Monthly Archives: April 2018

Interstellar objects

The rotation of ‘Oumuamua

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Hi there! Today we go back to ‘Oumuamua, you know, this interstellar object discovered last Fall. Its visit to our Solar system was the opportunity to observe it, and here we discuss on an analysis of the variations of its luminosity. I present you The excited spin state of 1I/2017 U1 ‘Oumuamua, by Michael J.S. Belton and collaborators. This study tells us that its rotation state might be complex, and that affects the way we figure out its shape. It has recently been published in The Astrophysical Journal Letters.

Outline

Remember 1I/’Oumuamua
Different modes of rotation
Observing the rotation
2 numerical algorithms
A cigar or a pancake?
The study and its authors

Remember 1I/’Oumuamua?

I already told you about ‘Oumuamua. This is the first identified object, which has been found in our Solar System but which undoubtedly originates from another System. In other words, it was formed around another star.
The Pan-STARRS survey identified ‘Oumuamua in October 2017, and the determination of its orbit proved it to be unusually eccentric. With an eccentricity close to 1.2, its orbit is a branch of a hyperbola rather than an ellipse. This means that it comes from very far, passes by while the Sun deviates it, and leaves us for ever.
This is the highest eccentricity ever recorded in the Solar System so far. Other objects had an eccentricity larger than 1, but which could have been caused by the gravitational perturbation of a planet. Not for ‘Oumuamua.
Its full name is actually 1I/2017 U1 (ʻOumuamua). 2017 because it was discovered in 2017, 1I as the first Interstellar object ever discovered (by the way, the International Astronomical Union has created this category for ‘Oumuamua), and the name ‘Oumuamua means scout in Hawaiian.

The announcement of its discovery motivated the observers all around the world to try to observe it and make photometric measurements. Here we discuss what these measurements tell us on the rotation and the shape. But before that, let me tell you something on the rotation.

Different modes of rotation

We will consider that our object is an ellipsoid. This is actually unsure, but let us assume it. We have 3 different axes, and we could imagine different configurations for its rotation:

  1. Tumbling rotation: the object rotates around its 3 axes, and basically this is a mess. We could be in a situation of dynamical chaos, like for the moon of Saturn Hyperion.
  2. Short-axis mode (SAM): the rotation is strongly dominated by a motion around the shortest axis. This is the case for many bodies in the Solar System, like the planets, our Moon… This does not mean that the rotation is strictly around one axis, but we will see that a little later.
  3. Long-axis mode (LAM): the rotation is strongly dominated by a motion around the longest axis.
The LAM and SAM modes.
The LAM and SAM modes.

These last two modes can actually cohabit with tumbling, i.e. a tumbling rotation may favor rotation around one axis.

If the rotation were strictly around one axis, then the body would look like a top. But this rotation axis may move with respect to the figure axis. This motion is named precession-nutation. The precession is the averaged path of the figure axis around the angular momentum, while the nutation contains the oscillations around it.

Now, imagine that you look at an object, which has such a rotation. How can you estimate it? There are ways.

Observing the rotation

Actually the brightness of a body not only depends on the distance from it, or on the insolation angle, but also on the surface facing you. This means that from the brightness, you can deduce something on the rotation state of the object. In particular, this surface brightness depends on its location with respect to the principal axis. If the object has the shape of a cigar, the reflected light from the long axis and from the short one will be different, and the lightcurve will present periodic variations. And the period of these variations is the rotation period. Easy, isn’t it?

Actually, not that easy. First, you assume that the surface has a constant albedo, i.e. that the ratio between the incident and the reflected lights is constant. But you do not know that. In particular, an icy surface has a higher albedo than a carbonaceous one. Another difficulty: a tumbling object, or even one with a precessional component in its rotation, will present a combination of different frequencies. Of course, this complicates the analysis.

However, you simplify the analysis in adding observations to your dataset. The authors used 818 observations over almost one month, spanning from Oct, 25 to Nov, 23, 2017. This includes observations from the Hubble Space Telescope, from the Magellan-Baade telescope at Las Campanas Observatory (Chile), from the Canada-France-Hawaii Telescope, from Pan-NSTARRS (these last facilities being based in Hawaii)…

Once the observations are obtained as raw data, they must be treated to correct from atmospheric and instrumental problems. And then it is not done yet, since the authors need an absolute luminosity of ‘Oumuamua, i.e. as if its distance to the observer were constant. The motion of ‘Oumuamua actually induced a trend in its distance to the Earth, and a trend in its luminosity, which the authors fitted before subtracting it the measured lightflux.

