Icarus 158, 343–359 (2002)doi:10.1006/icar.2002.6871

Origin of the Basaltic Asteroid 1459 Magnya: A Dynamicaland Mineralogical Study of the Outer Main Belt1

T. A. Michtchenko

IAG, Universidade de Sao Paulo, Sao Paulo, SP 05508-900, BrazilE-mail: tatiana@astro.iag.usp.usp.br

D. Lazzaro

Observatorio Nacional, Rio de Janeiro, RJ 20921-400, Brazil

S. Ferraz-Mello

IAG, Universidade de Sao Paulo, Sao Paulo, SP 05508-900, Brazil

and

F. Roig

Observatorio Nacional, Rio de Janeiro, RJ 20921-400, Brazil

Received December 20, 2001; revised March 12, 2002

The recent discovery of a relatively small basaltic asteroid in theouter main belt with no apparent link to (4) Vesta raised severalhypotheses on its origin. We present the results of a dynamical andmineralogical study of the region near (1459) Magnya intendedto establish its origin. The dynamical analysis shows that the re-gion is filled with high-order two-body and three-body mean mo-tion resonances and nonlinear secular resonances, which can leadto slow chaotic diffusion. The mineralogical analysis has not iden-tified any other asteroid with a composition similar to Magnya,nor the presence of fragments that could be securely related tothe catastrophic disruption of a differentiated parent body. Thevarious scenarios for the origin of Magnya are also discussed inthe face of both the results presented here and recently publishedresults. c© 2002 Elsevier Science (USA)

Key Words: asteroids; dynamics; spectroscopy; resonances.

geochemical differentiation and resurfacing. Its composition is

1. INTRODUCTION

Asteroid (4) Vesta has been known as the unique large objectof the main belt showing a basaltic crust. This basaltic crust wasinferred by McCord et al. (1970) and confirmed in all subsequentwork (McFadden et al. 1977, Binzel et al. 1997). The presence ofthis crust demonstrates that this object has undergone extensive

1 Based on observations made with the 1.52 m telescope at the European

Southern Observatory (La Silla, Chile) under the agreement with the CNPq/Observatorio Nacional.

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also similar to that of basaltic achondrite meteorites, specificallythe eucrites, diogenites, and howardites (HED). Due to this sim-ilarity, Vesta has been the center of an intense debate over thepast years, trying to establish whether it is the parent body ofthese meteorites or not (Drake 2001).

While the global surface composition of Vesta is very similarto that of eucrites, Vesta itself was not believed to be the imme-diate source of these meteorites (Wasson and Wetherill 1979).There seemed to be no mechanism sufficiently efficient to trans-port fragments to the Earth in the time scale of the inferred cos-mic ray exposure age of these meteorites. However, since the dis-covery of near-Earth asteroids (NEA) with similar composition(Cruikshank et al. 1991, Wisniewski 1991, Hicks and Grundy1995, Hicks et al. 1996), the problem of the delivery of HEDmeteorites to Earth was partially solved: they would be frag-ments of these near-Earth asteroids. Subsequent work has beendevoted to establishing if these near-Earth asteroids could them-selves be fragments of Vesta. This hypothesis was confirmed bythe identification of a Vesta dynamical family (Williams 1989,1992, Zappala et al. 1990, 1995) and the discovery that these ob-jects have a surface composition similar to Vesta (Binzel and Xu1993, Binzel et al. 1999, Burbine et al. 2001). Dynamical workshave also shown (Migliorini et al. 1997, Marzari et al. 1996)that the 3/1 mean resonance and the ν6 secular resonance canindeed transport fragments to near-Earth orbits. The traditionalscenario is the following: Great impacts excavated the surfaceof Vesta and produced a swarm of small fragments. Part of them

0019-1035/02 $35.00c© 2002 Elsevier Science (USA)

All rights reserved.

344 MICHTCHEN

were injected into the 3/1 mean-motion resonance and the ν6

secular resonance. Both resonances pumped up the eccentric-ities of these fragments, which were thus ejected due to closeencounters with terrestrial planets. Most of these fragments felldirectly into the Sun or escaped from the Solar System, but partof them remained in near-Earth orbits. Further collisions ejectedfragments into Earth-colliding orbits, which became the basalticachondritic meteorites recovered on Earth.

However, the above scenario still has some problems that needto be addressed and solved. The first of them is that the transporttime of objects from the 3/1 and ν6 resonances to NEA orbits istoo rapid to be compatible with the cosmic ray exposure time ob-served in basaltic achondrite meteorites (Migliorini et al. 1997,Gladman et al. 1997). This problem could be partially solvedconsidering a slow dissipation of the fragments after a colli-sional breakup, such as the Yarkowsky effect (Vokrouhlicky andFarinella 1998, 2000), which would increase the time elapsedbetween the ejection from Vesta and the entrance into the res-onances. Another intriguing problem is that the spectra of themembers of Vesta dynamical family, and of asteroids in the vicin-ity of Vesta having a V-type surface composition (hereafter wewill arbitrarily use the denomination “Vestoids” for all theseasteroids), do not match exactly the spectrum of Vesta itself.Burbine and Binzel (1997) showed that the spectra of Vestoidshave a redder slope, which has been interpreted as a space weath-ering effect (Hiroi et al. 1995, Hiroi and Pieters 1998, Pieterset al. 2000) probably associated to the size of the particles inthe regolith layer (Burbine et al. 2001). Another problem in theHED and Vesta’s spectra is the presence of a small absorptionfeature at 506.5 nm, not detected on all of the Vestoids (Vilaset al. 2000, Hiroi et al. 2001).

The recent identification of a small basaltic asteroid in theouter belt, (1459) Magnya (Lazzaro et al. 2000), raised a newpossibility for the source of V-type NEAs and HED, as wellas new problems. First, the presence of a basaltic surface im-plies in an extensive geochemical differentiation and resurfac-ing but, according to our current understanding (Ruzicka et al.1997), such processes should not occur on small-size objects(recall that Magnya has a diameter of 30 km according to IRASsurvey). This suggests a catastrophic disruption of a basaltic ob-ject with a diameter similar to that of Vesta (around 500 km), withMagnya a remnant of that collisional event. However, Magnyais not related to any of the nearby dynamical families (Williams1992, Zappala et al. 1995). The nearest family identified byZappala et al. (1995) is that of (137) Meliboea. This family isclustered at a proper semimajor axis of 3.10–3.11 AU, withno apparent extension that could include (1459) Magnya, at3.15 AU. Moreover, the C-type taxonomic classification ofMeliboea (Zellner et al. 1985), interpreted to be analogous to rel-atively unheated carbonaceous chondrite material, is incompat-ible with the required thermal history to form Magnya’s basalticmaterial.

A similar problem concerning the missing Psyche family wasaddressed recently by Davis et al. (1999). (16) Psyche is an

KO ET AL.

