Tag Archives: Binary asteroids

Forming Pluto’s satellites

Hi there! A team from the University of Hong Kong has recently explored a scenario of formation of the small satellites of Pluto. You know, there are 4 small bodies, named Styx, Nix, Kerberos, and Hydra, which orbit around the binary Trans-Neptunian Object Pluto-Charon. At this time, we don’t know yet how they were formed, and how they ended up at their present locations, despite the data that the spacecraft New Horizons sent us recently. The study I present you today, On the early in situ formation of Pluto’s small satellites, by Jason Man Yin Woo and Man Hoi Lee, simulates the early evolution of the Pluto-Charon system. It has recently been published in The Astronomical Journal.

The satellites of Pluto

The American Clyde W. Tombaugh discovered Pluto in 1930. He examined photographic plates taken at Lowell Observatory at Flagstaff, Arizona, USA, and detected a moving object, which thus could not be a star. The International Astronomical Union considered Pluto to be the ninth planet of the Solar System, until 2006. At that time, numerous discoveries of distant objects motivated the creation of the class of dwarf planets, Pluto being one of the largest of them.

The other American astronomer James W. Christy discovered a companion to Pluto, Charon, in June 1978. Still at Flagstaff.

The existence of far objects in our Solar System motivated the launch of the space missions New Horizons in 2006. New Horizons made a close approach of the system of Pluto in July 2015, and is currently en route to the Trans-Neptunian Object 2014MU69. The closest approach is scheduled for January, 1st 2019.

In parallel to the preparation of New Horizons, the scientific team performed observations of Pluto-Charon with the famous Hubble Space Telescope. And they discovered 4 small satellites: Nix, Hydra, Styx and Kerberos. You can find some of their characteristics below, which are due to New Horizons.

Charon Styx Nix Kerberos Hydra
Discovery 1978 2012 2005 2011 2005
Semimajor axis 17,181 km 42,656 km 48,694 km 57,783 km 64,738 km
Eccentricity 0 0.006 0 0.003 0.006
Inclination 0.8° 0.1° 0.4° 0.2°
Orbital period 6.39 d 20.16 d 24.85 d 32.17 d 38.20 d
Spin period 6.39 d 3.24 d 1.829 d 5.31 d 0.43 d
Mean diameter 1,214 km 10.5 km 39 km 12 km 42 km
Styx seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Styx seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Nix seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Nix seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Kerberos seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Kerberos seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute

Hydra seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute
Hydra seen by New Horizons © NASA / Johns Hopkins University Applied Physics Laboratory / Southwest Research Institute

We should compare these numbers to the ones of Pluto: a mean diameter of 2370 km, and a spin period of 6.39 d. This implies that:

  • Pluto and Charon are two large objects, with respect to the other satellites. So, Pluto-Charon should be seen as a binary TNO, and the other four objects are satellites of the binary.
  • Pluto and Charon are in a state of double synchronous spin-orbite resonance: their rotation rate is the same, and is the same that their mutual orbital motion. If you are on the surface of Pluto, facing a friend of yours on the surface of Charon, you will always face her. This is probably the most stable dynamical equilibrium, reached after dissipation of energy over the ages.

And the four small satellites orbit outside the mutual orbits of Pluto and Charon.

Proximity of Mean-Motion Resonances

We can notice that:

  • the orbital period of Styx is close to three times the one of Charon,
  • the orbital period of Nix is close to four times the one of Charon,
  • the orbital period of Kerberos is close to five times the one of Charon,
  • the orbital period of Hydra is close to six times the one of Charon.

Close to, but not exactly. This suggests the influence of mean-motion resonances of their orbital motion, i.e. the closest distance between Charon and Styx will happen every 3 orbits of Charon at the same place, so you can have a cumulative effect on the orbit. And the same thing would happen for the other objects. But this is actually not that clear whether that cumulative effect would be significant or not, and if yes, how it would affect the orbits. Previous studies suggest that it translates into a tiny zone of stability for Kerberos, provided that Nix and Hydra are not too massive.

