Category Archives: Asteroids: Centaurs

Origin and fate of a binary TNO

Hi there! I have already told you about these Trans-Neptunian Objects, which orbit beyond the orbit of Neptune. It appears that some of them, i.e. 81 as far as we know, are binaries. As far as we know actually means that there are probably many more. These are in fact systems of 2 objects, which orbit together.

The study I present you today, The journey of Typhon-Echidna as a binary system through the planetary region, by Rosana Araujo, Mattia Galiazzo, Othon Winter and Rafael Sfair, simulates the past and future orbital motion of such a system, to investigate its origin and its fate. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

Binary objects

Imagine two bodies, which are so close to each other that they interact gravitationally. You can say, OK, this is the case for the Sun and the planets, for the Earth and the Moon, for Jupiter and its satellites… Very well, but in all of those cases, one body, which we will name the primary, is much heavier than the other ones. This results as small bodies orbiting around the primary. But what happens when the mass ratio between these two bodies is rather close to unity, i.e. when two bodies of similar mass interact? Well, in that case, what we call the barycenter of the system, or the gravity center, is not close to the center of the primary, it is in fact somewhere between the two bodies. And the two bodies orbit around it. We call such a system a binary.

Binary systems may exist at every size. I am not aware of known binary giant planets, and certainly not in the Solar System, but we have binary asteroids, binary stars… and theory even predicts the existence of binary black holes! We will here restrict to binary asteroids (in the present case, binary minor planets may be more appropriate… please forgive me that).

So, you have these two similar bodies, of roughly the same size, which orbit together… their system orbiting around the Sun. A well-known example is the binary Pluto-Charon, which itself has small satellites. Currently some approximately 300 binary asteroids are known, 81 of them in the Trans-Neptunian region. The other ones are in the Main Belt and among the Near-Earth Asteroids. This last population could be the most populated by binaries, not only thanks to an observational bias (they are the easiest ones to observe, aren’t they?), but also because the YORP effect favors the fission of these Near-Earth Asteroids.

Anyway, the binary system we are interested in is located in what the authors call the TNO-Centaurs region.

The TNOs-Centaurs region

The name of that region of the Solar System may seem odd, it is due to a lack of consistency in the literature. Basically, the Trans-Neptunian region is the one beyond the orbit of Neptune. However, the Centaurs are the asteroids orbiting between the orbits of Jupiter and Neptune. This would be very clear if the orbit of Neptune was a legal border… but it is not. What happens when the asteroid orbits on average beyond Neptune, but is sometimes inside? You have it: some call these bodies TNO-Centaurs. Actually they are determined following two conditions:

  1. The semimajor axis must be larger than the one of Neptune, i.e. 30.110387 astronomical units (AU),
  2. and the distance between the Sun and the perihelion should be below that number, the perihelion being the point of the orbit, which is the closest to the Sun.

The distance between the Sun and the asteroid varies when the orbit is not circular, i.e. has a non-null eccentricity, making it elliptic.

When I speak of the orbit of an asteroid, that should be understood as the orbit of the barycenter, for a binary. And the authors recall us that there are two known binary systems in this TNOs-Centaurs region: (42355) Typhon-Echidna, and (65489) Ceto-Phorcys. Today we are interested by (42355) Typhon-Echidna.

(42355) Typhon-Echidna

(42355) Typhon has been discovered in February 2002 by the NEAT program (Near-Earth Asteroid Tracking). This was a survey operating between 1995 and 2007 at Palomar Observatory in California. It was jointly run by the NASA and the Jet Propulsion Laboratory. You can find below some orbital and characteristics of the binary around the Sun, from the JPL Small-Body Database Browser:

Typhon-Echidna
Semimajor axis 38.19 AU
Eccentricity 0.54
Perihelion 17.57 AU
Inclination 2.43°
Orbital period 236.04 yr

As you can see, the orbit is very eccentric, which explains why the binary is considered to be in this gray zone at the border between the Centaurs and the TNOs.

Discovery of Typhon in Feb. 2002, then known as 2002 CR<sub>46</sub>. © NEAT
Discovery of Typhon in Feb. 2002, then known as 2002 CR<sub>46</sub>. © NEAT

And you can find below the orbital characteristics of the orbit of Echidna, which was discovered in 2006:

Semimajor axis 1580 ± 20 km
Eccentricity 0.507 ± 0.009
Inclination 42° ± 2°
Orbital period 18.982 ± 0.001 d

These data have been taken from Johnston’s Archive. Once more, you can see a very eccentric orbit. Such high eccentricities do not look good for the future stability of the object… and this will be confirmed by this study.

