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.

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 r_C and r_E, they have the physical dimension of a distance, and are functions of all the parameters of the problems. r_E characterizes the stream, it is related to its velocity, while r_C 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

• You can find the study here. The authors also made it free available on arXiv, many thanks to them for sharing!
• Here is the webpage of Melaine Saillenfest,
• the ResearchGate profile of Benoît Tabone,
• and the one of Etienne Behar.

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.