ (or 1.44 Jupiter radii) by Demory et al. (2009) and so this is clearly smaller than the biggest exoplanets.

Case 2

If one demands that the exoplanet and star are part of the same system, then although they could exist in principle (as per the discussion above), there aren't any examples (yet). The curves in the plot above are not dependent on the type of star a planet orbits. Therefore, in principle, it might be possible for a $>1M_J$ planet to be found orbiting a (only just) smaller $<0.1 M_\odot$ star, even if it receives negligible insolation.

In practice, giant exoplanets appear to be rare around low mass stars, so it could be some time before an example is found. A compilation of 18 giant exoplanets that transit M-dwarfs, and hence having measured radii, contains none that are likely to be bigger than their host star (Kanodia et al. 2024).

Using the radial velocity technique, a close candidate might be GJ3512b which is an exoplanet with $M\sin i = 0.46 M_{\rm Jup}$ (i.e. this is a minimum mass, since the orbital inclination $i<90^{\circ}$) that orbits an M5.5V star quite similar to Proxima Cen (Morales et al. 2019). The star has an estimated radius of $(0.139 \pm 0.005) R_\odot$ and the age is thought to be a few billion years. Looking at the curves in the plot then a cold exoplanet with $i <=30^{\circ}$, and thus having $M >= M_{\rm Jup}$, might be comparable in size to the star. Unfortunately, the exoplanet doesn't transit so no radius measurement is available and it is unlikely to be inflated by stellar insolation because it is in a relatively wide orbit around a faint star

An interesting suggestion is that a young exoplanet might offer the best chance of being bigger than its host star. This is because the contraction timescale of a giant planet is longer than the pre main sequence contraction timescale of its star. The curves in the plot above for 1 Gyr and 10 Gyr show this effect, but it is even more extreme for ages $0.1$ Gyr. Thus the best chance of finding planets bigger than their host stars is to look at young systems in star forming regions. Some of these may already have been found using direct imaging, though in my opinion these quite high-mass "exoplanets" ($>5$ Jupiter masses) orbiting at very large distances ($>100$ au) are more like binary brown dwarfs.

Case 3

There are now examples of planets that orbits compact stars (neutron stars and brown dwarfs). In fact some of the first exoplanets discovered were around pulsars. Even the least massive of these "pulsar planets" is likely to be bigger than the $\sim$10 km radius of the neutron star it orbits.

There are also now examples of giant planets found around white dwarfs. Since white dwarfs are around the same size of the Earth, a giant planet would certainly be larger. The difficulty is in constraining the mass of the potential planet to be less than that of a brown dwarf (roughly 14 Jupiter masses). An example is WD 1856+534, which eclipses the brown dwarf and very likely has a mass less than 14 times that of Jupiter and is roughly the same size as Jupiter.

JWST has also directly imaged two planetary candidates around two white dwarfs (Mullally et al. 2024). These are likely to have mass in the range 1-7 Jupiter masses and must be far bigger than the white dwarfs, or they wouldn't be visible at all.

Answer 2

If by "bigger" you are referring to mass, disregarding radius, then the answer is strictly no for a regular "star"

A star is a body that has reached a stable state in which gravitational collapse is balanced by nuclear fusion in its core. A "planet" that was bigger (more massive) than a star would have a core that was hot and dense enough for fusion to begin, and so would be a star. A star that had less mass than a planet would not have a core that was hot and dense enough for fusion to start, and so would not be a star!

There is an exception: if you are willing to accept stellar remnants like white dwarfs and neutron stars as "stars" (they are hot but there is no fusion occurring) then these can be smaller (in diameter) but much more massive (weight) than a planet.

For convenience we normally consider bodies that are up to 13 times the mass of Jupiter to be "planets", 13-80 times the mass of Jupiter to be "brown dwarfs" (they don't have significant hydrogen fusion in their cores, but do have some deuterium and perhaps lithium fusion) and over 80 times the mass of Jupiter are "stars". By this definition "stars" must be more massive than planets.

A white dwarf would be about the size of a moon or small planet, but a mass of about 200-1300 times the mass of Jupiter. Neutron stars are even more extreme, with a size comparable to an asteroid, but a mass of several thousand Jupiters.

There are planets that are known to orbit around neutron stars. The planet would be physically larger than the star, but much much less massive. An example is PSR B1257+B12. The neutron star is about 10km in radius and has mass greater than the sun. Its planets are much less massive, but very roughly Earth sized.

Answer 3

The red dwarf EBLM J0555-57Ab is smaller than Saturn.

https://en.wikipedia.org/wiki/EBLM_J0555-57

Answer 4

Just from theoretical principles, suppose there is some mass $M_s$ above which a body undergoes gravitational collapse and becomes a star, and below which it doesn't. A body with mass $M_s+\epsilon$ would become a star, begin fusion, then radiate energy, becoming a body with mass less than $M_s$. However, it would continue being a star; once a body has undergone gravitational collapse, its density increases, and the mass needed to sustain gravitational collapse is lower. There would need to be a certain amount of energy radiated away before the body ceases being able to sustain fusion. So we should expect there to be a range from $M_s$ to whatever this lower mass is in which there exist both planets and stars.

On top of this, having a sharp boundary of $M_s$ would depend on all star candidates of the same mass being the same in terms of density, composition, temperature, etc. Variations in such characteristics would be another factor creating a "star or planet" band of mass.