THE ROTATION RATE DISTRIBUTION OF SMALL NEAR-EARTH ASTEROIDS A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Desire´e Cotto-Figueroa November 2008 c 2008 Desire´e Cotto-Figueroa. All Rights Reserved. This thesis titled THE ROTATION RATE DISTRIBUTION OF SMALL NEAR-EARTH ASTEROIDS by DESIREE´ COTTO-FIGUEROA has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Thomas S. Statler Professor of Physics and Astronomy Benjamin M. Ogles Dean, College of Arts and Sciences Abstract 3 COTTO-FIGUEROA, DESIREE,´ M.S., November 2008, Physics and Astronomy The Rotation Rate Distribution of Small Near-Earth Asteroids (101 pp.) Director of Thesis: Thomas S. Statler Rotation periods or lower limits for 34 Near-Earth Asteroids (NEAs) were ob- tained through optical light curves. Two codes were developed in order to obtain the true fraction of Fast-Rotating Asteroids (FRAs), F, using Fortran 95 and IDL. The first code models the shape of an asteroid and simulates its light curve. The second code, uses the results obtained from the observational program and the simulated light curves to obtain the probability density of F, P(F ). The observational and sta- tistical analysis indicates that the population of asteroids with D<150m is almost equally divided between fast and slow rotators, and that the majority of the popula- tion of asteroids with D>150m consists of slow-rotators. These results also indicate that selection effects have significantly influenced the currently known distribution of rotation periods of NEAs and therefore that it is not representative of the real population of NEAs. Approved: Thomas S. Statler Professor of Physics and Astronomy 4 To my husband Jos´e and our families. Acknowledgments First, I would like to acknowledge and thank my advisor, Thomas S. Statler, for all of his support and advice during the completion of this thesis. I would also like to thank the other members of my thesis defense committee, Alexander Nieman and Joseph C. Shields, for their helpful suggestions. I would also like to thank David Riethmiller for all of his hard work and contributions to this research. Furthermore I would like to thank Jess Wilhelm, Tomomi Watanabe, and Cristopher Haas for their help with the observations. A special thanks to Mangala Sharma, Kellen Murphy, Brett Ragozzine, Kyle Uckert, Sajida Khan, all of my friends and everyone else who supported or helped me in any way. Finally, I would like to thank my husband and our families for their endless love, support, and encouragement. 6 Table of Contents Page Abstract...................................... 3 Dedication..................................... 4 Acknowledgments................................. 5 ListofFigures................................... 8 ListofTables................................... 10 1 Introduction.................................. 11 1.1Near-EarthAsteroids........................... 11 1.2 The Rotation Rate Distribution of NEAs . 17 1.3TheYORPeffect............................. 23 2 ObservationalProgram............................ 28 2.1Data.................................... 28 2.2Reductions................................. 34 2.3LightCurves................................ 36 3 ModelingLightCurves............................ 39 3.1Introduction................................ 39 3.2TACO................................... 40 3.2.1 CodeDescription......................... 40 3.2.2 Gaussian Random Spheres . 41 3.2.3 BidirectionalReflectance..................... 43 3.2.4 HapkeParameters........................ 48 3.2.5 LibraryofSimulatedLightCurves............... 50 3.3SALSA................................... 56 4 ResultsandDiscussions............................ 59 4.1LightCurves................................ 59 4.2 Rotation Rate Distribution of Small NEAs . 63 4.3TruefractionofFRAs.......................... 69 4.4Discussion................................. 72 5 ConclusionsandFutureWork........................ 75 Bibliography.................................... 78 7 A Light Curves of NEAs . 84 8 List of Figures 1.1 The orbits of the three classes of NEAs: Amors, Apollos and Atens. 12 1.2 The orbits of the major planets and the location of asteroids. 16 1.3 The rubble pile asteroid 25143 Itokawa . 17 1.4 The Rotation Rate Distribution for Solar System Bodies. 18 1.5Thespinlimits............................... 20 1.6TheYarvkoskyeffect............................ 24 1.7TheYORPeffect............................. 27 1.8Radiationforces.............................. 27 2.1Anexampleofareduceddataimage................... 35 3.1Gaussianrandomspheres......................... 42 3.2Bidirectionalreflectance. ........................ 44 3.3Correctionformacroscopicroughness................... 