In addition to these data, let me add that the diameters of these two bodies are 162 ± 7 and 89 ±6 km, respectively, Typhon being the largest one. Moreover, water ice has been detected on Typhon, which means that it could present some cometary activity if it gets closer to the Sun.

The remarkable orbit of the binary, which is almost unique since only two binaries are known in the TNOs-Centaurs region, supplemented by the fact it is a binary, motivated the authors to specifically study its long-term orbital migration in the Solar System. In other words, its journey from its past to its death.

It should originate from the TNOs-Centaurs region

For investigating this, the authors started from the known initial conditions of the binary, seen as a point mass. In other words, they considered only one object in each simulation, with initial orbital elements very close to the current ones. They ran in fact 100 backward numerical simulations, differing by the initial conditions, provided they were consistent with our knowledge of them. They had to be in the confidence interval.

In all of these trajectories, the gravitational influence of the planets from Venus to Neptune, and of Pluto, was included. They ran these 100 backward simulations over 100 Myr, in using an adaptive time-step algorithm from the integrator Mercury. I do not want to go too deep in the specific, but keep in mind that this algorithm is symplectic, which implies that it should remain accurate for long-term integrations. An important point is the adaptive time-step: when you run numerical integrations, you express the positions and velocities at given dates. The separation between these dates, i.e. the time-step, depends on the variability of the force you apply. The specificity of the dynamics of such eccentric bodies is that they are very sensitive to close encounters with planets, especially (but not only) the giant ones. In that case, you need a pretty short time-step, but only when you are close to the planet. When you are far, it is more advisable to use a larger time-step. Not only to go faster, but also to prevent the accumulation of round-off errors.

It results from these backward simulations that most of the clones of Typhon are still in the TNOs-Centaurs regions 100 Myr ago.

But the authors also investigated the fate of Typhon!

It should be destroyed before 200 Myr

For that, they used the same algorithm to run 500 forward trajectories. And this is where things may become dramatic: Typhon should not survive. In none of them. The best survivor is destroyed after 163 Myr, which is pretty short with respect to the age of the Solar System… but actually very optimistic.

Only 20% of the clones survive after 20 Myr, and the authors estimate the median survival time to be 5.2 Myr. Typhon is doomed! And the reason for that is the close encounters with the planets. The most efficient killer is unsurprisingly Jupiter, because of its large mass.

Interestingly, 42 of these clones entered the inner Solar System. This is why we cannot exclude a future cometary activity of Typhon: in getting closer to the Sun, it will warm, and the water ice may sublimate.

All of these simulations have considered the binary to be a point-mass. Investigating whether it will remain a binary requires other, dedicated simulations.

Will it remain a binary?

The relevant time-step for a binary is much shorter than for a point mass, just because the orbital period of Typhon around the Sun is 236 years, while the one of Echidna around Typhon is only 19 days! This also implies that a full trajectory, over 200 Myr, will require so many iterations that it should suffer from numerical approximations. The authors by-passed this problem in restricting to the close encounters with planets. When they detected a close encounter in an orbital simulation of Typhon, they ran 12,960 simulations of the orbit of Echidna over one year. Once more, these simulations differ by the initial conditions, here the initial orbital elements of Echidna around Typhon.

The authors concluded that it is highly probable that the binary survived close encounters with planets, as a binary. In other words, if Typhon survives, then Echidna should survive.

The study and its authors

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

The activity of Chiron

Hi there! You may have heard of Chiron, which was he first Centaur discovered, in 1977. This minor planet may have rings, and seems to present some cometary activity, which cause needs to be discussed. This is the topic of the present study, i.e. Activity of (2060) Chiron possibly caused by impacts?, by Stefan Cikota, Estela Fernández-Valenzuela, Jose Luis Ortiz, Nicolás Morales, René Duffard, Jesus Aceituno, Aleksandar Cikota and Pablo Santos-Sanz. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

Chiron’s facts

Chiron was the first discovered Centaur, i.e. the first asteroid / small planet, which orbits between the orbits of Saturn and Uranus. It was discovered in 1977, in the sense that it was identified in 1977. But reexamination of past photographic plates show that it has in fact been observed since 1895. And from the reanalysis of the pre-discovery observations, it was easy to determine an orbit.