M-type asteroid traditionally considered to be the exposed coreof a collisionally disrupted differentiated body. However, noobserved dynamical family is associated with it. According tothese authors, the missing family cannot be explained on thebasis of observational bias generated by collisional evolution.Therefore, (16) Psyche is unlikely to be related to the breakupof a differentiated body.

On the other hand, the nonexistence of the Magnya familydoes not exclude the hypothesis of the catastrophic fragmen-tation of a large basaltic body in the region near Magnya. Infact, the preliminary dynamical analysis of this region (Lazzaroet al. 2000) revealed the presence of several mean-motion res-onances, which give rise to chaotic behavior and could help todisperse such hypothetical family. However, it is not yet clear ifthe chaotic diffusion rates are sufficiently large to drive objectsout of this region over time intervals smaller than the age of theSolar System. Therefore, we decided to perform a more com-plete study of the hypothesis of the catastrophic disruption of alarge body through the dynamical and mineralogical analyses ofthe phase space region around Magnya.

This paper is structured as follows. In Section 2, we presentthe spectral analysis method, which describes the proceduresinvolved, the input data, and other important details. The dy-namical analysis of the neighboring region of Magnya, togetherwith the estimate of the diffusion time scale, is presented inSection 3. Section 4 presents the results of the simulation of ahypothetical Magnya family and its dynamical evolution over500 Myrs. The mineralogical analysis of the Magnya region isgiven in Section 5, which tries to identify other possible rem-nants of a large basaltic asteroid. Some hypotheses on the originof Magnya, and the evolution of fragments to near-Earth orbits,are discussed in the last section.

2. SPECTRAL ANALYSIS METHOD

The spectral analysis method (SAM) has already been used tostudy the asteroidal and planetary motion, showing efficiency,sensitivity, and simplicity in implementation (Lazzaro et al.2000, Michtchenko et al. 2001, Michtchenko and Ferraz-Mello2001). The method is based on the well-known properties ofpower spectra (Powell and Percival 1979) and involves twomain steps. The first one is the numerical integration of the ade-quately chosen model, with online filtering of the short-periodicterms. The second step consists of the spectral analysis of theoutput of the numerical integrations and the construction of dy-namical maps. In this section we describe the features of themethod and apply it to the study of dynamics in the outer asteroidbelt.

In order to not introduce unnecessary complexity, and alsoto minimize the computational cost, the choice of the modelrequires a careful previous analysis of the dynamical problem.This is necessary because the computing times needed for the

construction of dynamical maps are significant. To study the dy-namics in the outer asteroid belt, a reliable model is to consider

ORIGIN OF THE BASALTIC

the asteroids as massless particles and to take into account thegravitational perturbations of the four major planets only. Werecall that the perturbations due to terrestrial planets and Plutohave a negligible effect on the asteroidal motion in the outer as-teroid belt. Moreover, the indirect effects of the terrestrial planets(e.g., when their masses are added to the mass of the Sun) causeonly small shifts (of the second order in the mass ratio, roughly3 × 10−11) in the location of the asteroidal mean-motion reso-nances (Murray and Holman 1999).

The exact equations of asteroidal motion, accounting for theperturbations of the major planets, were numerically integratedusing the accurate RA15 integrator (Everhart 1985). The ini-tial conditions of the simulation were uniformly distributed inthe space of osculating orbital elements. The resolution of thedynamical map provided by SAM increases with increasingnumber of conditions on the chosen grid. However, a largenumber of initial conditions also increases the computationalcost, and a good compromise is necessary between the avail-able computational resources and the grid resolution. In thiswork, a grid of 201 × 81 initial conditions was defined in the(a,e)-plane of semi-major axis and eccentricity, within the lim-its 3.05 AU ≤ a ≤ 3.25 AU (�a = 0.001 AU) and 0.0 ≤ e ≤ 0.4(�e = 0.005), respectively. The initial inclination and angularorbital elements of the test particles were fixed at the present val-ues of Magnya at JD 2451100.5 (I ≈ 15◦). The initial positionsof the planets were chosen at the same epoch. In this way, ourgrid of initial conditions covered almost all the outer asteroid beltbetween the 9/4 and 2/1 mean-motion resonances with Jupiter.

The total time span of the simulations has been carefully cho-sen to allow the detection of the main features of the asteroidaldynamics. The numerical integrations were performed over atime interval of 1 Myr, which roughly corresponds to 200,000orbital revolutions of the asteroids. This time interval also cor-responds to about 50 whole periods of circulation of the aster-oidal perihelia and nodes. Thus, the chosen time interval waslarge enough to allow an accurate and efficient averaging of thelong-period effects, and also to detect the occurrence of bothmean-motion and secular resonances in the outer asteroid belt.Further details will be presented in Section 2.1.

The application of the digital filtering procedure is an essentialstep in the construction of dynamical maps. The typical outputof a long numerical integration consists of the time series ofosculating orbital elements, which include both short- and long-periodic terms. Since we are interested only in the long-termfeatures of the asteroidal behavior, the information about theshort-term oscillations is unnecessary. Moreover, these short-period terms generate data output that is too large and makethe identification of the long-term oscillations inefficient. Forthis reason, the time series of the asteroids’ osculating elementshave been smoothed by digital filtering, to remove the short-period oscillations (those of the order of the asteroidal orbitalperiod). The filtering procedure was implemented online with

the numerical integration as described in detail by Michtchenkoand Ferraz-Mello (1995).

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The second step of the method used is the spectral analysis ofthe output of the numerical integrations. The orbital paths of thetest particles were Fourier-transformed using the standard FFTalgorithm. We extracted the information contained in the powerspectra of the orbital elements and stored it for further construc-tion of dynamical maps, averaged dynamical maps, and deter-mination of secular resonances as described in the following.

2.1. Spectral Number and Dynamical Map

Fourier transform allows us to distinguish between regularand chaotic motion, because regular and irregular trajectoriesbehave very differently and have different kinds of transforms.

The regular trajectories are conditionally periodic, such thatany orbital element ele(t) has a time dependence of the form:

ele(t) =∑

mA m exp(2π i m νt). (1)

Here, ν is a frequency vector whose components are the inde-pendent frequencies of motion, and m is an arbitrary integervector. When the independent frequencies are constant in time,the spectral composition of the regular motion may be obtainedfrom its Fourier transform.

For any smooth function ele(t), the amplitudes A m decreaserapidly with | m|, so that the sum in (1) is dominated by a fewterms. Therefore, the spectrum of regular motion is characterizedby a countable (and generally small) number of frequency com-ponents. It consists of the lines associated to the independentfrequencies whose number is equal to the number of degreesof freedom of the dynamical system and also to those corre-sponding to higher harmonics and linear combinations of theindependent frequencies. The half-width of each line is of theorder of�ν = 1

T , where T is the time-length of integration. Then,the total integration time T defines the resolution of the Fouriertransform: the longer is T , the smaller is �ν, and the finer thedetails in the Fourier spectrum that can be distinguished. Forsufficiently large T , each spectral peak may be approximated bythe Dirac δ-function.

