Forming Binary Near-Earth Asteroids From Tidal Disruptions

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Figure 2.1: Progenitor initial parameters of the reciprocal of elongation (c/a) and normalizedangular spin frequency (ω/ √ 2πGρ) are plotted as points. (solid line) This iscompared with the limiting curve for a cohesionless granular proloid with friction angleφ = 40 ◦ (Holsapple 2001; Richardson et al. 2005). (dashed line) The solutions for Jacobiand Maclaurin sequences representing theoretical axis ratios for rotating fluids.due to the small contribution rotation actually makes to tidal disruption at slower spins(Richardson et al. 1998).The 3 h spin rate simulations were only carried out for progenitors with an elongationof 1.0 and 1.25. Comparison to Richardson et al. (2005), as well as separate tests, indicatethat bodies with elongation of 1.5 or greater would be unstable at a 3 h spin rate, thus29
shedding mass and distorting prior to encountering the tidal forces of Earth (Fig. 2.1).The subset of results for 3 h will be presented independent of the bulk of the studies.The progenitors used in this work are all below the limit for cohesionless granularproloids with friction angle φ = 40 ◦ (Holsapple 2001). This limit, verified by Richardsonet al. (2005) as a rotational stability limit for numerical models of rubble piles, differsfrom the Maclaurin/Jacobi limits for fluid bodies (essentially a sequence of allowed equilibriumshapes). The Maclaurin/Jacobi sequence can be derived analytically and providesa useful fiducial for comparing less idealized models. For example Guibout & Scheeres(2003) determined that when a body is spinning beyond the Jacobi limit, the flow of materialon the surface of the body is towards the equator, whereas below the limit, the flowis towards the poles.2.2.3 Tidal encounters and initial conditionsThe hyperbolic encounters asteroids have with planets can be described by the close approachdistance q and the relative speed at infinity v ∞ . When v ∞ ≫ v esc (where v esc =√2GM/R), close approach is distributed with likelihood increasing as the square of thedistance. This means that an asteroid is four times more likely to encounter Earth at 4 R ♁than at 2 R ♁ . The v ∞ of these encounters depends on the bodies’ pre-encounter orbits.A distribution of expected encounter statistics was taken from a series of N-body simulationsof NEA migration from major source regions in the Main Belt (3:1 mean-motionresonance with Jupiter, ν 6 secular resonance, Mars crossers; Bottke et al. 2002, Bottke2004 personal communication; the distribution is similar to the impact speed distributionof Bottke et al. 1994). This was used to determine the expected v ∞ for the hyperbolicencounters with Earth (Fig. 2.2). Simulated parameters were selected to cover the mostfrequently occurring encounters and those previously shown to create very disruptive encounterslikely to form binaries, all sampled at a frequency to balance detail with compu-30
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 and 40: Chapter 2Formation of Binary Astero
Page 41: ∼ 60%, making a bulk density of
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
Page 97 and 98:
asteroids in the Main Belt is suffi
Page 99 and 100:
Figure 4.2: Percent of surviving NE
Page 101 and 102:
4.1.3 Binary evolutionBasic stabili
Page 103 and 104:
Table 4.1.Lifetimes for binary NEAs
Page 105 and 106:
which means it should have a critic
Page 107 and 108:
Figure 4.4: The total number of bin
Page 109 and 110:
the original eccentricity distribut
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Figure 4.6: Properties of the binar
Page 113 and 114:
Figure 4.8: Binary percentage for m
Page 115 and 116:
Figure 4.9: Effects of tidal evolut
Page 117 and 118:
quickly altered, or involved in bin
Page 119 and 120:
tidal disruption. However, the impl
Page 121 and 122:
Chapter 5ConclusionsA general concl
Page 123 and 124:
small additions to the angular mome
Page 125 and 126:
cently this large pool of observers
Page 127 and 128:
differences in results when a lower
Page 129 and 130:
Table A.1.Number of binaries produc
Page 131 and 132:
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.,
Page 139 and 140:
Storrs, A. D., Close, L. M., & Mena
Page 141 and 142:
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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