Category Archives: Comets

When a comet meets the Solar wind

Hi there! Today, let us talk about the environment of a comet. As you know, a comet is an active body, which emits ionized particles and dust. The Sun itself emits charged particles, which constitute the Solar wind. We discuss today of the interaction between these two emissions. The environment of charged particles around a comet has been measured by the spacecraft Rosetta, and this has motivated modeling these interactions. I present you Solar wind dynamics around a comet: The paradigmatic inverse-square-law model, by M. Saillenfest, B. Tabone, and E. Behar. This study has recently been accepted for publication in Astronomy and Astrophysics.

The spacecraft Rosetta

Let us first speak about the mission Rosetta. Rosetta was a European mission, which orbited the comet 67P/Churyumov–Gerasimenko between 2014 and 2016. It was named after the Rosetta Stone, which permitted the decipherment of Egyptian hieroglyphs. The mission Rosetta was supposed to give us clues on the primordial Solar System, i.e. on our origins, from the study of a comet.

It was launched in March 2004 from Kourou (French Guiana), and then started a 10-years journey, during which it made 3 fly-bys of the Earth and one of Mars. You can say: “why going back to Earth?” The reason is that Rosetta was supposed to orbit 67P/Churyumov–Gerasimenko (spoiler alert: it did it). For this orbital insertion to be possible, it had to arrive slowly enough… but also had to leave Earth fast enough, to get rid off its attraction, and also to shorten the journey. Fly-bys permitted to slow the spacecraft in exchanging energy with the Earth (or Mars).

Rosetta also visited two asteroids: (2867) Šteins, and (21) Lutetia, in September 2008 and July 2010, respectively. It was inserted into orbit around 67P in August 2014, released the lander Philae in November, and the mission ended in September 2016. In particular, Rosetta was present when 67P reached its perihelion in August 2015. At this point, the comet was at its closest distance to the Sun (1.25 astronomical unit, while its mean distance is almost thrice this number), where the cometary activity is maximal.

The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA
The asteroids (2867) Šteins (left) and (21) Lutetia (right), seen by Rosetta. © ESA

So, Rosetta consisted of two modules: the orbiter itself, and the lander Philae. The orbiter had 11 instruments on board, and the lander 10. These instruments permitted, inter alia, to map the comet and measure its geometry, to constrain its internal structure and its chemistry, and to characterize its environment.

This environment is strongly affected by the Solar wind, especially in the vicinity of the perihelion, but not only.

The Solar wind

The Solar corona emits a stream of charges particles, which is mainly composed of electrons, protons, and alpha particles (kind of charged helium). This emission is called Solar wind. It is so energetic, that the emitted particles go far beyond the orbit of Pluto, constituting the heliosphere. The heliosphere has the shape of a bubble, and its boundary is called the heliopause. Voyager 1 crossed it in August 2012, at a distance of 121 AU of the Sun. At the heliopause, the pressure of the Solar wind is weak enough, to be balanced by the one of the interstellar medium, i.e. the winds from the surrounding stars. Hence, Voyager 1 is in this interstellar space, but technically still in the Solar System, as under the gravitational attraction of the Sun.

Anyway, our comet 67P/Churyumov-Gerasimenko is much closer than that, and has to deal with the Solar wind. Let us see how.

The physics of the interaction

Imagine you are on the comet, and you look at the Sun… which should make you blind. From that direction comes a stream of these charged particles (the Solar wind), and you can consider that their trajectories are parallel if far enough from the comet. Of course, the Sun does not emit on parallel trajectories, i.e. the trajectories of all these particles converge to the Sun. But from the comet, the incident particles appear to arrive on parallel trajectories.

While a charged particle approaches the comet, it tends to be deflected. Here, the dominating effect is not the gravitation, but the Lorentz force, i.e. the electromagnetic force. This force is proportional to the electric charge of the particle, and also involves its velocity, and the electric and magnetic fields of the comet.

The authors showed in a previous paper that the trajectories of the charged particles could be conveniently described in assuming that the magnetic field obeys an inverse-square law, i.e. its amplitude decreases with the square of the distance to the comet. If you are twice further from the comet, then the magnetic field is four times weaker.