In the case of chaotic motion, the independent frequencies ofthe dynamical system vary with time, and the irregular trajec-tories are not conditionally periodic. The Fourier transform ofthe orbital elements is not a sum over Dirac δ-functions. Con-sequently, the power spectrum of chaotic motion is not discrete,showing broadband components. If the variation of the indepen-dent frequencies is large and fast enough to detect it over thechosen timespan T , the power spectrum yields a large amountof spectral peaks.

In Fig. 1, we illustrate the power spectra of regular and chaoticmotions. The power spectrum of the semi-major axis ofMagnya’s orbit is shown on the top panel. The bottom panelshows the power spectrum of a neighboring asteroid, (16029)

1999 DQ6, which is located close to Magnya in the space ofthe proper elements. Although both spectra seem to be similar,

346 MICHTCHEN

FIG. 1. Power spectra of the semi-major axis. Top: Magnya’s orbit obtainedover 1 Myr (spectral number N = 8). Bottom: Orbit of 16029 1999 DQ6 (spectralnumber N = 80).

the enlargement of the region around one spectral peak (zoomboxes) shows the qualitative difference between them. Indeed,the power spectrum of Magnya contains a small number of well-defined spectral lines, while the power spectrum of 1999 DQ6contains a broadband of unresolved spectral lines. In each powerspectrum, we can determine the number of peaks that are abovethe arbitrarily defined “noise,” and the value so obtained willbe called the spectral number N . In other words, the spectralnumber is the number of substantial peaks in the power spec-trum of the asteroidal semi-major axis. In this work, we consider“substantial” those peaks with an amplitude larger than 5% ofthat of the largest peak. According to this definition, the spectralnumber N corresponding to Magnya’s orbit is equal to 8. For1999 DQ6’s orbit, this number is much larger, and, in this case,we assign to the spectral number the value 80, arbitrarily definedas an upper limit of N .

The spectral number N can be used to qualify the chaoticityof asteroidal motion in the following way: small values of Ncorrespond to regular motion; large values indicate the onsetof chaos. It should be noted, however, that an orbit classifiedas regular can appear as chaotic if a larger time span is used

in the integrations. Indeed, if the diffusion rate of independent

KO ET AL.

frequencies is below the Fourier transform resolution (definedby the time span), the spectral analysis method is unable to detectchaos. In this work, the total integration times were chosen to belarge enough as to distinguish chaos generated by both two-bodymean-motion resonances and three-body resonances up to order10. Higher order resonances should appear in the dynamical mapjust by extending the integration time.

We also note that the mean-motion resonances strongly af-fect the semi-major axis variation, which justifies our choiceof the asteroidal semi-major axes as the basis for the spectralnumber calculation. On the other hand, to analyze the chaoticityintroduced by secular resonances, it would be more appropriateto use an action-like variable dependent on the eccentricity orthe inclination. Since the precession periods of the asteroidalperihelion and node are at least 1 order of magnitude largerthan the oscillation periods associated with mean-motion reso-nances, the integration time in this case should be significantlyincreased.

Once the spectral numbers N were determined for all theinitial conditions on the grid, we plot them on the plane of initialconditions using a shading scale. The calculated values of N ,in the range from 1 to 80, were coded by a gray level scale thatvaried logarithmically from white (log N = 0) to black (log N =1.9). Figure 2 shows the dynamical map of the outer main belt,

FIG. 2. Dynamical map of the outer asteroid belt. The values of the spec-tral number N , in the range from 1 to 80, are coded by gray levels that varylogarithmically from white (log N = 0) to black (log N = 1.9), and plotted onthe (a,e)-plane of initial osculating orbital elements. We used a grid of 201 × 81initial conditions, with �a = 0.001 AU and �e = 0.005. The lighter regions in-dicate regular motion, whereas the darker regions indicate chaotic motion. The

actual position of Magnya on the (a,e)-plane of initial conditions is indicatedby a plus sign.

ORIGIN OF THE BASALTIC

plotted on the plane of initial osculating (a,e). Since large valuesof N indicate the onset of chaos, the shading scale is related to thedegree of stochasticity of the initial conditions: lighter regionson the dynamical maps correspond to regular motion; darkertones indicate increasingly chaotic motion.

The domains of chaotic motion appear in Fig. 2 as black in-clined stripes of variable width, and they are associated withmean-motion resonances. There are both two-body meanmo-tion resonances with Jupiter and three-body mean-motion reso-nances with Jupiter and Saturn. The former correspond to criticalcombinations of the form mλ + mJλJ ∼ 0, and the latter ones tomλ + mJλJ + mSλS ∼ 0. Here, λ, λJ, and λS denote the meanmotions of the asteroid, Jupiter and Saturn, respectively, and m,mJ, and mS are integer. The order of the resonance is given by|m + mJ + mS| and define the width of the corresponding stripein Fig. 2. The mean-motion resonances were identified usingKepler’s third law. The main ones are labeled on the top of thegraph by the symbol mJ/m, in the case of two-body resonanceswith Jupiter, and the symbol mJ:mS:m, in the case of three-body resonances. The present position of Magnya on the (a,e)-plane of osculating initial conditions is marked by a plus sign.The large-scale chaos visible at the right-hand side of the graphis associated with the 2/1 mean-motion resonance with Jupiter.

2.2. Averaged Dynamical Map

Although the dynamical map obtained in the previous section are marked on the (a,e)-plane (left) and (a, I )-plane (right) by a

reveals the main features of the dynamics in the region under

FIG. 3. Averaged dynamical maps of the outer asteroid belt, corresponding to the grid of initial osculating elements in Fig. 2, on the (a,e)-plane (left) and onthe (a, I )-plane (right). The actual position of Magnya is indicated by a plus sign, and the location of 35 members of Meliboea family is shown by star symbols.There are three groups of the secular resonances labeled by 1, 2, and 3. The critical combinations of the frequencies of the asteroidal perihelion and node, g

plus symbol.

and s, and the planetary fundamental frequencies, g5, g6, g7, s6, and s7, are: fog + s − g5 − s7 and g + s − g6 − s6; and for group 3, g + 2g5 − 3s6, g + 2g7 −

ASTEROID 1459 MAGNYA 347

study, it suffers from limitations coming from the use of a grid inthe space of instantaneous osculating orbital elements. This factdoes not allow us, for example, to superimpose over this gridthe position of the real asteroids, because asteroidal motions inthis space present large variations. Then, in order to analyze thedistribution of the real objects in the region under study, we needto determine some kind of proper elements.

