Thursday, March 24, 2016

Why is Jupiter so Big?

WJupiter has about three-quarters of the total planetary mass. Why is so much concentrated in one planet? If Jupiter were divided into Earth-sized planets, there would be over three hundred of them. If Jupiter weren't so big, there might have been enough mass for many Earth-sized planets in our home solar system. That situation would be wonderful for interplanetary adventuring. Lots of places to go with the right amount of gravity. Maybe two in the liquid water zone, even bearing life. But Jupiter had to go and hog most of the mass, so our solar system, even though it has eight or nine planets, doesn't have much for friendly planets to visit. Granted, Venus has about the same mass, but if there were ten or twenty of the same size, things would be so much more interesting, and humanity would undoubtedly be much more interested in interplanetary adventuring.

Are solar systems in general going to be just as disappointing as our solar system? One giant planet with most of the mass, and some small numbers of littler ones. Why did Jupiter wind up with so much mass, and are the physical principles that caused it here going to cause it everywhere?

Recall that our solar system came about because there was a cloud of gas in the galaxy that was left alone for a while, and it cooled down. The creation of the galaxy resulted in a lot of heat, and that got dispersed among the gas that made it up, as there wasn't much else in the beginning. But there wasn't anything nearby heating up this particular gas cloud, and it radiated heat and started condensing. The gas pressure that kept it large against its self-gravitation gradually decreased, and gas flowed inward. Our old friend, angular momentum, had to be preserved, and that means that the collapsing spheroid of gas had to gradually shift over toward being a central spheroid surrounded by a rotating disk. Without too much angular momentum, the vast majority of the gas can collapse toward the central spheroid, which is gradually condensing and becoming a nuclear furnace. But the angular momentum keeps some small percentage of the mass spinning around in roughly circular orbits.

What is the distribution of mass plotted against the distance from the center of the newly forming star? Each circular ring of gas is under two forces, one is the force from the central mass of the sun, and that keeps it rotating at the same radial distance. The other is the force of the other rings. If two rings are close enough, the force between them is large, and they exchange angular momentum and approach each other. This is an unstable situation, and if the rings stayed rings, they would eventually all approach one another and become one single ring with all the planetary mass. The radius would be just right so that all the mass rotating at that radial distance would have the large majority of the angular momentum of the solar system, with just a bit in the star's rotation.

But all things do not stay the same. A ring in and of itself is unstable as well. The ring will do nothing as long as it is perfectly uniform, but a small perturbation in it will start attracting ring mass, and the ring will start getting heavier where the perturbation was and lighter on the opposite side of the orbit. This angular condensation works better when there is more mass in the ring, so it seems fairly clear that the disk will proceed with radial condensation and when it passes a certain point, angular condensation will start up. So, lots of mass radially condenses, as to Jupiter's orbit, and then the planet itself starts to form by angular condensation. This keeps going until there is a substantial angular concentration of mass. Then resonance effects start happening, and the large mass at Jupter's orbit, soon to be a planet, starts affecting the gas at other radii. The radial distribution of mass, during the radial condensation phase, would be unimodal, and the rest of the planets would have to form in the two tails of this distribution, where resonances allowed them to exist.

This is easy to translate to other solar systems. Ones which start in a cloud with no angular momentum will have no planets, and everything will condense into the stellar mass. Ones which have only a slight amount of angular momentum will have a hot Jupiter, and perhaps some planets between Jupiter and the star, unless tidal forces cause them to fall into the star and be annihilated. There would be some other planets at larger radii.

This simple explanation is incomplete on one major factor. How much mass in total is there in the planetary system? It is not solely angular momentum which creates planets. A giant planet with Jupiter's mass and Jupter's radius has just the same angular momentum as a giant planet with half Jupiter's mass and a radius equal to the square root of two times Jupiter's radius. What is the other variable that controls the size of planets?

One candidate is the rate of cooling of the original gas cloud. Before all this planetary disk business gets started, the pressure in the gas supports it against gravitational collapse. If the cooling only happens slowly, a lot of mass is maintained in the outer expanses of the gas cloud, and if it happens very quickly, compared to the time needed for collapse to take place kinematically, less is maintained at further radii.

Would it have been possible for a gas cloud to cool so quickly that all the mass condensed into the star, except for one blob of mass, equal to Earth's mass, orbiting at a large distance from the sun, and holding onto most of the angular momentum of the solar system? An Earth at about 80 AU would carry Jupiter's angular momentum, if that was what was required. This is not so far out that random stars in the neighborhood would influence its orbit, so this is a feasible situation. The alternate Earth is so far beyond the liquid water zone (LWZ) that it would be of little interest to us. A solar system with little total planetary mass and little total angular momentum would be another story. This could result in an Earth-sized planet alone in the solar system, but in the LWZ. We don't need a solar system with a Jupiter for life origination.

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