Discovery 1977
First observation 1895
Apparent magnitude 19
Absolute magnitude 6
Diameter 220 km
Semimajor axis 13.648 AU
Eccentricity 0.3823
Inclination 6.9497°
Orbital period 50.42 yr
Rotation 5.918 h

The orbital period of Chiron is a slightly longer than 50 years, which means that we dispose of astrometric observations over more than 2 periods. This orbit is highly eccentric, which results in large variations of the distance to the Sun, i.e. between 8.43 AU (astronomical units) at perihelion, and 18.86 AU at aphelion.

A spectral analysis of Chiron reveals a C-type, i.e. a carbonaceous, object. Moreover, it shows large variations of brightness, which are considered to be partly due to cometary activity, and partly due to rings. This cometary activity makes that Chiron, officially the asteroid (2060)Chiron, can also be called the comet 95P/Chiron.

Chiron observed at Kuma Kogen Astronomical Observatory, Japan. © 1997 by Akimasa Nakamura
Chiron observed at Kuma Kogen Astronomical Observatory, Japan. © 1997 by Akimasa Nakamura

The presence of rings around Chiron is not unanimously accepted in the scientific community. Unexpected stellar occultations by something orbiting close to Chiron could be interpreted either as cometary jets, or as rings. But the large variations of brightness and the discoveries of rings around Chariklo and Haumea speak for the presence of rings. The discovery of rings around Chariklo was very surprising, and showed that it is possible. The discovery around Haumea has shown that rings around such bodies were not exceptional. So, why not Chiron? In this study, the authors clearly state that they believe in the presence of rings, and they use it to study the brightness of Chiron. These rings would have a radius of 324 ± 10 km, which is inside the estimated Roche limit of Chiron, i.e. the particles constituting the rings could not accrete into a larger body.

But the central point is the cometary activity, i.e. evidence for cometary jets is reported.

Triggering a cometary activity

Classical comets behave this way: these are dirty snowballs, i.e. made of ice, dust, and some other elements. When approaching the Sun, the comet gets so warm that the ice is sublimated. But a Centaur with cometary activity is different, since it does not get closer to the Sun. Moreover, Chiron is essentially carbonaceous. So, another cause has to be found. And in such a case, it is often tempting to invoke impacts.

A problem is that impacts are not that frequent in that region of the Solar System. First because the gravitational action of the Sun tends to focus the orbits of the potential impactors, i.e. they will be more inclined to get closer to the Sun, and second because, the more distant from the Sun you are, the emptier the space appears, this is just a geometrical effect.
The consequences of these effects is that a collision of a 1km-radius comet is expected on a body like Chiron every 60 Gyr… while the age of the Solar System is 4.5 Gyr… quite unlikely.

Photometric observations

Anyway, Chiron is known to have some cometary activity, and the author tracked it from Calar Alto Observatory (CAHA) in Almeria, Spain, during 3 observation campaigns, between 2014 and 2016. The first campaign was primarily devoted to the study of the rotation of Chiron, and consisted of 3 runs in 2014, using the 3.5 and the 1.23 m telescopes. The second campaign was conducted in September 2015 on the 2.2 m telescope, with the CAFOS instrument (Calar Alto Faint Object Spectrograph), and looked for rotation, absolute magnitude, and cometary activity. The third campaign took place on 2016, September 2, to get a better constraint on Chiron’s absolute magnitude, once again with CAFOS.

The authors were particularly interested in the photometry, since cometary jets translate into variations of brightness. For that, they had to correct the variations due to observational constraints, and to the orientation of Chiron.

The 3.5m telescope at Calar Alto Observatory (CAHA). © Alfredo Madrigal
The 3.5m telescope at Calar Alto Observatory (CAHA). © Alfredo Madrigal

Observational constraints are likely to give artificial variations of photometry, since

  • the height of Chiron on the horizon varies, which means that the thickness of the atmosphere varies,
  • the wind might result in unstable images (seeing),
  • the detectors are different, even on the same instrument,etc.

To try to make things as proper as possible, the authors corrected the images from flat fielding, i.e. from the variations of the response of the CCD chip, and they observed a large enough field (at least 16 arcmin), to have the same stars as photometric references.