We have chosen the averaged orbital elements, defined asthe mean values of the smoothed time series resulting from thenumerical integrations, over the entire time span. By formal def-inition, the mean value of an oscillatory signal over a given timespan is provided by the amplitude of the spectral peak of fre-quency equal to 0, i.e., the term A0 in Eq. (1). Therefore, theFFT algorithm applied to the time series of the smoothed or-bital elements automatically yields the averaged values of thesemi-major axis: eccentricity and inclination. The averaged or-bital elements corresponding to each initial condition on thegrid of osculating elements can be plotted on the (a,e)- and(a, I )-planes, where a, e, and I are the averaged semi-major axis,eccentricity, and inclination, respectively. In this way, the gridof uniformly distributed osculating initial conditions is trans-formed by SAM into the maps of averaged elements, which werefer to as “averaged dynamical maps.” In Fig. 3, we present theaveraged dynamical maps of the outer asteroid belt, correspond-ing to the initial grid of Fig. 2. Figure 3 also shows the averagedelements of Magnya’s orbit, calculated in the same way. These

r group 1, g + s − g7 − s6 and g + s − g5 − s6; for group 2, g + s − g7 − s7,3s6 and g + g5 − 3s6 + g7.

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The interpretation of the averaged dynamical maps becomeseasier when preceded by some considerations about the mainfeatures of the asteroidal motion. The conditionally periodic reg-ular motion is characterized by a set of independent frequenciesthat are constant in time. The amplitudes of these frequenciesare also constant in time. In the domains of regular motion, theslight changes in the initial conditions lead to the small vari-ation of the independent frequencies and of their amplitudes.Consequently, the averaged elements suffer continuous varia-tion when the initial conditions are gradually changed. In thisway, the regions of regular motion are dominated by smoothedcurves of points in the averaged map. On the other hand, inthe case of chaotic motion, the diffusion processes cause thevariation of proper asteroidal frequencies in time, together withtheir amplitudes. Therefore, the mean values of the orbital ele-ments obtained over different time intervals will be different. De-pending on the magnitude of the chaotic process, small changesin the initial parameters can produce a large variation of theproper frequencies and averaged orbital elements. If the chosentime span and diffusion magnitude are large enough, the methodis able to detect the dispersion of the averaged orbital elements,and the domains of irregular motion are dominated by theerratic scatter of points. Finally, in the case of resonant mo-tion, the averaging makes all the resonant particles to appearat the libration centers, whereas the rest of the resonant spaceappears to be empty.

All these dynamical features can be found in the averageddynamical maps shown in Fig. 3. The regions of regular motionappear as domains of smoothed curves of points. The resonantparticles are distributed along the resonant libration centers, in-dicating the exact location of these resonances. They appear asvertical bands of different widths depending on the order of theresonance. They are labeled at the top of the graph. The mean-motion resonances overlap at eccentricities above 0.3 and giverise to chaotic motion. This region of the outer asteroid beltappears to be a continuous sea of strongly chaotic motion.

Another dynamical property reflected in the averaged dynam-ical maps is the occurrence of secular resonances in the outerasteroid belt. The features observed in Fig. 3 (left) as narrowstripes cutting the (a,e)-plane, and, in Fig. 3 (right), as largeempty bands on the (a, I )-plane, are groups of overlapping secu-lar resonances. The main ones are labeled by the correspondingcritical combination of the frequencies of the asteroidal peri-helion and node, g and s, with the fundamental frequencies ofplanetary theories, g5, g6, g7, s6, and s7 (see Section 2.3). Itshould be noted that the secular resonances do not appear in thedynamical maps of Fig. 2, because the total integration time wasnot large enough to detect the diffusive effects of the long-termacting secular resonances. On the other hand, these resonancesare visible on the averaged maps due to the effect of excitation ofthe asteroidal eccentricities and inclinations that reflects in theaveraged orbital elements. Thus, the averaged dynamical maps

indicate the exact location of the secular resonances on the spaceof the proper elements and allow the estimation of their widths.

KO ET AL.

Finally, the advantage of the averaged dynamical maps isthat the proper elements of real asteroids can be easily plot-ted over them. This is especially useful if we want to com-pare the distribution of asteroidal families with respect to theweb of resonances in the region under study. As an example,the distribution of 35 members of Meliboea family are shownin Fig. 3 (left) by star symbols. The proper elements of theseobjects were taken from the database of Milani and Knezevic(http://hamilton.dm.unipi.it/astdys), and the family was identi-fied by the hierarchical clustering method (HCM) at a cutoff levelof 110 m s−1. This family has been early identified by Zappalaet al. (1990), and it is the closest one to the present position ofMagnya. We will come back to this point in Section 4.

2.3. Proper Frequencies and Secular Resonances

The spectral analysis allows the efficient identification of themain long-term oscillations contained in the variation of theasteroidal orbit. In Fig. 4, we present the change of the mainoscillation modes in the eccentricity (top) and inclination (bot-tom), using the initial osculating semi-major axis as a para-meter. The initial values of the other orbital elements were fixedat those of Magnya. The proper frequencies of the perihelionlongitude (top) and node (bottom) are shown by large points,while their linear combinations with the fundamental frequen-cies of the planetary motion are shown by smaller points. Over

FIG. 4. The variation of the main oscillation modes in eccentricity (top)and inclination (bottom), using the initial osculating semi-major axis as a pa-rameter. The proper frequencies, g and s, are shown by large points; their linearcombinations with the planetary fundamental frequencies are shown by smallpoints. Discontinuities in the frequency evolution are associated with the pas-

sages through the mean-motion resonances. The large-scale chaos on the right-hand side is associated with the 2/1 mean motion resonance with Jupiter.

ORIGIN OF THE BASALTIC

the domains of regular motion, the value of the proper frequen-cies varies continuously when the semi-major axis is graduallyvaried. When the mean-motion resonances are approached, thefrequency evolution shows a discontinuity, characterized by theerratic scatter of values. The large-scale chaos at the right-handsides of both graphs is associated with the 2/1 mean-motionresonance with Jupiter.

It is known that the mean-motion resonances are the mainsource of chaotic behavior of the asteroids. However, any at-tempt to discuss the dynamical structure of the asteroid beltmust take into account also the secular resonances. The mainlinear secular resonances (of order 2), such as g − g5, g − g6,and s − s6, have been recognized in the asteroid belt for a longtime (Williams and Faulkner 1981). But much less attention hasbeen paid to the study of secular resonances of higher order. Toour knowledge, these resonances have only been discussed inthe work by Milani and Knezevic (1992, 1996). In the compu-tation of the asteroidal proper elements, these authors affrontedcomparatively large errors whenever a secular resonance wasencountered. This occurred not only for the asteroids actually indeep resonance (with a critical argument in a libration), but alsofor those in shallow resonance (critical argument circulating, butwith a very long period). Using their analytical algorithm, theyobtained the location in the asteroid belt of the nonlinear secularresonances up to order 4.

