Bias-Corrected Analysis of the
Physical and Compositional Properties of Asteroids
A Proposal submitted to NASA's "Planetary Geology and Geophysics Program"
2 May 2002
Principal Investigator:
Clark R. Chapman
Southwest Research Institute (SwRI)
Suite 426, 1050 Walnut St.
Boulder, CO 80302
Co-Investigators:
William J. Merline (SwRI)
Alan W. Harris (JPL, Consultant)
BACKGROUND AND OBJECTIVES
We propose to derive the first bias-corrected distributions of asteroid physical/compositional attributes (the "geography" of the belt) in fifteen years. Since the late 1980s,
there has been an explosive growth in relevant astronomical data, now assembled in the Planetary
Data System (PDS) and elsewhere, and it cries out for analysis. We propose to systematically
characterize ~3000 asteroids with good physical parameters in the context of >70,000 known
asteroids with good orbits. The statistical descriptions of asteroid populations (primarily main
belt out to the Jupiter Trojans), which we propose to derive, constitute the fundamental
framework for understanding the geophysical and compositional processes through which the
asteroids formed and have since evolved. When this three-year project is done, we will have
begun to take a giant step forward -- and enabled the rest of the small-body geoscience
community to participate -- in understanding the "big picture" of asteroid formative and
collisional processes, what they are made of and how their surfaces undergo space weathering,
the nature of dynamical families, relationships to the Near-Earth Asteroids and meteorites, and
the collisional formation of projectile populations that pummel the surfaces of terrestrial planets.
This work is central to the goals of the PG&G Program (see "Programmatic Notes"
section below). Though involving astronomical data, this research cannot and will not be
supported by NASA's Planetary Astronomy (PAST) Program; a similar proposal submitted to
PAST five years ago was summarily rejected because it is analysis of existing data rather than
acquisition of new telescopic data; hence it was deemed "non-responsive" to PAST program
guidelines. We were explicitly and officially informed that PG&G is the appropriate program for
this work; we were advised to submit our proposal to PG&G, which -- after several years while
the P.I. was engaged with NEAR -- we are now hereby doing.
Introduction
Unlike an individual planet, in which geological/geophysical understanding derives from
studying heterogeneous localities, the asteroid belt is a heterogeneous ensemble of innumerable
bodies. In order to understand how asteroids formed and evolved, and how they influence other
processes (crater formation, meteorite delivery), we must study and synthesize the diversity of
their physical properties. Three decades of intensive astronomical observations (reflectance
spectra from the UV to IR, emitted radiation, and variations in such quantities with time, such as
lightcurves) have established the approximate "geography" and structure of this population of
remnant planetesimals. Two fundamental features were found: (a) their mineralogical
compositions (indicated by spectra) vary with solar distance, from S-types predominating at the
inner edge of the belt out to the Jupiter Trojans where D-types predominate; (b) their sizes
(smaller ones vastly more numerous than larger ones) can be represented by a wavy power-lawlike size distribution that bespeaks a lengthy history of catastrophic collisions.
Yet the basis exists for much more sophisticated understanding. Justice has not been
done to the vast data that have been painstakenly obtained by asteroid observers and archived in
the PDS and other data banks. Most discussions of asteroid belt structure still reference the
heliocentric variation of taxonomic (compositional) types depicted in a 13-year-old diagram in
the "Asteroids II" "Big Picture" chapter by Bell et al. (1989), based on raw data from Tholen
(1984), uncorrected for the enormous observational biases that affect asteroid data. And the
most recent determination of the main-belt size distribution (Durda et al. 1998, not updated at the
"Asteroids 2001" conference) ignores earlier evidence (discussed below) that the size-distribution
actually varies enormously between asteroids at different heliocentric distances, of different
taxonomic types, and in different families.
The observational biases that affect asteroid data are not subtle; indeed, they are
enormous. Consider observing, at opposition, two different asteroids of the same size: an S-type
asteroid (with albedo 0.20) at 2.2 AU (near the belt's inner edge) is thirty-six times brighter than a
C-type asteroid (with albedo 0.04) at 3.2 AU (near the outer edge). Given a typical power-law
size distribution, a telescopic survey to a given limiting magnitude will see more than 200 times
as many of the first type as the second, even though they are equally numerous in reality! Here is
a concrete example: as of 1988 when the "Asteroids II" book (Binzel et al., 1989) was written, it
was understood from bias corrections that the Trojan population is "comparable with that of the
main belt" (French et al., 1989); yet, there were only 150 known Trojans at that time among the
many thousands of known asteroids.
The way to understand the structure of asteroid populations -- and what we propose here
to do -- is (a) to assemble all available high-quality, systematic data on asteroid physical
properties and (b) correct it for observational selection effects, in order (c) to derive statistical
distributions of physical properties (e.g. sizes, albedos, spectral reflectances, spins) as a function
of orbital parameters and family membership. This work will permit (d) robust studies of the
variations of these distributions and correlations with each other. Only through such un-biased
statistical studies can we reliably understand the structure of the asteroid belt. We propose to
delve into some of the most vital correlations and implications for asteroid geophysics; but,
primarily, we wish to provide rich opportunities for analysis by the planetary science community
by developing a framework against which to test competing models for the origin and evolution
of the asteroids.
