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Or a star smaller than a planet?

Which star and planet would be an example of this?

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    $\begingroup$ Do neutron stars count as "stars" for this? $\endgroup$
    – mmeent
    Oct 27 at 13:11
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    $\begingroup$ By "bigger" are you referring to volume or mass? $\endgroup$ Oct 27 at 15:37
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    $\begingroup$ Do brown dwarves count as stars or planets? Or neither? $\endgroup$ Oct 27 at 20:36
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    $\begingroup$ @DonBranson mostly... nasa.gov/feature/goddard/2021/… $\endgroup$
    – fraxinus
    Oct 28 at 6:00
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    $\begingroup$ Bigger than a star or bigger than their star? $\endgroup$
    – Mast
    Oct 28 at 11:38
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The answer depends on whether you mean is any planet bigger than any star, or whether the planet and star have to be in the same system and have been discovered/measured, rather than just that they could exist in principle.

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. Mass-radius plot for 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.

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 are rare around low mass stars, so it could be some time before an example is found. However, 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 $i \sim 30^{\circ}$ 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.

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    $\begingroup$ I have played around a little bit with the numbers to see if a specific planet with a specific host star can be larger. I.e. if we want to inflate a 'Hot' Jupiter orbiting the smallest M dwarf, $M=0.08M_{\odot}$ and assuming it sits on its main sequence, we get $R=0.1R_{\odot}$ and $T_{\rm eff}=2000 K$, then the incident flux when orbiting at 3 $R_{J}$ distance is about $\rm9\times 10^{7} erg cm^{-2}s^{-1}$, which is just below the empirical threshold value for HJ inflation ($\rm2\times 10^{8} erg cm^{-2}s^{-1}$). Now this is only the minimum stellar mass, but chances for $R_p>R_s$ seem slim. $\endgroup$ Oct 27 at 13:55
  • $\begingroup$ @AtmosphericPrisonEscape as you can see from the plot, "uninflated" planets of more than one Jupiter mass should be bigger than $0.1 R_\odot$ (indeed, Jupiter is, just). $\endgroup$
    – ProfRob
    Oct 27 at 17:19
  • $\begingroup$ Yes, but that is for any planet and star found. The plotted planets and stars are not orbiting pairs. I asked the question whether there is an actual star-planet combination that can fulfill the requirement to inflate the planet via the large L condition and fulfill $R_{p}>R_{s}$. $\endgroup$ Oct 27 at 19:27
  • $\begingroup$ @AtmosphericPrisonEscape the relationship between the mass and size of a cold planet (the solid line in the picture) is independent of the type of star the planet orbits. Therefore there is no reason in principle that a very low mass star should not have a $>1M_J$ planet that is bigger than it. In practice, giant planets around low mass stars are rare. $\endgroup$
    – ProfRob
    Oct 27 at 19:32
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    $\begingroup$ One possible solution would be a recently formed and therefore hot Hupiter, or one that had just collided with a terresital planet. $\endgroup$ Oct 28 at 15:46
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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.

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    $\begingroup$ That contradicts Prof Rob's answer, which has actual examples. Hot Jupiters vs Red Dwarfs, which are "regular stars" (not brown dwarfs). $\endgroup$
    – JDługosz
    Oct 27 at 22:41
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    $\begingroup$ @JDługosz such is the problem with accepting questions that use vague terms like "bigger" :D $\endgroup$
    – Caius Jard
    Oct 28 at 12:09
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    $\begingroup$ "bigger" is a different word than "heavier". What's vague about it? $\endgroup$
    – JDługosz
    Oct 28 at 14:43
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    $\begingroup$ @JDługosz, what's not vague about it? "Bigger" could refer either to bigger radius / volume or to bigger mass. Both senses are fairly common. Indeed, there is a highly upvoted comment on the question requesting exactly this clarification, to which the OP has not yet responded. $\endgroup$ Oct 28 at 15:26
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    $\begingroup$ @JohnBollinger Would you really say that a cardboard box filled with stuff is bigger than the same box when empty? I think that the speaker talking about a "bigger" object may implicitly refer to their masses and that the bigger one is also heavier, but the calling of one bigger is keying off the visible shape. If the two properties were not varying in the same direction, one would point out that "the bigger one is lighter". I submit that a native speaker would never call a smaller but heavier choice "bigger". $\endgroup$
    – JDługosz
    Oct 28 at 20:38
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The red dwarf EBLM J0555-57Ab is smaller than Saturn.

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

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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.

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