I do not mean that the magnetic field indeed obeys this law. It is in fact more complex. I just mean that if you model it with such an ideal law, you are accurate enough to study the trajectories of the Solar wind particles. And this is what the authors did.

By the way, the authors suggest that any magnetic field following an inverse-power law could work. Of course, the numbers would have been different, but the global picture of the trajectories would be pretty much the same. It seems, at this time, too challenging to determine which of these models is the most accurate one.

Reducing the problem

The authors used analytical calculations, i.e. maths, which are in fact close to the classical ones, you make to show that the gravitation results in elliptic, parabolic, or hyperbolic, trajectories.

A wonderful tool assisting such studies is the First Integrals. A First Integral is a quantity, which remains constant all along a trajectory. For instance, in a gravitational problem where no energy is dissipated, then the total energy (kinetic + potential energies) is conserved. This is a First Integral. Another First Integral in that problem is the norm of the total angular momentum. And the existence of these two quantities helps to understand the shape of the possible orbits.

The authors showed that this is quite similar here. Even if the equations are slightly different (anyway the inverse-square law is a similarity), they showed that the problems has 2 First Integrals. And from these 2 First Integrals, they showed that knowing only 2 parameters is in fact enough to characterize the trajectories of the Solar wind particles. These two parameters are called rC and rE, they have the physical dimension of a distance, and are functions of all the parameters of the problems. rE characterizes the stream, it is related to its velocity, while rC characterizes a given particle. If you know just these 2 parameters, then you can determine the trajectory.

An empty cavity around the comet

The authors give a detailed description of the trajectories. To make things simple: either the particles orbit the comet, or they just pass by. But anyway, there is an empty space around the comet, i.e. a spherical cavity in which no Solar wind particle enters.

To come: comparison with in situ measurements

The journey of Rosetta around 67P crossed the boundary of this empty cavity. In other words, we have measurements of the density of charged particles at different distances from the comet, and also for different distances from the Sun, since the orbital phase of the mission lasted 2 years, during which 67P orbited the Sun. The authors promise us that a study of the comparison between the model and the in situ measurements, i.e. the observations, is to come. We stay tuned!

Rosetta does not operate anymore, and has landed (or crashed…) on 67P in September 2016. It is still there, and has on-board a kind of modern Rosetta stone. This is a micro-etched pure nickel prototype of the Rosetta disc donated by the Long Now Foundation, as part of its Rosetta Project. The disc was inscribed with 6,500 pages of language translations. This is a kind of time capsule, aiming at preserving part of our culture. Maybe someone will one day find it…

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.

An active asteroid

Hi there! Today we will detail a recent study by Jessica Agarwal and Michael Mommert, entitled Nucleus of active asteroid 358P/Pan-STARRS (P/2012 T1). This study has recently been accepted for publication in Astronomy and Astrophysics, and consists in increasing our knowledge of a recently discovered object, i.e. P/2012 T1. This object proved to have some activity, like a comet. The authors realized several observations to try to characterize its activity, and infer some physical properties like its size and its rotation.

Comet vs. active asteroid

First of all, I would like to make clear what is a comet, and what is an active asteroid. I am very ambitious here, since these two notions actually overlap. For instance, our object is both an active asteroid, and a main-belt comet.

Let us say that a comet is an active asteroid, while an active asteroid is not necessarily a comet. The difference is in the nature of the activity.

A comet is a dirty snowball, i.e. you have water ice, and some silicates. Its orbit around the Sun is usually pretty eccentric, so that you have large variations of the distance Sun-object. The location of the orbit, at which the distance is the smallest, is called pericentre. When the comet approaches the pericentre, it approaches the Sun, heats, and part of its water ice sublimates. This results in a dusty tail (actually there are two tails, one being composed of ionized particles).

But when you see dust around a small body, i.e. when you see activity, this is not necessarily ice sublimation. There could be for instance rock excavated by an impact, or material expelled by fast rotation. In that case, you still have an active asteroid, but not a comet. One of the goals of this study is to address the cause and nature of P/2012 T1’s activity.

