Existence of planets larger than their host star?

The mass region of objects between ~ 0.5 Jupiter masses and 80 Jupiter masses (gas giants through to brown dwarfs and red dwarfs) is typified by an almost flat relationship with object diameter. There are planets out there which are larger than some of the smallest stars.

The smallest (currently fusing) star known, EBLM-J0555-57, is estimated to be slightly larger than Saturn (at about 59000 km radius with 85 times Jupiter's mass).

One of the largest planets known that isn't a suspected brown dwarf, WASP-79b is estimated to be twice Jupiter's diameter at 0.9 times Jupiter's mass. Many Hot jupiters and puffy planets with similar measurements are known.

How likely are there to be systems where a planet is larger than its host star? Are there any examples known?

I am looking for currently fusing stars only, which rules out pulsar planets, etc.

• Are you going purely on mass, or would you go by radius, allowing a "young" planet whose gas or dust field is still going thru the coalescence process? (not that I have any idea how to find those) – Carl Witthoft Mar 7 '19 at 15:59
• It has to be by radius, as stars are always more massive than planets. – Ingolifs Mar 7 '19 at 20:09

The answer to the question depends on the exact definition of planet that is used.

A possible example is the L dwarf 2M 0746+20 (2MASS J07464256+2000321) and its planet 2M 0746+20 b.

The radius of the planet is 12% greater than the radius of the star.

$$\begin{array}{lll} \hline \text{} & \text{Mass} & \text{Radius}\\ \hline \text{Planet} & 12.21 \cdot M_J & 0.970 \cdot R_J\\ \text{Star} & 83.79 \cdot M_J & 0.089 \cdot R_{Sun} = 0.866 \cdot R_J\\ \hline \end{array}$$

Note: The reported planet mass of $$12.21 (± 0.4) \cdot M_J$$ is slightly below the deuterium burning limit of 13 Jupiter masses.

Since the smallest stars are still the size of gas giant planets, the question ends up coming down to whether gas giants exist around stars at the bottom of the main sequence. Close-in gas giant planets are rare around low-mass stars, though there do seem to be long-period ones. This means the largest planetary radii for the systems in question are going to be similar to Jupiter, rather than inflated hot Jupiters. An exception would be the case of very young systems before the planets cool and shrink but in that case the star would also still be contracting so you probably don't win there.

A problem is that these stars are extremely faint, so the radial velocity method is tricky - this may change a bit once more RV instruments that operate in the infrared (e.g. the Habitable Zone Planet Finder) come online. The long orbital periods for giant planets around these stars would also require longer observation times to make a detection. Unfortunately the long orbital periods would make transits unlikely, so most probably we wouldn't be able to determine the planet's radius and would not know for certain that the planet is larger than the star.

Direct imaging has spotted a few objects of a few Jupiter masses at fairly wide separations from objects near the hydrogen-burning limit, e.g. 2MASS J02192210-3925225 with an object at the deuterium-burning limit is located about 150 AU from a 0.1 solar mass star. It's not entirely clear what to call these objects and they may be very low-mass brown dwarfs rather than planets. Furthermore these systems are so young that the stars have not yet contracted to their main sequence radii. For low-mass stars this can take several billion years, by which time the planets will have cooled off and become much fainter (and less detectable). These kind of wide-separation systems may also end up being disrupted by stellar encounters.

The other approach that works for detecting these kind of systems is gravitational microlensing, which tends to find objects near the system snowline, i.e. on scales more similar to our planetary system. An example of the kind of system that might have a planet larger than its star is KMT-2016-BLG-1107Lb, where the parameters suggest a ~3.3 Jupiter mass planet orbiting a ~0.087 solar mass star at ~0.34 AU. Unfortunately the uncertainties in the parameters are typically large because the lens systems are usually invisible. This means we also don't have radius information, so we can't say for sure that this system definitely has a planet larger than its star.

So it looks like systems do exist where a planet can be larger than the main-sequence star it orbits, though so far there is no confirmed case due to the difficulty of making the necessary observations.

Beyond red dwarfs, another possibility is that of a planet orbiting a type B subdwarf star.

Some features of such stars:

• Composed almost entirely of helium
• Thought to be formed through the merger of two white dwarfs or at a specific point in the evolution of some red giants
• Temperatures range from 20,000 K to 40,000 K
• Brightness is between 10 - 100 times the brightness of the Sun
• Mass is typically ~0.5 times the mass of the Sun
Two type-B Subdwarf stars with planets are known. V391 Pegasi is perhaps the closest to fulfilling the planet-larger-than-star criterion. Orbiting the star at ~1.7 AU is a 2.5 - 3.99 $$M_j$$ gas giant. This gas giant will receive more energy from its star per square metre than the Earth does from the sun, but this is not likely enough for the planet to heat up sufficiently to become sufficiently 'puffy' to overtake the star's size of 2.3 $$R_j$$.