Category Archives: Asteroids: Main Belt

Identifying an asteroid family

Hi there! Today’s post deals with an asteroid family, more precisely the Datura family. The related study is New members of Datura family, by A. Rosaev and E. Plávalová, it has recently been accepted for publication in Planetary and Space Science. The Datura family is a pretty recent one, with only 7 known members when that study started. The authors suggest that 3 other bodies are also members of this family.

Some elements of the dynamics of asteroids

Detailing the dynamics of asteroids would require more than a classical post, here I just aim at giving a few hints.
Asteroids can be found at almost any location in the Solar System, but the combination of the gravitational effects of the planets, of thermal effects, and of the formation of the Solar System, result in preferred locations. Most of the asteroids are in the Main Belt, which lies between the orbits of Mars and Jupiter. And most of these bodies have semimajor axes between 2.1 and 3.2 astronomical units (AU), i.e. between 315 and 480 millions of km. Among these bodies can be found interesting dynamical phenomena, such as:

  • Mean motion resonances (MMR) with planets, especially Jupiter. These resonances can excite the eccentricities of the asteroids until ejecting them, creating gaps known as Kirkwood gaps. At these locations, there are much less asteroids than nearby.
  • Stable chaos. Basically, a chaotic dynamics means that you cannot predict the orbit at a given accuracy over more than a given timespan, because the orbit is too sensitive to uncertainties on its initial conditions, i.e. initial location and velocity of the asteroid. Sometimes chaos is associated with instability, and the asteroid is ejected. But not always. Stable chaos means that the asteroid is confined in a given zone. You cannot know accurately where the asteroid will be at a given time, but you know that it will be in this zone. Such a phenomenon can be due to the overlap of two mean-motion resonances (Chirikov’s criterion).

Anyway, when an asteroid will or will not be under the influence of such an effect, it will strongly be under the influence of the planets, especially the largest ones. This is why it is more significant to describe their dynamics with proper elements.

Proper elements

Usually, an elliptical orbit is described with orbital elements, which are the semimajor axis a, the eccentricity e, the ascending node Ω, the pericentre ω, the inclination I, and the mean longitude λ. Other quantities can be used, like the mean motion n, which is the orbital frequency.

Because of the large influence of the major planets, these elements present quasiperiodic variations, i.e. sums of periodic (sinusoidal) oscillations. Since it is more significant to give one number, the oscillations which are due to the gravitational perturbers are removed, yielding mean elements, called proper elements. These proper elements are convenient to characterize the dynamics of asteroids.

Asteroid families

Most of the asteroids are thought to result from the disruption (for instance because of a collision) of a pretty large body. The ejecta resulting from this disruption form a family, they share common properties, regarding their orbital dynamics and their composition. A way to guess the membership of an asteroid to a family is to compare its proper elements with others’. This guess can then be enforced by numerical simulations of the orbital motion of these bodies over the ages.

Usually a family is named from its largest member. In 2015, 122 confirmed families and 19 candidates were identified (source: Nesvorný et al. in Asteroids IV, The University of Arizona Press, 2015). Many of these families are very old, i.e. more than 1 Gyr, which complicates their identification in the sense that their orbital elements are more likely to have scattered.
The Datura family is thought to be very young, i.e. some 500 kyr old.

A funny memory: in 2005 David Nesvorný received the Urey Prize of the Division of Planetary Sciences of the American Astronomical Society. This prize was given to him at the annual meeting of the Division, that year in Cambridge, UK. He then gave a lecture on the asteroid families, and presented the “Nesvorný family”, i.e. his father, his wife, and so on.

Datura’s facts

The asteroid (1270) Datura has been discovered in 1930. It orbits the Sun in 3.34 years, and has a semimajor axis of 2.23 AU. As such, it is a member of the inner Main Belt. Its orbit is highly elongated, between 1.77 and 2.70 AU, with an orbital eccentricity of 0.209. It rotates very fast, i.e. in 3.4 hours. Its diameter is about 8.2 km.

It is an S-type asteroid, i.e. it is mainly composed of iron- and magnesium-silicates.

This study

After having identified 10 potential family members from their proper elements, the authors ran backward numerical simulations of them, cloning each asteroid 10 times to account for the uncertainties on their locations. The simulations were ran over 800 kyr, the family being supposed to be younger than that. The simulations first included the 8 planets of the Solar System, and Pluto. The numerical tool is a famous code, Mercury, by John Chambers.

