Monday, May 7, 2018

Planet Nine makes some KBOs go wild

Hi, everyone! I’m Tali, an undergrad at the University of Michigan. Last summer, I worked on a Planet Nine project with Konstantin and Mike, and although we didn’t find Planet Nine (yet!), we did look further into the stability of objects in the presence of Planet Nine. Turns out, not everything is stable!

In his last post, Konstantin explained that the main cluster of anti-aligned objects is able to remain stable due to mean motion resonances with Planet Nine. Their orbits always cross Planet Nine’s orbit, but such resonances allow the objects to avoid collisions. Here’s an example of what the dynamics looks like: the green orbit is Planet Nine, and pink orbit is an anti-aligned Kuiper belt object. The little blue circle is Neptune’s orbit, and the star is the Sun (not to scale).

What we see here is that the anti-aligned object experiences librations (=bounded oscillations) in the direction its orbit points (the longitude of perihelion). Meanwhile, Planet Nine’s orbit slowly precesses and changes direction as well.

BUT, it turns out that being in resonance with Planet Nine is not enough for stability. That’s because Neptune is still in the picture. Let’s look back at the animation above. Notice that as the pink orbits wags back and forth, its perihelion distance (=the shortest distance from the orbit to the Sun) changes. The pink orbit stretches (and hugs Neptune’s orbit) and then circularizes (and detaches from Neptune). The wider the “wagging the tail” oscillations are, the more pronounced the in and out behavior becomes. If the object librates with too large of an amplitude, it comes suuuuuper close to Neptune. And when that happens, it either gets ejected from the solar system or its dynamics changes entirely, and its behavior is no longer relevant to Planet Nine.

SO, the stability of the anti-aligned objects can be summarized by the two gifs below. When the longitude of perihelion libration (tail-wagging) is mild, our object experiences small changes in perihelion distance, and thus remains at a safe distance from the inner solar system. But, if the librations become too wide (and too wild), the object goes unstable, thanks to Neptune.
STABLE LIBRATIONS



UNSTABLE BEHAVIOUR


Now, the anti-aligned population is not the only one we looked at. Planet Nine carves out an aligned cluster of objects as well, which experience librations in longitude of perihelion, but this time, inside the orbit of Planet Nine:

As you can see this object is in the perfect stable location - it stays far away from Neptune (blue) AND doesn’t cross Planet Nine’s orbit, and just quietly librates in longitude of perihelion. This object is all set for life. Nothing will make it budge from this configuration.

BUT, there are objects that seem to be aligned at first, but suffer because their libration amplitudes are too large. Here’s an example of such an object:


In the animation above, the orbit spins too far and crosses Planet Nine’s orbit. This is not good for two reasons: (i) Planet Nine starts having collisions with this object and knocking it about, and, (ii) UNLESS the object is in a resonance with Planet Nine, it gets swept by Planet Nine into the Neptune scattering region. If you look at the animation carefully after the pink orbit crosses the green orbit, you’ll see that the perihelion distance of the object is slowwwly decreasing. When it gets small enough - when the object starts interacting strongly with Neptune - we get the same output as for the unstable anti-aligned objects (i.e. instability and a crazy jumping dog.)

So, what’s the bottom line? Not all anti-aligned objects are stable! And not all aligned objects are stable. And it all depends on their perihelion distance, which is closely tied with their librations in longitude of perihelion.

Moreover, it turns out that what kind of objects we find surviving through the end of our simulations depends on the initial conditions we put in. What do I mean by initial conditions? Well, for example, we expect that different scenarios of Planet Nine’s formation would have affected the initial configuration of the Kuiper belt in different ways. So, suppose we start with two different initial conditions: a “narrow” Kuiper belt (objects initially within a narrow interval of perihelion distances) and a more widely spread “broad” Kuiper belt.  And now we integrate these populations forward, in the presence of Planet Nine, in two separate simulations. Do these populations end up creating the same Kuiper belt?

In our recently accepted paper, we find that they don’t! In fact, the stable aligned population discussed above is completely missing from the “narrow” Kuiper belt. So, as the astronomy community continues to find more and more of these distant Kuiper belt objects, we might be able to start to tell which initial Kuiper belt we started with, and maybe how Planet Nine formed…

Read our paper here to find out more about Planet Nine, initial conditions, and stability!

16 comments:

  1. thank you for the up-date.

    and i hope you will soon change the "although we didn’t find Planet Nine (yet!)" to "oh, here it is"

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    1. And when it is found, it would have to be named... and a whole lot of suitable names has already been used. Strangely, "Apate" hasn't been taken yet. In mythology, Apate is a sister of Eris. It might be appropiate due to Planet Nine's capacity to lead lots of TNOs astray.

