Hi there! Today, we go back to the famous comet 67P / Churyumov-Gerasimenko. As you may know, this comet was the target of the European space mission Rosetta. In particular, it was the first comet to be landed by a spacecraft, in November 2014. Rosetta gave us invaluable information on 67P, which could be extrapolated to many comets, with caution of course. Today we discuss Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation induced torques, by T. Kramer, M. Läuter, S. Hviid, L. Jorda, H.U. Keller and E. Kührt.

It addresses the following issue: when you try to assess the forces affecting the orbit and the rotation of the comet, you have troubles. Among these forces are the gravitational perturbations of the Sun and the planets, which are very well known, but also torques and forces due to non-gravitational effects. When the comet approaches the Sun, its ice sublimates, and the resulting outgassing deviates the comet and affects its rotation. This last effect is only poorly constrained, and this is why in situ observations, as made by Rosetta, are essential to understand them. This study has recently been accepted for publication in Astronomy and Astrophysics.

###### Outline

The discovery of 67P / Churyumov-Gerasimenko

A rugged terrain

The data brought by Rosetta

The torques affecting the comet

Modeling its rotation

What it tells us on the activity

The study and its authors

## The discovery of 67P / Churyumov-Gerasimenko

This comet has been discovered by chance in September 1969 at Alma Ata Observatory, now in Kazakhstan, then in USSR. Svetlana Ivanova Gerasimenko took images of a field containing the comet 32P/Comas Solá, and Klim Ivanovich Churyumov detected there a new object close to the edge of an image. This object appeared on several images, which permitted to characterize its motion. That object was itself a comet, a periodic one (“P”), and more precisely the 67th to be discovered. So was it named 67P / Churyumov-Gerasimenko. You can find below some of its characteristics.

Discovery | 1969 |
---|---|

Semimajor axis | 3.463 AU |

Perihelion | 1.243 AU |

Aphelion | 5.68 AU |

Eccentricity | 0.64 |

Inclination | 7.04° |

Orbital period | 6.44 yr |

Spin period | 12 h 24 min |

Diameter | 4 km |

Density | 0.53 g/cm^{3} |

As you can see, its orbit is pretty elongated, and has a period of almost 6.5 years. This means that every 6.5 years, 67P/Churyumov-Gerasimenko approaches the Sun, at its perihelion, and at that time gets heated. This results in the sublimation of some of its material, which deviates it and alters its spin. The last passage at the perihelion occurred in August 2015, while the next one will be in November 2021. Rosetta orbited the comet from 2014 to 2016, which encompassed the perihelion passage, allowing to observe and measure the peak and evolution of its cometary activity.

## A rugged terrain

We will see later that modeling the rotation of a planetary object requires to know its shape. Fortunately for us, we know this shape very accurately, thanks to Rosetta. Unfortunately for the authors, 67P/Churyumov-Gerasimenko is far from a ball.

This is actually a bilobal object, i.e. roughly like a bone, of some 4 km in its larger dimension. Moreover, its terrain is very rugged. Rosetta actually observed, over only two years, alterations in the terrain, e.g. a landslide associated with an outburst. This makes the behavior of the comet all the more difficult to constrain… For instance, if you want to consider an outburst, from which region will it emerge?

## The data brought by Rosetta

We know the shape and rotation state of 67P/Churyumov-Gerasimenko thanks to Rosetta/OSIRIS images. OSIRIS, for Optical, Spectroscopic, and Infrared Remote Imaging System, is an imager composed of 2 cameras, a WAC and a NAC (Wide-Angle and Narrow-Angle Camera, respectively). From images brought by OSIRIS, it was possible to build a set of approximately 25,000 control points. Multiple observations of these control points, at different dates, permitted to understand that

- the comet spun around a single axis, which orientation has been determined,
- its rotation period was 12 hours and
*something*(on purpose, I do not detail this*something*here), - the rotation state varies with time. Rosetta observed a reorientation of the spin axis of 0.5°, and a shortening of the rotation period by 21 minutes (this is why I did not detail the
*something*).

Moreover, these data permitted to elaborate a shape model of the comet, made of 3,996 triangular surface elements. From this shape model, you can determine what is called the tensor of inertia of the comet, i.e. its mass distribution, in assuming its composition to be homogeneous (you always have to make hypotheses).

Now, let us see how the rotation is affected.

## The torques affecting the comet

In the study, the comet is assumed to be rigid, i.e. its shape is constant. You have no elasticity, this is probably a good approximation over such a limited time span. The equations of the rigid rotation tell you that the angular momentum of the comet (the angular momentum is the tensor of inertia, which is multiplied by the rotation) is affected by two kinds of torques:

- the gravitational torque of the surrounding bodies, which is almost entirely due to the mass of the Sun,
- non-gravitational torques, due to ice sublimation and heating by the Sun.

You put all this into an equation, you solve it numerically, and you can predict it, and understand the rotation measurements… Easy, isn’t it? Well, not that easy, since you have only few constraints on the ice sublimation.

## Modeling its rotation

BUT you have measurements of the rotation. So, what you can do is fit the parameters you don’t know, to the observed rotation. And more particularly to the changes in the rotational state.

More precisely, the authors modeled the torque due to the sublimation of water ice with a Fourier representation, i.e. as a sum of periodic quantities. These contributions are assumed to have a period, which is due to the rotation of the comet, and they are treated separately. The authors managed to match the Fourier amplitudes with the observed torque. And now let us go to the conclusions.

## What it tells us on the activity

Fitting the Fourier coefficients to the observed rotation finally tell us that:

- you can constrain the active fraction of the surface, with respect to the different areas (the authors considered 38 different zones on the surface),
- the sublimation increases much faster than linearly with respect to insolation. In other words, when you are twice closer to the Sun, the quantity of sublimated water ice is much more than twice than before. This was already known from other studies, but the study of the rotation confirms this fact. You should see it as a validation of the method.

So, this paper shows that we can definitely make a link between water production and the changes in rotation rate. Outgassing also produces CO_{2}, but this is not considered, since this production is more uniform than the one of water, and so should not affect the reorientation of the spin axis.

## The study and its authors

- You can find the study here. The complete reference is Kramer T., Läuter M., Hviid S., Jorda L., Keller H.U. & Kührt E., 2019, Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation-induced torques,
*Astronomy and Astrophysics*, in press. The authors made it also freely available on arXiv, many thanks to them for sharing! And now, let us see the authors: - the website of Tobias Kramer, first author of the study,
- the webpage of Matthias Läuter,
- the IAU page of Laurent Jorda,
- the one of Horst Uwe Keller,
- and the ResearchGate profile of Ekkehard Kührt.

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.