This will be the first comprehensive bias-corrected analysis of asteroid taxonomic types
and sizes since Zellner's (1979) study and since two preliminary/partial updates by Gradie &
Tedesco (1982) and Chapman (1987; Gradie, Chapman & Tedesco, 1989). Since the mid-1980's
2
work, the available data on physical properties has grown by several times and numbered
asteroids have grown by an order of magnitude. Furthermore, there have been enormous
advances in taxonomic classification and in identifying asteroid families, critical elements for
this work.
Bias-Corrected Studies of Belt Structure: Scientific Background
We have mentioned two fundamental traits of asteroids: (a) variation of taxonomic type
(reflecting composition) with heliocentric distance (Fig. 1) and (b) the quasi power-law size
distribution. That these should demand the highest scientific and NASA programmatic interest
was stated by COMPLEX (1980) more than two decades ago and has underpinned NASA's
interest in asteroids ever since:
Altogether, the asteroids seem to constitute an ordered assemblage of primitive planetesimals and their
fragments in which there is preserved important information about the structure of the proto-planetary
nebula and the processes that produced the planetary bodies of the solar system.
Yet such "ordering" of asteroids is much more complex than that. Consider collisional
processes, which produce families and the projectile populations that crater terrestrial planets and
which, mediated via chaotic dynamics and the Yarkovsky effect, deliver meteorites to Earth. We
now realize that there may be very different collisional outcomes from collisions involving
bodies of different sizes ranging
from solid metallic cores, to
rocky shards, to porous bodies
like Mathilde, and finally to
cohesionless rubble piles.
Furthermore, there is not a
single, ubiquitous size
distribution; it varies not only by
compositional type but from
family to family, reflecting
different degrees of collisional
processing for older and younger
families. The seemingly simple
variation of composition with
solar distance is confounded by
the fact that some asteroids are
primitive planetesimals whereas
others have been geochemically
differentiated; furthermore,
spectral clues to composition
Figure 1. Proportions of taxonomic types vary with solar
must be read through the "tinted
distance (bias-corrected analysis by Chapman, 1987).
eyeglasses" of space-weathering
processes. Finally, dynamical
data offer another dimension of complexity pertaining to asteroid geophysics: lightcurves yield
not only spin periods, shapes, and spin-axis orientations, but modern adaptive optics observations
3
have demonstrated that a significant minority of asteroids are double bodies or have satellites
(Merline et al., 2002).
We must go beyond the simplistic apparent "ordering" of the main belt and study what
order and correlations exist among all of the observable parameters, which vary over enormous
ranges. Albedos vary by a factor of 20, spins vary from minutes to months, the variety of
taxonomic types has nearly consumed the alphabet, while masses for main-belt asteroids for
which we have reasonable statistics vary by more than a factor of a million. Given the greatly
augmented data archives on physical properties and the tens of thousands of asteroids now
known, against which we can assess biases, now is the time to perform this fundamental
research.
Among the many vital issues that will be elucidated by this work, we propose to focus on
several during the final phase of our project: hypotheses for formation of families, issues
involving true non-family asteroids, variations in size distributions for different taxonomic types,
trends indicative of space weathering, and the evolutionary histories of asteroid groups that are
dynamically isolated from the main belt (e.g. Hildas and Trojans).
Bias-Corrected Analyses: Historical Background and Data Bases
Observers have spent perhaps tens of thousands of nights obtaining data relevant to
asteroid physical properties. Yet the pace of archiving the data and synthesizing it into
fundamental understanding has slowed. As we have noted, such data are subject to enormous
biases. Bright asteroids (i.e. those that are closer, larger, and/or have higher albedos) are greatly
over-represented in most data bases. On the other hand, thermal radiometric surveys, like the
Infrared Astronomical Satellite (IRAS) survey, favor low-albedo rather than high-albedo objects.
Many recent surveys have focussed on specific goals, sometimes exclusively oriented to subsets
of asteroids within particular heliocentric rings or within particular dynamical families. Hence,
from the raw data catalogs, one simply cannot infer whether apparent correlations of, e.g.,
spectral properties with, e.g., spin period or orbital inclination are real or spurious. Hence, some
of the most important insights about the structure, geophysics, and cosmochemistry of asteroids
have been obtained from studies of the de-biased statistics of asteroid data.
The earliest efforts to de-bias asteroid data related not to the physical and compositional
properties of individual asteroids but simply to their astronomically observable properties during
discovery: magnitude (apparent brightness) and orbital properties (especially a, e, and i; cf.
Kiang 1966). Such analyses have also been pursued recently, for example by Jedicke & Metcalfe
(1998) who employed Spacewatch data to infer the magnitude distributions of asteroids in three
regions of the main belt (inner, middle, outer). But Jedicke et al. did not consider the physicallyvital issue of family membership; in fact, they could not, because of the nature of Spacewatch
data (designed to discover NEO's), which -- for example -- is insensitive to differences in orbital
eccentricity of main-belt asteroids. While Jedicke et al. were aware of issues involving
taxonomic types and albedos, they concluded that "any further attempt at converting our absolute
magnitudes to sizes is not justified after careful consideration of these factors."