The nonlinear secular resonances are those associated with acritical combination of the form: m · ν ∼ 0, where m is a vec-tor of integer coefficients and ν = (g, s, g5, g6, g7, s6, s7) is avector of the fundamental frequencies. Here, g and s are the as-teroidal proper modes of the perihelion and node, respectively,and g5, g6, g7, s6, and s7 are the fundamental frequencies ofthe planetary theories. For the resonances of order 6, the criti-cal combinations contain six frequencies, that is,

∑i |mi | = 6;

moreover,∑

i mi = 0 by the D’Alembert’s rule, and the num-ber of frequencies related to the nodes (s, s6, s7) must be even.Therefore, having the values of the asteroidal proper frequenciesover the grid of initial conditions, and knowing the precise val-ues of the fundamental planetary frequencies (Nobili and Milani1989), we can calculate the location of the nonlinear secular res-onances which occur in the region under study. Using SAM, wehave identified the location of the secular resonances up to or-der 6 in the region of the phase space around Magnya. Furtherdetails are given in Section 3.

To close this section, it should be noted that the spectral analy-sis method, although powerful, suffers from the same limitationsthat characterize all methods used for detecting the chaoticity ofmotion. Their common shortcoming is the nonexistence of anexact correlation between the indicator of chaos provided by themethods and the macroscopic instability of motion. The largevalues of the spectral number N , as well as the large frequencyvariations or the short Lyapunov times, can be taken as esti-mates of robust chaos. However, once an indication of chaos is

obtained, very long-term precise integrations of the dynamicalmodel are necessary in order to assess the significance of this

ASTEROID 1459 MAGNYA 349

chaos. In this work, we have performed very long-term integra-tions over a few sets of initial conditions, and the relevant resultsare detailed in Section 3.4.

3. DYNAMICAL MAPS OF THE MAGNYA REGION

A strong observational evidence for the relatively commonoccurrence of collisional disruption events in the asteroid beltis given by the existence of several dynamical families locatedat different heliocentric distances (Zappala et al. 1995). Thebreakup hypothesis for the origin of a V-type Magnya (crustalmaterial) assumes the collisional disruption of a differentiatedparent body. This implies that a dynamical family composed bymetallic, mantle, and crustal material should be formed. How-ever, there is no observed dynamical family associated withMagnya. We can think in two different explanations for thisintriguing missing-family problem. On one hand, our currentunderstanding of the formation of dynamical families is quiteincomplete, and the present models of the internal structure ofdifferentiated asteroids could even be wrong. On the other hand,there are some dynamical mechanisms acting in the region of thehypothetical Magnya’s family that could disperse the membersof a big family over time intervals comparable to the age of theSolar System. In this way, we would not be able to identify thefamily from the presently observed orbits.

Assuming the second hypothesis, we study the dynamics inthe region around Magnya, in order to detect the possible mech-anisms responsible for the eventual erosion of Magnya fam-ily. We arbitrarily defined a “Magnya region” as the region ofthe space of asteroidal osculating orbital elements in the range3.12 AU <a <3.16 AU, 0.15<e<0.35, and 0◦< I <25◦. UsingSAM, we constructed the dynamical maps of the Magnya region,which are shown in Fig. 5. Figure 5 (top) shows the map on the(a,e)-plane of osculating initial conditions. This map was ob-tained using a 81 × 81-points grid with �a = 0.0005 AU and�e = 0.0025. The initial inclinations of the test particles wereset to the actual value of the Magnya’s inclination (I ≈ 15◦).Figure 5 (bottom) shows the (e,I )-plane obtained with a 61 ×51-points grid with �e = 0.0025 and �I = 0.5◦. The initialsemi-major axes of the test particles are equal to that of Magnya.In both figures, the initial values of the other angular elementsof the test particles were also set to those of Magnya. The oscu-lating position of Magnya is marked by a plus symbol.

Figure 6 shows the averaged dynamical map of the Magnya re-gion. The positions of real objects in the Magnya region are plot-ted on the (a,e)-plane using � symbols. The numbered asteroidsin that region were extracted from the April 2001 version of theasteroid database of Lowell Observatory (ftp://ftp.lowell.edu/pub/elgb). Averaged values of the semi-major axis and eccen-tricity of these real objects were calculated over 600,000 yearsusing the same procedure described in Section 2.2. The positionof Magnya is marked by a plus symbol.

The high-order two-body and three-body mean-motion reso-nances occurring in the Magnya region are labeled on the top of

N

of the real objects are shown by a star symbol. Two bands, BI and BII, of the

350 MICHTCHE

FIG. 5. Dynamical maps of the “Magnya region” defined in Section 3.Top: (a,e)-plane of the osculating elements (the initial inclination was fixed atthe current value of the Magnya’s inclination); Bottom: (e,I )-plane (the initialsemi-major axis was fixed at the current value of the Magnya’s semi-majoraxis). The domains of chaotic motion (dark regions) are associated with themean motion resonances and are labeled on the top panel by correspondingsymbol. The bands of the secular resonances are indicated by the symbols fromBI to BIV (see Table I). The actual position of Magnya is shown by a plus sign.

the graph. We use the notation mJ/m for two-body resonances,or mJ : mS : m for three-body resonances, with m, mJ and mS

integers. There are several of these resonances in the Magnyaregion, all of them characterized by chaotic motions. In fact,the real objects, which are presently involved in any of thesemean-motion resonances (see Fig. 6), exhibit chaotic behav-ior. From previous studies (Nesvorny and Morbidelli 1998),

it is known that typical Lyapunov times associated with thesemean-motion resonances are of the order of 5 × 103 to 105 years,

KO ET AL.

while the secular frequencies suffer a relative change of 10−2

to 10−3 per million years. This indicates the possibility of animportant chaotic diffusion both in eccentricity and inclination.However, very long-term integrations need to be done in orderto estimate the actual diffusion rates.

Applying SAM to the Magnya region, we have also detectedthe occurrence of numerous nonlinear secular resonances. Insome cases, these resonances lie very close one to another andform groups with more or less parallel overlapping components.Four of such groups, composed by secular resonances up to order6, have been detected in the neighborhood of Magnya. They areplotted by continuous curves on the (a,e)- and (e,I )-planes inFig. 5 and labeled from BI to BIV. The components of eachgroup are listed in Table I. The long-term stability of asteroidalorbits evolving inside nonlinear secular resonances is still anopen problem, but, from previous studies (Milani and Knezevic1992), it is clear that these resonances would induce long-terminstabilities in the asteroidal motion.

To assess the actual effects of the instabilities induced by bothmean-motion and secular resonances, we have performed verylong-term simulations of Magnya together with seven other testparticles close to it. The initial osculating orbital elements ofthe test particles were set to those of Magnya, except the eccen-tricities which varied from 0.2 to 0.25 (the initial eccentricityof Magnya at epoch was 0.237). We must note that the initialeccentricities were chosen in such a way that none of the testparticles started inside any mean-motion resonance. The orbitalpaths were followed over 1 Gyr. The time series of the osculat-ing elements were smoothed by digital filtering to remove the

FIG. 6. Averaged dynamical maps of the Magnya region. The distribution

secular resonances are observed. The position of Magnya is indicated by a plussymbol.