The 10 asteroids identified by the authors include the 7 already known ones, and 3 new ones: (338309) 2002 VR17, 2002 RH291, and 2014 OE206. These are all sub-kilometric bodies. The authors point out that these bodies share a linear correlation between their node and their pericentre.

This study also shows that 2014 OE206 has a chaotic resonant orbit, because of the proximity of the 9:16 MMR with Mars. This resonance also affects 2001 VN36, but this was known before (Nesvorný et al., 2006). The authors also find that this chaotic dynamics can be significantly enhanced by the gravitational perturbations of Ceres and Vesta. Finally, they say that close encounters might happen between (1270) Datura and two of its members: 2003 SQ168 and 2001 VN36.

Another study

Now, to be honest, I must mention another study, The young Datura asteroid family: Spins, shapes, and population estimate, by David Vokrouhlický et al., which was published in Astronomy and Astrophysics in February 2017. That study goes further, in considering the 3 new family members found by Rosaev and Plávalová, and in including other ones, updating the Datura family to 17 members.

This seems to be a kind of anachronism: how could a study be followed by another one, which is published before? In fact, Rosaev and Plávalová announced their results during a conference in 2015, this is why they could be cited by Vokrouhlický et al. Of course, their study should have been published earlier. Those things happen. I do not know the specific case of this study, but sometimes this can be due to a delayed reviewing process, another possibility could be that the authors did not manage to finish the paper earlier… Something that can be noticed is that the study by Vokrouhlický is signed by a team of 13 authors, which is expected to be more efficient than a team of two. But the very truth is that I do not know why they published before. This is anyway awkward.

A perspective

I notice something which could reveal a rich dynamics: the authors show (their Figure 7) a periodic variation of the distance between (1270) Datura and 2003 SQ168, from almost zero to about twice the semimajor axis… This suggests me a horseshoe orbit, i.e. a 1:1 mean-motion resonance, the two bodies sharing the same orbit, but with large variations of their distance. If you look at the orbit of the smallest of these two bodies (here 2003 SQ168) in a reference frame which moves with (1270) Datura, you would see a horseshoe-shaped trajectory. To the best of my knowledge, such a configuration has been detected in the satellites of Saturn between Janus and Epimetheus, suggested for exoplanetary systems, maybe detected between a planet and an asteroid, but never between two asteroids…

By the way, 2003 SQ168 is the asteroid, which has the closest semimajor axis to the one of (1270) Datura, in Rosaev and Plávalová’s paper. Now, when I look at Vokrouhlický et al.’s paper, I see that 2013 ST71 has an even closer semimajor axis. I am then tempted to speculate that these two very small bodies are coorbital to (1270) Datura. Maybe a young family favors such a configuration, which would become unstable over millions of years… Speculation, not fact.

Update

This is actually not an horsehoe orbit. The large variation of the distance is due to the fact that 2003 SQ168 is on a orbit, which is close to the one of (1270) Datura, with a slightly different orbital frequency. Regarding 2013 ST71, a numerical simulation by myself suggests the possibility of a temporary (i.e. unstable) capture in a 1:1 MMR.

To know more…

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

Predicting the chemical composition of (4)Vesta

Hi there! Today I present you a study entitled Chlorine and hydrogen degassing in Vesta’s magma ocean, by Adam R. Sarafian, Timm John, Julia Roszjár and Martin J. Whitehouse. This study has recently been published in Earth and Planetary Science Letters. The goal here is, from the chemical analysis of meteorites which are supposed to come from Vesta, understand the evolution of its chemical evolution. In particular, how the degassing of its magma ocean impacts its chemical evolution.

(4)Vesta

I have presented the small planet (4)Vesta in that post. Basically, it is one of the largest Main-Belt asteroids, with a mean radius of some 500 km. The craters at its surface and the dynamical models of the early Solar System show that Vesta has been intensively bombarded. The largest of these impacts were energetic enough to melt Vesta and trigger its differentiation between a pretty dense core, a shallow magma ocean and a thin crust.

Despite having been visited by the spacecraft Dawn, the magma ocean has not been detected. Its presence is actually confirmed by the analyses of meteorites which fell on Earth.

