Hi there! I will present you today a fascinating paper. It aims at a comprehensive understanding of the system composed of an asteroid, (107) Camilla, and its two satellites. For that, the authors acquired, processed and used 5 different types of observations, from all over the world. A consequence is that this paper has many authors, i.e. 27. Its title is Physical, spectral, and dynamical properties of asteroid (107) Camilla and its satellites, by Myriam Pajuelo and 26 colleagues, and it has recently been published in Icarus. This paper gives us the shape of Camilla and its main satellites, their orbits, the mass of Camilla, its composition, its spin period,… I give you these results below.

###### Outline

The system of Camilla

5 different types of data

The orbit of the satellites

Spin and shape

The composition of these objects

The study and its authors

## The system of Camilla

The asteroid (107) Camilla has been discovered in 1868 by Norman Pogson at Madras Observatory, India. It is located in the

outer Main-Belt, and more precisely it is a member of the Cybele group. This is a group of asteroids, named after the largest of them (65) Cybele, which is thought to have a common origin. They probably originate from the disruption of a single progenitor. I show you below some Camilla’s facts, taken from the JPL Small-Body Database Browser:

Discovery | 1868 |
---|---|

Semimajor axis | 3.49 AU |

Eccentricity | 0.066 |

Perihelion | 3.26 AU |

Inclination | 10.0° |

Orbital period | 6.52 yr |

We have of course other data, which have been improved by the present study. Please by a little patient.

In 2001 the Hubble Space Telescope revealed a satellite of Camilla, S1, while the second satellite, S2, and has been discovered in 2016 from images acquired by the Very Large Telescope of Cerro Paranal, Chile. This makes (107) Camilla a ternary system. Interesting fact, there is at least another ternary system in the Cybele group: the one formed by (87) Sylvia, and its two satellites Romulus and Remus.

Since their discoveries, these bodies have been re-observed when possible. This resulted in a accumulation of different data, all of them having been used in this study.

## 5 different types of data

The authors acquired and used:

- optical lightcurves,
- high-angular-resolution images,
- high-angular-resolution spectrum,
- stellar occultations,
- near-infrared spectroscopy.

You record *optical lightcurves* in measuring the variations of the solar flux, which is reflected by the object. This results in a curve exhibiting periodic variations. You can link their period to the spin period of the asteroid, and their amplitudes to its shape. I show you an example of lightcurve here.

*High-angular-resolution imaging* requires high-performance facilities. The authors used data from the Hubble Space Telescope (HST), and of 3 ground-based telescopes, equipped with adaptive optics: Gemini North, European Southern Observatory Very Large Telescope (VLT), and Keck. Adaptive optics permits to correct the images from atmospheric distortion, while the HST, as a space telescope, is not hampered by our atmosphere. In other words, our atmosphere bothers the accurate observations of such small objects.

A spectrum is the amplitude of the reflected Solar light, with respect to its wavelength. This permits to infer the composition of the surface of the body. The *high-angular-resolution spectrum* were made at the VLT, the resulting data also permitting astrometry of the smallest of the satellites, S2. These spectrum were supplemented by *near-infrared spectroscopy*, made with a dedicated facility, i.e. the SpeX spectrograph of the NASA InfraRed Telescope Facility (IRTF), based on Mauna Kea, Hawaii. Infrared is very sensitive to the temperature, this is why their observations require dedicated instruments, which need a dedicated cooling system.

Finally, *stellar occultations* consist to record the light of a star, which as some point is occulted by the asteroid you study. This is particularly interesting for a faint body, which you cannot directly observe. Such observations can be made by volunteers, who use their own telescopes. You can deduce clues on the shape, and sometimes on the presence of a satellite, from the duration of the occultation. In comparing the durations of the same occultation, recorded at different locations, you may even reconstruct the shape (actually a 2-D shape, which is projected on the celestial sphere). See here.

And from all this, you can infer the orbits of the satellites, and the composition of the primary (Camilla) and its main satellite (S1), and the spin and shape of Camilla.

