Using the hierarchical method of family identification developed by Zappala et al., the results coming from the data set of proper elements computed by Williams (about 2100 numbered + about 1200 PLS 2 asteroids) and by Milani and Knezevic (5.7 version, about 4200 asteroids) are compared. Apart from some expected discrepancies due to the different data sets and/or low accuracy of proper elements computed in peculiar dynamical zones, a good agreement was found in several cases. It follows that these high reliability families represent a sample which can be considered independent on the methods used for their proper elements computation. Therefore, they should be considered as the best candidates for detailed physical studies

Cellino, Alberto

Farinella, Paolo

Zappala, Vincenzo

English

NASA Technical Reports Server

Asteroids, Comets, Meteors 1991, pp. 675-678
A COMPARISON BETWEEN FAMILIES OBTAINED FROM DIFFERENT PROPER
ELEMENTS
V. Zappa]A I, A. Cellino I, P. Farinella 2
x Osservatorio Astronomico di Torino, Italy
2 Dipartimento di Matematica, UniversitA di Pisa, Italy
Abstract. Using the hierarchical method of family identification developed by Zappal_ et al. [Astron.
J., 100, 2030 (1990)] we compare the results coming from the data set of proper elements computed
by Williams (about 2100 numbered + about 1200 PLS II asteroids) and by Milani and Kneievi_ (5.7
version, about 4200 asteroids). Apart from some expected discrepancies due to the different data sets
and/or low accuracy of proper elements computed in peculiar dynamical zones, a good agreement was
found in several cases. It follows that these high reliability families represent a sample which can be
considered independent on the methods used for their proper elements computation. Therefore, they
should be considered as the best candidates for detailed physical studies.
It is well known that asteroid dynamical falni]Jes are a fascinating, but until recently puzzling subject.
In fact, in spite of a noticeable effort carried out for several years by many authors, it has not long been
possible to achieve a satisfactory agreement among the different proposed family lists. In particular,
substantial disagreement exists for what concerns both the amount of existing families and the number
and identity of their members. A detailed review of this subject can be found in Valsecchi et al. (1989).
Moreover, a review by Chapman et al. (1989) emphasizes another difficulty, in a physical sense,
affecting many of the proposed families: in particular, only a few of them (mainly the most populous ones)
are self-consistent from a cosmochenfical point of view. In other words, most of the smaller clusterings
identified in the space of proper elements by different authors, are composed by asteroids whose taxonomic
types conflict with each other, in the sense that no plausible process of collisional origin from a single
plausible parent body could explain the observed variety of taxonomic types of their supposed members.
On the other hand, the most recent advances in the studies of the overall collisional evolution of
the asteroid belt (see, for a review, Davis et al., 1989) require some reliable estimates of the number
and physical properties of the presently existing dynamical families, since they can provide some crucial
constraints for the general evolutionary models proposed. At the same time, a knowledge of the main
physical properties of the family members could shed some fight on the general problem of the physics
of catastrophic impacts and their collisional outcomes.
There are many reasons for the inconsistencies found in the past among the different proposed family
lists. The main reasons are: different data sets used; different adopted methods of proper element
computations; different procedures for clustering identification.
Recently, Zappal_ et al. (1990) have carried out a new analysis, in which they used the biggest data
set (about 4100 objects) ever analyzed for family identification purposes, as well as a new identification
method. For what concerns the adopted proper elements, they used those computed by Milani and
Kneievi_ (1990), on the basis of a second-order, forth degree secular perturbation theory.
The new identification method is based on hierarchical clustering techniques of multivariate data
analysis. The basic idea is to compute all the mutual distances among the analyzed objects, on the basis
of some definition of a metric in the proper elements space (in particular, the adopted distance definition
is related to the incremental velocity needed for orbital change after ejection from a fragmented parent
body). In this way, it is possible to build some dendrograms, containing all necessary information about