Once this is done, the authors get a lightcurve, which is constant on average, but presents variations around its mean value. Unfortunately, the required treatment induced an uncertainty in the measurements, which the authors had to consider. But fortunately, these practical difficulties are well-known, and algorithms exist to extract information from such data.

2 numerical algorithms

Basically, you need to extract periods from the variations of the lightflux. For that, we dispose of the classical tool of Fourier Transforms, which in principle requires equally spaced data. But the recorded data are not equally spaced, and remember that you must consider the uncertainties as well.

Specific algorithms exist for such a purpose. The authors used CLEAN and ANOVA, to double-check their results. These algorithms allow in particular to remove the aliasing effect, i.e. a wrong measurement of a period, because of an appropriate spacing of the data. And now, the results!

A cigar or a pancake?

The authors found two fundamental periods in the lightcurves, which are 8.67±0.34 and 3.74±0.11 hours. Interestingly, they connected these measurements to the possible dynamics of rotation, and they found two possible solutions:

  1. Long-Axis Mode: In that case, the possible rotation periods are 6.58, 13.15 and 54.48 hours, the latter being the most probable one.
  2. Short-Axis Mode: Here, ‘Oumuamua would be rotating with respect to the short-axis, but also with oscillations around the long axis of periods 13.15 or 54.48 hours.

In both axis, the long axis would also precess around the angular momentum in 8.67 ± 0.34 hours. Moreover, the authors found constraints on its shape. Previous studies already told us that ‘Oumuamua is highly elongated, this study confirms this fact, and tells us that ‘Oumuamua could be somewhere between the cigar and the pancake. But once more, this result could be weakened by variations of the surface albedo of ‘Oumuamua.

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.

Asteroids: Main Belt

Analyzing a crater of Ceres

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Hi there! The space mission Dawn has recently visited the small planets Ceres and Vesta, and the use of its different instruments permits to characterize their composition and constrain their formation. Today we focus on the crater Haulani on Ceres, which proves to be pretty young. This is the opportunity for me to present you Mineralogy and temperature of crater Haulani on Ceres by Federico Tosi et al. This paper has recently been published in Meteoritics and Planetary Science.

Outline

Ceres’s facts
The crater Haulani
Dawn at Ceres
Different indicators
VIR and FC data
A young and bright region
Possible thanks to lab experiments
The study and its authors

Ceres’s facts

Ceres is the largest asteroid of the Solar System, and the smallest dwarf planet. A dwarf planet is a planetary body that is large enough, to have been shaped by the hydrostatic equilibrium. In other words, this is a rocky body which is kind of spherical. You can anyway expect some polar flattening, due to its rotation. However, many asteroids look pretty much like potatoes. But a dwarf planet should also be small enough to not clear its vicinity. This means that if a small body orbits not too far from Ceres, it should anyway not be ejected.

Ceres, or (1)Ceres, has been discovered in 1801 by the Italian astronomer Giuseppe Piazzi, and is visited by the spacecraft Dawn since March 2015. The composition of Ceres is close to the one of C-Type (carbonaceous) asteroids, but with hydrated material as well. This reveals the presence of water ice, and maybe a subsurface ocean. You can find below its main characteristics.

Discovery 1801
Semimajor axis 2.7675 AU
Eccentricity 0.075
Inclination 10.6°
Orbital period 4.60 yr
Spin period 9h 4m 27s
Dimensions 965.2 × 961.2 × 891.2 km
Mean density 2.161 g/cm3

The orbital motion is very well known thanks to Earth-based astrometric observations. However, we know the physical characteristics with such accuracy thanks to Dawn. We can see in particular that the equatorial section is pretty circular, and that the density is 2.161 g/cm3, which we should compare to 1 for the water and to 3.3 for dry silicates. This another proof that Ceres is hydrated. For comparison, the other target of Dawn, i.e. Vesta, has a mean density of 3.4 g/cm3.

