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.

Forming Mars

Hi there! Of course, you know the planet Mars. You can here from it these days, since it is exceptionally close to our Earth. Don’t worry, this is a natural, geometrical phenomenon.

Anyway, it is a good time to observe it. But I will not speak of observing it, today. We will discuss its formation instead, because the issue of the formation of Mars remains a challenge. This is the opportunity to present The curious case of Mars’ formation, by James Man Yin Woo, Ramon Brasser, Soko Matsumura, Stephen J. Mojzsis, and Shigeru Ida. Astronomy and Astrophysics will publish it pretty soon.

Mars is too small

The following table gives you comparative characteristics of Venus, the Earth, and Mars.

Venus Earth Mars
Semimajor axis 0.723 AU 1.000 AU 1.524 AU
Eccentricity 0.007 0.017 0.093
Inclination 3.39° 1.85°
Orbital period 224.7 d 365.25 d 686.96 d
Spin period -243.02 d 23.93 h 24.62 h
Mean diameter 12,104 km 12,742 km 6,779 km

The last line reveals a problem: Venus and the Earth are about the same size, while Mars is much smaller! But this is not the only problem: the compositions of the Earth and Mars are VERY different.

It is pretty easy to know the composition of the Earth: you just analyze samples. And for Mars? Just the same!

Interestingly, there are Martian meteorites on Earth. These are ejecta from impacts, which were ejected from Mars, and then traveled in the Solar System, until reaching our Earth.

In fact, over the tens of thousands of meteorites which have been found on Earth, a little more than one hundred were significantly different than the other ones, i.e. younger formation ages, a different oxygen isotopic composition, the presence of aqueous weathering products… Most of these meteorites were known as SNC, after the three groups they were classified into:

  • S for Shergottites, after the Shergotty meteorite (India, 1865),
  • N for Nakhlites, after the Nakhla meteorite (Egypt, 1911),
  • C for Chassignites, after the Chassigny meteorite (France, 1815).

Such a significant number of similar meteorites, which are that different from the other ones, suggests they come from a large body. Mars is an obvious candidate, which has been confirmed after the discovery that trapped gases in these meteorites are very similar to the ones, which are present in the atmosphere of Mars.

The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.
The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.

After that, the numerous space missions improved our knowledge of the Martian composition. And it finally appeared that both planets are essentially made of chondritic material. The Earth should accrete about 70% of enstatite chondrite (and same for the Moon), while Mars only about 50%. Chondrites are non-metallic meteorites, the enstatite chondrites being rich in the mineral enstatite (MgSiO3). These numbers are derived from the documented isotopic compositions of the Earth and Mars, i.e. the ratio of the different chemical elements. An isotope is a variant of a particular chemical element, which differs in neutron number.

If you want to convincingly simulate the formation of Mars, the product of your simulations should be similar to Mars in mass AND in composition. And this is very challenging. Let us see why, but first of all let us recall how to form planets from a disk.

Forming planets from a disk

At its early stage, a planetary system is composed of a proto-star, and a pretty flat disk, made of gas and dust. Then the dust accretes into clumps, which then collides to form planetary embryos, i.e. proto-planets. These embryos continue to grow with collisions, until forming the current planets. Meanwhile, the gas has dissipated.

Anyway, interactions between the protoplanets and between them and the gas can lead to planetary migration. This means that we cannot be sure whether the planets we know formed close to their current location. This makes room for several scenarios.

Two models of planetary formation

The obvious starting point is to assume that the planets formed close to their current locations. This so-called Classical model works pretty well for Venus, the Earth, Jupiter, Saturn… but not for Mars. The resulting Mars is too massive.

An idea for by-passing this problem is to start with a depletion of material at the location of Mars. This is equivalent to an excess inside the terrestrial orbit. In such a configuration, less material is available to the proto-Mars, which eventually has a mass, which is close to the present one.

You can get this excess of material inside the terrestrial orbit if you buy the Grand Tack scenario: when Jupiter formed, it created a gap in the inner disk, and the mutual interaction resulted in an inward migration of Jupiter, until reaching the present orbit of Mars. In moving inward (Type II migration), Jupiter pushed the material inward. Then, a 3:2 mean-motion resonance with Saturn occurred, which created another gap, and made Jupiter move outward, until its present location.

This way, you can form a planetary object, which is similar to Mars in mass and location.

But what about its composition?

The composition challenge

This is still a challenge. The composition of a planetary object is strongly affected by the one of the disk, where the object formed… which may not be its present location.

The authors added a free parameter to the model: the break location, which would split the protoplanetary disk into an inner and an outer region. The inner region would be rich in enstatite chondrites, while the outer one would be rich in ordinary chondrites.

A break location at 1.3 AU gives the best fit for the difference of composition between Mars and the Earth, for both formation scenarios (Classical and Grand Tack).

So, the Grand Tack with a break location at 1.3 AU could be the right scenario. But another possibility exists: the Classical scenario says that if Mars formed where it is, then it should be heavier. But what if Mars formed actually further from the Sun, and then migrated inward? Then, it would not need any depletion of material to have the right mass. And the break barrier should have been further than 1.3 AU. But you have to explain why it migrated inward.

Anticipating the composition

One of the good things with scenarios of formation is that thr gives more details on the outcomes, than actually observed. For instance, this study predicts the isotopic composition of 17O, 50Ti, 54Cr, 142Nd, 64Ni and 92Mo, in the Martian mantle. Further data, collected by space missions, will give additional constraints on these parameters, and test the validity of the present study. 8 missions are currently operational in orbit or on Mars, and InSight is en-route, after having been launched in May 2018. It should land on Mars on November 26, and will study its interior with a seismometer, and a heat transfer probe.

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.