Category Archives: Asteroids: Extreme Trans-Neptunian Objects

Asteroids: Extreme Trans-Neptunian Objects

How the Planet Nine would affect the furthest asteroids

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Hi there! You have heard of the hypothetical Planet Nine, which could be the explanation for an observed clustering of the pericentres of the furthest asteroids, known as eTNOS for extreme Trans-Neptunian Objects. I present you today a theoretical study investigating in-depth this mechanism, in being focused on the influence of the inclination of this Planet Nine. I present you Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth by Melaine Saillenfest, Marc Fouchard, Giacomo Tommei and Giovanni B. Valsecchi. This study has recently been accepted for publication in Celestial Mechanics and Dynamical Astronomy.

Outline

Is there a Planet Nine?
The secular dynamics of an asteroid
The Kozai-Lidov mechanism
Methodology
Results
To know more…

Is there a Planet Nine?

An still undiscovered Solar System planet has always been dreamed, and sometimes even hinted. We called it Tyche, Thelisto, Planet X (“X” for mystery, unknown, but also for 10, Pluto having been the ninth planet until 2006). Since 2015, this quest has been renewed after the observation of clustering in the pericentres of extreme TNOS. Further investigations concluded that at least 5 observed dynamical features of the Solar System could be explained by an additional planet, now called Planet Nine:

  1. the clustering of the pericentres of the eTNOs,
  2. the significant presence of retrograde orbits among the TNOs,
  3. the 6° obliquity of the Sun,
  4. the presence of highly inclined Centaurs,
  5. the dynamical detachment of the pericentres of TNOs from Neptune.

The combination of all of these elements tends to rule out a random process. It appears that this Planet Nine would be pretty like Neptune, i.e. 10 times heavier than our Earth, that its pericentre would be at 200 AU (while Neptune is at 30 AU only!), and its apocentre between 500 AU and 1200 AU. This would indeed be a very distant object, which would orbit the Sun in several thousands of years!

Astronomers (Konstantin Batygin and Michael Brown) are currently trying to detect this Planet Nine, unsuccessfully up to now. You can follow their blog here, from which I took some inspiration. The study I present today investigates the secular dynamics that this Planet Nine would induce.

The secular dynamics of an asteroid

The secular dynamics is the one involving the pericentre and the ascending node of an object, without involving its longitude. To make things clear, you know that a planetary object orbiting the Sun wanders on an eccentric, inclined orbit, which is an ellipse. When you are interested in the secular dynamics, you care of the orientation of this ellipse, but not of where the object is on this ellipse. The clustering of pericentres of eTNOs is a feature of the secular dynamics.

This is a different aspect from the dynamics due to mean-motion resonances, in which you are interested in objects, which orbital periods around the Sun are commensurate with the one of the Planet Nine. Some studies address this issue, since many small objects are in mean-motion resonance with a planet. Not this study.

The Kozai-Lidov mechanism

A notable secular effect is the Kozai-Lidov resonance. Discovered in 1961 by Michael Lidov in USSR and Yoshihide Kozai in Japan, this mechanism says that there exists a dynamical equilibrium at high inclination (63°) for eccentric orbits, in the presence of a perturber. So, you have the central body (the Sun), a perturber (the planet), and your asteroid, which could have its inclination pushed by this effect. This induces a libration of the orientation of its orbit, i.e. the difference between its pericentre and its ascending node would librate around 90° or 270°.

This process is even more interesting when the perturber has a significant eccentricity, since the so-called eccentric Kozai-Lidov mechanism generates retrograde orbits, i.e. orbits with an inclination larger than 90°. At 117°, you have another equilibrium.

Now, when you observe a small body which dynamics suggests to be affected by Kozai-Lidov, this means you should have a perturber… you see what I mean?

Of course, this perturber can be Neptune, but only sometimes. Other times, the dynamics would rather be explained by an outer perturber… which could be the Planet Nine, or a passing star (who knows?)

Methodology

Before mentioning the results of this study I must briefly mention the methodology. The authors made what I would call a semi-analytical study, i.e. they manipulated equations, but with the assistance of a computer. They wrote down the Hamiltonian of the restricted 3-body problem, i.e. the expression of the whole energy of the problem with respect to the orbital elements of the perturber and the TNO. This energy should be constant, since no dissipation is involved, and the way this Hamiltonian is written has convenient mathematical properties, which allow to derive the whole dynamics. Then this Hamiltonian is averaged over the mean longitudes, since we are not interested in them, we want only the secular dynamics.