The asteroid P/2012 T1

P/2012 T1, now named 358P, has been discovered in October 2012 by the Pan-STARRS-1 survey. Pan-STARRS stands for Panoramic Survey Telescope and Rapid Response System, it uses dedicated facilities at Haleakala Observatory, Hawaii, USA.

Discovery of P/2012 T1. © Pan-STARRS
Discovery of P/2012 T1. © Pan-STARRS

Its provisional name, P/2012 T1, contains information on the nature of the object, and its discovery. P stands for periodic comet, 2012 is the year of the discovery, and T means that it has been discovered during the first half of October.

Interestingly, this object appeared on images taken in December 2001 at Palomar Observatory in California, while acquiring data for the survey NEAT (Near-Earth Asteroid Tracking).

You can find below its orbital elements, from the Minor Planet Center:

Semi-major axis 3.1504519 AU
Eccentricity 0.2375768
Inclination 11.05645°
Period 5.59 y

From its orbital dynamics, it is a Main-Belt object. As a comet, it is a Main-Belt Comet.

New observations

Once an object is known and we know where it is, it is much easier to reobserve it. The authors conducted observations of 358P from the Southern Astrophysical Research (SOAR) telescope, and the Very Large Telescope.

The SOAR telescope is based on Cerro Pachón, Chile. This is a 4.1-m aperture facility, located at an altitude of 2,700 m. The authors took images with the Goodman High Throughput Spectrograph during one night, from July 27 to July 28, 2017. They wanted to analyze the reflected light by the asteroid at different wavelengths, unfortunately the observational constraints, i.e. cloud coverage, permitted only two hours of observations. Only the observations made with the VR filter, centered at 610 nm, were useful.

These data were supplemented by 77 images taken during 10 hours from August 17 to August 18, 2017, at the Very Large Telescope. This instrument depends on the European Southern Observatory (ESO), and is located on Cerro Paranal, once more in Chile, at an altitude of 2,635 m. The authors used the FOcal Reducer and low dispersion Spectrograph 2 (FORS2), which central wavelength is 655 nm.

The observations give raw images. The authors treated them to get reliable photometric and astrometric measurements of 358P, i.e. they corrected from the variations of the luminosity of the sky, in using reference stars, and from the possible instrumental problems. For that, they recorded the response of the instrument to a surface of uniform brightness, and used the outcome to correct their images.

Let us now address the results.

Measuring its rotation

Such a small (sub-kilometric) body is not spherical. This results in variations of luminosity, which depend on the surface element which is actually facing your telescope. If you acquire data during several spin periods of the asteroid, then you should see some periodicity in the recorded lightcurve.

The best way to extract the periods is to make a Fourier transform. Your input is the time-dependent lightcurve you have recorded, and your output is a frequency-dependent curve, which should emphasize the periods, which are present in the recorded lightcurve. If the signal is truly periodic, then it should exhibit a maximum at its period and its harmonics (i.e. twice the period, thrice the period, etc.), and almost 0 outside (not exactly 0 since you always have some noise).

In the case of 358P, the authors did not identify any clear period. A maximum is present for a rotation period of 8 hours, but the result is too noisy to be conclusive. A possible explanation could be that we have a polar view of the asteroid. Another possibility is that the albedo of the asteroid (the fraction of reflected light) is almost uniform.

Dust emission

The authors tried to detect debris around the nucleus of the comet, in widening the aperture over which the photometry was performed. They got no real detection, which tends to rule out the possibility of non-cometary activity.

A 530m-large body

Finally, the magnitude of the asteroid is the one of a sphere of 530 meters in diameter, with an albedo of 6%. This means that a higher albedo would give a smaller size, and conversely. The albedo depends on the composition of the asteroid, which is unknown, and can be only inferred from other asteroids. The authors assumed it to be a carbonaceous asteroid (C-type), as 75% of the asteroids. If it were an S-type (silicateous) body, then it would be brighter. A wide band spectrum of the reflected light would give us this information.