ORIGIN OF THE BASALTIC

TABLE IThe Groups of Nonlinear Secular Resonances

in the Magnya Region

Group Order 4 Order 6

BI g + s − g7 − s6 g + s + g6 − 2g7 − s7

g + s − g5 − s6 g + s − g5 + g6 − g7 − s7

g + s − 2g5 + g6 − s7

g + s − 2g5 + g7 − s6

BII g + s − g7 − s7 g + s + g5 − 2g7 − s7

g + s − g5 − s7 g + s + g5 − g6 − g7 − s6

g + s − g6 − s6 g + s − 2g5 + g7 − s7

g + s − g5 − g6 + g7 − s6

BIII g + s − g6 − s7 g + s + g5 − g6 − g7 − s7

g + s + g5 − 2g6 − s6

g + s − g5 − g6 + g7 − s7

g + s − 2g6 + g7 − s6

BIV s + 2g6 − 2g7 − s6

s − g5 + 2g6 − g7 − s6

s − 2g5 + 2g6 − s6

short-term oscillations, as well as the long-term oscillations withfrequencies g − g5 and g − g6. In Fig. 7, the resulting paths aresuperimposed over the averaged dynamical map of the Magnyaregion on the (a,e)-plane. Each path is indicated by a numberfrom 1 to 7. The path of Magnya (labeled by M) is confined toa very small domain, which indicates a quite regular behavior.On the other hand, the remaining test particles show an appre-ciable diffusion, originated by both mean-motion and nonlinearsecular resonances. The role of secular resonances is, in thiscase, to transport objects out by pushing them into the nearby

FIG. 7. Evolutionary paths of seven fictitious initial conditions in the veryneighborhood of Magnya. The path of Magnya is marked by M.

ASTEROID 1459 MAGNYA 351

mean-motion resonances, namely the 17/8 and 13:-6:-5 reso-nances. The estimated diffusion times are of the order of billionyears.

4. DYNAMICAL DISPERSION OF FAMILIES

The above results provide evidence to support the disper-sion of an asteroidal family in the Magnya region. To thor-oughly test this idea, we simulated a hypothetical Magnya fam-ily and studied its dynamical evolution over 500 Myrs. Wegenerated initial conditions of 50 fragments resulting from thebreakup of a Magnya-type parent body of 100 km in diameter.The breakup was simulated using a simple model of isotropicejection, in which the ejection velocities were distributed follow-ing a Maxwellian and did not depend on the mass of the frag-ments (e.g., Farinella and Davis 1992, Petit and Farinella 1993).We chose the parameters of the model such that we ended upwith the least dispersed fragments, corresponding to an average“effective” ejection velocity of ∼70 m s−1. The initial conditionswere then numerically propagated considering planetary pertur-bations from Earth to Neptune, and proper elements a, e, and Iwere determined as averages of a, e, and I over 10 Myrs, andsampled every 0.1 Myr.

Figure 8 shows the initial distribution of the fragments afterthe breakup (top) and their final distribution after 500 Myr ofevolution (bottom). For the sake of comparison, the fragmentsare superimposed on the averaged dynamical map of Fig. 6. A re-markable dispersion of the fragments at the end of the simulationis observed. The eccentricities were significantly excited dueto the chaotic diffusion along the numerous mean-motion res-onances (high-order two-body resonances and low-order three-body resonances) occurring in the region. The typical evolution-ary paths along these resonances are shown in Fig. 9. Magnya’spath is located between the 17/8 and 13:-6:-5 resonances, ate � 0.21, and does not show any significant diffusion (comparewith Fig. 7).

Using the hierarchical clustering method (Zappala et al. 1990),we found that about 20 to 30% of the original members of thefamily at a cutoff level of 110 m s−1 were still identified asmembers after 500 Myr. In other words, the family lost morethan 70% of its members during the simulation due to dif-fusion along mean-motion resonances. Since the evolutionarypaths in Fig. 9 have the properties of a quasi-random walk, thetemporal dispersion (diffusion) of the family is given by therelation

d2 =(

5

4

Da

a20

+ 2De + 2Dsin I

)t, (2)

where d is the average “distance” between the members of thefamily (in m s−1); t is the time; Da, De, Dsin I are the diffusioncoefficients of each proper element; and a0 is the average semi-major axis of the family. The diffusion coefficients are deter-

2

mined as the variance, σ , of the proper elements over 500 Myrs.According to typical values of these coefficients, we have d/

√t ∼

352 MICHTCHEN

FIG. 8. The evolution of the hypothetical Magnya family due to dynami-cal diffusion. Top: Initial family after the hypothetical breakup. Bottom: Finaldistribution of the fragments after 500 Myrs of evolution.

0.003–0.006. Then, we conclude that after a couple of billionyears of evolution the family would be sufficiently dispersed toavoid its detection at cutoff levels under 150 m s−1.

We can conclude that the numerous mean-motion and secularresonances acting in the Magnya region can produce signifi-cant diffusion and, consequently, dispersion of the hypotheticalMagnya family. Indeed, the effect of these resonances can result

in the loss of several family members, becoming impossible toidentify the family in a reliable way.

KO ET AL.

Moreover, we must note that our simulation of the hypo-thetical Magnya family assumed that the parent body was atMagnya’s present location at the time of breakup. In fact, theoverall dispersion of the family could have been significantly ac-celerated if the parent body was initially at another, more chaotic,place. Such a situation is achieved, for example, by locating theparent body at a slightly larger eccentricity or inclination thanMagnya’s ones (see Fig. 5). In this case, Magnya would be afragment of the family’s periphery, while the core of the familywould have been at a much more chaotic region, being rapidlydispersed. We will return to this point later in Section 6.

Our present simulations of Magnya’s family did not accountfor the possible effects of nonconservative forces, like Yarkovskyeffect. Recent studies showed that Yarkovsky orbital drift(Farinella and Vokrouhlicky 1999) plays an important role inspreading asteroidal families (Bottke et al. 2001, Nesvorny etal. 2002). It contributes to the mobility in semi-major axis,driving bodies into the mean-motion and secular resonances.Yarkovsky effect is actually relevant for small bodies. Simula-tions by Roig et al. (in preparation) showed that, for 5-km aster-oids in the Magnya region, this effect causes a drift in a of some0.02 AU per Gyr. The interaction between Yarkovsky effect andweak resonances could have introduced a significant additionalspread of Magnya’s hypothetical family over the age of the SolarSystem.

It is interesting to compare the results of our simulations ofthe fictitious Magnya family to the Meliboea family, which is

FIG. 9. Typical evolutionary paths of the fragments of our hypothetical

Magnya family. Averages of a, e, I were calculated over 10 Myrs and sampledevery 0.1 Myr.

