The size and spatial distribution of collisional debris from main belt asteroids is modeled over a 10 million year period. The model dust and meteoroid particles spiral toward the Sun under the action of Poynting-Robertson drag and grind down as they collide with a static background of field particles

Dermott, Stanley F.

Durda, Daniel D.

Gruen, Eberhard

Gustafson, Bo A. S.

English

NASA Technical Reports Server

Asteroids, Comets, Meteors 1991, pp. 223-226
Lunar and Planetary Institute, Houston, _ 0_ 1
COLLISIONAL AND DYNAMIC EVOLUTION OF DUST FROM THE
ASTEROID BELT
B.A.S. Gustafson 1, E. Grtin 2, S.F. Dermott 1, and D.D. Durda 1
1) Astronomy Department, University of Florida 211 SSRB, 32611 Florida, USA.
2) Max-Planck Institut ftir Kemphysik, Posffach 10 39 80, D-6900 Heidelberg 1, FRG.
ABSTRACT
The size and spatial distribution of collisional debris from main belt asteroids is modeled over
a 10 million year period. The model dust and meteoroid particles spiral toward the Sun under
the action of Poynting-Robertson drag and grind down as they collide with a static background
of field particles.
INTRODUCTION
Analysis of the solar system dust bands in the IRAS data using the SIMUL model (Dermott and
Nicholson, 1989) has established both the bands' origin in the prominent Hirayama families and
the transport of asteroidal dust to 1 AU (Dermott et al., 1992). Durda et al. (1992) show how
the production rate of 1 mm and larger debris from any one family varies stochastically over
time. The comminution or collisional break-up of smaller particles and their transport to 1 AU
is addressed in this article.
THE ASTEROID COMMINUTE EVOLUTION (ACE) MODEL
The present form of our Asteroid Comminute Evolution (ACE) model accounts for the collision
of asteroid fragments with a static background of field particles while the fragments spiral toward
the Sun under the action of Poynting-Robertson drag and radiation pressure. The combined
effects of gravitational forces due to the planets and radiation forces may be accounted for in
future models using a new secular perturbation theory by Gomes and Dermott (1992).
A body of given size and density is in a circular heliocentric orbit of given radius. A
collision breaks the body into fragments following a size distribution of the form
dN-c m- (I+I]) ,
dm
where dN is the number of fragments in the mass range m to m + din. The exponent r l usually
equals 0.83 with the largest fragment retaining 30% of the total mass (Fujiwara et al., 1977).
Conservation of mass defines the constant C. Fragments in the mass range from 10 -t2 to 101Sg
(from B-meteoroids to 4 or 5 km radius asteroids) are divided into 60 logarithmic size bins. For
computational convenience, every fragment is assumed to be homogeneous, of equal density, and
https://ntrs.nasa.gov/search.jsp?R=19930009976 2020-03-17T07:32:48+00:00Z
224 Asteroids, Comets, Meteors 1991
spherical in shape. To further reduce computational overhead while conserving mass, particles
are reassigned a mass equal to the arithmetic mean associated with its bin. Radiation pressure
instantly distorts the pre-break-up circular orbit to an ellipse with perihelion at the breakup point.
This distortion is important for small bodies and the smallest particles leave the solar system as
S-meteoroids. After break-up, particles within a given mass bin are placed in identical circular
orbits at the time averaged heliocentric distance of their orbits. Every particle bin is
characterized by the average particle mass and heliocentric distance in a two dimensional matrix.
Fragments smaller than the lower cut-off limit and any fragments on orbits beyond 5.425 AU are
assumed to escape the solar system, the accumulated mass of such 13-meteoroids is recorded.
Fragments collide with a population ofinterp_lanetary grains represented by the empirical
interplanetary flux model of Grtln et al. (1985). This distribution closely fits fluxes derived from
Pioneer 8, 9, ancl _OS-2 measurements. Th_mass distribution is observationally supported up
to approximately 100 g corresponding to meteoroids a few cmi_ radi_s: As the humber Of larger
field objects is small, their detailed distribution is not decisive to modeling over a few million
years. The number of fragments produced by particles in a given size bin in one time step is
calculated from the probability for catastrophic collisions per unit time multiplied by the time
interval and the number of particles. Average collision probabilities were used in these
simulations. In contrast, in the simulations by Durda et al. (1992) a random number generator
was used to investigate the extent of statistical fluctuations. Fragments instantly move to higher
orbits while the surviving particles lose height due to PR-drag at each time step.
RESULTS
The distribution of fragments is immediately distorted as radiation pressure expels the smallest
particles as 13-meteoroids. Dust sized particles (1 to 100 p.m in radius) are initially dispersed on
elliptic orbits and reside most of the time outside the orbit of the parent asteroid. PR-drag soon
reduces the size and eccentricity of their trajectories and the smallest particles are first to arrive
at 1 AU even though radiation pressure originally pushed them furthest out. A supply of fresh