The study and its authors

  • You can find the study here, on Astronomy and Astrophysics’ website. Moreover, the authors uploaded a free version on arXiv, thanks to them for sharing!
  • Here is the webpage of the first author, Jessica Agarwal,
  • and here the website of Michael Mommert.

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.

Some comets are not randomly distributed

Hi there! Everybody knows the comets, which may show us impressive tails, when they approach our Sun. This is due to what we call cometary activity. You can find comets in many places in the Solar System. Today we will focus on the 9 ones, which are located in the Main Asteroid Belt, i.e. between the orbits of Mars and Jupiter. This is the opportunity to present you Orbital alignment of Main-belt comets, by Yoonyoung Kim, Yougmin JeongAhn, and Henry H. Hsieh. This study has recently been published in The Astronomical Journal.

Comets in the Solar System

A comet is a small body, which presents some activity. This activity manifests as 2 tails, which are a gas tail and a dust tail. These two tails have different directions because the dust is heavier than the gas, and so is differently affected by the Sun. The Sun is actually responsible for at least part of this activity: if the body has water ice at its surface, the proximity of the Sun heats it enough to sublimate it.

We distinguish different classes of comets, from their orbital motion. The short-period comets have a period below 200 years, i.e. they make a close approach to the Sun periodically, with less than 200 years between two approaches. This is for instance the case of the famous Halley comet, or 1P/Halley, which period is 75 years. The comets with a period smaller than 20 years are called Jupiter-family comets, their orbits are strongly affected by the gravitational perturbation of Jupiter.
And we also have long-period comets, with periods larger than 200 years, up to several thousands of years, or even more… The extreme case is the one of the parabolic and hyperbolic comets, which eccentricities are close to or larger than 1. In such a case, we just see the comet once.

The Jupiter-family comets should originate from the Kuiper Belt, and have been so strongly perturbed by Jupiter that their semimajor axes became much smaller, reducing their orbital periods. However, we attribute the origin of the longer periods comets to the Oort cloud, which is thought to lie between 50,000 and 200,000 astronomical units (remember: the Sun-Earth distance is 1 AU). The comets we are interested in today are much closer, in the Main-Belt of asteroids.

The Main-Belt Comets

Main Belt Comets (MBCs) are comets, which are located in the asteroid belt. As such, they present some cometary activity. It appears that there is no general agreement on the way to identify them. Some asteroids present an activity, which is mainly driven by dust, and not by sublimation of water ice, so it could be relevant to call them active asteroids instead of comets. But they may have some sublimation driven activity as well.

The first identified MBC is 133P/Elst-Pizarro, which has been discovered in 1979 and is since then identified as an asteroid… and also as a comet since 1996. I mean, this is officially both a comet and an asteroid. The authors considered 9 MBC, there could be a little more of them, since classifying them is not that easy.

The comet Elst-Pizarro seen at La Silla Observatory. © ESO
The comet Elst-Pizarro seen at La Silla Observatory. © ESO

The MBC should originate from the Main-Belt. In this study, we are interested in the orbital dynamics. Let us talk about orbital elements.

Proper, forced, and osculating elements

As I have already told you in a previous post, we usually describe the orbit of a planetary body with 6 orbital elements, which characterize the ellipse drawn by the trajectory.

These orbital elements are

  • the semi-major axes (which would be the distance to the Sun, if the orbit were circular… this remains almost true for slightly eccentric orbits),
  • the mean longitude,
  • the eccentricity of the trajectory (0 means circular, the eccentricity must be smaller than 1 for the orbit to be elliptic),
  • the pericentre, i.e. location of the point of the trajectory, where the distance to the Sun is minimal,
  • the inclination, with respect to a given reference plane,
  • the ascending node, which locates the intersection between the reference plane and the orbit.

We call them osculating elements. These are the elements that the orbit would have at a given time, if it were exactly an ellipse. The real trajectory is very close to an ellipse, actually.

We will just keep in mind the two couples (eccentricity, pericentre), and (inclination, ascending node). Because these variables are coupled: without eccentricity, the pericentre is irrelevant, since the distance Sun-body is constant. And without inclination, the ascending node is irrelevant, since the whole trajectory is in the reference plane.