4
Another recent astronomical survey (the Sloan Digital Sky Survey) has provided data on
main-belt asteroids that is even coarser than that of Spacewatch, and the exhaustive statistical
analysis of SDSS data by Ivezic et al. (2001) is even less relevant to addressing the issues of
asteroid sizes and compositions that are of modern concern to small-body geoscientists and
meteoriticists. SDSS data are very insensitive to orbital parameters (errors are ±0.07 in a and
±17% in i); furthermore, one can infer from the unphysical results of Ivezic et al. concerning
NEOs that the SDSS 5-filter color data has not reliably distinguished between C/E/M type
asteroids and ordinary chondrite analogs (e.g. Q-types).
Physical property data required to meaningfully address modern issues in asteroid
geophysics and cosmochemistry must be precise enough for assignment to family membership
and for reliable taxonomic classification. The former requirement restricts us to ~70,000
multiple-opposition orbits, of which more than half are the numbered asteroids. The latter
requirement often requires either (a) crude color data plus independent albedo data or (b) good
quality vis/near-IR spectra (e.g. of the quality being obtained in the SMASS program [Xu et al.
1995; Bus & Binzel, 2002; http://smass.mit.edu/] and most other modern
spectroscopic/spectrophotometric observing programs). (In a minority of cases, lower quality
color data maps uniquely into a taxonomic type.)
The first bias-corrected analysis of asteroid colors and sizes (Chapman, Morrison, & Zellner,
1975) yielded the first fundamental understanding of the structure of the asteroid belt. It
introduced the C, S, M... "alphabet soup" taxonomy, which underlies modern analysis of asteroid
spectral data. That research first showed that the C-type (carbonaceous) asteroids are the chief
component of the main belt and that the apparently abundant S-types (silicaceous) are much less
numerous and are mostly restricted to the inner belt where -- as we were simultaneously learning
at that time -- resonance processes facilitate delivery of collisional fragments to Earth as
meteorites.
The next, and most definitive, study of asteroid physical properties from data corrected
for observational selection biases was by Zellner (1979) in the "Asteroids I" book. He studied
distributions of six taxonomic types (Bowell et al., 1978) in 15 different orbital element zones
(inner-to-outer main belt rings, the Hildas, the Trojans, several major asteroid families, etc.) and
discovered some remarkable features, some of which continue to confound us. For example the
size distribution of non-family C-types inside of 2.82 AU differs radically from the size
distribution of C-types farther out in the belt (Zellner's "C-types" included what we now call "Ptypes", but his conclusion remains valid).
Gradie and Tedesco's (1982) preliminary analysis of the compositional structure of the
asteroid belt corrected the then-still-unpublished Eight Color Asteroid Survey (ECAS) data for
observational biases, but did not consider other sources of physical data. Several years later,
Chapman (1987) worked to remove observational selection effects from a still larger, more
comprehensive sample of physical data; his preliminary results (cf. Gradie, Chapman & Tedesco,
1989, in "Asteroids II") remain the best available information concerning the distribution of
asteroid sizes and taxonomic type as a function of orbital properties, including family
membership. (His results utilized the Tholen taxonomy, augmented by S-type subgroups, and
analyzed results for 17 orbit zones). But, after 15 years, that analysis is badly obsolete. It is
5
almost shocking that no equivalent bias-corrected analysis of the structure of the asteroid belt has
been done since, despite the fact that the number of asteroids for which good physical
observations exists has perhaps tripled and the tabulation of numbered asteroids has increased by
more than an order-of-magnitude (see Table I).
Table 1. Numbers of Asteroids Available for Bias-Corrected Analysis
Year
No. with
Good Orbits
1975
1979
1982
1987
2002
~1800
2078
~2100?
3495
~70000
No. with
Good Phys. Data
82
752
656
939
~3000
Bias-Corrected Analysis Reference
Chapman, Morrison & Zellner (1975)
Zellner (1979)
Gradie & Tedesco (1982)
Chapman (1987); Gradie, Chapman & Tedesco (1989)
[THIS PROPOSAL]
In the late-80s analysis, Chapman devoted much effort to trying to sort out confusions
regarding competing lists of asteroid family memberships. Since then, there has been a
revolution in the dynamical understanding of asteroid families; not only is derivation of the
proper elements now well understood (Knezevic et al., 2002), but ~70,000 asteroid orbits are
now known well enough (D. Nesvorny, 2002) to use in compiling family membership lists,
compared with fewer than 3,400 published in "Asteroids II".