Anyway, the authors wondered why these four satellites are currently at their present location.

Testing a scenario of formation

They addressed this question in testing the following scenario: Charon initially impacted Pluto, and the debris resulting from the impact created the four small satellites. To test this scenario, they ran long-term numerical simulations of small, test particles, perturbed by Pluto and Charon. Pluto and Charon were not in the current state, but in a presumed early one, before the establishment of the two synchronous rotations, and with and without a significant initial eccentricity for Charon. The authors simulated the orbital evolution, the system evolving over the action of gravitational mutual interactions, and tides.

The long-term evolution is ruled by tides

The tides are basically the dissipation of energy in a planetary body, due to the difference of force exerted at different points of the body. This results in stress, and is modeled as a tidal bulge, which points to the direction of the perturber. The dissipation of energy is due to the small angular shift between the orientation of the bulge and the direction of the perturber. The equilibrium configuration of Pluto-Charon, i.e. the two synchronous rotations, suggest that the binary is tidally evolved.

The authors applied tides only on Pluto and Charon, and considered two tidal models:

  1. A constant time delay between the tidal excitation and the response of the tidal bulge,
  2. A constant angular shift between the tidal bulge and the direction of the perturber.

The tidal models actually depend on the properties of the material, and the frequency of the excitation. In such a case, the frequency of the excitation depends on the two rotation rates of Pluto and Charon, and on their orbital motions. The properties of the material, in particular the rigidity and the viscosity, are ruled by the temperatures of the objects, which are not necessarily constant in space and in time, since tidal stress tend to heat the object. Here the authors did not consider a time variation of the tidal parameters.

Other models, which are probably more physically realistic but more complex, exist in the literature. Let me cite the Maxwell model, which assumes two regimes for the response of the planetary body: elastic for slow excitations, i.e. not dissipative, and dissipative for fast excitations. The limit between fast and slow is indicated by the Maxwell time, which depends on the viscosity and the rigidity of the object.

Anyway, the authors ran different numerical simulations, with the two tidal models (constant angular shift and constant time delay), with different numbers and different initial eccentricities for Charon. And in all of these simulations, they monitored the fate of independent test particles orbiting in the area.

Possible scenario, but…

The authors seem disappointed by their results. Actually, some of the particles are affected by mean-motion resonances, some other are ejected, but the simulations show that particles may end up at the current locations of Styx, Nix, Kerberos, and Hydra. However, their current locations, i.e. close to mean-motion resonances, do not appear to be preferred places for formation. This means that we still do not know why the satellites are where they currently are, and not somewhere else.

What’s next?

The next target of New Horizons is 2014MU69, which we will be the first object explored by a spacecraft, which had been launched before the object was known to us. We should expect many data.

The study and its authors

You can find here

  • The study, made freely available by the authors on arXiv, thanks to them for sharing!
  • and the homepage of Man Hoi Lee.

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 system of (107) Camilla

Hi there! I will present you today a fascinating paper. It aims at a comprehensive understanding of the system composed of an asteroid, (107) Camilla, and its two satellites. For that, the authors acquired, processed and used 5 different types of observations, from all over the world. A consequence is that this paper has many authors, i.e. 27. Its title is Physical, spectral, and dynamical properties of asteroid (107) Camilla and its satellites, by Myriam Pajuelo and 26 colleagues, and it has recently been published in Icarus. This paper gives us the shape of Camilla and its main satellites, their orbits, the mass of Camilla, its composition, its spin period,… I give you these results below.

The system of Camilla

The asteroid (107) Camilla has been discovered in 1868 by Norman Pogson at Madras Observatory, India. It is located in the
outer Main-Belt, and more precisely it is a member of the Cybele group. This is a group of asteroids, named after the largest of them (65) Cybele, which is thought to have a common origin. They probably originate from the disruption of a single progenitor. I show you below some Camilla’s facts, taken from the JPL Small-Body Database Browser:

Discovery 1868
Semimajor axis 3.49 AU
Eccentricity 0.066
Perihelion 3.26 AU
Inclination 10.0°
Orbital period 6.52 yr

We have of course other data, which have been improved by the present study. Please by a little patient.