The HED meteorites

Every day, about 6 tons of material hit the surface of the Earth, after having survived the atmospheric entry. Mineralogists split these meteorites into several groups. 5% of these meteorites are HEDs, for Howardite-Eucrite-Diogenites. These are achondritic basaltic meteorites, which are supposed to present similarities with Vesta. This hypothesis has been proposed in 1970 after comparison of the spectrum of Vesta and the one of these meteorites, and enforced since by the observations and theoretical works. So, it is now accepted that these meteorites come from Vesta or bodies similar to it, and studying them is a way to study the chemical composition of Vesta.
In this study, only the Eucrites will be addressed. They represent most of the HEDs, and contain 2 phosphates: the merrillite and the apatite. Moreover, they are systematically depleted in volatile elements, compared to carbonaceous chondrites and the Earth.

Chemical analysis

The authors have analyzed the chemical composition of 7 samples of eucrites, which were found on Earth. They present a variety of thermal alteration. Comparing them would be like watching a movie of the process of evolution of the material during the degassing in the magma ocean. The analyses were conducted on two sites: the Natural History Museum Vienna, in Austria, and the Woods Hole Oceanographic Institution (MA, USA). The involved technology is the scanning electron microscopy, which consists in obtaining images from the interaction of the sample with a focused bean of electrons, supplemented with an energy-dispersive X-ray spectrometer. This spectrometer gives the spectral signature of the interactions of the electrons with the rock sample, and so reveals the elements which constitute it.

The authors were particularly interested in measuring the concentrations of halogen (fluorine, chlorine, bromine and iodine), of stable isotopes of the chlorine, isotopes of hydrogen, and water. Comparing the relative concentration of these elements in the seven samples would give information on their volatilization during the outgassing process of the magma ocean, in conditions that do not exist on Earth.

Conclusions

The samples show different compositions in volatile elements (H2, H20, and metal chlorides), which show that there is some outgassing in Vesta’s magma ocean. The authors show in particular a large variability in the ratio [Cl]/[K], i.e. chlorite with respect to potassium. This means that not only the thermal evolution tends to reject volatile elements, but also that they are effectively ejected. This might be a concern since the ocean cannot be seen at the surface of Vesta. Anyway, this does not preclude outgassing, either through the crust, which is supposed to be thin, and/or with the assistance of giant impacts, which created craters deep enough to reach the ocean.

This way, we have a signature of the history of a planetary body in material found on the Earth. These results might have implications beyond Vesta, i.e. could be extended to other dwarf planets, and so give us information on the chemical evolution of the Solar System.

I hope you enjoyed this article. As usual, I am interested in your feed-back. So please, leave me some comments, share it, and happy new year!

To know more…

  • The study, which can also be found on ResearchGate, thanks to the authors for sharing!
  • The webpage of Adam Robert Sarafian, grad student at the Woods Hole Oceanographic Institution (USA)
  • The webpage of Timm John, Freie Universität Berlin, Germany
  • The webpage of Julia Roszjár, Natural History Museum, Vienna, Austria
  • The webpage of Martin Whitehouse, Swedish Museum of Natural History, Stockholm, Sweden

Interesting polar craters on Vesta

Hi there! Today’s post is on the paper On the possibility of viscoelastic deformation of the large south polar craters and true polar wander on the asteroid Vesta, by Saman Karimi and Andrew J. Dombard, both at the University of Illinois at Chicago during the study; Saman Karimi is now at Johns Hopkins University. This study has recently been accepted for publication in Journal of Geophysical Research: Planets. It is a study of 2 craters of the small planet Vesta, Rheasilvia and Veneneia, which present two unusual features:

  1. they are located close to the South Pole,
  2. they are shallow with a central peak.

The authors have tried to explain these two properties.

The small planet Vesta

Vesta, or more precisely (4) Vesta, is the second largest object of the Main Asteroid Belt. It has a triaxial shape, i.e. (572.6 × 557.2 × 446.4) km, and is large enough to have a differentiated structure. It orbits at a distance of 2.36 AU from the Sun, i.e. 354 millions km, which implies an orbital period of 3.63 years. However, it rotates much more rapidly, in 5.3 hours. This rapid rotation is responsible for the high polar flattening, i.e. you can see from its shape that one of its axes is much smaller than the other ones. This axis is actually the rotation axis. This rotation around one axis permits to define easily the North and the South Poles, close to which are the 2 craters of interest.

(4) Vesta has been recently the target of the space mission Dawn. Dawn has been launched from Cape Canaveral in September 2007. It has orbited Vesta between July 2011 and September 2012, and is orbiting Ceres since March 2015. Dawn permitted invaluable progress on our knowledge of Vesta. It gave us an accurate cartography of the surface, which resulted in a count of the craters, measurements of its shape, of its gravity field, of its rotation… All of these data permit to constrain the interior. Many papers on Vesta followed, the paper I am presenting you is one of these.