At great expense to NASA, major efforts have been made since "Asteroids II" to
assemble, review, and archive asteroid data in the PDS Small Bodies Node (PDS-SBN). The
predecessor to these tables, the Tucson Revised Index of Asteroid Data (TRIAD, Zellner, 1989b,
in "Asteroids I") had, as a primary purpose, to support bias-corrected analyses of the ensemble of
asteroids. But similar utilization was never made of the updated version of TRIAD published as
the "Asteroids II Data Base" (Tedesco, 1989) nor of the PDS archives that have been amassed
subsequently. In addition to the PDS database, which is now many years behind schedule
ingesting some new asteroid data, there are many web sites providing access to recent data and,
of course, hundreds of papers and abstracts published in the last 15 years with pertinent data.
Although it is understandable that the printed version of the forthcoming "Asteroids III" volume
(Bottke et al., 2002) cannot contain a lengthy tabulation section, it is unfortunate that an effort
wasn't made, as it was for "Asteroids II", to collate available data into a single collection of
machine-readable files. Nevertheless, we have made a preliminary attempt (see "Selection of
Data" subsection below) to identify the additional data sets that exist, or will exist in the near
future, beyond those currently in the PDS-SBN. They provide a rich basis for understanding the
asteroid belt, and we propose to exploit that data along with the tabulations in the PDS.
Objectives of this Research
We propose to perform a comprehensive bias-corrected analysis of asteroid physical
properties for asteroids from the inner edge of the main belt out to, and including, the Jupiter
Trojans. We will also consider Near Earth Asteroids (NEA's), but only on a best-effort basis at
lower priority, for several reasons: First, much effort has recently been devoted to understanding
6
the very appreciable selection biases in NEA observations (cf. Bottke et al., 2002). Second, due
to observational difficulties, the sampling of NEO physical properties is rather sparse, often of
limited quality (although with spectacular exceptions, especially thanks to radar) and of a
generally less uniform character. Finally, NEA's are a dynamically transient class, with lifetimes
typically <10 Myr: we believe that a higher priority, more fundamental need is to analyze the
structure of the more permanent populations, which may date from primordial times, and which
serve as the source region for NEA's.
As in previous analyses, a prime goal is to determine the proportions of taxonomic types
at various distances from the Sun and among other dynamically defined groupings of asteroids.
A second primary goal is to determine the size distributions (not just magnitude distributions!)
for the same dynamical groups and, separately, for the different taxonomic types. A larger
emphasis than before will be placed on ascertaining such taxonomic and size distributions for the
now well-defined asteroid families, with the goal of testing existing hypotheses for the formation
and evolution of families. Subsidiary goals involve correlating the results with other physical
and orbital properties of asteroids (e.g. spins) in order to test models for processes that have acted
on asteroids, or may be currently acting. For instance, evolution of obliquities and spin periods,
space weathering, and other processes may be a function of size, distance from the sun, orbital
inclination, family youthfulness, and so on. Correlations of parameters derived from raw data
can be confusing and misleading whereas studies based on bias-corrected statistics are more
robust.
We do not claim that, in this focused research project, we can forge a new "big picture"
understanding of asteroid evolution. But that is surely a long-term goal, not only for ourselves
but also for the whole community of asteroid and meteorite researchers. Our construction of a
new, bias-corrected framework for addressing such issues will certainly be a major step in that
direction, whether or not it immediately yields a new paradigm.
TECHNICAL APPROACH AND METHODS
Task Statement Summary
 We will assemble data on asteroid physical properties from diverse sources, assess its quality,
and determine whether and how it may be integrated with other like data.
 We will derive taxonomies for the asteroids (a crude, basic taxonomy for the largest sample of
asteroids for which we have limited information and a more refined taxonomy for a subset of
asteroids supported by more comprehensive observations).
 We will calculate bias corrections, by assessing the observational selection factors affecting
each classified object (determined from known characteristics of the observing programs, but
reverting to the basic bias against apparently fainter objects when necessary). The latest family
identifications based on proper elements calculated by A. Milani and Z. Knezevic will be utilized
as dynamical buckets within which to assess observational completeness; remaining non-family
asteroids will be divided into further dynamical zones identical (but further subdivided) to those
7
of Zellner et al. (1985). The numbers of known, good-orbit asteroids, in various magnitude bins,
in these families/zones will constitute the total population from which we will derive the
observational bias factors to multiply the numbers of classified asteroids in order to estimate their
proportions in the true population.
 We will calculate the bias corrected proportions of taxonomic types as well as size
distributions within each family or zone.
 Our final task involves correlations, analyses, and interpretations of these products in terms of
asteroid geophysics and cosmochemistry.
While this project may seem ambitious, note that we will rely on procedures and datamanagement codes, previously developed by Dr. Chapman, which still exist and require only
modest augmentation. The massive increase in data volume can readily be processed by our
computers. Within the limitations of space, we amplify on our methodologies below.
Selection of Data
Primary physical data are albedos and spectral data. The former are vital because they
dramatically affect observational completeness and, when combined with observed brightness,
yield asteroid size. But albedos also, in combination with spectral data, define an asteroid's basic
spectral reflectance, indicative of globally averaged mineralogy. Since spectral data have been
obtained in highly heterogeneous ways, we must derive more uniform spectral parameters from
the data from which we will then compute taxonomic types. While asteroids have been observed
from the far UV into radio wavelengths, the most useful data (both because the data have been
taken for the largest sample of asteroids and because they are most mineralogically diagnostic)
are (a) spectral data through the visible band to about 3.5µm (especially those with good spectral
resolution; but broader-band colors, like UBVRIJHK, are also useful) and (b) thermal-IR data
that yield albedos and hence sizes.