Regarding the orientation of Chiron, variations of brightness can reveal:

  • the rotation of Chiron, which would present different surface elements to the observer,
  • the orientation of the rings.

These two effects were modeled, to be removed from the photometric measurements. And the result is…

Impacts from the rings

The authors do observe a small cometary activity on Chiron, which is pretty faint. It has actually been stronger in the past, a measurement in 1973 showed a peak with respect to another measurement in 1970, and since then the coma is monotonously decreasing. The authors interpret that as a possible small impact having occurred between 1970 and 1973, the associated coma tail having almost disappeared. This activity appears to be supplemented by a continuous micro-activity, which could be due to impacts by small particles falling from the rings.

The study and its authors

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

On the stability of Chariklo

Hi there! Do you remember Chariklo? You know, this asteroid with rings (see this post on their formation). Today, we will not speak on the formation of the rings, but of the asteroid itself. I present you the paper entitled The dynamical history of Chariklo and its rings, by J. Wood, J. Horner, T. Hinse and S. Marsden, which has recently been published in The Astronomical Journal. It deals with the dynamical stability of the asteroid Chariklo as a Centaur, i.e. when Chariklo became a Centaur, and for how long.

(10199)Chariklo

Chariklo is a large asteroid orbiting between the orbits of Saturn and Uranus, i.e. it is a Centaur. It is the largest known of them, with a diameter of ~250 km. It orbits the Sun on an elliptic orbit, with an eccentricity of 0.18, inducing variations of its distance to the Sun between 13.08 (perihelion) and 18.06 au (aphelion), au being the astronomical unit, close to 150 millions km.
But the main reason why people are interested in Chariklo is the confirmed presence of rings around it, while the scientific community expected rings only around large planets. These rings were discovered during a stellar occultation, i.e. Chariklo occulting a distant star. From the multiple observations of this occultation in different locations of the Earth’s surface, 2 rings were detected, and announced in 2014. Since then, rings have been hinted around Chiron, which is the second largest one Centaur, but this detection is still doubtful.
Anyway, Chariklo contributes to the popularity of the Centaurs, and this study is focused on it.

Small bodies populations in the Solar System

The best known location of asteroids in the Solar System is the Main Belt, which is located between the orbits of Mars and Jupiter. Actually, there are small bodies almost everywhere in the Solar System, some of them almost intersecting the orbit of the Earth. Among the other populations are:

  • the Trojan asteroids, which share the orbit of Jupiter,
  • the Centaurs, which orbit between Saturn and Uranus,
  • the Trans-Neptunian Objects (TNOs), which orbit beyond the orbit of Neptune. They can be split into the Kuiper Belt Objects (KBOs), which have pretty regular orbits, some of them being stabilized by a resonant interaction with Neptune, and the Scattered Disc Objects (SDOs), which have larger semimajor axes and high eccentricities
  • the Oort cloud, which was theoretically predicted as a cloud of objects orbiting near the cosmological boundary of our Solar System. It may be a reservoir of comets, these small bodies with an eccentricity close to 1, which can sometimes visit our Earth.

The Centaurs are interesting from a dynamical point of view, since their orbits are not that stable, i.e. it is estimated that they remain in the Centaur zone in about 10 Myr. Since this is very small compared to the age of our Solar System (some 4.5 Gyr), the fact that Centaurs are present mean that the remaining objects are not primordial, and that there is at least one mechanism feeding this Centaur zone. In other words, the Centaurs we observe were somewhere else before, and they will one day leave this zone, but some other guys will replace them.

There are tools, indicators, helpful for studying and quantifying this (in)stability.