Impacts in the Solar System

The Solar System bodies are impacted since the beginning of their formation. During the early ages of the Solar System, the impacts were more frequent than now, because of the presence of a protoplanetary disk composed of small objects before they accrete into larger ones. For instance, the Late Heavy Bombardment (LHB) is known as an episode of intense bombardment which occurred approximately 4 billion years ago. Some models consider that it could have been triggered by a gravitational interaction between giant planets and a former asteroid belt, which has destabilized it. For instance a previous version of the Nice model stated that the LHB could have been the consequence of a former 2:1 mean-motion resonance between Jupiter and Saturn during their migration. That resonance would have raised the orbital oscillations of these planets, which would have favored the destabilization of the asteroid belt and the bombardment of the terrestrial planets.

Meteorites are signatures of impacts on the Earth. Actually, many small objects are destroyed when they enter our atmosphere, this is why we get these small meteorites on the surface. Atmosphereless bodies usually present signatures of bombardment, for instance the Moon is known for its craters. When such a body does not present evidence of craters, it could mean that its surface has been recently renewed by some internal processes, due to tectonic or volcanic activity. So, counting the impacts is a way to age the surfaces.

When large enough, impacts can be responsible for dramatic events such as: the creation of the Moon, which has probably been split from the Earth by an impact, the creation of the rings of Saturn, which could be made of a large impactor, the destruction of the outer envelope of the proto-Mercury, or the extinction of the dinosaurs.

The study I present here deals with two impact basins at the South Pole of Vesta: Rheasilvia and Veneneia, with diameters of 505 and 395 km, respectively. You can compare these numbers with the dimensions of Vesta, and you understand how significant the impacts creating these craters should have been in the history of Vesta.

A viscoelastic rheology

The issue is: how does the surface respond to a large impact? It depends on its structure, of course. Basically, when you hit the surface, you create a crater, ejecta being expelled. After that, the surface of the asteroid tends to relax, i.e. the deformation due to the impact is kind of damped, but the final aspect will not be the initial one, since some material has been displaced, some other ejected, and the heating due to the impact tends to molten the surface. During the process of relaxation, the material tends to converge to the center of the basin, while it was pushed to the edges when the impact occurred, this can result in a central peak. Measuring the topography of the crater, i.e. its width, its depth, and the height of its central peak, can give constraints on the way the surface responds. This response characterizes the rheology of the surface, which is basically viscoelastic. Elastic would mean that the surface would recover its initial shape without any energy loss, and viscous means that you have actually some energy loss, which results in a permanent deformation once the surface is relaxed.

This study

The study first points out the two peculiarities of the two craters, and test the hypothesis that the impacts occurred close to the equator As a consequence Vesta would have been reoriented, this would explain why the impacts are now located close to the South Pole. This would mean that the surface is molten enough to result in the current topography of the craters and in the present polar flattening of Vesta.

To try to understand these facts, the authors assumed that the impactors hit Vesta close to its equator, and ran numerical simulations to check whether Vesta was able to reach its current state, which implies reshaping and reorientation. The numerical simulations consist to propagate the response to the impact not only in time, but also on the surface of Vesta. For that, the surface is discretized on a mesh, and finite elements modeling is used. This is a classical way to integrate Partial Derivative Equations (PDE). A key parameter is the temperature: if the impact is energetic enough, then Vesta heats enough to be molten enough to create the central peak, relax the crater, and reshape according to its new orientation state.

The reader should be aware that such simulations require high computation facilities, and take a long time. This is the reason why the authors ran only 8 of them, with different assumptions to cover most of the physically acceptable properties for the lithosphere of Vesta. These properties are in this study ruled by 6 parameters: the crustal thickness, the temperatures of the surface and of the mantle, the crustal thermal conductivity, the background heat flux, and the isostatic compensation. This last parameter characterizes the capacity of the surface to recover its gravity after the shock of the impact, which displaced the internal masses. This particularly affects the height of the central peak.

None of these 8 simulations result in a Vesta which is close enough to the observed one, since it does not heat enough. This means that the shape of Vesta is not a direct consequence of these two impacts, which probably occurred close to the South Pole, even if impacts at this latitude have a low probability.

A question for the authors

I am no specialist of impacts, but I wonder: if we have two tangent impacts instead of perpendicular ones, I guess they would have resulted in craters with a limited depth, but a strong reorientation of Vesta. The authors do not mention this possibility in the paper, and I would be interested in their opinion on this issue.

