Massive 'forbidden planet' orbits a strangely tiny star only 4 times its

TOI 5205b, that is a good one here and very interesting. shows properties and it orbits very close to the red dwarf star., "The host star, TOI-5205, is just about four times the size of Jupiter, yet it has somehow managed to form a Jupiter-sized planet, which is quite surprising!" exclaimed Kanodia, who specializes in studying these stars, which comprise nearly three-quarters of our galaxy yet can't be seen with the naked eye...The time frame in which this happens is crucial. "TOI-5205b's existence stretches what we know about the disks in which these planets are born," Kanodia explained. "In the beginning, if there isn't enough rocky material in the disk to form the initial core, then one cannot form a gas giant planet. And at the end, if the disk evaporates away before the massive core is formed, then one cannot form a gas giant planet. And yet TOI-5205b formed despite these guardrails. Based on our nominal current understanding of planet formation, TOI-5205b should not exist; it is a "forbidden" planet."

Forbidden planets could be a fun topic :)

ref - TOI-5205b: A Short-period Jovian Planet Transiting a Mid-M Dwarf,, 21-Feb-2023. “Abstract We present the discovery of TOI-5205b, a transiting Jovian planet orbiting a solar metallicity M4V star, which was discovered using Transiting Exoplanet Survey Satellite photometry and then confirmed using a combination of precise radial velocities, ground-based photometry, spectra, and speckle imaging. TOI-5205b has one of the highest mass ratios for M-dwarf planets, with a mass ratio of almost 0.3%, as it orbits a host star that is just 0.392 ± 0.015 M⊙. Its planetary radius is 1.03 ± 0.03 RJ, while the mass is 1.08 ± 0.06 MJ..."
The total dust and gas for a postulated protoplanetary disc around a 0.392 solar mass red dwarf (MMSN model) could be 1.305136E+03 earth masses. The 1.08 Mjup exoplanet is about 3.432456E+02 earth masses.

From the ref paper.

“6. Summary We present the discovery of TOI-5205b, a Jovian exoplanet orbiting a solar metallicity mid-M dwarf. TOI-5205b was first identified from TESS photometry, and then characterized using a combination of ground-based photometry, RVs, spectroscopic observations, and speckle imaging. The large mass ratio of the planet (∼0.3%) necessitates a disk that is ∼10% as massive as the host star, thereby stretching our current understanding of protoplanetary disks around M dwarfs. The typical scaling relations used to estimate disk properties are hard-pressed to reproduce the primordial disks that are massive enough to form such a planet. However there is significant scatter in disk dust mass measurements and scaling relations, which could still explain such massive planets around mid-M dwarfs. TOI-5205b has a large transit depth of 7%, which makes it an excellent candidate for transmission and emission spectroscopy, both from the ground (high-resolution) and space (JWST). Atmospheric characterization could help constrain the metallicity of the planet and could offer clues about their formation history. The large sample of M dwarfs being observed by TESS is already improving our understanding of planet formation around M dwarfs. While the first few discoveries were limited to the early-M dwarfs, we are now starting to find that it is indeed possible to form these gas giants around mid-M dwarfs. As we go from a sample of these planets around solar-type stars to mid-M dwarfs, there is a unique opportunity to study planet formation at its extremes, spanning more than a 2× range in stellar mass, and 100× in luminosity!”
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Jan 11, 2023
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With the number of stars out there, even wildly improbably configurations are going to exist in abundance. Maybe this system only existed because of a sequence of unique gravitation interactions. Theories may be too rigid, but not entirely wrong. Also, we must take great care in exoplanet analysis because the data is skewed towards what is easiest to detect with our instruments, there is a lot of data we're missing because we can't detect it. Detecting this system is super easy because the planet has a massive effect on it's parent star. You can't not see it. An analog to our solar system at over 200ly might not be detectable with our current technology.
I can find 4 exoplanets like this, near or slightly larger than Jupiter mass found around very small mass stars.

The star masses range 0.092 solar mass up to 0.392 solar mass (TOI-5205 b in this report). I used mass of exoplanet 0.9 to 1.1 Mjup to find them in my database (updated from site).

Their semi-major axis range 0.0199 au to 1.74 au.

TOI-5205 b, OGLE-2018-BLG-1647/KMT-2018-BLG-2060, OGLE-2018-BLG-1367/KMT'2018-BLG-0914, KMT-2018-BLG-1743 b

These exoplanets will have the same issues that TOI-5205 b does when it comes to origin.
Nov 10, 2020
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Are we absolutely certain that it is a "rocky" gas giant? Why not a binary star that has failed to form because of a lack of total mass?
This is a good question which as evidence for disk instability driven direct collapse as a dominant mode of large planetesimal formation grows both within our solar system and in young protoplanetary systems observed by long baseline interferometry the difference between planet and star is getting blurrier and harder to define. Now there is evidence that accretion is still significant i.e. it isn't either or but both since stellar metallicity has been found to correlate fairly strongly with the number and mass of planets given our limited sample sizes but it looks like large planetesimals form far more early on than traditionally assumed in more chaotic turbulent conditions. There is even evidence that stars can and do form this way around more massive parent stars or given the dominant planar alignment of many of the S stars around Sagittarius A* quite possibly generalized accretion itself as the coalescence of particulate grains in gas and dust serves as a means to allow the bulk accretionary flow to rapidly expel angular momentum.

If memory serves were was even a recent paper which studied the radiation outflows of accreting protostars over time and found that contrary to expectations the flow seemed to occur in discrete bursts which energetically appear to be on average several Jupiter masses worth of material. Or in essence the collision of gaseous planetary masses may be the dominant mode of star formation i.e. stars may form from "planets" rapidly falling inwards due to gravitational interactions in the main coalescence stage with the planets left over being remnants of this process.

This may on a related note help resolve some of the apparent conundrums of super massive black hole growth as if the bulk accretionary flow is occurring in the disk around instability (plus subsequent accretion and collisions) derived compact objects.
After all many of those S stars appear to be young and very massive the sorts of stars which may undergo supernovae in a few million years with potentially more massive siblings that have already exploded. When accretion resumes what will happen to those compact objects left behind? might they not continue to grow until they become black holes which continue to in fall and collide into more and more massive compact bodies ultimately falling into the SMBH?

Lots of questions to investigate and mysteries to resolve out there.