Sir Chaos wrote:
The Roche limit is a hard inner limit for orbital radius
Umm. It's one hard inner limit. I think that in the case of a rather dense planet and a very diffuse star the Roche limit might be inside the star's surface! And remember that the Roche limit is proportional to the cube root of the ratio of the density of the star to the density of the planet. The Sun's Roche limit would be about 1.56 r☉
for a planet as dense as Earth, but 3.12 r☉
— twice as far — for a planet as diffuse as Saturn.
Given that planets can have migrated inwards, availability of primordial material in the protoplanetary disk is not a strict limit. That is, a planet or planetismals can form out in a large and thick part of the disk and then migrate inwards to a more circumscribed or sparser region. That leaves three 'hard' inner limits that I can think of. The one that actually binds is the outermost of them.
• There's the temperature limit. Large black-body temperatures mean that the volatiles of a planet evaporate to space in a process of Jeans Escape. I guess
that that means that a gas giant leaves behind a rocky-metallic residue that forms a rocky planet — it might not have formed a core in the original, but there has got to have been some dust and junk included when the gas giant coalesced, and that won't undergo Jeans Escape whereever in the planet it starts out from. However, when things get really hot even materials that aren't normally thought of as volatile (a) melt, which doesn't matter much, because they just form oceans (b) evaporate, which matters more, because they are then liable to Jeans Escape depending on their molecular mass, and ultimately (c) break down chemically into elemental gasses and simple molecules. There's an article on catastrophic evaporation of rocky planets
that suggests that the limit is about 2000 K but that the evaporation takes significant time so that planets may be observed* that have formed at a cooler radius and migrated in, or have been caught as their star grows brighter with age. Such planets have a sunny face over 2000 K, metals and silicates evaporating on the dayside, blowing to the nightside as an atmosphere, and condensing on the night side. This is a transient stage, as the vapours involved don't have molecular masses all that much greater than oxygen's 32 (iron vapour is 56, silica 60) so they evaporate to space by the Jeans process; the planets lose mass, their escape velocity falls, and the Jeans process gets more rapid. I would definitely
be up for featuring a system with one of these things in a hard-science exploration campaign. But they are transient and rare so I don't think I'd build a generator to recognise them. Anyway, black body temperature of about 2000 K is one hard limit.
• Then you have the tidal disruption limit, the Roche limit. Again, this is further out for gas giants than it is for rocky and especially rocky-metallic planets. If gas giants have cores then it is possible that when they reach the Roche limit they start losing hydrogen and helium from their surfaces while denser constitutent remain at the core. Such planets get denser as they get smaller, and their Roche limit moves inwards. Simultaneously they get hotter and their escape velocity falls, so they start preferentially losing hydrogen and helium to Jeans escape, which again tends to make them denser and their Roche limit move inwards. Maybe gas giants that are disrupted by tidal effects leave rocky corpses.
• And finally there's the surface of the star itself. This can be further out than the Roche limit if the planet is 14.8 times the density of the star, which is within the bounds of possibility. And Earthlike planet could orbit at the surface of a star with specific gravity of 0.373 or less, which is less dense than Sol but about right for a main-sequence star hotter than about A3 or any giant. It can only be outside the temperature limit if the star's surface is cooler than 2000K, which is only the case for L-type and late T-type brown dwarfs. The thing here is that any star that is low-density enough for the Roche limit for rocky-metallic planets to be within the surface is too hot for the temperature limit to be within the surface. So it must alway be one of the other constraints which binds.
* E.g. KIC 12557548b