Some links

And please do not forget to comment! Thanks!

How Ceres and Vesta shape the asteroid belt

Hi! Today I will tell you about a recent study made in Serbia on the dynamical influence of the small planets Ceres and Vesta on the Asteroid Belt. This study, Secular resonances with Ceres and Vesta by G. Tsirvoulis and B. Novaković, has been accepted for publication in Icarus.

The Asteroid Main Belt

There are many small bodies in the Solar System, here we just focus on the so-called Main Belt, i.e. a zone “full” of asteroids, which lies between the orbits of Mars and Jupiter. The word “full” should be taken with care, since there are many asteroids populating it, but if we cross it, we would be very unlikely to meet one. This zone is essentially void. It is estimated that the total mass of these asteroids is only 4% of the mass of the Moon.

It is called “Main Belt” since the first asteroids were discovered in this zone, and it was long thought that most of them were in this Main Belt. At this time, hundreds of thousands of them have been identified, but the Kuiper Belt, which lies behind the orbit of Neptune, might be even more populated.

The dynamics of these bodies is very interesting. It could contain clues on the early ages of the Solar System. Moreover, they are perturbed by the planets of the Solar System, especially the giant planets.

As a consequence, they have pretty complex dynamics. Their orbits can be approximated with ellipses, but these are not constant ellipses. They are precessing, i.e. their pericentres and nodes are moving, but their semi-major axes, eccentricities and inclinations are time-dependent as well. To represent their dynamics, so-called proper elements are used, which are kind of mean values of these orbital elements, and which are properties of these bodies.

Ceres and Vesta

Ceres and Vesta, or more precisely 1 Ceres and 4 Vesta, are the two largest objects of the Main Belt, with mean radii of 476 and 263 km, respectively. So large objects could present complex interior structures, this is one motivation for the US space mission Dawn, which has orbited Vesta between July 2011 and September 2012, and is currently in orbit around Ceres, since March 2015.

This space mission has given, and is still giving, us invaluable data on these two bodies, like a cartography of the craters of Vesta, and the recent proof that Ceres is differentiated, from the analysis of its gravity field.

The orbital resonances

The asteroids are so small bodies than they are subjected to the gravitational influence of the planets, in particular Jupiter. The most interesting dynamical effect is the orbital resonances, which occur when a proper frequency of the orbit of the asteroid (for instance its orbital frequency, or the frequency of precession of its orbital plane, known as nodal precession) is commensurate with a proper frequency of a planet. In such a case, orbital parameters are excited. In particular, an excitation of the eccentricity results in a destabilization of the orbit, since the asteroid is more likely to collide with another body, and/or to be finally ejected from the Main Belt.

This results in gaps in the Main Belt. The most famous of them are the Kirkwood Gaps, which correspond to mean-motion resonances between the asteroids and Jupiter. When the orbital frequency of the asteroid is exactly three times the one of Jupiter, i.e. when its orbital period is exactly one third of the one of Jupiter, then the asteroid is at the 3:1 resonance, its eccentricity is excited, and its orbit is less stable. We thus observe depletions of asteroids at the resonances 3:1, 5:2, 7:3, and 2:1.

Another type of resonance are the secular resonances, which involve the precession of the pericentres and / or of the node (precession of the orbital plane) of the asteroid. In such a case, this is a much slower phenomenon, since the periods involved are of the order of millions of years, while the orbital period of Jupiter is 11.86 years.

The asteroid families

An analysis of the dynamics (proper elements) and the physical properties of the asteroids shows that it is possible to classify them into families. The asteroids of these families are thought to originate from the same body, which has been destroyed by a collision. They are usually named among the largest of these bodies, for instance Vesta is also the name of a family.

This study

In this study, the authors investigate the dynamical influence of Vesta and Ceres on the Main Belt. They particularly focus on the secular resonances, in identifying four of them, i.e. resonances with the precessions of the pericentres and nodes of these two bodies.

For that, they perform numerical integrations of the motion of 20 test particles over 50 Myr, perturbed by the 4 giant planets, with and without Ceres and Vesta, and show significant influence of these bodies for some of the particles.

Finally, they show that some asteroid families do cross these resonances, like the Hoffmeister family.

Some links

  • The study, Secular resonances with Ceres and Vesta by G. Tsirvoulis and B. Novakovic, accepted for publication in Icarus, and made freely available by the authors on arXiv (thanks to them for sharing)
  • The web site of Georgios Tsirvoulis
  • The web site of Bojan Novaković
  • The mission DAWN