It appears that Ceres is highly craterized, as shown on the following map. Today, we focus on Haulani.

Topographic map of Ceres, due to Dawn. Click to enlarge. © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
Topographic map of Ceres, due to Dawn. Click to enlarge. © NASA/JPL-Caltech/UCLA/MPS/DLR/IDA

The crater Haulani

The 5 largest craters found on Ceres are named Kerwan, Yalode, Urvara, Duginavi, and Vinotonus. Their diameters range from 280 to 140 km, and you can find them pretty easily on the map above. However, our crater of interest, Haulani, is only 34 km wide. You can find it at 5.8°N, 10.77°E, or on the image below.

The crater Haulani, seen by <i>Dawn</i>. © NASA / JPL-Caltech / UCLA / Max Planck Institute for Solar System Studies / German Aerospace Center / IDA / Planetary Science Institute
The crater Haulani, seen by Dawn. © NASA / JPL-Caltech / UCLA / Max Planck Institute for Solar System Studies / German Aerospace Center / IDA / Planetary Science Institute

The reason why it is interesting is that it is supposed to be one of the youngest, i.e. the impact creating it occurred less than 6 Myr ago. This can give clues on the response of the material to the impact, and hence on the composition of the subsurface.
Nothing would have been possible without Dawn. Let us talk about it!

Dawn at Ceres

The NASA mission Dawn has been launched from Cape Canaveral in September 2007. Since then, it made a fly-by of Mars in February 2009, it orbited the minor planet (4)Vesta between July 2011 and September 2012, and orbits Ceres since March 2015.

This orbit consists of several phases, aiming at observing Ceres at different altitudes, i.e. at different resolutions:

  1. RC3 (Rotation Characterization 3) phase between April 23, 2015 and May 9, 2015, at the altitude of 13,500 km (resolution: 1.3 km/pixel),
  2. Survey phase between June 6 and June 30, 2015, at the altitude of 4,400 km (resolution: 410 m /pixel),
  3. HAMO (High Altitude Mapping Orbit) phase between August 17 and October 23, 2015, at the altitude of 1,450 km (resolution: 140 m /pixel),
  4. LAMO (Low Altitude Mapping Orbit) / XMO1 phase between December 16, 2015 and September 2, 2016, at the altitude of 375 km (resolution: 35 m /pixel),
  5. XMO2 phase between October 5 and November 4, 2016, at the altitude of 1,480 km (resolution: 140 m / pixel),
  6. XMO3 phase between December 5, 2016 and February 22, 2017, at the altitude varying between 7,520 and 9,350 km, the resolution varying as well, between
  7. and is in the XMO4 phase since April 24, 2017, with a much higher altitude, i.e. between 13,830 and 52,800 km.

The XMOs phases are extensions of the nominal mission. Dawn is now on a stable orbit, to avoid contamination of Ceres even after the completion of the mission. The mission will end when Dawn will run out of fuel, which should happen this year.

The interest of having these different phases is to observe Ceres at different resolutions. The HAMO phase is suitable for a global view of the region of Haulani, however the LAMO phase is more appropriate for the study of specific structures. Before looking into the data, let us review the indicators used by the team to understand the composition of Haulani.

Different indicators

The authors used both topographic and spectral data, i.e. the light reflected by the surface at different wavelengths, to get numbers for the following indicators:

  1. color composite maps,
  2. reflectance at specific wavelengths,
  3. spectral slopes,
  4. band centers,
  5. band depths.

Color maps are used for instance to determine the geometry of the crater, and the location of the ejecta, i.e. excavated material. The reflectance is the effectiveness of the material to reflect radiant energy. The spectral slope is a linear interpolation of a spectral profile by two given wavelengths, and band centers and band depths are characteristics of the spectrum of material, which are compared to the ones obtained in lab experiments. With all this, you can infer the composition of the material.

This requires a proper treatment of the data, since the observations are affected by the geometry of the observation and of the insolation, which is known as the phase effect. The light reflection will depend on where is the Sun, and from where you observe the surface (the phase). The treatment requires to model the light reflection with respect to the phase. The authors use the popular Hapke’s law. This is an empirical model, developed by Bruce Hapke for the regolith of atmosphereless bodies.