debris is constantly produced as larger particles collide with the meteoric complex, break-up, and
produce miniature dust clouds analogous to the break-up of the asteroid. The Size and spatial
distribution changes rapidly at f'trs_ but dust below 10-Sg (10 l,tm) reach a nearly sieadydistribution at 1 AU over the first 05 years. Figure 1 shows the size distribution at 1 AU
resulting from the break-up of a 100 km radius asteroid, of 2.5 g cm "_ _nsity, near the outer
edge of the astergid belt (3 AU). Particles ranging up to approximately 10-5g (100 i.tm) arrive
at 1 AU after 10 ° years (dashed line) and alsoap_r-to reacha nearly steady=size distribution
with larger particles still arriving over the 107 year period (solid curve). The distribution of dust
from an asteroid on the inner edge of the main belt (2 AU) shown in Figure 2 confirm the overall
features shown in Figure 1 and meteoroids in the 10 .4 to 103g range appear to have reached an
equilibrium distribution. Meteoroids of 10-2g or about a millimeter arrive from 2 AU after 106
years (Figure 2) and their numbers did not change from 106 to 107 years. Intermediate size
meteoroids are destroyed and feed the dust population. _iie the compu_on_ in_ca_ that
some millimeter sized meteoroids arrive from a break-up at '3 AU their numbersi_ _small that
they are not seen in Figure 1. The dust size distribution (below 10"Sg or 100 Bin) esi_blished
over the first 106 years remains rem_ka-b_ stabie in both figures. =
Asteroids,Comets,Meteors1991 225
=
1025
i lo2o 
1016 [1010[
105
100
-12
I I I I I
Break-up at 3 AU
_"-'"_"1:"_"_':2""._._ - . _
106yr
-10 -8 -8 -4 -2
LOG( MASS ) [g]
0
Figure I. Size distribution
of collisionally evolved
astcroidaldebris at I AU,
105, 106, and 107 years
after the break-up of an
asteroidnear the outer edge
of the main belt. The
original power law size
distributionis altered as
debris collide,grind down,
and spiralin to Earth'sorbit
under the actionof PR-drag.
Fragments in the sizerange
10-5 to I0"llg (or 100 to I
_tm) reach 1 AU within the
first 10 6 years and their size
distribution then remains
remarkably stable.
Figure 2. Size distribution
at 1 AU of collisionally
evolved debris from an 1026
asteroid that broke up near
the inner edge of the _ loeo
asteroid belt. A nearly !
steady size distribution is
attained within the first [_ 1018
million years after the
break-ul,x Meteoroids in I010
the 10-'g or 1 mm size
range reach the Earth's
orbit after 10 6 years but 1°6
intermediate size particles
are ground down before 1°°
they reach the Earth.
-12
i l t l I
2""22.............. Break-up at 2 AU
_ _ _ ""-.. ....
i__ 6
i _,, lOyrs
I ,,, I I t t
-10 -0 -8 -4 -2
LOG(MASS) [Z]
226 Asteroids, Comets, Meteors 1991
These arc significant results as particles in the 10 to 100 gm size range axe thought to produce
most of the zodiacal light (R6ser and Staude, 1978). Particles in this size range are also routinely
collected in the stratosphere (Brownie, 1985) where atmospheric entry heating favors the
survival of asteroidal debris over cometary dust (Flynn, 1992). Asteroids including the major
Hirayama families may have extended associated dust populations reaching 1 AU produced as
member asteroids collide, as suggested from analysis of the IRAS solar system dust bands
(Dermott et al., 1992). Collisions with the meteoric complex generally break fragments into
smaller pieces before they reach 1 AU and alter the original size distribution but do not preclude
significant amounts of collisionally evolved asteroid dust from reaching the Earth's orbit. This
is also the size range particles to be collected by the Cosmic Dust Collection Facility (CDCF)
planned to fly on the Space Station Freedom. The CDCF might be expected to collect asteroidal
dust particles for analysis.
l
ACKNOWLEDGEMENTS
B.A.S. Gustafson acknowledges support from the Alexander Yon Humboldt Stiftung during his
stay at the Max-Planck Institut f'tir Kemphysik where this work was initiated. Partial support
from NASA Grant No. NAGW-1257 is also acknowledged.
References
Brownle¢, D.E. (1985) Cosmic dust: Collection and research. Ann, Rev. Earth. planet.
Sci., 13, pp.134-150.
Dermott S.F., and Nicholson P.D. (1989) IRAS dust bands and the origin of the zodiacal
cloud.HighlightsofAstronomy, 8,pp. 259-266. _=__ : 7
Dermott S.F.,Durda D.D., Gomes R.S.,Gustafson B.A.S.,Jayaraman S.,Xu Y.-L.,and
Nicholson P.D. (1992) The originand evolutionofthe zodiacaldusicioud. These
proceedings.
Durda D.D, Dermott S.F., and Gustafson B.A.S. Modeling of asteroidal dust production_ _
rates. These proceedings, r : -
Flynn G.J. (1992) Large micrometeorites: Atmosphenc entry survwal, relatao_ {omffinbelt
asteroids, and implication for the cometary dust flux. These_pr_:_n_'_.
Fujiwara, A., _motoG., and Tsukamot 0 A. (1977) Destruction of basaltic bodies by
high-velocity impact. Icarus, 31, pp. 277-28_-8.
Gomes R.S., and Dermott S.F. (1992). To be submitted tO Icarus
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meteoritic complex. Icarus, 62, pp. 244-272.
ROser S., and Staude H.J. (1978) The zodiacal light from 1500 A to 60 micron. Astron.
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Collisional and dynamic evolution of dust from the asteroid belt

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