In 2001 the Hubble Space Telescope revealed a satellite of Camilla, S1, while the second satellite, S2, and has been discovered in 2016 from images acquired by the Very Large Telescope of Cerro Paranal, Chile. This makes (107) Camilla a ternary system. Interesting fact, there is at least another ternary system in the Cybele group: the one formed by (87) Sylvia, and its two satellites Romulus and Remus.

Since their discoveries, these bodies have been re-observed when possible. This resulted in a accumulation of different data, all of them having been used in this study.

5 different types of data

The authors acquired and used:

  • optical lightcurves,
  • high-angular-resolution images,
  • high-angular-resolution spectrum,
  • stellar occultations,
  • near-infrared spectroscopy.

You record optical lightcurves in measuring the variations of the solar flux, which is reflected by the object. This results in a curve exhibiting periodic variations. You can link their period to the spin period of the asteroid, and their amplitudes to its shape. I show you an example of lightcurve here.

High-angular-resolution imaging requires high-performance facilities. The authors used data from the Hubble Space Telescope (HST), and of 3 ground-based telescopes, equipped with adaptive optics: Gemini North, European Southern Observatory Very Large Telescope (VLT), and Keck. Adaptive optics permits to correct the images from atmospheric distortion, while the HST, as a space telescope, is not hampered by our atmosphere. In other words, our atmosphere bothers the accurate observations of such small objects.

A spectrum is the amplitude of the reflected Solar light, with respect to its wavelength. This permits to infer the composition of the surface of the body. The high-angular-resolution spectrum were made at the VLT, the resulting data also permitting astrometry of the smallest of the satellites, S2. These spectrum were supplemented by near-infrared spectroscopy, made with a dedicated facility, i.e. the SpeX spectrograph of the NASA InfraRed Telescope Facility (IRTF), based on Mauna Kea, Hawaii. Infrared is very sensitive to the temperature, this is why their observations require dedicated instruments, which need a dedicated cooling system.

Finally, stellar occultations consist to record the light of a star, which as some point is occulted by the asteroid you study. This is particularly interesting for a faint body, which you cannot directly observe. Such observations can be made by volunteers, who use their own telescopes. You can deduce clues on the shape, and sometimes on the presence of a satellite, from the duration of the occultation. In comparing the durations of the same occultation, recorded at different locations, you may even reconstruct the shape (actually a 2-D shape, which is projected on the celestial sphere). See here.

And from all this, you can infer the orbits of the satellites, and the composition of the primary (Camilla) and its main satellite (S1), and the spin and shape of Camilla.

The orbits of the satellites

All of these observations permit astrometry, i.e. they give you the relative location of the satellites with respect to Camilla, at given dates. From all of these observations, you fit orbits, i.e. you numerically determine the orbits, which have the smallest distances (residuals), with the data.

This is a very tough task, given the uncertainty of the recorded positions. For that, the authors used their own genetic-based algorithm, Genoid, for GENetic Orbit IDentification, which relies on a metaheuristic method to minimize the residuals. Many trajectories are challenged in this iterative approach, and only the best ones are kept. These remaining trajectories, designed as parents, are used to generate new trajectories which improve the residuals. This algorithm has proven its efficiency for other systems, like the binary asteroid (22) Kalliope-Linus. In such cases, the observations lack of accuracy and many parameters are involved.

You can find the results below.

S/2001 (107) 1
Semimajor axis 1247.8±3.8 km
Eccentricity <0.013
Inclination (16.0±2.3)°
Orbital period 3.71234±0.00004 d
S/2016 (107) 2
Semimajor axis 643.8±3.9 km
Eccentricity ~0.18 (<0.23)
Inclination (27.7±21.8)°
Orbital period 1.376±0.016 d

You can deduce the mass of (107) Camilla from these numbers, i.e. (1.12±0.01)x1019 kg. The ratio of two orbital periods probably rule out any significant mean-motion resonance between these two satellites.