Previous spectral data analyzed by Chapman (1987) included 24-color spectrophotometry, ECAS, and the 52-Color Survey (see PDS-SBN: http://pdssbn.astro.umd.edu). Now there
are new spectra from many programs, most notably SMASS (with ~2,000 spectra publicly
available and counting). Other spectral data sets in the PDS-SBN include UBV color data; 3micron spectrophotometry including that of Rivkin and Lebofsky et al. (~100 spectra); some
spectra from Sawyer's thesis; the 7-color IRTF asteroid survey (~126 asteroids); and CCD spectra
of 85 asteroids by Vilas. Numerous reflectance spectra, primarily of selected asteroid families,
have been published in a series of papers by A. Doressoundiram, the late F. Migliorini, D.
Lazzaro, M. A. Barucci, E. Dotto, M. Florczak, and their colleagues. JHK colors for 56 asteroids
in three families are by Veeder et al. (1995). Specific spectral studies have been made of
asteroids beyond the main belt (e.g. spectra of 49 Hildas plus Thule by Dahlgren et al. [1997] and
spectra of 32 Trojans by Jewitt & Luu [1990]). We have used the NASA ADS Astronomy
Abstract Service to identify many more papers -- far too many to list here -- containing spectra of
one, a few, or up to a few dozen asteroids; countless additional papers (often in association with
lightcurve photometry) report UBV colors.
8
There are supplementary spectral data sets that are or will be of use in the time frame of
this research. For example tens of thousands of colors in the 2µm region are scheduled to be
available by the end of 2002 from the Two-Micron All Sky Survey ("2MASS"; Sykes et al.,
2001). I,J,K magnitudes of 1233 asteroids are available from the DENIS Survey (Baudrand et
al., 2001). We will compare our results with UV spectral data sets and with broad, non-specific
color surveys such as the SDSS, but we will not use them in our bias-corrected analysis for
reasons previously explained.
The IRAS Minor Planet Survey (IMPS) still constitutes the major source of thermal IR
data, although groundbased radiometry is superior in some particular instances. IMPS has
recently been substantially augmented and revised under the title "Supplemental IRAS Minor
Planet Survey" (Tedesco et al., 2002), which refines albedos for about 15% of objects tabulated
in IMPS and augments the sample by 24%, yielding a total of 2228 asteroids (including 69
Trojans). Additional sampling of fainter asteroids has been performed by the space-based
observatories MSX and ISO (cf. Tedesco & Desert, 2002).
Supplemental physical data bases include: the Asteroid Photometric Catalogue (APC),
which contained 8600 lightcurves of more than 1000 asteroids in the 5th update (Piironen et al.,
2001); the Harris Lightcurve Catalog of derived parameters, maintained by Alan Harris, Co-I of
this proposal, who will construct an updated compilation as part of his work on this project; the
new MIDAS mid-IR spectral program (Lim et al., 2001) and previously released IRAS Low-Res
mid-IR spectra (Walker & Cohen, 1999); and early SBN compilations of asteroid polarimetric
properties (which provide complementary estimates of albedo). Also vital for calculating bias
corrections (and an integral part of determining albedos from thermal IR surveys) are the
absolute magnitude H and slope parameter G. Current tabulations are available, for example, on
Ted Bowell's web site (ftp://ftp.lowell.edu/pub/elgb/astorb.html); but we intend to revise these
along with making estimates of errors in the quantities.
The above list of data sources is not exhaustive. At the beginning of the proposed
research project, we will more thoroughly assess the availability and character of all relevant data
sets. The data will be assembled and all information relevant to inherent observational biases
will be recorded both (a) from information in published descriptions of the observing programs
and (b) from interviews with the observers if the published descriptions are insufficiently
informative.
Synthesis of Asteroid Taxonomies
A critical element of this research is to classify each asteroid into a useful taxonomic type
or sub-type, despite the often heterogeneous nature of the data. We will follow several precepts.
First, rather than developing any new taxonomic classification, the prime taxonomy will be that
of Tholen (1984), based both on visible and near-IR spectral reflectances within the bandpasses
of ECAS and on albedo (albedo is particularly useful for separating the almost-redundant spectral
classes E, M, and P). However, many researchers (e.g. Chapman, 1987; Bus, 1999) have found it
useful to extend the Tholen taxonomy in several respects, particularly to take account of colors or
spectra at wavelengths in the 1 - 3µm region and to reflect the more subtle variations observable
within the broader classes. Here again, we will endeavor to develop a taxonomy that is
9
compatible with the new Bus "feature-based" taxonomy (itself explicitly an extension of the
Tholen taxonomy). We will add additional sub-types to account for variations seen at longer
wavelengths that are not highly correlated with the shorter wavelength data.
