Sunday, May 1, 2016

For Every Hot Jupiter is there a Cold Saturn?

Right now we here on Earth have seen quite a few solar systems, but only partially. Our detection methods are quite selective as to finding exo-planets. We see them preferentially if they are larger and closer to their star, by one method, or if they have an orbital alignment that puts them in transit across the face of their star. Other methods might have other selectivity, but we need a bit larger dishes to stop with all this selectivity and start looking for a whole solar system.

Until we do this, one big question is left unanswered. How many origin planets are there in our galaxy? We can throw out the stars where planets would be hard-pressed to produce life, like in the central bulge, but for all of them in the galactic disk, what’s the probability that a given star, F through M class, has a planet with a LWZ (liquid water zone), much less all the other conditions that the origination of life needs.

This makes a big deal of difference for the visiting of our planet by aliens, or by an alien probe, or by an alien seeding vessel. If there are lots of planets that some alien civilization might reach, then maybe they just haven’t gotten here yet. If there are virtually none, then the distances to get to us are too large. There is a lot more to be said about alien strategies for star travel, but for now, let’s think about how many planets there might be.

One way planets get thrown out of the solar system or into the deep cold reaches of it is through planetary migration. Why would planetary migration happen? For a one-planet solar system, it doesn’t, except if the planet is so close to the star that tidal effects make a difference. So let’s talk about two planet solar systems.

Everybody knows about resonances. That is where the period of one planet is a fraction of another’s, with both the numerator of the fraction and the denominator being small integers. Some resonances are very stable, others unstable. So, if the two planet solar system starts out away from a stable resonance, it will drive itself to one, most likely the closest one. You can think of a resonance like a ball rolling back and forth, up and down, on a circular frame. If the ball was in the bottom of the frame, unmoving, it would stay there. So if the two planets were perfectly on orbital radii with a perfect resonance, they would stay there. If they were only close, they would go back and forth around it. If you measured the periods at one instance in time, they would not be in resonance, but if you came back a million years later and measured them again, they would be different, but still close to the resonance.

All stable resonances have limits. Just like with the ball rolling on the circular frame, if the velocity at the bottom is too large, it will hit the end of the circular frame and pop out. How high that velocity has to be depends on the height of the frame. If it only goes up 10 degrees, it will be easier to get the velocity up to pop out than if it goes up 75 degrees. What is the equivalent for planets near a resonance? It is the strength of the coupling between them. And what makes coupling stronger? You guessed it. The villain is eccentricity.

When one or both of the planets in our toy solar system has a lot of eccentricity, orbital variation will eventually bring one close to the other, and then there will be a big kick in angular momentum, instead of the small steady kicks they receive in circular orbits. This is the equivalent of the circular frame being quite low. Planets with eccentricity have a hard time staying in stable resonances.

So why would a planet have high eccentricity? Because it was born with it. When the planetary disk starts to condense, and the initial star forms, the disk might be going around in circular orbit around the disk, but certainly not necessarily. There could have been some preliminary condensing going on at a secondary place, and if that happens, orbits won’t wind up circular. There will be circularization, but not necessarily enough.

So here’s the punch line: If the gas cloud that eventually turns into a solar system has two centers of condensation, but one is too weak and too close in to form a binary star system, and a couple of planets get formed, they may have too much eccentricity to be able to form a stable resonance. This means that they will get moved. The inner one will go in and the outer one will go out. Everybody knew that because everybody knows angular momentum gets conserved, and if the inner planet loses some, the outer planet has to get some, the exact amount.

So, we have some selectivity that shows us what has been nicknamed “Hot Jupiters”, meaning large planets near their star. To get the Jupiter in close from a formation location far out, there has to be another large planet that Is shoved into farther orbits. Our selectivity is very negative for these “cold Saturns”, as they won’t cause the star to wobble much and won’t be crossing it for much time relative to its orbital preiod, if any at all.

So much for a two planet solar system. We talked about the relationship between the two largest planets, because that’s almost all that matters in solar systems where there are two big ones. Our solar system is like that. Little planets just scatter before the wind when a big planet comes calling. Maybe they get cast into the star, or more likely, shot out into some elliptic orbit with large radii, just the thing that life origination wouldn’t like. Maybe some would be pushed back toward the interior by the Saturn equivalent, but a solar system with high eccentricity for the big planets at the start is a bad bet for planets with life.

This means that the thing we see most easily, a hot Jupiter, is a clue that the solar system has no origin planet. If we can do a survey of how many there are, we will be able to exclude that percentage, and use it to narrow down the list of solar systems with origin planets. A hot Jupiter with low eccentricity is not an exclusion as being nearby to a star circularizes quite well.

We will need to figure out some other clues to get that list down to where it should be in order to make an estimate, but at least we have a start. On the other hand, maybe there are other reasons for hot Jupiters.

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