Spectroscopy of 3 Outer Solar System Small Bodies 

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The Late Heavy Bombardment

On the Moon, the Nectarian and early-Imbrium basins were formed around 3.8 to 4.1 billion years ago. Additionally, nearly all lunar impact melt breccia samples have ages between 3.8 and 4.0 Gy old (e.g., Cohen et al., 2000; Norman et al., 2006). During this time it is suspected that a spike in impacts occurred throughout the inner Solar System, potentially caused by orbital excitation due to sweeping resonances in the Main Belt resulting from planet migration. Evidence for the Late Heavy Bombardment (LHB) has also been suggested for Mercury, Mars, and Earth. It has also been argued that the LHB was simply the end of a monotonically decreasing flux of impacts from 4.5 to 4.0 Ga. They purport that the sample of lunar impact melts is highly biased and that we find no material older than 4.0 because the younger impacts erased the underlying older ones (Chapman et al., 2007). Models of the young small body population, though limited, show that the declining bombardment scenario is extremely unlikely (Bottke et al., 2007).

Effects currently shaping the Solar System

The four processes predominantly shaping the current structure of the Solar System are gravity, collisions, and the Yarkovsky and YORP effects.
• Gravity is the most important force shaping our Solar System. It was responsible for forming the minor bodies and planets through accretion, and acts as the “glue” keeping them in their solid form. It is the force keeping all bodies in orbit around the Sun and maintains the distribution present in the Solar System. Gravitional interactions are also responsible for displacing much of the mass in the original asteroid belt and Transneptunian population.
• Collisions link the original asteroid and Kuiper belts to the current one. Asteroids are thought to have originally accreted to very large sizes, from ∼100 to 1000 kilometers in diameter (Johansen et al., 2007; Cuzzi et al., 2008; Morbidelli et al., 2009a). Throughout the age of the Solar System, most bodies collided creating smaller fragments which eventually resulted in the current size distribution. Collisions affect the surfaces of all bodies in the Solar System, evidenced by the existence of impact craters on all bodies, even ones with young surfaces such as the Earth.
• The Yarkovsky Effect is a thermal radiation force that changes the semi-major axis of a small body’s orbit. The force can cause small asteroids to migrate over time into resonances which eventually excite their orbits into Mars-crossing or near-Earth orbits, thus resupplying these unstable populations. It is also responsible for the gradual dispersion of asteroid collisional families in orbital element space over time. The Yarkovsky and YORP effects are discussed in Bottke et al. (2006).
Diurnal Effect: Sunlight reaching the asteroid on the “day” side is absorbed, heating the surface, and is later reradiated as thermal energy in a different direction (the “night” side), after the body has already rotated. As the photons are radiated from the surface they take angular momentum with them, causing an uneven push to the object. For prograde rotators this pushes the body outward, increasing the semi-major axis, and the opposite is true for retrograde rotators. This effect is more important for larger bodies (100 m . D . 40 km) Seasonal Effect: Throughout an asteroids orbit, the “night” side that radiates more energy than the “day” side faces the direction of the orbital motion. The radiation emitted acts as a breaking force, slowing the motion and causing the body to drift inward (lowering the semi-major axis). This effect is more important for smaller bodies ( 1 m . D . 100 m).
• YORP: The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, similar to Yarkovsky, is driven by reflection and re-emission of sunlight. YORP controls the asteroid spin vector, rotation rate, and the rate of Yarkovsky drift. It is driven by the asymmetric shape of the body that creates a “windmill” effect. It is particularly effective for objects with diameters less than ∼10 km over 108 years and faster for smaller bodies (Rubincam, 2000).

Spectroscopy

Spectroscopy is a measure of emission or reflectance of a source. The incoming light is dispersed according to wavelength. For non-cometary Solar System bodies, the light reflecting off the surface of the body is divided by a spectrum of a solar-like star to determine the reflectance relative to that of the original light source, the Sun. If the resulting spectrum is flat, the light is reflected equally across all measured wavelengths. If the spectrum has a positive slope, more light is reflected at longer wavelengths. Localized dips in the spectrum indicate a particular material is absorbing light at that wavelength. Analyzing these absorption features provides crucial information about the composition on the surfaces of these bodies.
For asteroids, signatures at 1 and 2 microns are indicative of olivine and pyroxene. For TNOs, features at 1.5 and 2 microns are indicative of H2O. A feature at 2.15 microns reveals nitrogen, and a large array of strong absorptions in the visible and near-infrared represent methane. Reflected light penetrates only a few microns below the surface, so spectroscopy probes only the utmost surface layer. Any information about the interior can only be inferred by density measurements.

