Last time we explored the new theory of Sergei Nayakshin & Aaron Boley – the origin of terrestrial planets in the cores of diffuse proto-planets. How do such objects form and are their core conditions sufficient for Marvin Herndon‘s provocative theory of Whole-Earth Decompression?
According to the new planet formation theory, large gaseous proto-planets form far away from the proto-Sun, about 50-100 AU. The initial disk of gas and dust forms large spiral structures of over-density, which in the cooler outer-reaches can form Jeans Mass blobs. A Jeans Mass is a mass which is collapsing, under its own gravity, just a bit faster than sound can travel across its span. Sound waves act to even out density changes, so they act to maintain a diffuse cloud in a diffuse state. Gravity acts to clump gas/dust together, creating over-dense regions. Once a significant over-density sets in, the collapse is inexorable so long as excess energy and momentum can be radiated or spun away.
A Jeans Mass equal to Jupiter (1.899E+27 kg), assuming a ~50 K starting temperature and a mean molecular mass of ~3.9E-27 kg, is 1.59 AU in radius (!) At this point its free-fall time is ~21 years, but before too long the internal temperature rises, from infalling gas/dust, to the point where the gas/dust mix is no longer transparent and the object starts convecting internally as it contracts. That’s typically at about ~1000-2000 K, when hydrogen starts becoming opaque to the IR being emitted. Roughly the proto-planet has to contract to about 1/40th its initial size before the temperature rises to ~2,000 K. Then it radiates at about that temperature and contraction slows down as internal pressure climbs and the blob doesn’t lose heat quick enough.
I’m being a bit vague on all the tricky physics as it gets rather complicated – modellers compute the evolution of such blobs as “proto-stars” and have computers crunch the numbers for a few hundred layers within the proto-star, slowly evolving the system through time. A proto-Jupiter would settle down within a few thousand years to something like a red-hot equilibrium, cooling off over a few million years to become the planet we know today.
However, to make a terrestrial planet from a proto-planet, it can’t stay put in the outer nebula disk, out past 50 AU, while collapsing. Instead a whole bunch of other Jeans Mass blobs have formed from those big spiral shocks in the nebula. All sorts of tidal effects are tugging at the proto-planet and being so diffuse its Roche Limit is much, much bigger than what it is for a planet. Migration has set in and the proto-planet is losing orbital angular momentum to the nebula’s loose gas/dust. By the time it hits the region of the asteroids much of its envelope can be stripped away by the tidal effects of the spiral shocks, other proto-planets and the central proto-Sun.
But is that enough for Herndon’s Compressed Earth concept? Here’s the thing. Central pressure of an object varies with the square of the density and the radius – BUT for a constant mass and changing density, that density is also proportional to the inverse cube of the radius. Thus squared density means the inverse sixth power of the radius, which after cancelling means the inverse fourth power of the radius. In hard numbers it means a proto-Jupiter 10 times as big as final Jupiter, will have 1/10,000th of the central pressure. Roughly ~2500 bars. Interestingly Herndon quotes an old cosmochemical theory from A. Eucken which had the terrestrials form in proto-planet cores at that pressure. But between 10 times Jupiter’s radius and its current radius is 10 times more binding energy for the proto-Sun to make off with proto-Earth’s excess gas-giant mass. Whether the conditions near the proto-Sun are enough to strip away the gaseous envelope of a near fully developed gas giant is thus an open question. Eucken’s ideas require a hot, extended proto-planet and might be correct, but Herndon’s Whole-Earth Decompression theory seems to require a nearly fully condensed Gas-Giant with a central pressure of ~multi-millions of atmospheres. That might not be achieveable and still result in a Sun-stripped planetary core.
But what if the proto-Sun was vigorous enough? Herndon assumes Earth was compressed to ~64% of its present size. That means a former density about 3.8 times higher and a former surface gravity ~2.44 times higher. Interestingly the Faint Young Sun paradox, the unexpectedly clement climate of Earth around a once fainter Sun, could be solved by a higher surface pressure causing pressure broadening of the greenhouse-effect-causing infra-red absorption of the carbon dioxide in Earth’s atmosphere. The original suggestion is that Earth once had much more nitrogen, which is possible. But an Earth 64% of its current size would have roughly 6 times higher atmospheric pressure from the same amount of gas – as both the surface area and gravity vary inversely with the square of the radius, thus combined it means the surface pressure varies with inverse fourth power of the radius.
Over time the Earth’s internal structure “relaxes”, releasing the energy stored in its constituent molecular structures from all that compression, with some extra energy from radioactive decay and Herndon’s theorized georeactor – a natural nuclear breeder reactor in the Earth’s core. Imagine a spring slowly returning to a less compressed state after a part of a very heavy load is removed. Most of the energy is stored up as gravitational potential energy as the Whole Earth rises against its own gravity, but some will go into heating the mantle and maybe the core. Eventually some final equilibrium will be achieved, though just when is yet to be determined by Herndon.