A major issue, given the heterogeneous data base, concerns the quality and diversity of
spectral and albedo data. Some useful but coarse colorimetric and albedo data are available for a
very large sample of asteroids; the high-quality data that permit analysis of taxonomic sub-types
are available for a much smaller sample of objects. It would be a shame to sacrifice the
mineralogical specificity of the high quality data, but also a shame to severely restrict the sample
size to just the most thoroughly observed asteroids. Accordingly, we will construct and analyze
two primary lists of taxonomic classifications: (a) all asteroids for which we can reasonably
assign a high probability of being a C, S, P/D, or "other" classification and (b) a large but
considerably smaller group for which good, more specific taxonomic classification is possible.
In both cases, following Chapman's (1987) approach, we will determine if an asteroid is uniquely
classifiable; if not, we will list all allowable types in decreasing order of probability.
It is often possible to classify asteroids even from limited data. For example, Chapman
(1987) demonstrated that approximately half of the region of (B-V)/(U-B) space occupied by
asteroids uniquely maps into one of the Tholen classes A, S, G, T, C, D, B, and F. So with just
UBV data alone, even lacking an IRAS albedo, quite a few asteroids may be uniquely classified
into the lower-precision taxonomy. Combined with even very low precision radiometry, such
limited color data will uniquely classify most asteroids. Similar approaches can be used for other
limited data sets (e.g. I,J,H,K colorimetry).
Bias Corrections
The principle behind bias correction introduced by Zellner (1979) is very straightforward.
Within each dynamical zone, each physically classified asteroid is assumed to be a random
sample of the collection of all other "known" asteroids (but without observed physical properties)
within the same zone and of the same brightness (taken to be the mean opposition magnitude).
The bias-corrected number of asteroids with a particular taxonomy within the zone is thus the
number of observed asteroids with that taxonomy multiplied by the ratio of all "known" asteroids
of that magnitude to the number of all classified asteroids of that magnitude. This assumes that
all "known" asteroids are, in fact, complete; at the faintest magnitudes, we may need to multiply
the cataloged numbers by a correction factor based on surveys of fainter asteroids...but we expect
that the large number of known asteroids (>70,000) will be sufficient to generally avoid the
necessity of applying such completion factors.
Reapplication of Zellner's approach, without change, should provide a useful bias
correction. But the approach has assumptions that were never precisely true and are less true
today. It assumes that, within each zone, the biases are random, that they are due to biases
against fainter asteroids alone, and that the relevant measure of brightness is mean opposition
magnitude. In recent years, astronomers have been blessed with more powerful equipment,
allowing studies of asteroids far from opposition and with less selection by apparent magnitude
alone. In particular, there have been many more goal-directed observing programs, especially
studies of particular families (e.g. by the Italian observers) or particular zones (e.g. the SMASSII
10
study by Bus [1999], which concentrated on 2.69 to 2.815 AU). Our adoption of many more
zones, especially those defined by family, should mitigate against many such biases.
We will study other potential biases, as well. For example, darker asteroids tend to be
farther out, thus they are observed at lower phase angles on average, which may be somewhat
counterbalanced by their steeper phase relations; such issues have not been examined previously
as a source of bias. We must also ensure that certain kinds of asteroids are not over-represented,
either directly or indirectly, by the design and execution of the various observing programs.
Determination of Distributions by Size and Taxonomic Class
Best-estimate sizes will be calculated for all classified asteroids based on IRAS (SIMPS),
other radiometric programs, or independent estimates of diameter. In the case of IRAS, we will
re-compute albedos in light of the updated values of H,G that we will develop, using the Harris &
Harris (1997) revision algorithm. Bias-corrected frequencies of asteroids as a function of
dynamical zone (e.g. family) and diameter will be assembled for each taxonomic class. From
such data, we can then construct plots analogous to those in Figs. 1 and 2, but based on this much
more comprehensive analysis of the much larger data base now available. We will assess the
statistical and systematic errors in the results. These data will constitute our core results on the
"geography" and structure of the asteroid belt, which will be a valuable framework for the
planetary science community at large.
Correlations of Asteroid Statistics and Geophysical/Cosmochemical Interpretations
Having done all of this work, we propose to begin analyzing the results in terms of
understanding the evolution of asteroid populations. No doubt, intriguing features of the plots
described above will jump out and cry out for interpretation. So we will explore some obvious,
unexpected features of the size- and orbital-distributions.
Sizes and taxonomies are not the only important physical descriptors of asteroids. We
will also correlate these derived parameters with other physical properties that have geophysical
or cosmochemical relevance. In particular, parameters derived from lightcurves like spin period
and obliquity should give us a complementary perspective about physical processes (e.g.
collisional processing) inferred from our size distributions, for example. So we will correlate our
bias-corrected size and compositional data with the lightcurve parameters (for which we also
propose to provide an updated compilation). By application to a single family, we can test via
such parameter correlations the predictions of modern hypotheses for family formation by
collisional disruption followed by dynamical dispersal.