Stability, Lyapunov time, and MEGNO

Usually, an orbiting object is considered as “stable” (actually, we should say that its orbit is stable) if it orbits around its parent body for ever. Reasons for instability could be close encounters with other orbiting objects, these close encounters being likely to be favored by a high eccentricity, which could itself result from gravitational interactions with perturbing objects.
To study the stability, it is common to study chaos instead. And to study chaos, it is common to actually study the dependency on initial conditions, i.e. the hyperbolicity. If you hold a broom vertically on your finger, it lies in a hyperbolic equilibrium, i.e. a small deviation will dramatically change the way it will fall… but trust me, it will fall anyway.
And a good indicator of the hyperbolicity is the Lyapunov time, which is a timescale beyond which the trajectory is so much sensitive on the initial conditions that you cannot accurately predict it anymore. It will not necessarily become unstable: in some cases, known as stable chaos, you will have your orbit confined in a given zone, you do not know where it is in this zone. The Centaur zone has some kind of stable chaos (over a given timescale), which partly explains why some bodies are present there anyway.
To estimate the Lyapunov time, you have to integrate the differential equations ruling the motion of the body, and the ones ruling its tangent vector, i.e. tangent to its trajectory, which will give you the sensitivity to the initial conditions. If you are hyperbolic, then the norm of this tangent vector will grow exponentially, and from its growth rate you will have the Lyapunov time. Easy, isn’t it? Not that much. Actually this exponential growth is an asymptotic behavior, i.e. when time goes to infinity… i.e. when it is large enough. And you have to integrate over a verrrrry loooooooong time…
Fortunately, the MEGNO (Mean Exponential Growth of Nearby Orbits) indicator was invented, which converges much faster, and from which you can determine the Lyapunov time. If you are hyperbolic, the Lyapunov time is contained in the growth rate of the MEGNO, and if not, the MEGNO tends to 2, except for pretty simple systems (like the rotation of synchronous bodies), where it tends to zero.

We have now indicators, which permit to quantify the instability of the orbits. As I said, these instabilities are usually physically due to close encounters with large bodies, especially Uranus for Centaurs. This requires to define the Hill and the Roche limits.

Hill and Roche limits

First the Roche limit: where an extended body orbits too close to a massive object, the difference of attraction it feels between its different parts is stronger than its cohesion forces, and it explodes. As a consequence, satellites of giant planets survive only as rings below the Roche limit. And the outer boundary of Saturn’s rings is inner and very close to the Roche limit.

Now the Hill limit: it is the limit beyond which you feel more the attraction of the body you meet than the parent star you both orbit. This may result in being trapped around the large object (a giant planet), or more probably a strong deviation of your orbit. You could then become hyperbolic, and be ejected from the Solar System.

This paper

This study consists in backward numerical integrations of clones of Chariklo, i.e. you start with many fictitious particles (the authors had 35,937 of them) which do not interact with each others, but interact with the giant planets, and which are currently very close to the real Chariklo. Numerical integration over such a long timespan requires accurate numerical integrators, the authors used a symplectic one, i.e. which presents mathematical properties limiting the risk of divergence over long times. Why 1 Gyr? The mean timescale of survival (called here half-life, i.e. during which you lose half of your population) is estimated to be 10 Myr, so 1 Gyr is 100 half-lives. They simulated the orbits and also drew MEGNO maps, i.e. estimated the Lyapunov time with respect to the initial orbital elements of the particle. Not surprisingly, the lower the eccentricity, the more stable the orbit.

And the result is: Chariklo is in a zone of pretty stable chaos. Moreover, it is probably a Centaur since less than 20 Myr, and was a Trans-Neptunian Object before. This means that it was exterior to Neptune, while it is now interior. In a few simulations, Chariklo finds its origin in the inner Solar System, i.e. the Main Belt, which could have favored a cometary activity (when you are closer to the Sun, you are warmer, and your ice may sublimate), which could explain the origin of the rings. But the authors do not seem to privilege this scenario, as it supported by only few simulations.

What about the rings?

The authors wondered if the rings would have survived a planetary encounter, which could be a way to date them in case of no. But actually it is a yes: they found that the distance of close encounter was large enough with respect to the Hill and Roche limits to not affect the rings. So, this does not preclude an ancient origin for the rings… But a specific study of the dynamics of the rings would be required to address this issue, i.e. how stable are they around Chariklo?

To know more

And 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.

Forming the rings of Chariklo

Hi there! Today’s article is on the rings of the small planet Chariklo. Their origin is being discussed in Assessment of different formation scenarios for the ring system of (10199) Chariklo, by Mario Melita, René Duffard, Jose-Luis Ortiz and Adriano Campo Bagatin, which has recently been accepted for publication in Astronomy and Astrophysics.

