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"Planet Nine" update: Possible resonances beyond the Kuiper belt?

Posted by Emily Lakdawalla

08-03-2016 11:34 CST

Topics: trans-neptunian objects, explaining science, dwarf planets beyond Neptune

When Konstantin Batygin and Mike Brown announced the possible existence of a distant planet, my first question was "what do the dynamicists think?" Several were quoted in the media surrounding the announcement, but yesterday leading dynamicist Renu Malhotra (with coauthors Kat Volk and Xianyu Wang) posted to ArXiv the first formal response I've seen. In brief, Malhotra and coauthors are on board with the idea of a possible outer planet, and found that it may have shaped the orbits of extremely distant Kuiper belt objects in another way beyond the several ways that Batygin and Brown proposed.

Before I continue with the story, I want to mention that you can hear from Batygin and Brown directly tonight through a Planetary Radio Live webcast! I'll be onstage as well.

Possible orbit of a perturbing

Caltech/R. Hurt (IPAC) [Diagram was created using WorldWide Telescope.]

Possible orbit of a perturbing "ninth planet"
The six most distant known objects in the solar system with orbits exclusively beyond Neptune (magenta), including Sedna (dark magenta), all mysteriously line up in a single direction. Also, when viewed in three dimensions, they tilt nearly identically away from the plane of the solar system. Another population of Kuiper belt objects (cyan) are forced into orbits that are perpendicular to the plane of the solar system and clustered in orientation. Batygin and Brown show that a planet with 10 times the mass of the earth in a distant eccentric orbit (orange) anti-aligned with the magenta orbits and perpendicular to the cyan orbits is required to maintain this configuration.

In the paper, Malhotra points out that because the orbits of the extremely distant Kuiper belt objects like Sedna, 2010 GB174, 2004 VN112, 2012 VP113, and 2013 GP136 are so eccentric, then they are likely to have had close encounters with the putative planet. Close encounters with a massive planet change orbits of smaller worlds. It's relatively easy for small worlds, so tenuously connected to the Sun, to get ejected from the solar system entirely. If there is an undiscovered distant planet affecting their orbits, the fact that the little worlds still remain in our solar system means either that they've had relatively few encounters, or else they're protected from close encounters with the planet by being in resonances. This is how Pluto is still a member of our solar system even though its orbit crosses Neptune's: because Pluto orbits the Sun twice for every three times Neptune does, Pluto and Neptune are never actually close to each other, so Neptune doesn't get a chance to eject Pluto.

Armed with this hypothesis, Malhotra, Volk, and Wang investigated whether the worlds we know about could be in resonances with the one that Batygin and Brown suggested. In short, they can. It's complicated because we have short observational arcs on these distant, slow-moving worlds, so the analysis has to include a detailed understanding of the uncertainties on the worlds' orbits. The analysis suggests that Sedna's orbital period is in a 3:2 resonance with the putative planet; 2010 GB174 in a 5:2; 2994 VN112 in a 3:1 resonance; 2004 VP113 in 4:1; and 2013 GP136 in 9:1.

If all this is true (and I should note here that the paper has not been peer-reviewed yet), Malhotra et al.'s work constrains the mass and location of the possible planet in different ways than Batygin and Brown's does. In this new paper, in order to keep the smaller worlds corralled into resonant orbits, the possible planet has to have a mass of at least 10 times that of Earth. The orbital plane can be one of two: either inclined at 18 degrees or 48 degrees. In the low-inclination case, the orbit eccentricity would be less than 0.18; in the high-inclination case, it could be much larger. There are many places along the possible orbits that the putative planet could not be, or else it would have close encounters with the discovered worlds.

Is this proof for a ninth planet? No. From their conclusion:

Our analysis supports the distant planet hypothesis, but should not be considered definitive proof of its existence. The orbital period ratios have significant uncertainties, so the near-coincidences with N/1 and N/2 ratios may simply be by chance for a small number of bodies. The long orbital timescales in this region of the outer solar system may allow formally unstable orbits to persist for very long times, possibly even to the age of the solar system, depending on the planet mass; if so, this would weaken the argument for a resonant planet orbit. It would be pertinent to examine this question quantitatively in future work.

More work is always needed -- but this work is cool because it suggests new constraints on where to look for the possible undiscovered world.