Finally, we propose to focus our preliminary interpretive analyses of our data products in
five specific areas:
 Origin and evolution of families. What do de-biased size distributions and percentages of
asteroids of different taxonomic types within each family say about the degree of compositional
heterogeneity (vs. partial differentiation) of the parent body and degree of collisional evolution of
11
the family members? Are the numbers of anomalous objects within families consistent with
being non-family interlopers?
 Non-family asteroids. Does the heliocentric
variation in proportions of taxonomic types follow
the trends previously observed, now that all wellidentified families are excluded? (Previous studies
considered only 5 main-belt families; all other
families were lumped into zones of "non-family"
asteroids.) Does the overall size distribution of
non-family asteroids suggest that they are all
thoroughly collisionally evolved within old
families that are now dynamically dispersed, or do
they possibly reflect a size distribution more like
that of a primordial accretionary population?
 Size distributions of different taxonomic types.
As shown in Fig. 2, there are enormous differences
in the degree to which the sizes of different
taxonomic types follow quasi-power-laws (e.g. the
S- and M-types) or major departures from such
linearity (e.g. the C-types). These differences are
even more pronounced in certain heliocentric
zones. Are these consistent with published
inferences about the compositions and internal
structures of these bodies and their responses to
collisions and collisional processing? For the first
time, we will be able to address these questions
cleanly, both within individual families and for
non-family members, since the larger data base will
have enabled us to extend bias-corrected size
distributions over a greater range of sizes.
 Space weathering. Are trends in taxonomic
sub-types (especially among the S-types) with
heliocentric distance and size consistent with
models for space weathering? It has often been
noted that small S types and those toward the inner edge of the belt trend toward the appearance
of Q-types (ordinary chondrite analogs), but past studies of raw data uncorrected for
observational biases have been partially muddied by failure to distinguish the separate variations
with size and distance, and for family- and non-family asteroids.
Figure 2. Bias corrected size distributions
for different taxonomic classes (Chapman,
1987); see adjacent text.
 Groups dynamically isolated from the main belt. We will explore the possibility that asteroids
in exceptional dynamical zones beyond the main belt (e.g. the Hildas and Trojans) have had
histories markedly different from those in the main belt. Asteroids in such dynamical classes
formed in different environments, and have different dynamical longevities, physical structures,
12
and average collision velocities; such histories may result in anomalous size distributions, which
will be revealed in our bias-corrected data (such anomalies have been suspected previously).
PROGRAMMATIC NOTES: IMPACT ON ASTEROID SCIENCE AND RELEVANCE
TO NASA AND PG&G GOALS
This research addresses the fundamental attributes of asteroids, which are among the high
priority targets of past, ongoing, and contemplated NASA missions. Asteroids, as remnants of
primordial planetesimal populations, as meteorite parent bodies, and as the bodies which -- by
impact cratering -- continue to be the dominant modifier of planetary surfaces, are a central focus
of NASA's Solar System Exploration Program.
Our ultimate goals address issues central to the PG&G Program: "...synthesis, analysis,
and comparative study of data that will improve the understanding of...geophysical processes...,
the origin and evolution of the solar system...". Our analytical techniques are those traditionally
employed by astronomers, synthesizing global data for an ensemble of unresolved bodies, and
they may be unfamiliar to some geoscientists. But it is essential to address asteroid populations
this way, since spatially resolved "geological" traits of asteroids are known for only the few
visited by spacecraft. We emphasize that global data on physical traits of asteroids (taxonomic
types, sizes, lightcurve parameters) directly relate to geoscience attributes of asteroids (their
mineralogical composition and geophysical characteristics) and to their geophysical evolution
(through hypervelocity collisions, space weathering processes, and dynamical movement into
different cratering regimes) as well as their relationship to other geological objects, like
meteorites.
We must insist on the core relevance of our proposal to the PG&G Program for an
additional programmatic reason. The P.I. submitted a similar proposal in 1997 to the Planetary
Astronomy (PAST) Program, figuring that astronomical analysis of astronomical data in the
PDS-SBN was the proper role of PAST. Not true (even if it should be)! Apparently PAST has
forsaken meaningful data analysis and now requires its P.I.'s to obtain new telescopic data. Thus
the vast sums NASA has spent archiving such data in the PDS have largely gone to waste as data
languish there. Astronomers publish their obvious, apparent-at-first-glimpse "results" from their
observing runs, then rush off to spend their minimal funds on the next observing run, rarely
performing comprehensive analyses and syntheses. Thus asteroid astronomers, just like Mars
remote-sensing astronomers, are obliged to analyze and synthesize data under the PG&G
program.
Chapman's 1997 Planetary Astronomy proposal to analyze bias-corrected statistics of
asteroids was summarily rejected, for programmatic reasons alone, with the following comments:
"Major weakness: This proposal is not an observational task (as explicitly stated by the PI). The
Planetary Astronomy Program is directed strictly at observational tasks, so this proposal is nonresponsive to program guidelines. The Planetary Geology and Geophysics Program, which
supports tasks for analysis of data, is a suitable place for this task." The Review Panel's
Summary Statement also included the following "Suggestion for the Proposer": "Submit
13
proposal to Planetary Geology and Geophysics Program or other program for which data analysis
is within scope."