A

982 Franklina 49.9 A

ORIGIN OF THE BASALTIC

located in the neighborhood of Magnya (star symbols in Fig. 3).This dynamical family appears at values of a, e, and I slightlysmaller than those of Magnya and shows a rather large dispersionof its members. The family accounts for 35 members, detected ata cutoff level of 110 m s−1, and it is reduced to only 10 membersat a cutoff level of 100 m s−1. Meliboea family shows clear tracesof the action of weak mean-motion and secular resonances inthe region. Assuming that the diffusion rates around Meliboeaare similar to those we estimated around Magnya, we concludethat this family is the result of a relatively recent breakup, whichhappened less than 1 Gyr ago.

5. MINERALOGICAL MAP OF THE MAGNYA REGION

Substantial evidence for the break-up of a Magnya’s parentbody would be provided by finding additional V-type (basaltic)asteroids such as Magnya and olivine-rich (A-type) and metal-rich (M-type) asteroids, which should be liberated from the man-tle and nucleus, respectively, of a differentiated parent body.Therefore, we analyzed the compositions, as suggested by tax-onomic types, in a large region Magnya: 3.05 < a < 3.25, e <

0.4 and I > 0. In this region, 604 numbered asteroid are foundof which only 123 asteroids (20% of the sample) do have a tax-onomic classification. Among these, almost 73% come from theS3OS2 survey (Lazzaro et al. 2001), which specifically observedasteroids in the neighborhood of Magnya trying to increase thecompositional knowledge of this region. The taxonomic clas-sification of the remaining asteroids were obtained from twoother large surveys: ECAS (Zellner et al. 1985, Tholen 1989)and SMASS (Binzel et al. 2001).

The taxonomic classification of these 123 asteroids is givenin Table II, together with their diameter and albedo. When-ever the IRAS albedo was not available, the diameter was com-puted assuming the mean albedo of the taxonomic type (0.12 forS-type, 0.05 for C- and D-type). For the X-type asteroids withno albedo, it was assumed a value of 0.08, which is the meanalbedo of the asteroids in this region. It is worth recalling that,in Tholen’s taxonomic scheme, an X-type spectrum is “degen-erate” and it would be identified as an E-, M-, or P-type only onthe basis of the albedo: high, medium, or low, respectively. Eachof these classes are interpreted in terms of very different heatinghistories: while the E and M classes are linked to differenti-ated bodies, the P class is believed to be primitive. Assumingan albedo of about 0.38 for these X-type objects (the highestalbedo in the region), the diameters would decrease somehow,but the results would not change significantly.

Since a high or low albedo can indicate a preferential compo-sition, we also included in our analysis the asteroids with knownIRAS albedo (Tedesco 1997). This increased the sample of as-teroids with a compositional indication to 174, about 30% of thetotal number of asteroids in the region.

The distribution of all the numbered asteroids in the (a,e)- and(e, I )-planes around Magnya is given in Fig. 10, indicating the

associated mineralogical composition of the asteroids. In thisfigure the letter “D” indicates a dark composition, i.e., asteroids

STEROID 1459 MAGNYA 353

TABLE IITaxonomic Classification of Asteroids in the Region

around Magnya

Asteroid Diameter Albedo ECAS SMASS S3OS2

57 Mnemosyne 112.6 .21 S S S95 Arethusa 136.0 .07 C Ch C96 Aegle 169.9 .05 T T

137 Meliboea 145.4 .05 C152 Atala 87.7 D Sl181 Eucharis 106 .11 S Xk X199 Byblis 104.2 X D250 Betina 79.8 .26 M Xk286 Iclea 96.9 .05 CX Ch C314 Rosalia 56.8 .09 C328 Gudrun 122.9 .04 S357 Ninina 106.1 .05 CX C373 Melusina 95.8 .04 C C375 Ursula 152.7 C Xc399 Persephone 49.1 .18 X439 Ohio 76.6 .03 X: D448 Natalie 47.8 .06 C451 Patientia 225.0 .08 CU C457 Alleghenia 30.1 X489 Comacina 139.4 .04 C X491 Carina 97.3 .07 C X493 Griseldis 46.4 .06 X501 Urhixidur 77.4 .08 X508 Princetonia 142.3 .04 C C509 Iolanda 53.0 .27 S S511 Davida 326.1 .05 C C X601 Nerthus 73.3 .04 X C C602 Marianna 124.7 .05 C C612 Veronika 37.7 .04 D618 Elfriede 120.3 .06 C C640 Brambilla 80.8 .07 G C663 Gerlinde 100.9 .03 X X665 Sabine 51.1 .39 X676 Melitta 80.0 .05 XC680 Genoveva 83.9 .05 XC X683 Lanzia 82.0 .08 C696 Leonora 75.8 .08 XC X702 Alauda 194.7 .06 C B C704 Interamnia 316.6 .07 F B C746 Marlu 69.8 .04 P C756 Lilliana 71.5 .05 D760 Massinga 71.3 .23 SU S762 Pulcova 137.1 .04 F C768 Struveana 43.2 X X780 Armenia 94.4 .05 X784 Pickeringia 89.4 .05 C786 Bredichina 91.6 .07 C788 Hohensteina 103.7 .08 C791 Ani 103.5 .03 C C805 Hormuthia 66.9 .05 CX849 Ara 61.8 .27 M886 Washingtonia 90.6 .07 C893 Leopoldina 76.1 .05 XF C894 Erda 36.1 .16 X912 Maritima 83.2 .11 C921 Jovita 58.5 .03 C928 Hildrum 66.8 .07 C943 Begonia 69.2 .04 ST X977 Philippa 65.6 .05 C X