 
See other posts from March 2016

 

Or read more blog entries about: trans-neptunian objects, explaining science, dwarf planets beyond Neptune

Comments:

Brian Schmidt: 03/08/2016 12:37 CST

Something I've never understood about resonances: are they actively "managed" by the orbits to stay in resonance, or are they just one result of non-resonant orbits that keep changing until they become resonant, collide, or eject? I get the impression that it's the former, but I don't understand why (e.g. if a disturbance makes a body drift slightly out of resonance, I don't see what makes it drift back into resonance as opposed to drifting into greater instability).

Emily Lakdawalla: 03/08/2016 02:44 CST

Brian, dynamics are not my forte, but my understanding is that resonances can be stable or unstable ones. If they're stable, you get situations like Pluto and the "twotinos" or like a confined ring of a giant planet, like the F ring, where small deviations get corrected to confine things in a specific region of dynamical space. If they're unstable, you get a gap where there are few objects, like the Cassini division or one of the Kirkwood gaps in the Main Belt. Whether you get a concentration or a gap depends on whether it is "uphill" or "downhill" dynamically away from the gap -- if it's uphill, things stay, if downhill, things leave. That's my (very simplistic) understanding anyway.

Catherine Cowie: 03/08/2016 03:09 CST

I ran my own numerical check from Malhotra et al’s barycentric calculations of semi-major axes (Kepler makes that relatively easy, with a³=P², and all that). The periods of 2010 GB₁₇₄ and (148209) 2000 CR₁₀₅ are somewhat weakly related to Sedna’s; P₁/P₂ is ~ 1.737, and P₁/P₅ is ~3.459, to use the notation in the paper. However, the ratio P₂/P₅ is 1.991 or very close to 2/1 – so if Malhotra et al. were ascribing a 5/2 resonance for 2010 GB₁₇₄ with the hypothetical planet (P'/P₂), then (148209) 2000 CR₁₀₅ would be close to a 5/1 resonance – to a similar margin of error. That makes for a fairly impressive set of mean motion resonances with relatively small integer ratios. It’s not compelling, but it is tantalising.

David Frankis: 03/08/2016 04:56 CST

This is a really interesting paper. I'm no expert, but don't the constraints from this paper contradict those from Batygin and Brown? B & B's Planet Nine's inclination is similar to Malhotra and al's low-inclination solution - but that's also relatively low eccentricity. The high-inclination solution could also have high eccentricity, but its inclination is completely different from B & B's.

Andy Hastings: 03/08/2016 05:46 CST

Is that Nobel Laureate Brian Schmidt? :D Great work as always, Emily!

Stephen: 03/08/2016 07:50 CST

"planet nine"? Don't you mean "dwarf planet six"? After all if this object is inside the Kuiper Belt then it presumably has not yet cleared its orbit as required by the IAU.

Jean-Luc Margot: 03/08/2016 08:14 CST

Stephen: A 10 Earth mass planet would clear its orbit all the way out to 3000 astronomical units. Figure and paper available at http://mel.epss.ucla.edu/jlm/epo/planet/nine.html

Jehochman: 03/08/2016 11:04 CST

Over at Wikipedia (https://en.wikipedia.org/wiki/Talk:Planet_Nine#Semi-major_axis) we are trying to figure out how to include this paper. It does seem to contract Batygin and Brown with regard to eccentricity of P9's orbit and inclination. Is there any explanation for the discrepancy? Are these results within the margin of uncertainty of B&B's work? B&B seem to have run a bunch of supercomputer simulations, and say that the large eccentricity is necessary and that a 30 inclination is the best fit for observations. A high precision n-body simulation would seem to over-rule a theoretical analysis of resonances if the two studies didn't produce compatible results. Perhaps the theoretical analysis of orbital resonances has failed to take into account some nuances, or makes the wrong assumptions.

Steven: 03/09/2016 03:40 CST

Maybe the conflict is from their error margins on the objects orbits. Or if the error margins are less clearly resolved in B&B's work. Not sure.

Steven: 03/09/2016 03:43 CST

And don't forget the paper over at http://arxiv.org/abs/1602.06116v3 on the fine positioning of Cassini lending details to Saturn's orbit. One of their preferred regions seems to overlap one of the segments of the above paper.

Stargazed: 03/09/2016 04:56 CST

Where can I find a recording of yesterday's Planetary Radio Live webcast?

