Hi there
Hot-Jupiters are fascinating objects, and the fact that so many have been discovered in the past years, makes me think about planet Mercury, its formation and evolution in the past.
There's one question that came into my mind recently: Is it possible, that Mercury is the core of an ancient "Hot-Jupiter" or "Hot-Neptune", which lost its atmosphere over time? The average density, interior structure and large core of Mercury, are unique in our solar system and may fit to the core of a much larger planet.
Are there any scientific studies to this topic or additional information on the web?
Extremely unlikely if not completely impossible. Mercury's surface is cratered at saturation level which strongly implies that it's been a rocky object since at least the LHB.
Furthermore, at an orbital radius of 56 mil km, a gas giant could barely be considered a 'hot Jupiter' most of which have MUCH smaller orbital radii. True objects of this type seem to be stable over large timescales, so if Mercury had ever been a gas giant it would be reasonable to expect that it would still be so in the current era.
A gas giant planet that boiled off its atmosphere, leaving only the core is called a chthonic planet.
As nprev noted, radiative heating at Mercury's orbital distance is not nearly enough to burn off a gas giant's atmosphere.
There's also some evidence that systems with hot Jupiters develop by the hot Jupiter clearing out the entire inner system, so if Mercury had ever been a Jupiter-mass planet, Venus wouldn't be here -- maybe not Earth, Mars, or even Jupiter, either.
There's some fun, somewhat uncertain math regarding the ability of a world to hold a gas in its atmosphere given the molecular weight of the gas, the escape velocity of the world, and the atmosphere's temperature. (It's that last factor that makes it so uncertain, because temperature and atmospheric composition can vary with altitude in complex ways.) For different putative values of albedo, distance from the Sun, mass, radius, etc., you can see what the minimum distance is that will maintain H2 and He.
Incidentally, there are probably some hot gas dwarfs out there: Worlds that are made of silicates and metal but are so hot that they are gaseous, but still hold together gravitationally. I've done some tinkering with this math and find that an earthlike mass could probably make this work, while a marslike mass probably could not.
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