Why are the four gas giants not all the same size?

[nhnifong]

As distance increases from the sun, less mass is needed to achieve the same Hill sphere diameter. With their current masses, (Correction) Neptune has the largest Hill sphere. If these gas giants each had a similar collection area from which to gather mass, why do they taper off in size as one gets more distant from the sun?

Hill sphere diameter in km

Edited August 19, 2013 by nhnifong

[Anton P. Nym]

I don't know enough to answer the question, but I know barely enough to point out that those Hill radii are today's results and not the results from the formation of the solar system ~4B years ago. I suspect they were considerably different back then.

-- Steve

[sojourner]

Uranus has the largest Hill sphere.

Neptune?

As for why Jupiter is larger, I would guess it had more material to feed on when the solar system was forming. Hill sphere size is only part of the equation, not the sole determinant.

Edited August 19, 2013 by sojourner

[K^2]

As far as I know, accretion disks are denser closer to the star, so there is more stuff to collect for a gas giant close in. I don't know if it explains all of it, but it might be the big part of the puzzle.

[PakledHostage]

There's also the added complexity that the planets may not have formed in their current positions. For example, for some initial conditions, the Nice model predicts that Uranus and Neptune may have actually switched places during the evolution of the solar system. More generally, the Nice model "proposes the migration of the giant planets from an initial compact configuration into their present positions, long after the dissipation of the initial protoplanetary gas disk."

[Stochasty]

In addition to possible migration suggested by the Nice model, and to density variations in the accretion disk during planet formation, it should be noted that Jupiter is just beyond the ice line. It has been suggested that this is no accident: volatiles boiled off from the inner solar system may have concentrated near Jupiter's orbit, allowing it to grow more quickly.

Unfortunately, we only have indirect evidence of the formation of a single solar system at present, so there's very little data with which to use for comparison of various theories.

Edited August 19, 2013 by Stochasty

[nhnifong]

Interesting model pakled. I'd be very interested in finding out what the distribution of gas giants looks like in the population models they've run, but I was unable to find such results in the papers cited. They could be getting a general smattering of gas giants, or it could be so accurate as to produce the four giants of our system every time, with approximately correct masses.

Unfortunately, we only have indirect evidence of the formation of a single solar system at present, so there's very little data with which to use for comparison of various theories.

Perhaps the James Webb Space Telescope will help with that

Edited August 19, 2013 by nhnifong

[Stochasty]

I'd be very interested in finding out what the distribution of gas giants looks like in the population models they've run.

I attended a plenary talk given by one of the authors of the Nice model a couple of years ago where he discussed this. As I recall, he commented that roughly half their simulations resulted in Uranus and Neptune switching places, and half did not. The outward migration due to the resonance between Jupiter and Saturn was a consistent feature across all runs, though.

Edit: Nevermind; misread your post. You were asking about model statistics during the formation, not during the migration; I know less about that. The plenary only covered from just after formation up through migration, and didn't discuss the actual formation. (I'm not sure they can model formation nearly as accurately.)

Edited August 19, 2013 by Stochasty