Forming Binary Near-Earth Asteroids From Tidal Disruptions

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2.2 Method2.2.1 SimulationsAll simulations were done using pkdgrav, a parallelized tree code designed for efficientN-body gravitational and collisional simulations (Richardson et al. 2000; Leinhardt et al.2000; Stadel 2001; Leinhardt & Richardson 2002; Richardson et al. 2005). The simulationsused a timestep of 10 −5 yr/2π, (about 50 seconds, or ∼ 2% of the dynamical timefor the particles) and all simulations were initially run for 10,000 timesteps (∼ 5.8 days).Simulations that produced binaries or systems of bound bodies were run an additional20,000 timesteps to reach a total of 30,000 timesteps (∼ 17.4 days). The collisions ofindividual particles were governed by coefficients of restitution, both normal (ε n ) andtangential (ε t ), which determine how much energy is dissipated during collisions. Thenormal coefficient of restitution, ε n , was fixed at 0.8 in these simulations, similar to previousstudies, and ε t was fixed at 1.0 (no surface friction). Previous work has shown thatε n has little effect on the outcome of a tidal disruption so long as ε n < 1.0 (Richardsonet al. 1998).2.2.2 ProgenitorsThe rubble pile models used in these simulations consist of identical rigid spheres boundto one another by gravity alone. There were five separate progenitors used in the simulations,each with different elongations: 1.0, 1.25, 1.5, 1.75, and 2.0 (here elongationis defined as e = a/c with a, b and c representing the long, intermediate and short axislength of a tri-axial ellipsoid; in our simulations, b was set to ∼ c). The bodies were allconstructed using particles with an internal density of 3.4 g cm −3 , but the bulk densityof the body would vary depending on its packing efficiency, which was usually around27
∼ 60%, making a bulk density of ∼ 2.0 g cm −3 . Each progenitor consisted of approximately1,000 particles; the exact number varied between 991 and 1021 depending on thefinal overall shape 1 . Recent work by Richardson et al. (2005) shows that the resolutionof a rubble pile simulation can have an effect on the outcome: as resolution increases, thegranular behavior becomes more fluid-like, aiding disruption. To justify our use of 1000particles, we assume the smallest building block for rubble piles in the inner solar systemis ∼150 m, based on SPH collision studies and the observed spin rate cutoff of km-sizedasteroids (Benz & Asphaug 1999; Pravec et al. 2002). With 150 m particles, a sphericalclose-packed rubble pile with 1000 particles is ∼ 3.3 km in diameter. This diameter isnearly as large as the largest observed NEA binary primary, but also has enough resolutionto model ejected fragments which may remain bound to each other, and to allowaccurate measurement of size ratios.The progenitors were given one of four rotation rates: 3, 4, 6, or 12 h periods. Largeasteroid (D > 40 km) spin rates have been shown to follow a Maxwellian distribution,but small asteroids (D < 10 km) have an excess of fast and slow rotators (Pravec et al.2002). Studies have attempted to fit the population of small asteroids with 3 differentMaxwellians, with a combination of fast, moderate, and slow rotation rates of ∼ 6.4, 11.3,and 27.5 h (Donnison & Wiper 1999). However, with the large proportion of fast-rotatingNEAs (possibly as high as 50%) observed to be primaries of binary systems, they mayhave already experienced a tidal disruption and had their spin state altered (Margot et al.2002; Scheeres et al. 2004). Our selections were made to sample fast rotators (3, 4 h), aswell as some moderate ones (6, 12 h). No spin periods longer than 12 h were simulated1 The packing algorithm uses hexagonal closest packing, which depends on a certain level of symmetryto construct bodies out of a finite number of perfect spheres. This results in variation in the number ofparticles for various shapes. Similarly, due to boundary algorithms and the finite size of the building blocks,the bulk density can vary slightly.28
Page 1 and 2: AbstractTitle of Dissertation:Formi
Page 3 and 4: Forming Binary Near-Earth Asteroids
Page 5 and 6: PrefaceMuch of the work in this dis
Page 7 and 8: AcknowledgementsI would not have ma
Page 9 and 10: 2.3 Results and Discussion . . . .