Spin and shape

The authors used their homemade algorithm KOALA (Knitted Occultation, Adaptive-optics, and Lightcurve Analysis) to determine the best-fit solution (once more, minimization of the residuals) for spin period, orientation of the rotation pole, and 3-D shape model, from lightcurves, adaptive optics images, and stellar occultations. And you can find the solution below:

Camilla
Diameter 254±36 km
a 340±36 km
b 249±36 km
c 197±36 km
Spin period 4.843927±0.00004 h

This table gives two solutions for the shape: a spherical one, and an ellipsoid. In this last solution, a, b, and c are the three diameters. We can see in particular that Camilla is highly elongated. Actually a comparison between the data and this ellipsoid, named the reference ellipsoid, revealed two deep and circular basins at the surface of Camilla.

Moreover, a comparison of the relative magnitudes of Camilla and its two satellites, and the use of the diameter of Camilla as a reference, give an estimation of the diameters of the two satellites. These are 12.7±3.5 km for S1 and 4.0±1.2 km for S2. These numbers assume that S1 and S2 have the same albedo. This assumption is supported for S1 by the comparison of its spectrum from the one of Camilla.

The composition of these objects

In combining the shape of Camilla with its mass, the authors deduce its density, which is 1,280±130 kg/m3. This is slightly larger than water, while silicates should dominate the composition. As the authors point out, there might be some water ice in Camilla, but this pretty small density is probably due to the porosity of the asteroid.

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.

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.

Does Neptune have binary Trojans?

Hi there! Jupiter, Uranus and Neptune are known to share their orbits with small bodies, called Trojans. This is made possible by a law of celestial mechanics, which specifies that the points located 60° ahead and behind a planet on its orbit are stable. Moreover, there are many binary objects in the Solar System, but no binary asteroid have been discovered as Trojans of Neptune. This motivates the following study, Dynamical evolution of a fictitious population of binary Neptune Trojans, by Adrián Brunini, which has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society. In this study, the author wonders under which conditions a binary Trojan of Neptune could survive, which almost means could be observed now.

The coorbital resonance

The coorbital resonance is a 1:1 mean-motion resonance. This means that the two involved bodies have on average the same orbital frequency around their parent one. In the specific case of the Trojan of a planet, these two objects orbit the Sun with the same period, and the mass ratio between them makes that the small body is strongly affected by the planet, however the planet is not perturbed by the asteroid. But we can have this synchronous resonance even if the mass ratio is not huge. For instance, we have two coorbital satellites of Saturn, Janus and Epimetheus, which have a mass ratio of only 3.6. Both orbit Saturn in ~16 hours, but in experiencing strong mutual perturbations. They are stable anyway.

In the specific problem of the restricted (the mass of the asteroid is negligible), planar (let us assume that the planet and the asteroid orbit in the same plane), circular (here, we neglect the eccentricity of the two orbits) 3-body (the Sun, the planet and the asteroid) problem, it can be shown that if the planet and the asteroid orbit at the same rate, then there are 5 equilibriums, for which the gravitational actions of the planet and the Sun cancel out. 3 of them, named L1, L2 and L3, are unstable, and lie on the Sun-planet axis. The 2 remaining ones, i.e. L4 and L5, lag 60° ahead and behind the planet, and are stable. As a consequence, the orbits with small oscillations around L4 and L5 are usually stable, even if the real configuration has some limited eccentricity and mutual inclination. Other stable trajectories exist theoretically, e.g. horseshoe orbits around the point L4, L3 and L5. The denomination L is a reference to the Italian-born French mathematician Joseph-Louis Lagrange (1736-1813), who studied this problem.

The Lagrange points, in a reference frame rotating with Neptune.
The Lagrange points, in a reference frame rotating with Neptune.

At this time, 6,701 Trojans are known for Jupiter (4269 at L4 and 2432 at L5), 1 for Uranus, 1 for the Earth, 9 for Mars, and 17 for Neptune, 13 of them orbiting close to L4.