The Centaur (10199)Chariklo

As a Centaur, (10199)Chariklo orbits around the Sun, between the orbits of Saturn and Uranus. It has been discovered in February 1997 thanks to the Spacewatch program, which was a systematic survey conducted at Kitt Peak National Observatory in
Arizona, USA. It orbits about the Sun in 63 years, has an orbital inclination of 23°, and an eccentricity of 0.17, which results in significant variations of its distance to the Sun. Moreover, it orbits close to the 4:3 mean-motion resonance with Uranus, which means that it performs 4 revolutions around the Sun while Uranus performs almost 3.

(10199)Chariklo is considered to be possibly a dwarf planet. A dwarf planet is not a planet, since the International Astronomical Union reserved this appellation for only 8 objects, but looks like one. As such, it is large enough to have a pretty spherical shape, with a mean radius of 151 km. It has a pretty fast rotation, with a period of 7 hours. Something unusual to notice: its equatorial section is almost circular (no problem), but its polar axis is the longest one, while it should be the shortest if Chariklo had been shaped by its rotational deformation.

The planetary rings

Everybody knows the massive rings of Saturn, which can be seen from the Earth with any telescope. These rings are composed of particles, which typical radius ranges from the centimeter to some meters. These particles are mostly water ice, with few contamination by silicates.
The spacecrafts Voyager have revealed us the presence of a tiny ring around Jupiter, mainly composed of dust. Moreover, Earth-based observations of Uranus and Neptune revealed rings in 1978 and 1984, respectively. We now know 13 rings for Uranus, which should be composed of submillimetric particles, and 5 rings for Neptune. Interestingly, one of the rings of Neptune, Adams, is composed of 5 arcs, i.e. 5 zones of surdensity, which seem to be pretty stable.

It is usually assumed that rings around a planet originate from the disruption of a small body, possibly an impactor. A question is : why do these rings not reaccrete into a new planetary body, which could eventually become a satellite of a planet? Because its orbit is above the Roche limit.

The Roche limit

The Roche limit is named after the French astronomer and mathematician Édouard Albert Roche who discovered that when a body was too close from a massive object, it could just not survive. This allowed him to say that the distance Mars-Phobos which was originally announced when Phobos was discovered was wrong, and he was right.

Imagine a pretty small object orbiting around a massive planet. Since the object has a finite dimension, the gravitational force exerted by the planet has some variation over the volume of the object. More precisely, it decreases with the square of the distance to the planet. If the internal cohesion in the body is smaller than the variations of the gravitational attraction which affect the body, then it just cannot survive, and is tidally disrupted.

It was long thought than you need a very massive central object to get rings around. This is why the announcement of the discovery of rings around Chariklo, in 2014, was a shock.

The rings of Chariklo

The discovery of these rings has been announced in March 2014, and was the consequence of the observation of the occultation by Chariklo of the star UCAC4 248-108672 in June 2013 by 13 instruments, in South America. This was a multichord observation mostly aiming at characterizing a stellar occultation observed from different sites, to infer clues on the shape of the occulting body, and possibly discover a satellite (see this related post). In the case of Chariklo, short occultations before AND after the main one have been measured, which meant a ring system around Chariklo. The following video, made by the European South Observatory, illustrates the light flux drops due to the rings and to Chariklo itself.

Actually two rings were discovered, which are now named Oiapoque and Chuí. They have both a radius close to 400 km, Oiapoque being the inner one. These two rings are separated by a gap of about 9 km. Photometric measurements suggest there are essentially composed of water ice.

This study

This study investigates and discusses different possible causes for the formation of the rings of Chariklo.

Tidal disruption of a small body: REJECTED

It can be shown that, for a satellite which orbits beyond the Roche limit, i.e. which should not be tidally disrupted, the tides induce a secular migration of its orbit: if the satellite orbits faster than the central body (here, Chariklo) rotates around its polar axis, then the satellites migrates inward, i.e. gets closer to the satellite. In that case, it would eventually reach the Roche limit and be disrupted; this is the expected fate of the satellite of Mars Phobos. However, if it orbits above the synchronous orbit, which means that its orbital angular velocity is smaller than the rotation of Chariklo, then it would migrate outward.
In the case of Chariklo, the synchronous orbit is closer than the Roche limit. The rotation period of Chariklo is 7 hours, while the rings’ one is 20 hours. As a consequence, tidal inward migration until disruption is impossible. It would have needed Chariklo to have spun much slower in the past, while a faster rotation is to be expected because of the loss of rotational energy over the ages.

