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The Centaur object (11990) Chariklo
The Centaur object (10199) Chariklo was discovered in 1997 and it is the largest known Centaur with an equivalent radius of 119 km (Fornasier et al., 2014). Chariklo showed a sustained decrease in its brightness of about 0.6 magnitudes between its discovery and 2008 (Belskaya et al., 2010). In the same time period, the absorption feature at 1.5 and 2 µm in its spectrum revealed the presence of water ice (Brown & Koresko, 1998; Brown, 2000; Dotto et al., 2003), with the subsequent disappearance of the water ice feature in the following years (Guilbert et al., 2009).
To explain this intriguing behavior, Guilbert-Lepoutre (2011) proposed a thermophysical model where Chariklo experiences cometary activity. How-ever, no cometary activity has been detected so far around Chariklo by direct imaging and an upper limit for the dust production rate has been estimated in 2.5 kg s−1 (Guilbert et al., 2009; Fornasier et al., 2014). Simi-larly, no gas emission has been detected so far around Chariklo. Search for CO emission puts an upper limit of ∼1028 mol s−1 at heliocentric distance of 13.5 au (Bockelee-Morvan et al., 2001). The increased sensitivity of the Atacama Large Millimeter Array (ALMA) will detect fainter CO emission or put tighter upper limits (see Appendix B)).
An alternative explanation was given for these observational features after the discovery of rings around Chariklo. The stellar occultation by Chariklo in 2013 revealed the presence of a ∼400 km radius ring system. The observation of this occultation involved about a dozen of observation sites spread in South-America from small 40 cm telescopes up to 1.5 m telescopes (including a station near Santiago de Chile, from which I contributed to the ring discovery (Braga-Ribas et al., 2014b)). The higher signal to noise ratio observations at the 1.5-m Danish tele-scope actually revealed two rings at ingress and egress (ie before and after the occultation by Chariklo’s main body). Several other stations detected the rings. These detections, even unresolved, helped to constraint the orien-tation and size of the system. The observations fitted well to two concentric and circular rings of radius 390.6 km and 400.3 km respectively.
After the reappearance of the water ice features in 2013 and with the ring model deduced from stellar occultations, the photometric and spectrometric behavior of Chariklo was consistently explained by the changing orientation of icy rings as seen from Earth. Under the assumption of a spherical body, the reflectivity of the rings was found to be ∼ 9 %, while a spheroidal body lowered the estimate to ∼ 6 % (Duffard et al., 2014; Braga-Ribas et al., 2014b) that compares to Chariklo’s dark surface (geometric albedo near 4%). This will be discussed again on Chapter 3.
Chariklo’s ring formation is not yet understood, but some mechanisms have been proposed. Rings can form around a differentiated Centaur object after close encounter with giant planets (Hyodo et al., 2016). While this favors the formation of Chariklo’s ring during its Centaur stage (before its migration from the transneptunian region), close encounter of Centaurs with giant planet are unlikely (Wood et al., 2017). For Melita et al. (2017), the formation of rings after a collision is unlikely during the lifetime of Chariklo as a Centaur and is more likely in the primordial transneptunian belt where collisions were more frequent. Finally, Chariklo’s rings are stable under perturbations by planetary encounters, suggesting that rings around Centaurs may be a common feature if an efficient ring formation mechanism exist (Araujo et al., 2016).
Conversion factor and read-out noise
Both cameras were tested to determine the conversion factor g and read-out noise (RON) for different configurations. The factor g gives the conversion between the number of electrons e− recorded by the camera into digital counts, or Analog-Digital Units (ADUs), in the recorded image. The factor g is expressed in electrons per ADU (e−/ADU). This basic quantity is used below to express the RON in comparable units (i.e. e− ) so the performances of both cameras can be consistently compared. Knowing g, it is possible to estimate the SNR given a star magnitude, a telescope collecting area, and the sky brightness. In practice, several other conditions will determine the final SNR achieved in a particular observation. Among these are the star altitude, the star color, the moon light background, linked to its phase and angular distance from the star, the seeing, telescope shaking by wind, to name some. However, it is useful to have some quantitative way to compare the expected performances of the cameras under typical conditions.
The conversion factor g is calculated using the ’photon transfer curve’ (PTC) (Janesick, 2001) which basic steps are summarized here. The camera is illuminated by a source of white light with constant and uniform intensity. A centered squared region of each image is used and the rest of the image is discarded. This is done to take only the region with the most uniform illumination, and to avoid the so-called ’amplifier glow’ typically present in the borders of CMOS-based cameras. Images are taken with the acquisi-tion software ’Genika Astro’ by Airylab using different level of illumination, starting from no light (detector totally covered) and increasing the illumi-nation level up to the saturation of the detector. This is repeated changing the parameters of interest in each camera such as CM OSgain (respectively EMgain for the EMCCD camera) and binning factor.The tests were per-formed at room temperature of ∼20 C, keeping the detector temperature constant with the camera cooling system activated.
