My planet is a gas giant, it is called Klarloth (Inspired by a character from "Star Mouse" by Fredric Brown).
Klarloth is a strange planet. For one thing, the planet is large in size, more larger than usual for a gas giant (Most gas giants above $1$ $M_J$ tend to get denser, not bigger, as they gain mass, mostly hovering at around $1-1.5$ $R_J$). Characteristics of Klarloth:
Radius: 285,000 km
Parent Star: None, Klarloth is a rogue planet.
Mass: 500 $M_J$
Yes, you heard that right. Klarloth is 500 times the mass of Jupiter.
Not even a star, not even a brown dwarf. Klarloth is a PLANET.
The reason is well (relatively) mundane, when you get to it.
The nebula, where the planet Klarloth formed was deficient in deuterium/lithium for some reason. I will figure out why in a later question. But for now, let's assume the fact that for some reason, the presence of deuterium/lithium in the nebula that formed planet Klarloth, was non-existent. Meaning that even if it wasn't a star, Klarloth couldn't effectively be a brown dwarf, as they was not enough deuterium in the nebula that it could fuse and generate energy. Even without deuterium, lithium wasn't present the nebula that formed Klarloth, so even if deuterium wasn't present, it couldn't resort to fusing lithium for energy. (How? and Why? is happened is out of the scope of the question, as I have handwaved the chances of such a nebula occuring, so I am primarily concerned with how- [REVEALED LATER IN QUESTION])
The next reason, however is a bit more exciting.
You see, Klarloth, although primarily made of hydrogen, has a core made of heavier elements. Although Klarloth has plenty of hydrogen, the reason why it cannot fuse it despite it being wayyyy more massive than $80$ $M_J$, is especially, there is no hydrogen in the core.
The situation is similar to a AGB Star (Red Giant, blue supergiant, red hypergiant etc etc). Let's take Betelguese for an analogy of Klarloth (I know that a red supergiant is a poor analogy for a supermassive planet, but I cannot find any other reference)
Betelguese still has more than half of it's hydrogen remaining. However, it is paradoxically fusing heavier elements. If current calculations are current, Betelguese is still fusing either helium or carbon.
The main reason is not because of lack of hydrogen. Betelguese still has plenty of hydrogen. But the hydrogen has been shunted out of the core. In other words, you have plenty of food at the table, but the food has been shunted out of reach, leaving only plates on the table. Meaning that, Betelguese's core is now littered with heavier elements like carbon/oxygen. The hydrogen has been shunted out to the outside of the core, where it is not hot enough to fuse.
My planet Klarloth, similarly also faces a similar situation, although in this case, there is NO fusion going on. The planet started out as a ball of rock which grew up in size and gained tons of hydrogen gas, which continued to grow up, till it reached $500$ $M_J$.
As of today, Klarloth's core is composed of the following chemicals in the given ratios-
- 55% Iron, mostly in the form of oxides.
- 16% Oxygen, bound to iron as oxides.
- 29% Thorium sulfide
Basically, the planet Klarloth has such a large core of heavy metals, that at a certain radius, it should be able to displace hydrogen from the center. Meaning that hydrogen is now in an envelope surrounding the core of heavy metals.
The only thing that is left to calculate, is the radius of the core....
Basically, I want to find how big the core has to be, so that it can displace hydrogen from the center, preventing it from fusing.
So, if an electron-degenerate iron core about 2 times as wide as Germany, can halt silicon fusion in a red supergiant (before collapsing into a neutron star in a fraction of a second, of course, but that's completely unrelated to the question's scope), I figure that, the core of the planet can be small and still prevent fusion in the core. Sadly, my planet is not a red supergiant, so my previous assumptions in the previous sentence were proven wrong. I figure that the core of the planet has to be much larger to order to prevent fusion of hydrogen in the core. I simply want a supermassive planet. I have solved the deuterium/lithium deficit problem, now I just need to find out the radius of the core, at what size it can displace enough hydrogen from the center, to stop fusion.
My dear Worldbuilders, I present you with this question:-
- How large (in radius) should the core of my supermassive planet be, to prevent fusion of hydrogen?
Bonus question (Not necessary to answer, I just added in, just because I thought it might be related)
- How massive should the core of the planet be?
The reason I have added the hard-science tag is because, I need calculations and stuff to check the answer, the resultant required radius of Klarloth's core.
Remember that although ironically handwavium has been used in a question tagged hard-science, handwavium has only been used for parts of the story that are not the scope of the question (explaining how it formed, why it has a deficit of deuterium/lithium etc). The main problem here is to find the radius of the core of Klarloth.
Note about the Hydrogen envelope, surrounding the heavy-element core:-
The envelope (you can call it the "mantle" of Klarloth. Gas giants don't really have a "crust"), is composed of 90% hydrogen and 10% helium.
Note that the core of the gas giant isn't a "fuzzy core" like Jupiter. If that was the case, results would be disastrous, as the hydrogen could seep in and ignite fusion. Klarloth's core is a proper, well-defined core.