A common way to do this is to expand the Hamiltonian following small parameters, i.e. the eccentricity, the inclination… But not here! You cannot do this since the eccentricity of the Planet Nine (0.6) and its inclination are not supposed to be small. So, the authors average the Hamiltonian numerically. This permits them to keep the whole secular dynamics due to the eccentricity and the inclination.

Once they did this, they looked for equilibriums, which would be preferential dynamical states for the TNOs. They also detected chaotic zones in the phase space, i.e. ranges of orbital elements, for which the trajectory of the TNOs would be difficult to predict, and thus potentially unstable. They detected these zones in plotting so-called Poincaré sections, which give a picture of the trajectories in a two-dimensional plane that reduces the number of degrees-of-freedom.

Results

And the authors find that the two Kozai-Lidov mechanisms, i.e. the one due to Neptune, and the one due to the Planet Nine, conflict for a semimajor axis larger than 150 AU, where orbital flips become possible. The equilibriums due to Neptune would disappear beyond 200 AU, being submerged by chaos. However, other equilibriums appear.

For the future, I see two ways to better constrain the Planet Nine:

  1. observe it,
  2. discover more eTNOs, which would provide more accurate constraints.

Will Gaia be useful for that? Anyway, this is a very exciting quest. My advice: stay tuned!

To know more…

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Asteroids: Extreme Trans-Neptunian Objects

Discovery of 6 new Extreme Trans-Neptunian Objects

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Hi there! You know the Trans-Neptunian Objects, these bodies which orbit beyond the orbit of Neptune… There are the furthest known objects in the Solar System. Today I will particularly tell you on the most distant of them, which have a semimajor axis larger than 150 AU, while Neptune is at 30 AU… Yes, we can observe some of them. 6 have been recently discovered by the OSSOS survey, in OSSOS. VI. Striking biases in the detection of large semimajor axis Trans-Neptunian Objects, by Cory Shankman and 11 collaborators (full list at the end). This paper has recently been published in The Astronomical Journal. In this study, the authors particularly focus on the possible observational biases, and discuss the Planet Nine hypothesis.

Outline

The OSSOS survey
The Canada-France-Hawaii Telescope
Observational biases
Statistical tests
This study
What about the Planet Nine?
To know more…

The OSSOS survey

I should probably write OSSOSurvey instead, since it stands for Outer Solar System Origins Survey. It is a systematic observation program that ran on the Canada-France-Hawaii Telescope (CFHT) between 2013 and 2017, devoted to the discovery and orbit determination of Trans-Neptunian Objects. For that, the program used an imager with a field of 1×1 degree, to image 21 square degree fields, in different parts of the sky. During the 4 years, these fields were regularly re-observed to follow the motion of the discovered objects. 16 months of astrometric observations are required to obtain an accurate orbit.
The authors announce that OSSOS permitted the detection of more than 830 TNOs, with a “40% detection efficiency at r(ed)-band magnitude 24.4-24.5”. OSSOS followed another survey, CFEPS, for Canada-France-Hawaii Ecliptic Plane Survey, which discovered some 200 Kuiper Belt Objects, i.e. Trans-Neptunian Objects, which are not as far as the objects we discuss today. This makes more than 1,000 small objects discovered by the CFHT.

Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.
Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.

The Canada-France-Hawaii Telescope

The Canada-France-Hawaii Telescope is a joint facility of the University of Hawaii, the French Centre National de la Recherche Scientifique, and the Canadian National Research Council. It has also partnerships with institutions based in the two Chinas, South Korea, and Brazil. It has a 3.58-m telescope, which is functional since 1979.
It is ideally situated, close to the summit of the Mauna Kea mountain, Hawaii (altitude: 4,204 m). It is equipped of different instruments, to observe in the visible to infrared bands. One of them, the wide field imager MegaCam, was used for OSSOSurvey.

Observational biases

If you are looking for stars to the West, you will find some. But only on the West, and brighter than a given magnitude. Does that mean that there are no fainter stars, and no stars in the opposite direction? Of course not. You have found only those stars because your observation means and protocol precluded from discovering other stars. This is an observational bias.