Collision between a former satellite of Chariklo and another body: VERY UNLIKELY

If the rings are the remnants of a former satellite of Chariklo, then models of formation suggest that this satellite should have had a radius of about 3 km. The total mass of the rings is estimated to be the one of a satellite of 1 km, but only part of the material would have stayed in orbit around Chariklo.
The occurence of such an impact is almost precluded by the statistics.

Collision between Chariklo and another body: UNLIKELY

We could imagine that the rings are ejectas of an impact on Chariklo. The authors estimate that this impact would have left a crater with a diameter between 20 and 50 km. Once more, the statistics almost preclude it.

Three-body encounter: POSSIBLE

Imagine an encounter between an unringed Chariklo and another small planet, which itself has a satellite. In that case, favorable conditions could result in the trapping of the satellite in the gravitational field of Chariklo, and its eventual disruption if it is below the Roche limit. The author estimate that it would require the largest body to have a radius of about 6.5 km, and its (former) satellite a radius of 330 meters.

The authors favor this scenario, but I do not see how a satellite of a radius of 330 m could generate a ring, which material should correspond to a 1 km-radius body.

Beyond Chariklo

The quest for rings is not done. Since 2015, another Centaur, (2060)Chiron, is suspected to harbor a system of rings. This could mean that rings are not to be searched around large bodies, as long thought, but in a specific region of the Solar System. Matt Hedman has proposed that the weakness of ice at 70K, which is its temperature in that region of the Solar System, favors the formation and the stability of rings.

To know more

That’s all for today! I hope you liked it. As usual, you are free to comment. You can also subscribe to the RSS feed, and follow me on Twitter.

On the dynamics of small bodies beyond Neptune

Hi there! Today I will present you a study on the possible dynamics of some Trans-Neptunian Objects (TNOs). This study, Study and application of the resonant secular dynamics beyond Neptune by M. Saillenfest, M. Fouchard, G. Tommei and G.B. Valsecchi, has recently been accepted for publication in Celestial Mechanics and Dynamical Astronomy.
This is a theoretical study, which presents some features of the dynamics that could one day be observed. This manuscript follows another one by the same authors, in which a theory of the “resonant secular dynamics” is presented. Here it is applied to small bodies, which are thought to be in mean-motion resonances with Neptune. This study results from a French-Italian collaboration.

The Kozai-Lidov mechanism

The dynamics that is presented here uses the so-called Kozai-Lidov mechanism. This is a mechanism which has been simultaneously and independently discovered in Russia (by Lidov) and in Japan (by Kozai), and which considers the following configuration: a massive central body, another massive one called the perturber, and a test-particle, i.e. a massless body, which orbits the central one. This problem is called the Restricted 3-body problem. Originally, the central body was the Earth, the perturber the Moon, and the test-particle an artificial satellite of the Earth. In such a case, the orbit of the test-particle is an ellipse, which is perturbed by the perturber; this results in variation of the elliptical elements, i.e. eccentricity, inclination… moreover, the orientation of the ellipse is moving…

To describe the problem, I need to introduce the following orbital elements:

  • The semimajor axis a, which is half the long axis of the orbit,
  • the mean anomaly M, which locates the satellite on the ellipse,
  • the eccentricity e, which is positive and smaller than 1. It tells us how eccentric the orbit is (e=0 means that the orbit is circular),
  • the pericentre ω, which is the point of the orbit which is the closest to the central body (undefined if the orbit is circular),
  • the inclination I, which is the angle between the orbital plane and the reference plane,
  • the ascending node Ω, which locates the intersection between the orbital plane and the reference plane.

The Kozai-Lidov mechanism allows a confinement of the pericentre with respect to the ascending node, and it can be shown that it results in a raise of the eccentricity of the inclination. Exploiting such a mechanism gives frozen orbits, i.e. configurations for which the orbit of an artificial orbiter, even inclined and eccentric, will keep the same spatial orientation.

These recent years, this mechanism has been extended for designing space missions around other objects than the Earth, but also to explain the dynamics of some exoplanetary systems, of small distant satellites of the giant planets, and of Trans-Neptunian Objects, as it is the case here. In this last problem, the central body is the Sun, the perturber is a giant planet (more specifically here, it is Neptune), and the test-particle is a TNO, with the hope to explain the inclined and eccentric orbit of some of them. A notable difference with the original Kozai-Lidov problem is that here, the test-particle orbits exterior to the perturber. Another difference is that its dynamics is also resonant.