The Trojans of Neptune

You can find an updated list of them here, and let me gather their main orbital characteristics:

Location Eccentricity Inclination Magnitude
2004 UP10 L4 0.023 1.4° 8.8
2005 TO74 L4 0.052 5.3° 8.3
2001 QR322 L4 0.028 1.3° 7.9
2005 TN53 L4 0.064 25.0° 9.3
2006 RJ103 L4 0.031 8.2° 7.5
2007 VL305 L4 0.060 28.2° 7.9
2010 TS191 L4 0.043 6.6° 8.0
2010 TT191 L4 0.073 4.3° 7.8
2011 SO277 L4 0.015 9.6° 7.6
2011 WG157 L4 0.031 22.3° 7.1
2012 UV177 L4 0.071 20.9° 9.2
2014 QO441 L4 0.109 18.8° 8.3
2014 QP441 L4 0.063 19.4° 9.3
2004 KV18 L5 0.187 13.6° 8.9
2008 LC18 L5 0.079 27.5° 8.2
2011 HM102 L5 0.084 29.3° 8.1
2013 KY18 L5 0.121 6.6° 6.6

As you can see, these are faint bodies, which have been discovered between 2001 and 2014. I have given here their provisional designations, which have the advantage to contain the date of the discovery. Actually, 2004 UP10 is also known as (385571) Otrera, a mythological Queen of the Amazons, and 2005 TO74 has received the number (385695).

Their dynamics is plotted below:

Dynamics of the Trojans of Neptune, at the Lagrangian points L4 and L5 (squares).
Dynamics of the Trojans of Neptune, at the Lagrangian points L4 and L5 (squares).

Surprisingly, the 4 Trojans around L5 are outliers: they are the most two eccentric, the remaining two being among the three more inclined Trojans. Even if the number of known bodies may not be statistically relevant, this suggests an asymmetry between the two equilibriums L4 and L5. The literature has not made this point clear yet. In 2007, a study suggested an asymmetry of the location of the stable regions (here), but the same authors said one year later that this was indeed an artifact introduced by the initial conditions (here). In 2012, another study detected that the L4 zone is more stable than the L5 one. Still an open question… In the study I present today, the author simulated only orbits in the L4 region.

Binary asteroids

A binary object is actually two objects, which are gravitationally bound. When their masses ratio is of the order of 1, we should not picture it as a major body and a satellite, but as two bodies orbiting a common barycenter. At this time, 306 binary asteroids have been detected in the Solar System. Moreover, we also know 14 triple systems, and 1 sextuple one, which is the binary Pluto-Charon and its 4 minor satellites.

The formation of a binary can result from the disruption of an asteroid, for instance after an impact, or after fission triggered by a spin acceleration (relevant for Near-Earth Asteroids, which are accelerated by the YORP effect), or from the close encounter of two objects. The outcome is two objects, which orbit together in a few hours, and this system evolves… and then several things might happen. Basically, it either evolves to a synchronous spin-spin-orbit resonance, i.e. the two bodies having a synchronous rotation, which is also synchronous with their mutual orbit (examples: Pluto-Charon, the double asteroid (90) Antiope), or the two components finally split… There are also systems in which only one of the components rotates synchronously. Another possible end-state is a contact binary, i.e. the two components eventually touch together.

At this time, 4 binary asteroids are known among the Trojans asteroids of Jupiter. None is known for Neptune.

Numerical simulations

The author considered fictitious binary asteroids close to the L4 of Neptune, and propagated the motion of the two components, in considering the planetary perturbations of the planets, over 4.5 Byr, i.e. the age of the Solar System. A difficulty for such long-term numerical studies is the handling of numerical uncertainties. Your numerical scheme includes a time-step, which is the time interval between the simulated positions of the system, i.e. the locations and velocities of the two components of the binary. If your time-step is too large, you will have a mathematical uncertainty in your evaluation. However, if you shorten it, you will have too many iterations, which means a too long calculation time, and the accumulations of round-off errors due to the machine epsilon, i.e. rounding in floating point arithmetic.
A good time step should be a fraction of the shortest period perturbing the system. Neptune orbits the Sun in 165 years, which permits a time step of some years, BUT the period of a binary is typically a few hours… which is too short for simulations over the age of the Solar System. This problem is by-passed in averaging the dynamics of the binary. This means that only long-term effects are kept. In this case, the author focused on the Kozai-Lidov effect, which is a secular (i.e. very long-term) raise of the inclination and the eccentricity. Averaging a problem of gravitational dynamics is always a challenge, because you have to make sure you do not forget a significant contribution.
The author also included the tidal interaction between the two components, i.e. the mutual interaction triggering stress and strain, and which result in dissipation of energy, secular variation of the mutual orbits, and damping of the rotation.
He considered three sets of binaries: two with components of about the same size, these two samples differing by the intensity of tides, and in the third one the binary are systems with a high mass ratio, i.e. consisting of a central body and a satellite.