This is a very important issue for understanding surveys, i.e. how to extrapolate the catalog of discovered objects to the existing but unknown ones? Observational biases can be due to:

  • The direction in which you observe. Since our sky is moving, this is strongly correlated to the observation date.
  • The weather. Hard to see something behind a cloud.
  • Your field of view. Is there something behind this tree?
  • The limitations of your instrument.
  • The albedo of your object. How efficiently does it reflect the incident Solar light?
  • …

There is something very significant in the name of CFEPS… E stands for ecliptic, which is the orbital plane of the Earth. The Solar System is roughly planar (with many exceptions of course), and it made sense to look for objects with a small orbital inclination. Consequence: most of the objects discovered by CFEPS have a low inclination… observational bias, which was in fact a way to optimize the chances to discover objects. But it would be wrong to conclude from these discoveries a lack of objects with a small inclination.

OSSOS had observational biases as well, mostly due to the absence of observations in the direction of the Galactic Plane, and to the allocated observation time. The Galactic Plane is full of stars, which complicates the observations of faint objects. This is why the authors maximized their chances in avoiding that part of the sky. As a consequence, OSSOS could not detect objects with an ascending node (the point where the orbit of the object crosses the ecliptic) between -120° and -20°, and had a poor sensitivity between 115° and 165°.

In the specific case of extreme TNOs, there is another bias due to their dynamics: a small object orbiting at a distance of 150 AU has no chance to be detected from the Earth. So, the only detected objects came close enough, which means that their orbits is highly elongated, i.e. highly eccentric. The 8 objects considered in this study, i.e. 6 newly discovered and 2 already known, have a pericentric distance between 31 and 50 AU, which involves an eccentricity between 0.727 and 0.932 (the eccentricity of the Earth is some 0.016). Among the extreme TNOs, only the highly eccentric ones can be detected. This does not mean that they are all highly eccentric.

The reason why the scientific community became excited about the Planet Nine is that a clustering of the orbits of the extreme TNOs was identified in other data, in particular a clustering of the pericentres of the objects. It was then concluded that this clustering was the dynamical signature of the Planet Nine, proving its existence. OSSOS gives independent data, are they clustered?

Answering such a question is not straightforward when the data are scattered. Looking at them with the naked eye is not enough, there are mathematical tools which can measure the statistical relevance of an hypothesis. In particular, the Planet Nine hypothesis should be compared with the null hypothesis, i.e. an equal distribution of the pericentres of the extreme TNOs.

Statistical tests

A common tool is the Kolmogorov-Smirnov test, or KS-test. The idea is to determine a distance between your sample and the one that a given law would give you. If the distance is small enough, then it makes sense to conclude that your sample obeys the law you tested.
This test has been refined as Kuiper’s test, which is insensitive to cyclic transformations of the variables. Cyclic phenomena are everywhere in orbital dynamics.

This study

The following table presents you the 8 eTNOs presented in this study.

Name Semimajor axis Eccentricity Inclination Magnitude
2013 GP136 150.2 AU 0.727 33.5° 23.1
2013 SY99 735 AU 0.932 4.2° 24.8
2013 UT15 200 AU 0.780 10.7° 24.1
2015 KH163 153 AU 0.739 27.1° 24.7
2015 RY245 226 AU 0.861 6° 24.6
2015 GT50 312 AU 0.877 8.8° 24.5
2015 RX245 430 AU 0.894 12.1° 24.1
2015 KG163 680 AU 0.940 14° 24.3

All of them have been discovered by OSSOS, the first two ones being known before that study. The 6 other ones are the 6 newly discovered. We can see that all have huge semimajor axes and eccentricities. You can see the high relative magnitudes in the red band during their discoveries. Their discoveries were made possible by their high eccentricities, which reduce significantly the minimal distances to the Sun and to the Earth.

And now their orbits are drawn!

Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.
Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.

Do they look clustered?

What about the Planet Nine?

The Kuiper’s test used by the authors say that the orbital elements of the detected eTNOS are statistically consistent with a uniform repartition. We must be careful with words. This means that there is no evidence of clustering in this sample. That does not mean that there is no Planet Nine. We should keep in mind that 8 objects do not constitute a statistically relevant sample.

My feeling is that if you were skeptical about the existence of the Planet Nine, you remain skeptical. However, if you believed in it, there is still room for belief. The fact is that this study does not comfort the existence of the Planet Nine.

To know more…

  • The study, made freely available by the authors on arXiv. You can also find a presentation of the study by the authors themselves here.
  • A presentation by Nature.
  • The website of the OSSOS survey, and its Twitter.
  • The quest for the Planet Nine.

And the authors of the study:

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.