47 3.4Uniformdistributionofpointsonasphere................ 51 3.5Object1.................................. 52 3.6LightcurveforObject1inFigure3.5.................. 52 3.7Object2.................................. 53 3.8LightcurveforObject2inFigure3.7.................. 53 3.9Object1atadifferentorientation.................... 54 3.10LightcurveforObject1inFigure3.9 ................. 54 3.11Object2atadifferentorientation.................... 55 3.12LightcurveforObject2inFigure3.11................. 55 3.13 Light curve for one single rotation of a simulated Object . 58 3.14 Light curve in Figure 3.13 after been processed with SALSA. 58 4.1 Light curve for 2008 CP . 60 4.2 Light curve for 2006 CL9. ........................ 61 4.3 Light curve for 2006 CL9 folded to the derived period. 61 4.4 Light curve for 2007 CQ5. ........................ 62 4.5 Distribution of NEAs with our results . 65 4.6 Probability density for the true fraction of FRAs . 71 A.1 Light curve for 2006 CL9. ........................ 84 A.2 Light curve for 2006 CN10......................... 85 A.3 Light curve for 2006 CY10......................... 85 A.4 Light curve for 2005 YT55......................... 86 A.5 Light curve for 2006 CL10. ........................ 86 A.6 Light curve for 2006 BN55......................... 87 A.7 Light curve for 2006 UQ17......................... 87 A.8 Light curve for 2006 PA1. ........................ 88 9 A.9 Light curve for 2006 WU29. ....................... 88 A.10 Light curve for 2006 UN216. ....................... 89 A.11 Light curve for 2006 YU1. ........................ 89 A.12 Light curve for 2007 DB61......................... 90 A.13 Light curve for 2007 CQ5. ........................ 90 A.14 Light curve for 2007 DD. 91 A.15 Light curve for 2007 DW. 91 A.16 Light curve for 2006 VC. 92 A.17 Light curve for 2006 VD13......................... 92 A.18 Light curve for 2007 CO26......................... 93 A.19 Light curve for 2007 DF8. ........................ 93 A.20 Light curve for 2007 AH12......................... 94 A.21 Light curve for 2007 DD49......................... 94 A.22 Light curve for 2007 DY40......................... 95 A.23 Light curve for 2007 DS84. ........................ 95 A.24 Light curve for 2007 EV. 96 A.25 Light curve for 2007 EF. 96 A.26 Light curve for 2007 EQ. 97 A.27 Light curve for 2007 WF55......................... 97 A.28 Light curve for 2008 AF4. ........................ 98 A.29 Light curve for 2007 PS9.......................... 98 A.30 Light curve for 2007 TU24......................... 99 A.31 Light curve for 2006 JY25. ........................ 99 A.32 Light curve for 2008 CC71......................... 100 A.33 Light curve for 2008 CP. 100 A.34 Light curve for 2008 CR116. ....................... 101 10 List of Tables 1.1 Classes of NEAs . 12 2.1 Orbital parameters of NEAs and Observational circumstances. 30 2.1 Orbital parameters of NEAs and Observational circumstances. 31 2.1 Orbital parameters of NEAs and Observational circumstances. 32 2.1 Orbital parameters of NEAs and Observational circumstances. 33 4.1 Rotation periods or lower limits for each observed NEA . 66 4.1 Rotation periods or lower limits for each observed NEA . 67 4.1 Rotation periods or lower limits for each observed NEA . 68 11 Chapter 1 Introduction 1.1 Near-Earth Asteroids Asteroids are rocky and metallic objects, left over pieces from the formation of the solar system about 4.6 billion years ago. Almost two hundred thousand asteroids have been discovered within the solar system and the vast majority is found within the main belt between the orbits of Mars and Jupiter. Near-Earth Asteroids (NEAs) are asteroids with perihelion1 distance less than 1.3 astronomical units (AU )2.There are three classes of NEAs: the Amors, the Apollos and the Atens (see Figure 1.1). NEAs are categorized into these classes according to their orbital semi-major axis and their perihelion and aphelion3 distances (see Table 1.1). The typical lifetime of a NEA is about ten million years (Gladman et al. 2000). NEAs eventually get destroyed by a collision with an inner planet, are ejected from our Solar System or end up in a Sun-grazing state. As their typical lifetime is less than the age of our Solar System, it is thought that NEAs are objects from the main belt constantly delivered to their current orbits by various mechanisms. Bottke et al. (2002) estimated that the replenishment rate from the main belt, in order to have 1The perihelion is the point in the orbit where the object is closest to the Sun. 2The mean distance from the Earth to the Sun is one astronomical unit. 1AU =1.5x1011m 3The aphelion is the point in the orbit where the object is furthest from