Bidirectional Reflectance Models

Interpreting a spectrum is not necessarily straightforward. Many factors need to be taken into account. The viewing geometry can affect overall reflectance levels and the overall slope. The depth probed is dependent on many factors, such as the opacity of the material, the wavelength of the light, and the grain size. As grain size increases, albedo levels decrease and absorption features widen and deepen. The relative abundances of each material is significant since some molecules are more optically active (and therefore dominate a spectrum’s signature) than others. Intimate mixtures of materials are also not necessarily linear combinations of their individual components. Temperatures affect spectra and often cause phase changes in materials such as ices. Therefore linearly combining laboratory spectra of samples taken under limited conditions cannot adequately reproduce a spectrum of a small body in space. Luckily, there are models that take into account these factors by approximating radiative transfer equations. The most commonly used spectral models include the Hapke (Hapke, 1981, 1993) and Shkuratov (Shkuratov et al., 1999) models. In this work only Hapke modeling is applied, and it is described in this section. For a full description of the theory see Hapke (1993).
Hapke theory provides an approximate solution to the radiative transfer equation that describes the
emission, absorption, and scattering of light on a nonuniform particulate surface. Exact solutions have been derived (i.e., Chandrasekhar, 1960), but other theories have either required too much computation or were too general. Hapke theory has few free parameters and is comparable with exact solutions within the accuracy of the observational measurements. Shkuratov et al. (1999) created a one-dimentional model intended particularly for understanding lunar regolith. The approximations and assumptions simplify the model making it depend on fewer variables than for Hapke (1981, 1993). Poulet et al. (2002) perform a comparison of the Hapke and Shkuratov models and find the main differences is the treatment of the phase function, which is a free parameter Hapke model but is fixed in the Shkuratov model. Also, because of the manner in which the materials are mixed, the Hapke model is a valid approximation for a wider variety of situations. For example, the Shkuratov model ignores the angle dependence of reflectance so it is not appropriate for analysis of resolved surfaces.

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Table of contents :

I Introduction and Background 
1 Background 
1.1 The Current Structure of the Solar System
1.1.1 Planets
1.1.2 Dwarf Planets
1.1.3 Comets
1.1.4 Asteroids
1.1.5 Centaurs and TNOs
1.2 Solar System Evolution
1.2.1 Solar System Formation
1.2.2 Planet Migration: The Nice Model
1.2.3 Passing Star, Companion Star, and Rogue Planet Theories
1.2.4 The Late Heavy Bombardment
1.2.5 Effects currently shaping the Solar System
1.3 The surfaces of small bodies
1.3.1 Composition
1.3.2 Surface Evolution
2 Observational Data 
2.1 Methods of investigating surface composition
2.1.1 Photometry
2.1.2 Spectroscopy
2.2 Telescopes and Instruments
2.2.1 IRTF
2.2.2 VLT
2.3 Data Reduction
2.3.1 Calibration files
2.3.2 Photometry Reduction
2.3.3 Spectroscopy Reduction
2.4 Observational Programs
3 Methods of Analysis 
3.1 Classification Methods
3.1.1 G-mode analysis
3.1.2 Principal Component Analysis
3.2 Bidirectional Reflectance Models
3.2.1 Hapke Model
3.2.2 Shkuratov Model
3.3 Space Weathering Models
3.3.1 Hapke Model
3.3.2 Brunetto Model
II The Inner Solar System 
4 Taxonomy of Asteroids 
4.1 Need for a new taxonomy
4.2 The Data
4.3 The Taxonomy
4.3.1 The end members: A, V, R, O, Q
4.3.2 The S-complex: S, Sa, Sq, Sr, Sv
4.3.3 The w-notation
4.3.4 The end members: D, K, L, T
4.3.5 C- and X- Complexes: B, C, Cb, Cg, Cgh, Ch, X, Xc, Xe, Xk
4.4 Taxonomy Web Application
4.5 IR-only taxonomy
4.6 Limits of only visible or near-IR coverage
4.6.1 Visible: The 1-micron band uncertainty
4.6.2 Near-IR: S-complex and Q-types
4.6.3 Near-IR: C- and X- complexes
4.7 Albedo Distributions among Taxonomic Classes
4.8 Conclusion
III The Outer Solar System 
5 Photometric Analysis of TNOs and Centaurs 
5.1 State of Understanding
5.2 Taxonomy of TNOs
5.3 Results
5.4 Discussion
5.4.1 26375 (1999 DE9)
5.4.2 Ixion (29878)
5.4.3 Thereus (32532)
5.4.4 47932 (2000 GN171)
5.4.5 Bienor (54598)
5.5 Conclusion
5.6 Final Color Results from the second ESO Large Program
6 Spectroscopy of 3 Outer Solar System Small Bodies 
6.1 Introduction
6.2 Modeling
6.3 Discussion
6.3.1 (52872) Okyrhoe
6.3.2 (73480) 2002 PN34
6.3.3 (90482) Orcus
6.3.4 Limits on the presence of CH4 and CO2 on Orcus
6.4 Conclusion
7 A search for Ethane on Pluto and Triton 
7.1 Background on Pluto and Triton
7.2 Introduction
7.3 Modeling
7.4 Discussion
7.5 Conclusion
7.6 Mission to Pluto: New Horizons
IV Synthesis of Research and Conclusions 
8 The surface variation of small bodies across the solar system 
8.1 The Early Solar System
8.2 Compositional trends in the Solar System today
8.2.1 Variation across the Main Asteroid Belt
8.2.2 Variation among Centaurs, in the Kuiper Belt and beyond
8.3 Water throughout the solar system
9 Comparison of systems around solar-like stars 
9.1 Evolution of Debris Disks
9.2 Formalhaut
9.3 Epsilon Eridani
9.4 Beta Pictoris
9.5 Composition of Dust Excess Emission
10 Conclusions and Perspectives 
Acknowledgments 
A Bus-DeMeo Taxonomy 
A.1 Table of Observationsa and Designations
A.2 371 Asteroid Spectra from Bus-DeMeo Taxonomy
B TNO Photometry 
B.1 Observational Circumstances
B.2 Observed Magnitudes using the V, J, H, and Ks Filters
B.3 Mean TNO Colors
C List of Publications 
C.1 Published Articles: First Author
C.2 Published Articles: Co-Author
C.3 Conference Proceedings
C.4 IAU Circulars
C.5 Invited Talks
C.6 Public Outreach
List of Tables

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