And these variables are the sums of a proper and a forced component. Imagine you are a MBC. You want to have your own motion around the Sun. This gives you the proper (or free) component, which is actually ruled by your initial conditions, and the interaction with the Sun (what we call the 2-body, or Kepler, problem). Unfortunately for you, there is this big guy perturbing your motion (Jupiter is his name). He is heavy enough to force your motion to follow his. This gives you a forced motion, and the actual motion is the sum of the proper and the forced ones. The forced motion tends to align your pericentre and your ascending node with the ones of Jupiter. The authors studied these motions.

The Main-Belt Comets are clustered

And their conclusions is that the MBC are clustered, in particular the pericentres. They tend to be aligned with the one of Jupiter. This could have been anticipated, but the authors found something more: the MBC are more clustered than the others asteroids, which lie in that region of the outer main-belt.

For quantifying this more clustered, they ran several statistical tests, which I do not want to detail (the Kolmogorov-Smirnov test, the F-test, and the Watson’s U2 test). These tests show that this excess of clustering happened very unlikely by chance. In other words, there is something. And this is more obvious for comets, for which the sublimation activity is overwhelming. This permits the authors to make a link between this activity, i.e. the presence of water ice, and this clustering. And to suggest favorable conditions for the detection of cometary activity for Main-Belt objects.

Where are the other MBCs?

Based on the result that the eccentricities of MBCs are secularly excited by Jupiter, the authors suggest to look for them in the fall night sky, when Jupiter’s perihelion is at opposition.
We would not necessarily be looking for new bodies, but also for cometary activity of already known bodies. Because of the variations of the distance with the Sun, the sublimation of water ice is not a permanent phenomenon. Remember that Elst-Pizarro has been classified as a comet 17 years after its discovery.

Clustering of TNOs suggests the existence of the Planet Nine

I would like to finish with a reminder that the Planet Nine was hinted that way, in 2016. A clustering among the orbits of Trans-Neptunian Objects was statistically proven. Since then, the Planet Nine has not been detected (yet), but other clues have suggested its presence, like the obliquity of the Sun.

More generally, I would say that big objects strongly affect the orbits of small ones, and in observing the small ones, then you can deduce something on the big ones!

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.

9 interstellar asteroids?

Hi there! You may have recently heard of 1I/’Oumuamua, initially known as C/2017 U1, then A/2017 U1 (see here), where C stands for comet, A for asteroid, and I for interstellar object. This small body visited us last fall on a hyperbolic orbit, i.e. it came very fast from very far away, flew us by, and then left… and we shall never see it again. ‘Oumuamua has probably been formed in another planetary system, and its visit has motivated numerous studies. Some observed it to determine its shape, its composition, its rotation… and some conducted theoretical studies to understand its origin, its orbit… The study I present you today, Where the Solar system meets the solar neighbourhood: patterns in the distribution of radiants of observed hyperbolic minor bodies, by Carlos and Raúl de la Fuente Marcos, and Sverre J. Aarseth, is a theoretical one, but with a broader scope. This study examines the orbits of 339 objects on hyperbolic orbits, to try to determine their origin, in particular which of them might be true interstellar interlopers. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

‘Oumuamua

I detail the discovery of ‘Oumuamua there. Since that post, we know that ‘Oumuamua is a red dark object, probably dense. It is tumbling, i.e. does not rotate around a single rotation axis, in about 8 hours. The uncertainties on the rotation period are pretty important, because of this tumbling motion. Something really unexpected is huge variations of brightness, which should reveal either a cigar-shaped object, or an object with extreme variations of albedo, i.e. bright regions alternating with dark ones… but that would be inconsistent with the spectroscopy, revealing a reddish object. This is why the dimensions of ‘Oumuamua are estimated to be 230 × 35 × 35 meters.

Artist's impression of 'Oumuamua. © ESO/M. Kornmesser
Artist’s impression of ‘Oumuamua. © ESO/M. Kornmesser

One wonders where ‘Oumuamua comes from. An extrapolation of its orbit shows that it comes from the current direction of the star Vega, in constellation Lyra… but when it was there, the star was not there, since it moved… We cannot actually determine around which star, and when, ‘Oumuamua has been formed.