Torbjörn Larsson: 03/09/2016 09:39 CST

This is encouraging, and as the thread notes, confusing. The best of both worlds! @Stephen: "it presumably has not yet cleared its orbit as required by the IAU." To remain in orbit after 4.5 billion years it is gravitationally dominant in its orbit, as is obvious from the bodies that it bosses around, i.e. it has cleared out any masses that would mess with it. I dunno where the mass limit goes, but it would take a pretty large body to threaten its dominance. Brown claims somewhere, because he knew this misunderstanding of the dynamics/IAU criteria (the latter of which could have been formulated better) would come up, that Planet None would be the most "planetary" planet of all if it exists. I take it the system is sparse of mass out there...

Torbjörn Larsson: 03/09/2016 09:42 CST

Oops. Planet Nine. (But fun miseplling.)

David Frankis: 03/09/2016 10:42 CST

Jehochman, the obvious resolution of the discrepancy is that there's no planet out there, and the observed small body effects are coincidences. I think a critical couple of questions are: Do the orbital periods of these TNOs rule out a planet as predicted by B & B? Does the clustering of the perihelia of these (are they exactly the same TNOs? - I haven't had time to check) rule out a planet as described by Malhotra et al? Torbjörn - I considered arguing for calling it 'Planet Thirteen' on the basis of Bode's Law, a particular bugbear of Brown's...

agmartin: 03/09/2016 02:35 CST

The difference between the papers: In B & B 's simulations the objects were captured in weak resonances and hopped between them, IIRC one of them once said they couldn't determine its semi-major axis because there were so many possible resonances objects could be in. Malhotra et al appear to have started with the assumption that the first objects discovered would most likely to be in the strongest resonances.

Catherine Cowie: 03/09/2016 04:02 CST

Looking at Batygin & Brown and Malhotra & al. again today, I am slightly disappointed that the latter did not examine the case for mean-motion resonances for a slightly wider group of objects. B & B originally identified 16 ETNOs with q > 30 AU and a > 150 AU, eight of which were dynamically stable in their modelling over 4 Gyr of orbital evolution; B & B used this lack of long-term stability to argue why the other 8 ETNOs would not necessarily show evidence of orbital clustering. Looking at all 16 they concluded spatial confinement was a reality for all 6 most distant objects (a > 250 AU) which were dynamically stable, and 2 of the other 10 with 150 AU < a < 250 AU. Looking at these others, I’d like someone to plot the orbit of a ninth, which I suspect is not too far from being part of the opposite ‘wing’ of confined orbits to the one which Sedna is on, and thus is temporarily confined. So of the six objects with a > 250 AU which B & B examined, Malhotra & al. exclude two (2007 TG₄₂₂ and 2013 RF₉₈) as their perihelions are within 40 AU (~36 AU); although these objects are less dynamically stable than the other four objects because of their closer proximity to Neptune at perihelion, this should not preclude them being influenced by the proposed Planet Nine (or Thirteen, pace Frankis) into mean motion resonances (the inclination of these bodies means their closest approach is not ‘really’ quite so close). Of the 150 AU < a < 250 AU population, Malhotra & el. examined two more, one of which is spatially confined according to B & B, while the other is not (this is the one which is weakly in the 9:1 resonance). It’s perhaps easy to select examples which demonstrate the effect you’re trying to measure, but less so to look for examples of the similar population to see if they provide confounding null results. Do any of the other ten or so ETNOs falsify or weakly confirm Malhotra et al.’s proposals?

Catherine Cowie: 03/09/2016 04:10 CST

Whoops. Belay that! B & B only found six objects to be dynamically stable in terms of semi-major axis in their orbital modelling; not eight. The two that I’d incorrectly included in this ‘stability’ group are not surprisingly, the exact two which I namechecked in the second paragraph, that Malhotra & al. did not consider for possible resonances. Mea culpa.

Jehochman: 03/09/2016 07:41 CST

I looked at the longitudes allowed by Cassini, and the longitudes allowed by Malhotra, and found there are just four possible locations (assuming only 48 degrees is workable because B&B rules out the low eccentricity type orbit). These four areas were approximately (1) Leo Minor/Ursa Major, (2) Camelopardis - middle (3) Camelopardalis - right, (4) Pisces. The very cool thing is that none of these areas seemed to heavily intersect the Milky Way. What would be good is for the Cassini group and B&B to run their simulations at 48 degrees inclination and see what results each gets. If there's a hard contradiction then we know somebody is wrong. If they can all agree on a compact set of locations, then the search is that much easier.