With the images acquired, the average signal S in units of ADU is calcu-lated. Then, the same images with same level of illumination are taken in pairs and subtracted to each other, and from the difference-image the vari-ance σdiff2 is calculated. Subtracting pairs of images eliminates the effect of pixel-to-pixel variations leaving only the photon noise. The variance in the original image is calculated as σ2 = σdiff2 /2 where it is assumed that noises add in quadrature. Then, from a plot of σ2 vs S the slope m is obtained using a linear fit. From that, the conversion factor g is: g = 1 (e ADU−1) (2.1).
CMOS camera
The CMOS camera permits to change a gain factor (CM OSgain) as well as a gamma factor. The CM OSgain have a direct impact in the amount of readout noise (see Table 2.2). On the other hand, the gamma factor introduces a non-linearity in the relation between the incident light and the signal in ADUs (see Figure 2.1). This is useful in some applications1 but obviously unwanted in the case of stellar occultations, e.g. for analyzing tenuous atmospheres or diffraction effects by airless bodies and their rings. In that case, the retrieval of physical parameters of the body under study (e.g. atmospheric density profiles or ring optical depths) are directly linked to the linearity of the device.
Stellar occultation by 2007 UK126
The TNO (229762) 2007 UK126 is a scattered disc object (SDO) with a semi major axis of 73.8 au, orbital eccentricity of 0.492, orbital period of 634.13 yr, and an inclination of 23.34. It possess a satellite but its orbit is not well determined to provide a mass value for the system (Santos-Sanz et al., 2012).
An occultation by this TNO was observed from North-America in 2014 November 15. There were seven positive detection and two negatives chords providing a well constrained elliptical fit. This is a good example of the most usual case where there is only one multi-chord occultation of an object. Given the size of the object of about 680 km, the reasonable assumption of a body in hydrostatic equilibrium was adopted (Tancredi & Favre, 2008).
For an homogeneous body in hydrostatic equilibrium, the shape can be a Maclaurin spheroid or a Jacobi ellipsoid. In this case, with only one occultation observed, only the Maclaurin possibility was analyzed. As there was no extra information of the pole position of the object, the object is assumed randomly orientated. Nonetheless, given the good constraint given by occultations chords (see Figure 3 and Table 4 in BR16), I adopted the simplification that the position angle of the pole axis was fixed and hence given by position angle of the semi minor axis of the elliptical fit. With the apparent center of the ellipse constrained by the elliptical fit, the remaining free parameter is the polar aspect angle (the angle between the polar axis and the line of sight). Then the approach is to use the apparent oblateness 0 to constrain the tridimensional shape and size under the assumption of an Maclaurin spheroid. As stated in BR16, the apparent oblateness 0 = 1 − (b0/a0) and true oblateness = 1 − (c/a) for an spheroid are related by: 0 = 1 − q cos2() + (1 − )2 sin2().
Table of contents :
1 Introduction
2 Characterization of cameras and time acquisition
2.1 Conversion factor and read-out noise
2.1.1 CMOS camera
2.1.2 EMCCD camera
2.2 Dead times
2.2.1 CMOS camera
2.2.2 Kite camera
2.3 Accuracy of time registration
2.4 Test at the sky and SNR estimation
3 Physical characterization by stellar occultations
3.1 2007 UK126 and 2003 AZ84
3.1.1 Stellar occultation by 2007 UK126
3.1.2 Stellar occultation by 2003 AZ84
3.2 Size and shape from multi-epoch stellar occultations
3.2.1 Body models
3.2.2 Bayesian approach
3.2.3 Shape and size of the Centaur object (10199) Chariklo
4 The dynamics of rings around a non-spherical body
4.1 Two simple cases of non axisymmetric potential
4.2 Lindblad resonances
4.2.1 Single-mass anomaly
4.2.2 Triaxial ellipsoid
4.2.3 Summary of the section
4.3 Corotation resonance
4.3.1 Azimuthal dependence of the corotation potential
4.3.2 Stability of the corotation fixed points
4.4 Evolution of a debris disk: Lindblad resonances
4.4.1 Torques at Lindblad resonances
4.4.2 Angular momentum deposition
4.4.3 Truncation of the disk
4.4.4 Clearing the corotation zone: time scales
4.5 Applications to Chariklo’s ring system
4.5.1 Lindblad resonances
4.5.2 Corotation resonances
4.6 Discussion
5 Conclusions
A Potential of a homogeneous triaxial ellipsoid
A.1 Axisymmetric part of the potential
A.2 Resonant terms
B Search for gas emmision from Chariklo with ALMA
C Other observations