Anyway, it was a breakthrough discovery, as the first certain interstellar object, with an eccentricity of 1.2. But other bodies have eccentricities larger than 1, which make them unstable in the Solar System, i.e. gravitationally unbound to the Sun… Could some of them be interstellar interlopers? This is the question addressed by the study. If you want to understand what I mean by eccentricity, hyperbolic orbit… just read the next section.

Hyperbolic orbits

The simplest orbit you can find is a circular one: the Sun is at the center, and the planetary object moves on a circle around the Sun. In such a case, the eccentricity of the orbit is 0. Now, if you get a little more eccentric, the trajectory becomes elliptical, and you will have periodic variations of the distance between the Sun and the object. And the Sun will not be at the center of the trajectory anymore, but at a focus. The eccentricity of the Earth is 0.017, which induces a closest distance of 147 millions km, and a largest one of 152 millions km… these variations are pretty limited. However, Halley’s comet has an eccentricity of 0.97. And if you exceed 1, then the trajectory will not be an ellipse anymore, but a branch of hyperbola. In such a case, the object can just make a fly-by of the Sun, before going back to the interstellar space.

Wait, it is a little more complicated than that. In the last paragraph, I assumed that the eccentricity, and more generally the orbital elements, were constant. This is true if you have only the Sun and your object (2-body, or Kepler, problem). But you have the gravitational perturbations of planets, stars,… and the consequence is that these orbital elements vary with time. You so may have a hyperbolic orbit becoming elliptical, in which case an interstellar interloper gets trapped, or conversely a Solar System object might be ejected, its eccentricity getting larger than 1.

The authors listed three known mechanisms, likely to eject a Solar System object:

  1. Close encounter with a planet,
  2. Secular interaction with the Galactic disk (in other words, long term effects due to the cumulative interactions with the stars constituting our Milky Way),
  3. Close encounter with a star.

339 hyperbolic objects

The authors identified 339 objects, which had an eccentricity larger than 1 on 2018 January 18. The objects were identified thanks to the Jet Propulsion Laboratory’s Small-Body Database, and the Minor Planet Center database. The former is due to NASA, and the latter to the International Astronomical Union.

Once the authors got their inputs, they numerically integrated their orbits backward, over 100 kyr. These integrations were made thanks to a dedicated N-body code, powerful and optimized for long-term integration. Such algorithm is far from trivial. It consists in numerically integrating the equations of the motion of all of these 339 objects, perturbed by the Sun, the eight planets, the system Pluto-Charon, and the largest asteroids, in paying attention to the numerical errors at each iteration. This step is critical, to guarantee the validity of the results.

Some perturbed by another star

And here is the result: the authors have found that some of these objects had an elliptical orbit 100 kyr ago, meaning that they probably formed around the Sun, and are on the way to be expelled. The authors also computed the radiants of the hyperbolic objects, i.e. the direction from where they came, and they found an anisotropic distribution, i.e. there are preferred directions. Such a result has been obtained in comparing the resulting radiants from the ones given by a random process, and the distance between these 2 results is estimated to be statistically significant enough to conclude an anisotropic distribution. So, this result in not based on a pattern detected by the human eye, but on statistical calculations.

In particular, the authors noted an excess of radiants in the direction of the binary star WISE J072003.20-084651.2, also known as Scholz’s star, which is currently considered as the star having had the last closest approach to our Solar System, some 70 kilo years ago. In other words, the objects having a radiant in that direction are probably Solar System objects, and more precisely Oort cloud objects, which are being expelled because of the gravitational kick given by that star.

8 candidate interlopers

So, there is a preferred direction for the radiants, but ‘Oumuamua, which is so eccentric that it is the certain interstellar object, is an outlier in this radiant distribution, i.e. its radiant is not in the direction of Scholz’s star, and so cannot be associated with this process. Moreover, its asymptotical velocity, i.e. when far enough from the Sun, is too large to be bound to the Sun. And this happens for 8 other objects, which the authors identify as candidate interstellar interlopers. These 8 objects are

  • C/1853 RA (Brunhs),
  • C/1997 P2 (Spacewatch),
  • C/1999 U2 (SOHO),
  • C/2002 A3 (LINEAR),
  • C/2008 J4 (McNaught),
  • C/2012 C2 (Bruenjes),
  • C/2012 S1 (ISON),
  • C/2017 D3 (ATLAS).