VIR and FC data

The authors used data from two Dawn instruments: the Visible and InfraRed spectrometer (VIR), and the Framing Camera (FC). VIR makes the spectral analysis in the range 0.5 µm to 5 µm (remember: the visible spectrum is between 0.39 and 0.71 μm, higher wavelengths are in the infrared spectrum), and FC makes the topographical maps.
The combination of these two datasets allows to correlate the values given by the indicators given above, from the spectrum, with the surface features.

A young and bright region

And here are the conclusions: yes, Haulani is a young crater. One of the clues is that the thermal signature shows a locally slower response to the instantaneous variations of the insolation, with respect to other regions of Ceres. This shows that the material is pretty bright, i.e. it has been less polluted and so has been excavated recently. Moreover, the spectral slopes are bluish, this should be understood as a jargony just meaning that on a global map of Ceres, which is colored according to the spectral reflectance, Haulani appears pretty blue. Thus is due to spectral slopes that are more negative than anywhere else on Ceres, and once more this reveals bright material.
Moreover, the bright material reveals hydrothermal processes, which are consequences of the heating due to the impact. For them to be recent, the impact must be recent. Morever, this region appears to be calcium-rich instead of magnesium-rich like anywhere else, which reveals a recent heating. The paper gives many more details and explanations.

Possible thanks to lab experiments

I would like to conclude this post by pointing out the miracle of such a study. We know the composition of the surface without actually touching it! This is possible thanks to lab experiments. In a lab, you know which material you work on, and you record its spectral properties. And after that, you compare with the spectrum you observe in space.
And this is not an easy task, because you need to make a proper treatment of the observations, and once you have done it you see that the match is not perfect. This requires you to find a best fit, in which you adjust the relative abundances of the elements and the photometric properties of the material, you have to consider the uncertainties of the observations… well, definitely not an easy task.

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.

Zodiacal dust

Dust coorbital to Jupiter

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Hi there! You may have heard of the coorbital satellites of Jupiter, or the Trojans, which share its orbit. Actually they are 60° ahead or behind it, which are equilibrium positions. Today we will see that dust is not that attached to these equilibrium. This is the opportunity to present you a study divided into two papers, Dust arcs in the region of Jupiter’s Trojan asteroids and Comparison of the orbital properties of Jupiter Trojan asteroids and Trojan dust, by Xiaodong Liu and Jürgen Schmidt. These two papers have recently been accepted for publication in Astronomy and Astrophysics.

Outline

The Trojan asteroids
Production of dust
Non-gravitational forces affect the dust
Numerical simulations
Some stay, some don’t…
Lucy is coming
The study and its authors

The Trojan asteroids

Jupiter is the largest of the planets of the Solar System, it orbits the Sun in 11.86 years. On pretty the same orbit, asteroids precede and follow Jupiter, with a longitude difference of 60°. These are stable equilibrium, in which Jupiter and every asteroid are locked in a 1:1 mean-motion resonance. This means that they have the same orbital period. These two points, which are ahead and behind Jupiter on its orbit, are the Lagrange points L4 and L5. Why 4 and 5? Because three other equilibrium exist, of course. These other Lagrange points, i.e. L1, L2, and L3, are aligned with the Sun and Jupiter, and are unstable equilibrium. It is anyway possible to have orbits around them, and this is sometimes used in astrodynamics for positioning artificial satellites of the Earth, but this is beyond the scope of our study.

Location of the Lagrange points.
Location of the Lagrange points.

At present, 7,206 Trojan asteroids are list by the JPL Small Body Database, about two thirds orbiting in the L4 region. Surprisingly, no coorbital asteroid is known for Saturn, a few for Uranus, 18 for Neptune, and 8 for Mars. Some of these bodies are on unstable orbits.

Understanding the formation of these bodies is challenging, in particular explaining why Saturn has no coorbital asteroid. However, once an asteroid orbits at such a place, its motion is pretty well understood. But what about dust? This is what the authors investigated.

Production of dust

When a planetary body is hit, it produces ejecta, which size and dynamics depend on the impact, the target, and the impactor. The Solar System is the place for an intense micrometeorite bombardment, from which our atmosphere protects us. Anyway, all of the planetary bodies are impacted by micrometeorites, and the resulting ejecta are micrometeorites themselves. Their typical sizes are between 2 and 50 micrometers, this is why we can call them dust. More specifically, it is zodiacal dust, and we can sometimes see it from the Earth, as it reflects light. We call this light zodiacal light, and it can be confused with light pollution.