Survival of the binaries

The authors find that for systems with strong tides, about two thirds of the binaries should survive. The tides have unsurprisingly a critical role, since they tend to make the binary evolve to a stable end-state, i.e. doubly synchronous with an almost circular mutual orbit. However, few systems with main body + satellite survive.

Challenging this model

At this time, no binary has been found among the Trojans of Neptune, but this does not mean that there is none. The next years shall tell us more about these bodies, and once they will be statistically significant, we would be able to compare the observations with the theory. An absence of binaries could mean that they were initially almost absent, i.e. lack of binaries in that region (then we should explain why there are binaries in the Trans-Neptunian population), or that the relevant tides are weak. We could also expect further theoretical studies, i.e. with a more complete tidal dynamics, and frequency-dependent tides. Here, the author assumed a constant tidal function Q, while it actually depends on the rotation rate of the two bodies, which themselves decrease all along the evolution.

So, this is a model assisting our comprehension of the dynamics of binary objects in that region. As such, it should be seen as a step forward. Many other steps are to be expected in the future, observationally and theoretically (by the way, could a Trojan have rings?).

The study and its author

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.

A new contact binary

Hi there! Today I will tell you on the discovery that an already known Trans-Neptunian Object is in fact probably a contact binary. This is the opportunity for me to present you 2004 TT357: A potential contact binary in the Trans-Neptunian Belt by Audrey Thirouin, Scott S. Sheppard, and Keith S. Noll. This study has recently been published in The Astrophysical Journal.

2004 TT357‘s facts

As suggested by its name, 2004 TT357 was discovered in 2004. More precisely in August by a team led by Marc W. Buie, at Kitt Peak Observatory, Arizona, USA, on the 4-m Mayall telescope. From its magnitude, its radius is estimated to be between 87 and 218 km, depending on the albedo of the asteroid, i.e. the fraction of Solar light which is reflected by its surface. This albedo is unknown. You can find below its orbital elements.

Orbital elements of 2004 TT357
Semimajor axis 54.97 AU
Eccentricity 0.43
Inclination
Orbital period 408 y

These elements show that 2004 TT357 is in a 5:2 mean-motion resonance in Neptune, i.e. it performs 2 revolutions around the Sun while Neptune makes 5. This makes 2004 TT357 a Scaterred Disc Resonant Object. Its high eccentricity is probably at least partly due to this resonance.

Contact binaries

In astronomy, a binary object is a group of two objects, which are so linked together that they orbit around a common barycenter. Of course, their separation is pretty small. There are binary stars, here we speak about binary asteroids.
A contact binary is a kind of extreme case, in which the two components touch each other. In some sense, this is a single object, but with two different lobes. This was probably a former classical binary, which lost enough angular momentum so that the two objects eventually collided, but slowly enough to avoid any catastrophic outcome. It is thought that there is a significant fraction of contact binaries in the Solar System, i.e. between 5% and 50%, depending on the group you are considering.

Characterizing a known object as a contact binary is not an easy task, particularly for the Trans-Neptunian Objects, because of their distance to us. Among them, only (139775) 2001 QG298 is a confirmed contact binary, while 2003 SQ317 and (486958) 2014 MU69 are probable ones. This study concludes that 2004 TT357 is a probable one as well.