Do we know just one, or 9 interstellar objects? Or between 1 and 9? Or more than 9? This is actually an important question, because that would constrain the number of detections to be expected in the future, and have implications for planetary formation in our Galaxy. And if these objects are interstellar ones, then we should try to investigate their physical properties (pretty difficult since they are very small and escaping, but we did it for ‘Oumuamua… maybe too late for the 8 other guys).

Anyway, more will be known in the years to come. More visitors from other systems will probably be discovered, and we will also know more on the motion of the stars passing by, thanks to the astrometric satellite Gaia. Stay tuned!

The study and its authors

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

The Brazil Nut Effect on asteroids

Hi there! You know these large nuts called Brazil nuts? Don’t worry, I will not make you think that they grow on asteroids. No they don’t. But when you put nuts in a pot, or in a glass, have you ever noticed that the biggest nuts remain at the top? That seems obvious, since we are used to that. But let us think about it… these are the heaviest nuts, and they don’t sink! WTF!!! And you have the same kind of effect on small bodies, asteroids, planetesimals, comets… I present you today a Japanese study about that, entitled Categorization of Brazil nut effect and its reverse under less-convective conditions for microgravity geology by Toshihiro Chujo, Osamu Mori, Jun’ichiro Kawaguchi, and Hajime Yano. This study has recently been published in The Monthly Notices of the Royal Astronomical Society.

Brazil Nut and Reverse Brazil Nut effects

The idea is easy to figure out. If you have a pot full of different nuts, then the smallest ones will be naturally closer to the bottom, since they are small enough to fill the voids between the largest ones. For the same reason, if you fill a bucket first with stones and then with sand, the sand will naturally reach the bottom, flowing around the stones. Flowing is important here, since the sand pretty much behaves as a fluid. And of course, if you put the sand in the bucket first, and then the stones, the stones will naturally be closer to the top. Well, this is the Brazil Nut Effect.

OK, now let us make the story go one step further… You have an empty bucket, and you put sand inside… a third of it, or a half… this results as a flat structure. You put stones, which then cover the sand, lying on its surface… and you shake. You shake the bucket, many times… what happen? the sand is moving, and makes some room for the stones, or just some of them, which migrate deeper… if you shake enough, then some of them can even reach the bottom. This is the Reverse Brazil Nut Effect.

And the funny thing is that you can find this effect on planetary bodies! Wait, we may have a problem… when the body is large enough, then the material tends to melt, the heaviest one migrating to the core. So, the body has to be small enough for its interior being ruled by the Brazil Nut Effect, or its reversed version. If the body is small enough, then we are in conditions of microgravity. The authors give the examples of the Near-Earth Asteroid (433)Eros, its largest diameter being 34.4 km, the comet 67P/Churyumov-Gerasimenko, which is ten times smaller in length, and the asteroid (25143)Itokawa, its largest length being 535 meters. All of these bodies are in conditions of microgravity, and were visited by spacecraft, i.e. NEAR Shoemaker for Eros in 2001, Rosetta for Churyumov-Gerasimenko in 2014, and Hayabusa for Itokawa in 2003. And all of these space missions have revealed pebbles and boulders at the surface, which motivated the study of planetary terrains in conditions of microgravity.

Eros seen by NEAR Shoemaker. © NASA/JPL-Caltech/JHUAPL
Eros seen by NEAR Shoemaker. © NASA/JPL-Caltech/JHUAPL

I mentioned the necessity to shake the bucket to give a chance to Reverse Brazil Nut Effect. How to shake these small bodies? With impact, of course. You have impactors everywhere in the Solar System, and small bodies do not need impactors to be large to be shaken enough. Moreover, this shaking could come from cometary activity, in case of a comet, which is true for Churyumov-Gerasimenko.

The authors studied this process both with numerical simulations, and lab experiments.