Resonant and secular dynamics

The authors do not speak of resonant secular dynamics, but of dynamics that is both resonant and secular. The difference is that the involved resonance is not a secular one. Let me explain.

The authors consider that the TNO is in a mean-motion resonance with Neptune. This implies an integer commensurability between its orbital period around the Sun and the one of Neptune, with results in large variations of its semi-major axis. If we look at the orbital elements, this affects the mean anomaly M, while, when a resonance is secular, M is not affected.

So, these objects are in a mean-motion resonance with Neptune. Moreover, they have an interested secular dynamics. By secular, I mean that the mean anomaly is not affected, but something interesting involves the node and/or the pericentre. And this is where comes Kozai-Lidov. The paper studies the objects which are trapped into a mean-motion resonance with Neptune, and which are likely to present a confinement of the pericentre ω, which could explain a significant eccentricity and a high inclination.

For that, they make an analytical study, which theory had been developed in the first paper, and which is applied here.

Why an analytical study?

The modern computing facilities allow to simulate the motion of millions of test-particles over the age of the Solar System, in considering the gravitational interaction of the planets, the galactic tide, a star passing by… and this results in clusters of populations of fictitious TNOs. Very well. But when you do that, you do not know why this particular object behaves like that. However, an analytical study will give you zones of stability for the orbits, which are preferred final states. It will tell you: there will probably be some objects in this state, BECAUSE… and in the case of this study, the because has something to do with the Kozai-Lidov mechanism. Moreover, the because also gives you some confidence in your results, since you have an explanation why you get what you get.

To make things short, a numerical study shows you many things, while an analytical one proves you a few things. A comprehensive study of the problem requires combining the two approaches.

This paper

This paper specifically deals with fictitious objects, which are in mean-motion with Neptune, and are likely to be affected by the Kozai-Lidov mechanism. After many calculations presented in the first paper, the authors show that the problem can be reduced to one degree of freedom, in a Hamiltonian formalism.

The Hamiltonian formalism is a common and widely used way to treat problems of celestial mechanics. It consists in expressing the total energy of the problem, i.e. kinetic + potential energy, and transform it so that trajectories can be described. These trajectories conserve the total energy, which may seem weird for a physical problem. Actually there is some dissipation in the dynamics of TNOs, but so small that it can be neglected in many problems. The most recent numerical studies in this topic consider the migration of the planets, which is not a conservative process. In the paper I present you today, this migration is not considered. This is one of the approximations required by the analytical study.

The remaining degree of freedom is the one relevant to the Kozai-Lidov mechanism. The one associated with the mean-motion resonance is considered to be constant. For that it involves the area enshrouded by the libration of the resonant argument, which is constant (hypothesis of the adiabatic invariant). So, the authors get a one degree-of-freedom Hamiltonian, for which they draw phase spaces, showing the trajectory in the plane q vs. ω, q=a(1-e) being the distance between the Sun and the pericentre of the TNO, i.e. its closest distance to the Sun. These phase portraits depend on other parameters, like the mean-motion resonance with Neptune that is considered, and a parameter η, which combines the inclination and the eccentricity.

The results are a catalog of possible trajectories, some of them presenting a confinement of the pericentre &omega;. For a large cloud of objects, this would result in an accumulation of pericentres in a constrained zone. The authors try to find confirmation of their results with existing objects, but their limited number and the inaccuracy on their location make this comparison inconclusive. They also point out that the orbits of Sedna and 2012VP113 cannot be explained by this mechanism.

Perspectives

The future observations of TNOs will give us access to more objects and more accurate trajectories, and it is to be hoped that some of them will fit into the trajectories found by the authors. That would be a great success for that, and that would be deserved regarding the effort necessary to achieve such an analytical study.

As I said, such a problem needs analytical and numerical studies, but some of the authors (Marc Fouchard and Giovanni Valsecchi) are also involved in such a numerical exploration, which starts from a fictitious Oort cloud and simulates the excitation of the eccentricity and inclination of some of the objects.

For the two studies to meet, it should also be investigated how the planetary migration, which results from models of formation and evolution of the Solar System, affects the zones of stability due to the Kozai-Lidov mechanism.

Finally, we should not forget the quest for the Planet Nine. As the authors honestly point out, an additional planet could break down some of the conclusions.

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