Observations at Lowell Observatory

Lowell Observatory is located in Flagstaff, Arizona, USA. It has been founded by Percival Lowell in 1894, and among its achievements is the discovery of the former planet Pluto in 1930, by Clyde Tombaugh. Currently, the largest of its instruments is the 4.3-m Discovery Channel Telescope (DCT), which has been partly funded by Discovery Communications. This telescope has its first light in April 2012, it is located in the Coconino National Forest near Happy Jack, Arizona, at an altitude of 2,360 meters.

The Discovery Channel Telescope. © Lowell Observatory
The Discovery Channel Telescope. © Lowell Observatory

The authors used this telescope, equipped with the Large Monolithic Imager (LMI). They acquired two sets of observation, in December 2015 and February 2017, during which they posed during 600 and 700 seconds, respectively. 2004 TT357 had then a mean visual magnitude of 22.6 and 23, respectively.

The Large Monolithic Imager. © Lowell Observatory
The Large Monolithic Imager. © Lowell Observatory

Analyzing the data

You can find below the photometric measurements of 2004 TT357.

The first set of observations. The measurements are represented with the uncertainties.
The first set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.

We can see pretty significant variations of the incoming light flux, these variations being pretty periodic. This periodicity is the signature of the rotation of the asteroid, which does not always present the same face to the terrestrial observer. From these lightcurves, the authors measure a rotation period of 7.79±0.01 h. From the curves, the period seems twice smaller, but if we consider that the asteroid should be an ellipsoid, then its geometrical symmetries tell us that our line of sight should be aligned twice with the long axis and twice with the short axis during a single period. So, during a rotation period, we should see two minimums and two maximums. This assumes that we are close to the equatorial plane.

Another interesting fact is the pretty high amplitude of variation of the incident light flux. If you are interested in it, go directly to the next section. Before that, I would like to tell you how this period of 7.79±0.01 h has been determined.

The authors used 2 different algorithms:

  • the Lomb periodogram technique,
  • the phase dispersion minimization (PDM).

Usually periodic signals are described as sums of sinusoids, thanks to Fourier transforms. Unfortunately, Fourier is not suitable for unevenly-spaced data. The Lomb (or Lomb-Scargle) periodogram technique consists to fit a sinusoid to the data, thanks to the least-squares method, i.e. you minimize the squares of the departure of your signal from a sinusoid, in adjusting its amplitude, phase, and frequency. PDM is an astronomical adaptation of data folding. You guess a period, and you split your full time interval into sub-intervals, which duration is the period you have guessed. Then you superimpose them. If this the period you have guessed is truly a period of the signal, then all of your time intervals should give you pretty the same signal. If not, then the period you have guessed is not a period of the signal.

Let us go back now to the variations in the amplitude.

Physical interpretation

The authors assume that periodic magnitude variations could have 3 causes:

  • Albedo variations
  • Elongation of the asteroid
  • Two bodies, i.e. a binary.

The albedo quantify the portion of Solar flux, which is reflected by the surface. Here, the variations are too large to be due to the variations of the albedo.

The authors estimate that, if 2004 TT357 were a single, ellipsoidal body, then a/b = 2.01 and c/a = 0.38, a,b, and c being the 3 axis of the ellipsoid. This is hardly possible if the shape corresponds to an equilibrium figure (hydrostatic equilibrium, giving a Jacobi ellipsoid). Moreover, this would mean that 2004 TT357 would have been ideally oriented… very unlikely

As a consequence, 2004 TT357 is probably a binary, with a mass ratio between 0.4 and 0.8. Hubble Space Telescope observed 2004 TT357 in 2012, and detected no companion, which means it is probably a contact binary. Another way to detect a companion is the analysis of a stellar occultation (see here). Fortunately for us, one will occur in February 2018.

A star occultation in February 2018

On 5 February 2018, 2004 TT357 shall occult the 12.8-magnitude star 2UCAC 38383610, in the constellation Taurus, see here. This occultation should be visible from Brazil, and provide us new data which would help to determine the nature of 2004 TT357. Are you interested to observe?

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.