Numerical simulations

The numerical simulations were conducted with a DEM code, for Discrete Element Modeling. It consisted to simulate the motion of particle which touch each others, or touch the wall of the container. These particles are spheres, and you have interactions when contact. These interactions are modeled with a mixture of spring (elastic interaction, i.e. without dissipation of energy) and dashpot (or damper, which induces a loss of energy at each contact). These two effects are mixed together in using the so-called Voigt rheology.

In every simulation, the authors had 10,224 small particles (the sand), and a large one, named intruder, which is the stone trying to make its way through the sand.

The simulations differed by

  • the density of the intruder (light as acryl, moderately dense as glass, or heavy as high-carbon chromium steel),
  • the frequency of the shaking, modeled as a sinusoidal oscillation over 50 cycles,
  • the restitution coefficient between the sand of the intruder. If it is null, then you dissipate all the energy when contact between the intruder and the sand, and when it is equal to unity then the interaction is purely elastic, i.e. you have no energy loss.

Allowing those parameters to vary will result in different outcomes of the simulations. This way, the influence of each of those parameters is being studied.

A drawback of some simulations is the computation time, since you need to simulate the behavior of each of the particles simultaneously. This is why the authors also explored another way: lab experiments.

Lab experiments

You just put sand in a container, you put an intruder, you shake, and you observe what is going on. Well, said that way, it seems to be easy. It is actually more complicated than that if you want to make proper job.

The recipient was an acryl cylinder, put on a vibration test machine. This machine was controlled by a device, which guaranteed the accuracy of the sinusoidal shaking, i.e. its amplitude, its frequency, and the total duration of the experiment. The intruder was initially put in the middle of the sand, i.e. half way between the bottom of the recipient and the surface of the sand. If it reached the bottom before 30,000 oscillation cycles, then the conclusion was RBNE, and if it raised from the surface the conclusion was BNE. Otherwise, these two effects were considered to be somehow roughly balanced.

But wait: the goal is to model the surface of small bodies, i.e. in conditions of microgravity. The authors did the experiment on Earth, so…? There are ways to reproduce microgravity conditions, like in a parabolic flight, or on board the International Space Station, but this was not the case here. The authors worked in a lab, submitted to our terrestrial gravity. The difficulty is to draw conclusions for the asteroids from Earth-based lab experiments.

At this point, the theory assists the experimentation. If you write down the equations ensuing from the physics (I don’t do it… feel free to do so if you want), these equations ruling the DEM code for instance, you will be able to manipulate them (yes you will) so as to make them depend on dimensionless parameters. For instance: your size is in meters (or in feet). It has the physical dimension of a length. But if you divide your size with the one of your neighbor, you should get something close to unity, but this will be a dimensionless quantity, as the ratio between your size and your neighbor’s. The size of your neighbor is now your reference (let him know, I am sure he would be delighted), and if your size if larger than 1, it means that you are taller than your neighbor (are you?). In the case of our Brazil Nut experiment, the equations give you a gravity, which you can divide by the local one, i.e. either the gravity of your lab, or the microgravity of an asteroid. The result of your simulation will be expressed with respect to this ratio, which you can then re-express with respect to the microgravity of your asteroid. So, all this is a matter of scale. These scaling laws are ubiquitous in lab experiments, and they permit to work in many other contexts.

Triggering the Reverse Brazil Nut effect

And here are the results:

  • The outcomes of the experiments match the ones of the numerical simulations.
  • The authors saw practically no granular convection, i.e. the sand initially at the bottom does not migrate to the top. This is here an analogy with fluid mechanics, in which water at the bottom can raise to the top, especially when it warms (warm water is less dense than cold one).
  • Densest intruders are the likeliest to migrate to the bottom.
  • The authors identified 3 distinct behaviors for the particles, depending on a dimensionless acceleration Γ.

These behaviors are:

  1. Slow Brazil Nut Effect,
  2. Fast BNE, for which the intruder requires less oscillation cycles to raise,
  3. Fluid motion, which may induce RBNE. This is favored by rapid oscillations of the shaking.

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, and (NEW) Instagram.