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    2. I like Erebus, god of darkness, considering its distance and us being in the dark for so long about its existence

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  2. I am so hyped by your probable future discovery! Please keep making updates about the science and more about the search itself!

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  4. Hi, would you please explain the chronology of these events: "the formation of Planet Nine is a two-step process. Particularly, originating in the inner solar system, Planet Nine is envisioned to have been scattered out to a wide orbit by the giant planets (possibly during the transient period of dynamical instability prescribed by the Nice model: Tsiganis et al. 2005; Nesvorný 2011; Batygin et al. 2012a). Since the hypothesized current orbit of Planet Nine has a high perihelion (q 9 > 250 AU), gravitational influence of the solar system’s birth cluster (Morbidelli & Levison 2004; Adams 2010) or dynamical friction from an extended massive planetesimal disk (Eriksson et al. 2018) is then invoked to perturb the orbit and raise Planet Nine’s perihelion distance."
    The migration of the giant planets under the Nice model would happen when there is no gas in the disk, contrary to what would be expected when the Sun is part of a cluster. How could the cluster have influenced after the phase of instability? Thank you.

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    1. "The migration of the giant planets under the Nice model would happen when there is no gas in the disk, contrary to what would be expected when the Sun is part of a cluster. How could the cluster have influenced after the phase of instability? Thank you."

      In the press the dynamical instability in the Nice model is typically described as taking place several hundred million years after the formation of the Solar System so that it coincides with the Late Heavy Bombardment.

      But in the last few years questions have been raised about its timing. Initially this was due to a paper by Kaib and Chambers http://adsabs.harvard.edu/abs/2016MNRAS.455.3561K published at roughly the same time as Batygin and Brown's paper about Planet Nine. Kaib and Chambers showed that the orbits of the terrestrial planets could become eccentric during the migration of the giant planets leading to the loss of one or more.

      Because of this and some other recent papers some now think the giant planet migration occurred shortly after the gas disk dissipated and before the formation of the terrestrial planets.

      Pushing Planet Nine's ejection back slightly until after the gas disk is gone may also allow the birth cluster to break up some making it less likely for Planet Nine to be lost if the Solar System encountered more than one star.

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  6. The new object spotted by OSSOS mentioned here:
    https://twitter.com/astrokiwi/status/994983595835056136
    looks like part of its its orbit would be close to tangent to that proposed for Planet Nine. Would you expect many like this to be observed?

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  7. I like the analysis shown here. . There are many steps along the path ahead. I was curious if you have an estimated range of surface gravity? - and would the planet be able to keep hydrogen gas or helium gas in its atmosphere? If it were formed closer to the sun, would that history mean less hydrogen gas / retention? jdk

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    1. My personal guess is that the Grand Tack scenario makes it very unlikely that it formed closer to the Sun than Jupiter, or between Jupiter and Saturn, or it would have absorbed mass that went into them and made the Grand Tack impossible.

      Also, I think since it had to be almost ejected from the Solar System, it's most likely that ejection was caused by Jupiter or Saturn - as Uranus and Neptune would have felt much stronger "recoil" pushing them inwards.

      So I think Planet Nine was originally formed between Uranus and Saturn. But I think it's also possible that there was a "gentler" meeting with Uranus or even Neptune that pushed them outwards and Planet Nine inwards, where it was ejected by Jupiter or Saturn.

      So from the place I expect it to be formed at, I think it might have a core that might be a little denser or more massive than that of Uranus or Neptune, while it was also far enough away from the Sun to keep holding a hydrogen and helium atmosphere.

      (And I think the formation was already complete when Planet Nine was ejected - if it was ejected during the period when it was still drawing hydrogen and helium from the disc, then it gained less of them, and more of its mass would be from its core - then it would be denser and smaller)

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  8. There isn't much to help narrow where in its orbit Planet 9 might be right now. All we have is that it is more likely to be nearer its aphelion, because an object in an elliptic orbit spends more time there, and not likely to be near perihelion because we would have detected it. For the same reason, it is more likely to be in the part of its orbit where, from our vantage, it crosses in front of the Milky Way.

    Is there nothing more that can be done to narrow that down? Like, I don't know, historic observations of Neptune's position, same as observations of Uranus' position lead astronomers to Neptune? If some think Cassini's motions could have been affected by Planet 9, then it seems slight anomalies in all the planets' positions ought to be detectable.

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