We fervently hope -- with this firm, official statement from the NASA review process -that the PG&G Panel will accept that this proposal is strictly and wholly within its core purview
and that it will not downgrade the proposal's "Relevance" to the PG&G program because of a
(false) perception that it may be relevant to PAST.
WORK PLAN, PUBLICATIONS AND DATA PRODUCTS, PERSONNEL,
EQUIPMENT, AND BUDGET NOTES
Dr. Clark R. Chapman will oversee this research and conduct much of it. He led the
original bias-corrected studies of the structure of the asteroid belt (Chapman et al., 1975), helped
develop the TRIAD data base -- the grandparent of all subsequent asteroid data bases -- which
served as the basis for the Zellner (1979) bias-corrected analysis. He also performed the biasanalysis reported in the Gradie, Chapman & Tedesco (1989) "Asteroids II" chapter on the
structure of the asteroid belt. He was also the lead author of the "Asteroids II" chapter on
physical properties of asteroid families. He is thus intimately familiar with how to perform bias
corrections to the vastly larger data base now available; indeed, he will apply the methodologies
and code, which he developed earlier, to this project.
Dr. Harris is an expert on asteroid dynamics as well as an observational astronomer
responsible for maintaining the PDS data base on asteroid lightcurves. Recently, he has been
responsible for assessing the progress of the Spaceguard Survey and analyzing all of the
observational biases that affect its discovery statistics. Dr. Harris' responsibilities in the research
proposed here involve updating H,G data with error bars and applying them to determine albedos
by the radiometric method, analyzing photometric biases (e.g. due to different phase relations for
high- and low-albedo asteroids), and evaluating sources of uncertainty in visible band spectral
data. He will also assess the correlations of physical properties derived in this program with
statistics of asteroid spin properties. Dr. Harris is currently an employee of JPL; however, by the
April 2003 start date of this work, he expects to have taken retirement from JPL or in any case to
be only part-time employed there, and will therefore be available as a private consultant to SwRI
for the amount of time committed in this proposal.
Dr. Merline, who has worked with Dr. Chapman on various small-body projects during
the past decade, is currently a very active observer of asteroids, using state-of-the-art adaptive
optics facilities and reduction techniques, at Keck, CFHT, Gemini, and HST to search for
asteroid satellites. Previously, he has developed much expertise in the calibration and
assessment of astronomical photometric and spectroscopic data and in the geophysical
interpretation of astronomical and spatially-resolved imaging data on asteroids. He has particular
expertise in the evaluation of errors, both systematic and random, in spectroscopic and imaging
data sets as well as in algorithm development and handling of large data bases. His role in this
project will be to assist in the collection, tabulation, and evaluation of the observational data
bases. Using his experience in instrumentation and observations, he will gather information on,
14
and evaluate, the observational techniques, strategies, and observational biases. He will lead the
effort on error analysis, and statistical interpretation of significance of the bias-corrected results.
We expect to assemble all of the data and refine our design of the analysis program
during the first half of the first year. The work of ingesting all of the data into the analysis
program will consume much of the remaining year. During the second year, we will derive all of
the bias-corrected statistics of asteroid distributional properties (e.g. as a function of asteroid
family membership) and begin correlating the results with other asteroid properties (e.g. spin
parameters, meteorite parent body models). During the final year, we will study additional
interrelationships of asteroid properties, test available models for the cosmochemical and
collisional evolution of the asteroids, and synthesize our results for publication in the refereed
literature. It is anticipated that publishable results on narrower aspects of the research can be
submitted before the end of the first year of research.
In addition to publication of the bias-corrected distributions and our interpretations and
synthesis, we will generate intermediate products that should be valuable to the community:
 We will prepare a comprehensive, annotated bibliography defining the entire data base that
we analyze and make it available on a web site. This will include thorough descriptions of the
data and references to publications and on-line availability. We will include the data themselves
in cases where the data are from obscure sources not readily available. This compilation will
permit anyone else to find all of the raw data themselves without repeating the time-consuming
"Selection of Data" process we propose for the beginning of our first year. The compilation will
be published on the web early during our second year.
 We will prepare a file, for submission to the PDS-SBN, of all classified asteroids employed in
our research. The file will include asteroid number, validated H,G values developed in the
analysis, best-estimate diameter, best-estimate albedo, and derived taxonomic classification in
one or both of the simpler and more refined schemes described above (including lowerprobability classifications). We will provide error estimates for tabulated values. This will be
the most comprehensive list of asteroid physical properties ever assembled and will enable users
to parse the data according to their own wishes (e.g. defining different dynamical boxes as family
definitions evolve). It will be published on the web by the end of the second year and submitted
to the PDS at that time.
This kind of analysis places rather modest demands on computing resources, so we will
require no additional equipment to support this research. We have budgeted minimal travel:
attendance by one person at one national/international meeting per year to present results
(budgeted as DPS meetings: the venues for 2 meetings are known, the third is budgeted for
Washington D.C.).
15