Page 11 and 12: List of Tables1.1 Binary NEA proper
Page 13 and 14: 4.8 Percentage of migrated binaries
Page 15 and 16: of the system mass M by way of Kepl
Page 17 and 18: the largest lightcurve amplitudes o
Page 19 and 20: 1.1.3 Binary Main-Belt asteroidsRec
Page 21 and 22: Lightcurve discoveriesA lightcurve
Page 23 and 24: Figure 1.1: (Top) The primary rotat
Page 25 and 26: 1.2.1 CaptureIn this scenario two a
Page 27 and 28: ever, understanding the mechanism i
Page 29 and 30: off the equator or off one end of a
Page 31 and 32: 3 Denotes a secure result with no a
Page 33 and 34: nostic.Recent results have demonstr
Page 35 and 36: another intermediate source of NEAs
Page 37 and 38: 1.5.2 Rubble pilesThe evidence for
Page 39: Chapter 2Formation of Binary Astero
Page 43 and 44: shedding mass and distorting prior
Page 45 and 46: Figure 2.3: Snapshots of a tidal di
Page 47 and 48: Figure 2.4: Normalized probability
Page 49 and 50: Figure 2.5: Normalized probability
Page 51 and 52: Figure 2.6: (a) Satellite eccentric
Page 53 and 54: various complications of measuring
Page 55 and 56: etween ω pri and L bin ), with clo
Page 57 and 58: prolate-like), the oblate-like bodi
Page 59 and 60: Figure 2.9: Plots comparing T-PROS
Page 61 and 62: Figure 2.10: Comparison of S-class
Page 63 and 64: 2.3.5 Triples and hierarchical syst
Page 65 and 66: a/R pri based on a simple conversio
Page 67 and 68: Figure 2.13: The eccentricity dampi
Page 69 and 70: Main Belt. Work by Chauvineau & Far
Page 71 and 72: (1992), with a target range of slig
Page 73 and 74: The observations were made from the
Page 75 and 76: peaked period, with a lower signifi
Page 77 and 78: and suggests that it is possibly a
Page 79 and 80: fit for the period of the lightcurv
Page 81 and 82: Table 3.2.Orbital, physical and lig
Page 83 and 84: Figure 3.2: Asteroid lightcurves.70
Page 85 and 86: Figure 3.4: Asteroid lightcurves.72
Page 87 and 88: 3.4.4 Spin and shape properties amo
Page 89 and 90: Figure 3.7: The lightcurve amplitud
Page 91 and 92:
Typically observations of eclipse o
Page 93 and 94:
Chapter 4Steady-State Model of the
Page 95 and 96:
values between 0.2-0.6. There is on
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asteroids in the Main Belt is suffi
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Figure 4.2: Percent of surviving NE
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4.1.3 Binary evolutionBasic stabili
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Table 4.1.Lifetimes for binary NEAs
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which means it should have a critic
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Figure 4.4: The total number of bin
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the original eccentricity distribut
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Figure 4.6: Properties of the binar
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Figure 4.8: Binary percentage for m
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Figure 4.9: Effects of tidal evolut
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quickly altered, or involved in bin
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tidal disruption. However, the impl
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Chapter 5ConclusionsA general concl
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small additions to the angular mome
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cently this large pool of observers
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differences in results when a lower
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Table A.1.Number of binaries produc
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Thus the reaccumulated bodies in th
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of 2.2 h observed is significantly
Page 135 and 136:
Benner, L. A. M., Nolan, M. C., Ost
Page 137 and 138:
V7.0:LCREF TAB, 35, 4Harris, A. W.,
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Storrs, A. D., Close, L. M., & Mena
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122Pravec, P., Kušnirá, P., Hicks
Page 143 and 144:
Shepard, M. K., Schlieder, J., Nola
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Forming Binary Near-Earth Asteroids From Tidal Disruptions

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