Measuring an asteroid from its shadow

Hi there! Today’s post is on the paper Results from the 2014 November 15th multi-chord stellar occultation by the TNO (229762) 2007 UK126, by Gustavo Benedetti-Rossi and 28 colleagues, which has recently been published in The Astronomical Journal. It explains us what 22 simultaneous observations of the same event, i.e. the occultation of a star by an asteroid, tell us about this asteroid.

The asteroid (229762) 2007 UK126

(229762) 2007 UK126 is a Trans-Neptunian Object, which was discovered in October 2007. Its highly eccentricity orbit (0.49) makes it a probable scattered disc object, i.e. its eccentricity should have been pumped by the planets, in particular Neptune. Its estimated rotation period is 11.05 hours. The Hubble Space Telescope has revealed the presence of an orbital companion.

Even at its perihelion, this object is further than Neptune, which makes it difficult to observe. The stellar occultations permit to bypass this problem.

The strategy of observation

The idea is this: while a pretty dark object passes just between you and a star, you do no see the star anymore. The dark object occults it. This occultation contains information.

This is the reason why some planetary scientists try to predict occultations from simulations of the motion of asteroids in the sky, maintaining lists of such events. These predictions suffer from uncertainties on the orbit of the asteroid, this motivates the need to refine the predictions just before the predicted event. For that, astrometric observations of the object are performed, to better constrain its orbital ephemerides.

Once the occultation is predicted with enough accuracy, the observers are informed of the date and the places from where to observe. Multiple observations of the same event, at different locations, represent a set of data which will then be inverted to get information on the asteroid. For these observations to be conducted, amateur astronomers are solicited. They usually constitute networks, which efficiency is doped by their enthusiasm.

The observation of a stellar occultation consists to measure the light flux received from the star during a time interval which includes the predicted event, and when the occultation happens, then a flux drop should be registered. For an observation to be useful, the observer should take care to have an accurate time reference. Moreover, a clear sky, preferably with no wind, makes the measurements more accurate. Some flux drops could be actually due to clouds passing by!

What can these observations tell us?

The first information we get from these occultations addresses the motion of the asteroid: the date and length of the occultation is an information, because we know where the asteroid was on the celestial sphere when this happened. When no occultation is detected, this is an information as well, even if it is frustrating.
Observing at different places permits to observe the occultation of the star by different parts of the asteroid. This is called a multi-chord occultation. From the duration of the event, we can deduce the size of the object with a much better accuracy than direct observation. Such a technique could also detect companions, as it might have been the case for the Main-Belt asteroid (146)Lucina in 1982.

A compelling information on a planetary body is its mass. The best way to measure its mass is by observing the orbit of a companion, if there is one. If there is none, or if its orbit cannot be observed, then we can combine the different measurements of its radius with the measurement of its rotation period and the assumption that its shape is at an hydrostatic equilibrium, i.e. a balance between its own gravity, its rotation, and possibly the gravitational (tidal) attraction of a planetary companion. In the absence of a companion, the equilibrium figure is an oblate, MacLaurin spheroid, which has a circular equatorial section, and a rotation axis which is smaller than the two other ones. If a companion is involved, then the object could be a Jacobi ellipsoid, i.e. an ellipsoid with 3 different principal axes.

This study

This study gathers the results of 20 observations of the stellar occultation of the star UCAC4 448-006503 by the TNO (229762) 2007 UK126 in November 2014, all over the United States, and 2 negative observations, i.e. no flux drop measured, in Mexico. One of the difficulties is is to be accurate on the exact times of the beginning (ingress) and the end (egress) of the event, i.e. the star disappearance and reappearance. This is the reason why the authors of the study split into two teams, which treated the same data separately, with their own techniques (denoted GBR and MWB, since conducted by Gustavo Benedetti-Rossi and Marc W. Buie, respectively).

And here are some of their results:

Before GBR MWB
Longest radius (km) 339+15-10 340+12-8
Equivalent radius (km) 299.5±38.9 319+14-7 319+12-6
Circular fit radius (km) 324+27-23 328+26-21
Apparent oblateness 0.106+0.050-0.040 0.118+0.055-0.048
Density (kg/m3) <1740 <1620

This table tells us that, before the occultation, only a mean radius was known, and with a much larger uncertainty than now. It also tells us that assuming the asteroid to be circular instead of elliptical gives a larger uncertainty. Wait… why circular and not spherical? Why elliptical and not ellipsoidal? Because the occultation is ruled by the projection of the shape of the asteroid on the celestial sphere, which is a 2D surface. So, we observe a surface, and not a volume, even if our assumptions on the shape (remember, the MacLaurin spheroid) give us a 3D information.
This is why the oblateness is just an apparent oblateness. It is actually biased by the projection on the celestial sphere. This oblateness is defined by the quantity (a-b)/a, where a and b are the two axes of the projected asteroid, with a > b.

To know more…

You can find the study on the web site of The Astronomical Journal. It has also been freely made available by the authors on arXiv. Thanks to the authors for sharing! Here is the webpage of the RECON and IOTA networks, which were of great help for the observations.

The authors

Here are their web pages or research profiles:

I hope you enjoyed this post. As usual, please let me know what you think about it. Happy holidays to everybody, and see you soon!

4 thoughts on “Measuring an asteroid from its shadow”

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