Stephen: 03/09/2016 10:45 CST

Torbjörn Larsson: “To remain in orbit after 4.5 billion years it is gravitationally dominant in its orbit, as is obvious from the bodies that it bosses around, i.e. it has cleared out any masses that would mess with it. “ First of all it is only your own presumption that this putative object has had its current orbit for the past 4.5 billion years. AFAIK that has yet to be demonstrated. Secondly, even putting that objection aside your statement really only applies to LARGE masses. Or at least those large in comparison to its own size. Small objects are not going to “mess” with its own motion as much, so your objection is arguably less applicable to objects more the size of a typical Kuiper belt object like Eris. I notice, for example, that small objects continue to cross the Earth’s own orbit despite 4.5 billion years. The very fact that this object has been detected through orbital interactions with Kuiper Belt objects strongly suggests that its orbital clearing process, at least as far as they are concerned, is still on-going. I would also note that the IAU does not define how far down the size scale for objects a would-be planet has to clear its orbit of in order for any smaller orbital-crossing riffraff (e.g. 2101 Adonis in Earth’s case) not to affect its classification. For example, Pluto crosses Neptune’s orbit yet its failure to clear out that interloper does not seem to have affected the IAU’s classification of Neptune—even though Pluto’s failure to clear out Neptune would seem to be one of the reasons Pluto was downgraded. (That said I note the IAU’s original missive simply asserted—as distinct from demonstrated—the planet status of the Lucky Eight. One wonders whether a similar executive decree will elevate this new body?)

Stephen: 03/09/2016 10:57 CST

Has anybody suggested a name yet for this hypothetical body? Probably not. Even granted it is still early days I am going to put my spoke in now: "Cerberus", the monstrous multi-headed dog who guarded the gates of the underworld in Greek mythology and was known as the "hound of Hades" (Since Hades==Pluto, "Cerberus" might have been a better title for a Pluto's major satellite, but that honour has gone to "Charon".)

Michael Richmond: 03/10/2016 07:48 CST

Stephen, Alas, "Cerberus" is already taken, as the name of asteroid 1865. Please check the list of existing minor planet names at http://www.minorplanetcenter.net/iau/lists/MPNames.html and try again.

Jeff Rabb: 03/11/2016 04:28 CST

I may be getting ahead of things, but judging by all the other planets in our solar system, any object that large will almost certainly have moons. My suggestions for those are: Acheron, Cocytus, Phlegethon, Lethe. They are 4 of the 5 rivers that surrounded the Greek Underworld (the fifth, Styx, is already taken for one of Pluto's moons. Additionally, we should consider: Rhadamanthus, Minos, and Aeacus - the three judges before all souls entering the Underworld were required to stand before to be judged.

David Frankis: 03/12/2016 10:16 CST

I watched the Planetary Radio Live event in the hope that someone might have asked about this. They didn't, but Batygin was pretty insistent that the corralling effect on the TNO orbits only works if Planet Nine's orbit is eccentric (which makes sense - a circular orbit wouldn't create a preferred direction in space).

khall1980: 03/12/2016 01:46 CST

This goes out for all the pluto lovers and supporters that pluto is not only a planet but a double planet system.. Now lets get down business well all grown up pluto being the 9th planet now well 9-10 by dent of being a double planet system with Charon.. eris being number 11 Eris 12 makemake 13 haumea 14 Quaoar and 15 Sedna and 16 2012 vp 113... many others that were either found or discovered from the late 90s to present.. now heres a thought im not speaking dynamically here im speaking naturally.. planets are planets simple as that.. if they are round or nearly round and orbit the sun its a planet.. period.. now as far as this renewed planet 9 is an insult to what we have learned and grew up with .. as far as pluto.. pluto is number 9 and it always will be in my eyes.. this supposed renewed planet 9 would be something like 20+ or 30 + or 40 and so on.. so lets do it by the year of discovery not by dynamics

David Frankis: 03/18/2016 10:14 CDT

There's a new blog post up at Findplanetnine (http://www.findplanetnine.com/2016/03/where-is-planet-nine.html ), about a new paper by Brown and Batygin. While the blog post doesn't discuss the Malhotra et al paper, the linked paper does. They say, basically, that the high eccentricity of Planet Nine means that there aren't just a few key mean motion resonances that matter, so you can't assume the TNOs are in simple resonances. What's more, they say that Malhotra el al's solutions wouldn't corral the TNO orbits in the way observed.

Anonymous: 04/16/2016 10:51 CDT

I find this article very interesting. If Planet Nine does exist, could there be life on that planet. I wonder. What if, once LightSail launches, what if it could go to where Planet Nine is possible locate to study it and learn more about this mysterious planet.

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