the existing clusterings of objects, having mutual distances smalhr than any given value d. They are then
compared with analogous dendrograms obtained for fictitious populations of quasbrandomly generated
objects, in order to find a crytical value of distance ("quasi-random level") for which the chsterings found
cannot be due to pure chance. These clusterings are defined as asteroid families in the gappalg et al.
(1990) paper.
https://ntrs.nasa.gov/search.jsp?R=19930010081 2020-03-17T08:17:41+00:00Z
676 Asteroids. Comets, Meteors 1991
• _i_ _-_
.:-: .... z:: ::, .
In this way a new list of 21 families has been obtained, which includes , i_n _dd_ion to the -we_ known
and already firmly estal_lished Eos, Themis and Koronis fan_'flies, at least i2-odaer___c_li_pear :
to be highly reliable. These results must be compared with those obtained by other studies on the same
subject available in the literature. In particular, one of the outstanding previou s analyses iS that carried
out by Williams (1979), who used his own theory of proper _ele_pents computation (Williams 1969), and
analyzed a large data set of 1796 numbered objects, in addition to a sample of the best orbits from
the PLS survey. By applying a subjective method of clustering identification, Williams recognized 104
families. More recently, Williams (i989) hM redone his analysisinc!uding a largersample of numbered
asteroids (2065), and found again a large number of families:i _7.-='_::_::-_-__:?_-_-__ :
It is interesting to infer whether the discrepancies between the WiUiams (1979, 1989) an_th_Zappal_
et nl. (1990) family lists are mostly due to the different identification methods used, or to the _nt
sets of adopted proper _ements_ ÷ --b _ _-:_-_-- :: __ _ :::=_: _:_-- _ _:-_:_:=_:-::_?_;_::_--_ :- ....
An obvious procedure to discriminate among these two possibilities is to apply the same method of
clustering identification to the two different samples of asteroid proper elements, in_this_paper, we present
the results of such an exercise, in which the Zappalh et al. (1990) identification method has been-applied
separately to the extended data set (4258 objects) of the 5.7 version of_teroid proper elements by Milani
and Kne_evi_, as well as t O the Williams (1989) proper elements lists, including 1968 numbered objects
and 1227 PLSs. ...... :: .... :: : ;:._=L .... - =--::: - ! ::--
The overall results of the present analysis are shown in Table 1, which shows,_ respe_tiveiy: ihe ,tliober . :
of resulting clusterings found using the Williams data set, the corresponding number of clusterings c_ing
" "' St ' " " _ ........from the Milani and Kne_.ewc data set, and the number of "intersection clu ermgs , Le., those _'ho are
found to be composed (at least partially) by the same objects in both the samp!cs. Table 1 shows -
separately the cases corresponding to clusterings composed by a number N > 5 and N > 1Oof objects.
As can be seen, the agreement is quite good, mainly in the case of the most populous (N > 10) groupings.
This can indicate that the global differences between the Williams (1979, 1989) and the Zappalh et al.
(1990) classifications are probably mostly due to the different adopted methods of clustering identification,
than to a substantial difference of the proper elements data sets.
Table 2 shows in a more detailed way the results of the present analysis for what concerns the
clusterings having N ___10 members. In particular, for each of them, the number of Williams numbered
objects (complete down to the number 2065), the number of PLS objects in the Williams data set,
the number of the corresponding Milani and Kne_.evi6 numbered asteroids (ire. , thgse having number <
2065), and the Milani and Kne_evi_ numbered objects beyond the 2065 are shown, respectively, as well
as the number of common objects present in both classifications. It is evident that the agreement can
be considered quite good, in the sense that for these clusterings the intersection is generally very cl_
to the number of common objects having number < 2065, which is the maximum possible intersection
of the tWO data sets. The next step of this analysis will be obviously to compute Mflani and Kne_evi_
proper elements for the PLS asteroids having the best determined osculating elements, and to use them
-Table I
Wi]lianls
N_ 5 26
N > 10 15
20
14
Intersection
16
14
- -:5 :. .:: !: ::-::- : :: •
h
|
Asteroids, Comets, Meteors 1991 677
Table II
Family
[Zappal& et al. (1990)] list
Williams
Num. PLS
31 + 35 4 5
32 5 3
MK 57
Num H.Num.
5 12
9 32
33 4 29 2 21
41 17 9 25 77
44
45
46
48
8 7
14 2
7 5
5 5
54 2951
8 12
1183(*)
135(*)
808(*)
17 21
6 14
3 2O
54 101
Intersection remarks
Vesta
5 F-type
2
16 Eunomia
13
54
61 89 9 80 i27 79
71 75 38 72 165 71
3 10 2 12 1
1 16 1
33 4
1 18
4 7
Adeona (Alexandra)
Maria
Koronis
