Artist's view of 'Oumuamua. © ESO/M. Kornmesser

The rotation of ‘Oumuamua

Hi there! Today we go back to ‘Oumuamua, you know, this interstellar object discovered last Fall. Its visit to our Solar system was the opportunity to observe it, and here we discuss on an analysis of the variations of its luminosity. I present you The excited spin state of 1I/2017 U1 ‘Oumuamua, by Michael J.S. Belton and collaborators. This study tells us that its rotation state might be complex, and that affects the way we figure out its shape. It has recently been published in The Astrophysical Journal Letters.

Remember 1I/’Oumuamua?

I already told you about ‘Oumuamua. This is the first identified object, which has been found in our Solar System but which undoubtedly originates from another System. In other words, it was formed around another star.
The Pan-STARRS survey identified ‘Oumuamua in October 2017, and the determination of its orbit proved it to be unusually eccentric. With an eccentricity close to 1.2, its orbit is a branch of a hyperbola rather than an ellipse. This means that it comes from very far, passes by while the Sun deviates it, and leaves us for ever.
This is the highest eccentricity ever recorded in the Solar System so far. Other objects had an eccentricity larger than 1, but which could have been caused by the gravitational perturbation of a planet. Not for ‘Oumuamua.
Its full name is actually 1I/2017 U1 (ʻOumuamua). 2017 because it was discovered in 2017, 1I as the first Interstellar object ever discovered (by the way, the International Astronomical Union has created this category for ‘Oumuamua), and the name ‘Oumuamua means scout in Hawaiian.

The announcement of its discovery motivated the observers all around the world to try to observe it and make photometric measurements. Here we discuss what these measurements tell us on the rotation and the shape. But before that, let me tell you something on the rotation.

Different modes of rotation

We will consider that our object is an ellipsoid. This is actually unsure, but let us assume it. We have 3 different axes, and we could imagine different configurations for its rotation:

  1. Tumbling rotation: the object rotates around its 3 axes, and basically this is a mess. We could be in a situation of dynamical chaos, like for the moon of Saturn Hyperion.
  2. Short-axis mode (SAM): the rotation is strongly dominated by a motion around the shortest axis. This is the case for many bodies in the Solar System, like the planets, our Moon… This does not mean that the rotation is strictly around one axis, but we will see that a little later.
  3. Long-axis mode (LAM): the rotation is strongly dominated by a motion around the longest axis.
The LAM and SAM modes.
The LAM and SAM modes.

These last two modes can actually cohabit with tumbling, i.e. a tumbling rotation may favor rotation around one axis.

If the rotation were strictly around one axis, then the body would look like a top. But this rotation axis may move with respect to the figure axis. This motion is named precession-nutation. The precession is the averaged path of the figure axis around the angular momentum, while the nutation contains the oscillations around it.

Now, imagine that you look at an object, which has such a rotation. How can you estimate it? There are ways.

Observing the rotation

Actually the brightness of a body not only depends on the distance from it, or on the insolation angle, but also on the surface facing you. This means that from the brightness, you can deduce something on the rotation state of the object. In particular, this surface brightness depends on its location with respect to the principal axis. If the object has the shape of a cigar, the reflected light from the long axis and from the short one will be different, and the lightcurve will present periodic variations. And the period of these variations is the rotation period. Easy, isn’t it?

Actually, not that easy. First, you assume that the surface has a constant albedo, i.e. that the ratio between the incident and the reflected lights is constant. But you do not know that. In particular, an icy surface has a higher albedo than a carbonaceous one. Another difficulty: a tumbling object, or even one with a precessional component in its rotation, will present a combination of different frequencies. Of course, this complicates the analysis.

However, you simplify the analysis in adding observations to your dataset. The authors used 818 observations over almost one month, spanning from Oct, 25 to Nov, 23, 2017. This includes observations from the Hubble Space Telescope, from the Magellan-Baade telescope at Las Campanas Observatory (Chile), from the Canada-France-Hawaii Telescope, from Pan-NSTARRS (these last facilities being based in Hawaii)…

Once the observations are obtained as raw data, they must be treated to correct from atmospheric and instrumental problems. And then it is not done yet, since the authors need an absolute luminosity of ‘Oumuamua, i.e. as if its distance to the observer were constant. The motion of ‘Oumuamua actually induced a trend in its distance to the Earth, and a trend in its luminosity, which the authors fitted before subtracting it the measured lightflux.

Once this is done, the authors get a lightcurve, which is constant on average, but presents variations around its mean value. Unfortunately, the required treatment induced an uncertainty in the measurements, which the authors had to consider. But fortunately, these practical difficulties are well-known, and algorithms exist to extract information from such data.

2 numerical algorithms

Basically, you need to extract periods from the variations of the lightflux. For that, we dispose of the classical tool of Fourier Transforms, which in principle requires equally spaced data. But the recorded data are not equally spaced, and remember that you must consider the uncertainties as well.

Specific algorithms exist for such a purpose. The authors used CLEAN and ANOVA, to double-check their results. These algorithms allow in particular to remove the aliasing effect, i.e. a wrong measurement of a period, because of an appropriate spacing of the data. And now, the results!

A cigar or a pancake?

The authors found two fundamental periods in the lightcurves, which are 8.67±0.34 and 3.74±0.11 hours. Interestingly, they connected these measurements to the possible dynamics of rotation, and they found two possible solutions:

  1. Long-Axis Mode: In that case, the possible rotation periods are 6.58, 13.15 and 54.48 hours, the latter being the most probable one.
  2. Short-Axis Mode: Here, ‘Oumuamua would be rotating with respect to the short-axis, but also with oscillations around the long axis of periods 13.15 or 54.48 hours.

In both axis, the long axis would also precess around the angular momentum in 8.67 ± 0.34 hours. Moreover, the authors found constraints on its shape. Previous studies already told us that ‘Oumuamua is highly elongated, this study confirms this fact, and tells us that ‘Oumuamua could be somewhere between the cigar and the pancake. But once more, this result could be weakened by variations of the surface albedo of ‘Oumuamua.

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.

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