It is difficult to estimate the production of dust. The intensity of the micrometeorite bombardment can be estimated by spacecraft. For instance, the spacecraft Cassini around Saturn had on-board the instrument CDA, for Cosmic Dust Analyzer. This instrument not only measured the intensity of this bombardment around Saturn, but also the chemical composition of the micrometeorites.

Imagine you have the intensity of the bombardment (and we don’t have it in the L4 and L5 zones of Jupiter). This does not mean that you have the quantity of ejecta. This depends on a yield parameter, which has been studied in labs, and remains barely constrained. It should depend on the properties of the material and the impact velocity.

The small size of these particles make them sensitive to forces, which do not significantly affect the planetary bodies.

Non-gravitational forces affect the dust

Classical planetary bodies are affected (almost) only by gravitation. Their motion is due to the gravitational action of the Sun, this is why they orbit around it. On top of that, they are perturbed by the planets of the Solar System. The stability of the Lagrange points results of a balance between the gravitational actions of the Sun and of Jupiter.

This is not enough for dusty particles. They are also affected by

  • the Solar radiation pressure,
  • the Poynting-Robertson drag,
  • the Solar wind drag,
  • the magnetic Lorentz force.

The Solar radiation pressure is an exchange of momentum between our particle and the electromagnetic field of the Sun. It depends on the surface over mass ratio of the particle. The Poynting-Robertson drag is a loss of angular momentum due to the tangential radiation pressure. The Solar wind is a stream of charged particles released from the Sun’s corona, and the Lorentz force is the response to the interplanetary magnetic field.

You can see that some of these effects result in a loss of angular momentum, which means that the orbit of the particle would tend to spiral. Tend to does not mean that it will, maybe the gravitational action of Jupiter, in particular at the coorbital resonance, would compensate this effect… You need to simulate the motion of the particles to know the answer.

Numerical simulations

And this is what the authors did. They launched bunches of numerical simulations of dusty particles, initially located in the L4 region. They simulated the motion of 1,000 particles, which sizes ranged from 0.5 to 32 μm, over more than 15 kyr. And at the end of the simulations, they represented the statistics of the resulting orbital elements.

Some stay, some don’t…

This way, the authors have showed that, for each size of particles, the resulting distribution is bimodal. In other words: the initial cloud has a maximum of members close to the exact semimajor axis of Jupiter. And at the end of the simulation, the distribution has two peaks: one centered on the semimajor axis of Jupiter, and another one slightly smaller, which is a consequence of the non-gravitational forces. This shift depends on the size of the particles. As a consequence, you see this bimodal distribution for every cloud of particles of the same size, but it is visually replaced by a flat if you consider the final distribution of the whole cloud. Just because the location of the second peak depends on the size of the particles.

Moreover, dusty particles have a pericenter which is slightly closer to the one of Jupiter than the asteroids, this effect being once more sensitive to the size of the particles. However, the inclinations are barely affected by the size of the particles.

In addition to those particles, which remain in the coorbital resonance, some escape. Some eventually fall on Jupiter, some are trapped in higher-order resonances, and some even become coorbital to Saturn!

As a conclusion we could say that the cloud of Trojan asteroids is different from the cloud of Trojan dust.

All this results from numerical simulations. It would be interesting to compare with observations…

Lucy is coming

But there are no observations of dust at the Lagrange points… yet. NASA will launch the spacecraft Lucy in October 2021, which will explore Trojan asteroids at the L4 and L5 points. It will also help us to constrain the micrometeorite bombardment in these regions.

The study and its authors

You can find below the two studies:

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.

Asteroids: Trans-Neptunian Objects

Forming Pluto’s satellites

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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.

Outline

The satellites of Pluto
Proximity of Mean-Motion Resonances
Testing a scenario of formation
The long-term evolution is ruled by tides
Possible scenario, but…
What’s next?
The study and its authors

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° 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.

Asteroids: Main Belt

The system of (107) Camilla

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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.

Outline

The system of Camilla
5 different types of data
The orbit of the satellites
Spin and shape
The composition of these objects
The study and its authors

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.