Eos
Themi_
Hertha
(*) Families not found in the Zappal£ et al. (1990) paper, due to the smaller data set used with respect
to the present analysis. Here, they are identified by their least-numbered asteroid.
for carrying out a new updated list of asteroid dynamical fanlilies (Zappalg et al., in preparation).
Table 1 shows that the method for clustering identification by Zappal£ et al. (1990), even in the case
of smaller permitted clusterings, can allow us to identify less than 30 "families" by making use of the
Williams' data set. This number has to be compared with the high number of families found by Williams
(117) using the same data set. This discrepancy can be explained, in our opinion, if we admit that the
Williams' cryterion of family identification was too liberal.
Figure 1 shows a general tentative classification of asteroid families; for a specific discussion of this
subject, see the Farinella et al. paper published elsewhere in the present book. The figure shows a typical
stalactite diagram for the asteroids having proper orbital semiaxes ranging between 2.500 and 2.825 AU
(corresponding, respectively, to the 1/3 and the 2/5 mean motion resonances with Jupiter). The stalactite
diagram shows, for different levels of the distance, the resulting clusterings of objects. The width of a
stalactite at each level is given by the number of objects belonging to the clustering at that distance level.
The dashed level is the "quasi-random level", or the distance level under which no clusterings are found
in the case of fictitious populations of quasi-randomly generated objects (for a detailed explanation of
this, see the Zappalg et al., 1990 paper).
As can be seen in the Figure, there are fundamentally three kinds of stalactites. The type II is sharp
and deep, and corresponds to the families which are well defined and have been found by both Williams
(1979, 1989) and Zappal£ et al. (1990), with a large intersection of common objects. Type III are less
sharp, and their members grow gradually as long as the distance level increases, so that the level at which
one "cuts" the stalactite in order to define the fanfily membership is crucial. Numerical simulations (see
Bendjoya et al. in this book) show that in such cases one has to make a choice between two main possi-
bilities: (1) to cut the stalactite at a low level, losing probably a significant anmunt of family members;
this is in general the choice performed in the gappal£ et al. (1990) paper. (2) to be "liberal", cutting the
678 Asteroids, Comets. Meteors 1991
j_
m
stalactite at higher levels, but taking into account that in this way a very large percentage of interlopers
can be included in the assumed family; this has been generally done by Williams (1979, 1989). Finally,
type IV stalactites are those that do not reach at present the rank of possible families On the basis of the
Zappalh et al. (1990) cryterion. Instead, they have often been considered as real families by Williams
(1979, 1989).
References.
Chapman C. R., Paolicchi P., gappalg V., Binzel R. P., and Bell J. F. (1989) Asteroids families: physical
properties and evolution. In Asteroids II (R. P. Binzel, T. Gehrels, and M. Shapley Matthews, eds.), pp.
386-415. University of Arizona Press, Tucson: _
Davis D. R., Weidenschilling S. 9., Farinella P., Paolicchi P., and Binzel R. P. (1989) Asteroids ¢0Llisional
history: effects on sizes and spins. In .Asteroids !I (R. P. Binzel, T. Gehrels, and M. Shapley Matthews,
eds.), pp. 805-826. University of Arizona Press, Tucson.
Milani A., and Kneievi¢ g. (1990) Secular perturbation theory and computation of asteroid proper ele-
ments. C.elestial Mechauics, 49, 247-411.
Valsecchi G., Carusi A., Kneievi_ Z., Kresgk L, and Williams ]. G. (1989) Identification of asteroid dy-
namical families. In Asteroids I[ (R. P. Binzel, T. Gehrels, and M. Shapley Matthews, eds.), pp. 368-385.
University of Arizona Press, Tucson.
Williams J. G. (1969) Secular perturbation in the Solar System. Ph. D. Thesis, University of California,
Los Angeles. : _ ...... _ =
Williams J. G. (1979) Proper elements and family memberships of the asteroids. In Asteroids (T. Gehrels,
ed.), pp. 1040-1063. University of Arizona Press, Tucson.
Williams J. G. (1989) Proper elements and family memberships. In Asteroids II (R. P. Binzel, T. Gehrels,
and M. Shaphy Matthews, eds.), pp. 1034-i072. University of Aiizona Piess, Tucson.
Zappalg V., Cellino A., Farinella P., and Kneievi_ Z. (1990) Asteroid families. I. Identification by hier-
archical clustering and reliability assessment. Astron. J., 10_O0,2030-2046.
Figure 1
100
10 objects
xf< /
type III II II
J
!
S
=
=


A comparison between families obtained from different proper elements

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server