## The orbits of the satellites

All of these observations permit astrometry, i.e. they give you the relative location of the satellites with respect to Camilla, at given dates. From all of these observations, you fit orbits, i.e. you numerically determine the orbits, which have the smallest distances (residuals), with the data.

This is a very tough task, given the uncertainty of the recorded positions. For that, the authors used their own genetic-based algorithm, *Genoid*, for GENetic Orbit IDentification, which relies on a metaheuristic method to minimize the residuals. Many trajectories are challenged in this iterative approach, and only the best ones are kept. These remaining trajectories, designed as *parents*, are used to generate new trajectories which improve the residuals. This algorithm has proven its efficiency for other systems, like the binary asteroid (22) Kalliope-Linus. In such cases, the observations lack of accuracy and many parameters are involved.

You can find the results below.

S/2001 (107) 1 | |
---|---|

Semimajor axis | 1247.8±3.8 km |

Eccentricity | <0.013 |

Inclination | (16.0±2.3)° |

Orbital period | 3.71234±0.00004 d |

S/2016 (107) 2 | |
---|---|

Semimajor axis | 643.8±3.9 km |

Eccentricity | ~0.18 (<0.23) |

Inclination | (27.7±21.8)° |

Orbital period | 1.376±0.016 d |

You can deduce the mass of (107) Camilla from these numbers, i.e. (1.12±0.01)x10^{19} kg. The ratio of two orbital periods probably rule out any significant mean-motion resonance between these two satellites.

## Spin and shape

The authors used their homemade algorithm *KOALA* (Knitted Occultation, Adaptive-optics, and Lightcurve Analysis) to determine the best-fit solution (once more, minimization of the residuals) for spin period, orientation of the rotation pole, and 3-D shape model, from lightcurves, adaptive optics images, and stellar occultations. And you can find the solution below:

Camilla | |
---|---|

Diameter | 254±36 km |

a | 340±36 km |

b | 249±36 km |

c | 197±36 km |

Spin period | 4.843927±0.00004 h |

This table gives two solutions for the shape: a spherical one, and an ellipsoid. In this last solution, a, b, and c are the three diameters. We can see in particular that Camilla is highly elongated. Actually a comparison between the data and this ellipsoid, named the *reference ellipsoid*, revealed two deep and circular basins at the surface of Camilla.

Moreover, a comparison of the relative magnitudes of Camilla and its two satellites, and the use of the diameter of Camilla as a reference, give an estimation of the diameters of the two satellites. These are 12.7±3.5 km for S1 and 4.0±1.2 km for S2. These numbers assume that S1 and S2 have the same albedo. This assumption is supported for S1 by the comparison of its spectrum from the one of Camilla.

## The composition of these objects

In combining the shape of Camilla with its mass, the authors deduce its density, which is 1,280±130 kg/m^{3}. This is slightly larger than water, while silicates should dominate the composition. As the authors point out, there might be some water ice in Camilla, but this pretty small density is probably due to the porosity of the asteroid.

## The study and its authors

- The study, made freely available by the authors on arXiv, thanks to them for sharing!
- The webpage of Myriam Virginia Pajuelo Cubillas, first author of the study,
- The website of Benoît Carry,
- the one of Frédéric Vachier,
- the webpage of Michaël Marsset,
- the ResearchGate profile of Jérôme Berthier,
- the one of William J. Merline,
- the one of Peter M. Tamblyn,
- the ResearchGate profile of Al Conrad,
- the webpage of Alexander Storrs,
- the ResearchGate profile of Bradley Timerson,
- the webpage of David W. Dunham,
- the ResearchGate profile of Steve Preston,
- the website of Arthur Vigan,
- the ResearchGate profile of Bin Yang,
- the one of Pierre Vernazza,
- the website of Laurent Bernasconi,
- the one of David Romeuf,
- the webpage of Raoul Behrend,
- the one of Christophe Dumas,
- the one of Jack Drummond,
- the one of Jean-Luc Margot,
- the one of Pierre Kervella,
- the one of Franck Marchis,
- and the website of Julien H. Girard.

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.