983 Gunila 73.9 .05 XD X

N

354 MICHTCHE

TABLE II—Continued

Asteroid Diameter Albedo ECAS SMASS S3OS2

986 Amelia 50.9 .12 D1000 Piazzia 47.7 .09 C1005 Arago 57.8 .07 X1030 Vitja 64.1 .03 X1035 Amata 50.7 .05 C1041 Asta 57.3 .06 C1069 Planckia 39.5 .21 S1102 Pepita 39.3 .20 C S1115 Sabauda 68.8 .07 C1213 Algeria 33.2 .08 C1243 Pamela 70.1 .05 C1282 Utopia 53.1 .06 X1306 Scynthia 67.5 .05 S D1317 Silvretta 49.7 CX: X1330 Spiridonia 55.5 .05 P C1357 Khama 50.2 .03 XCU1369 Ostanina 41.6 .10 C1436 Salonta 62.9 .03 X1444 Pannonia 27.6 .13 C1459 Magnya 29.4 .12 V1461 Jean-Jaques 33.3 .16 M1469 Linzia 59.0 .07 X1477 Bonsdorffia 28.1 .05 XU1520 Imatra 53.6 .06 C1546 Izsak 36.1 X1571 Cesco 23.9 X1637 Swings 45.5 .08 C1701 Okavanko 35.4 S1765 Wrubel 42.3 .11 DX X1794 Finsen 37.3 .05 C1828 Kashirina 27.9 .10 C1952 Hesburgh 35.5 .10 CD:1999 Hirayama 34.0 .09 C2040 Chalonge 28.7 Ch2104 Toronto 41.5 X2152 Hannibal 46.9 .05 Ch2332 Kalm 29.6 .12 C2374 Vladvysotskij 23.9 C2375 Radek 36.0 D2582 Harimaya-Bash 28.9 .13 Xc2655 Guangxi 27.4 X2813 Zappala 32.6 .07 T2829 Bobhope 38.3 .09 C2892 Filipenko 56.1 .05 C2929 Harris 22.8 T3106 Morabito 33.0 C3139 Shantou 41.7 .11 C3162 Nostalgia 26.2 C3259 Brownlee 40.6 S3300 McGlasson 33.8 S3925 Tret’yakov 41.9 .05 C4112 Hrabal 48.6 .02 C4730 1980 XZ 25.1 .10 C4889 Praetorius 18.8 .21 C5461 1983 HB1 26.2 D5651 Traversa 21.8 X5959 Shaklan 19.9 .17 C6051 Anaximenes 18.1 X7496 Miroslavholub 18.1 C7604 1995 QY2 8.7 C9219 1995 WO8 22.7 C

10007 1976 YF3 22.8 C

KO ET AL.

identified as C-, P-, or D-type, which are not compatible with thefragmentation of a differentiated body. All other compositionsare identified by their classical Tholen’s taxonomic letter, i.e., S-,M-, X-, E-, and V-type (Tholen 1989). The dots indicate asteroidswith no taxonomic identification. The yellow and black dots in-dicate asteroids with a moderate to high albedo (larger than 0.11)and with a low albedo (linked to “dark” asteroids), respectively.The gray dots indicate asteroids with no albedo determination.

Figure 10 shows that, apart from Magnya, no other V-typeasteroid has yet been observed in this region. We want to stressthat this result does not mean that they do not exist! In fact,the taxonomic classification in the outer asteroid belt has beenlimited only to the larger asteroids (D > 20 km), as we can easilyverify in Fig. 11. Recalling that Vestoids have diameters no largerthan 10 km, it seems reasonable to expect that several other V-type asteroids with diameters of a few kilometers might still beobserved in the Magnya region.

Among the asteroids with some kind of mineralogical identi-fication in the region around Magnya, about 10% to 20% havea composition (or albedo) that could be related to either thebreakup of a differentiated parent body or to bodies that have un-dergone extensive heating and differentiation. There is Magnyaitself, together with probably 1 XE-type, 6 M-type, and 1 A-type.There are also other nine asteroids with an X-type spectra butwith no albedo, which could be linked to a differentiated body,but not surely. Finally, there are 11 S-type, which could be re-lated to extensive differentiation, but, again, not surely. In thefollowing, we will discuss the possible link of these objects tothe fragmentation of Magnya’s parent body.

Asteroids with an X-type spectra are the most complex tobe interpreted. As we already mentioned, they can be relatedto completely differentiated (E or M) or primitive bodies (P)depending on their albedos. In the region around Magnya thereare six M-type asteroid that could be fragments of the nucleus ofa completely differentiated body. Among them, asteroid (849)Ara is spatially very close to Magnya. However, we have to becautious because some asteroids classified as M-type show the3-µm band associated to water and hydrated minerals (Rivkinet al. 2000), and this is incompatible with an extensive heatingand differentiation.

Another asteroid, (665) Sabine, can be classified as XE-typedue to its very high albedo (0.38). Could it be related to Magnya’sparent body? The V and XE spectra are both related to achondritemeteorites (Gaffey et al. 1993), more precisely, to the HED andthe enstatite achondrites (or aubrites), respectively. But thesemeteorites cannot be linked to the same parent body. Therefore,on the basis of our present knowledge, we cannot state thatMagnya and Sabine came from the same parent body, althoughboth are most probably fragments of bodies that have undergoneextensive heating and differentiation. Moreover, Rivkin et al.(2000) have also identified the presence of the 3-µm band insome E-type asteroids. If such a feature is found in Sabine, itwould invalidate the idea of an extensive heating history for it.

Notwithstanding, it is worth noting that Magnya and Sabine arespatially very close to each other (see Fig. 10).

355

ORIGIN OF THE BASALTIC ASTEROID 1459 MAGNYA

10

11

N

356 MICHTCHE

Finally, there are those asteroids classified as X-type but withno albedo determination. One of them, 768 Struveana, is partic-ularly close to Magnya and could be related to Magnya’s parentbody.

What about the 11 S-type asteroids in this region? Some timeago, the S-type composition was associated with differentiatedbodies (Bell et al. 1979). But today, much evidence indicatesthat the S-type class encompasses compositions produced froma low degree of partial melting through complete melting andigneous differentiation and may include some unmelted objects(Gaffey et al. 1993). To provide a strong link between the S-type asteroids in this region and the breakup of Magnya’s parentbody, more precise mineralogical studies of these objects areurged, especially for the following two: (760) Massinga and(982) Franklina. The first one is spatially very close to Magnya,whereas the second one has a spectrum that can be classifiedas A-type. We recall that the classical model for differentiatedbodies consists of a crust of pyroxene (V- or S-type), a mantleof olivine (A-type), and a nucleus of metal (M-type). There-fore, Franklina could be a fragment of the mantle of Magnya’sparent body, although the large distance between Magnya andFranklina does not seem to support a genetic relation betweenthem.

If a Magnya family existed a long time ago and was dis-persed by the dynamical diffusion in the Magnya region, somemembers of this former family should still be in the neigh-borhood, because diffusion times are sufficiently slow to al-low their survival over the age of the Solar System. From theabove analysis of the mineralogical composition in the regionaround Magnya, we conclude that at least four asteroids, beyondMagnya itself, could be the remnants of this hypothetical fam-ily. They are (665) Sabine (XE-type), (760) Massinga (S-type),(849) Ara (M-type), and (768) Struveana (X-type). On the otherhand, is important to state that none of these asteroids can besecurely linked to the fragmentation of an unique differentiatedbody.

6. DISCUSSION ON THE ORIGIN OF MAGNYA

In the previous sections, we presented a dynamical and min-eralogical analysis of the region around the basaltic asteroid(1459) Magnya. Here, we will discuss what conclusions on thepossible origin of this body can we draw from them. First ofall, from the dynamical analysis we conclude that the region isfilled with high-order resonances, which lead to a slow chaotic

diffusion of the objects. We also confirm previous studies, which do not identify any dynamical family in this region.

FIG. 10. Spatial distribution, in averaged orbital elements, of numbered asteroids in the “Magnya region” with their taxonomic classification. The lettersstand for: “D”—dark composition, “S”—S class, “M”—M class, ‘A”—A class, “V”—V class (Magnya). Dots indicate asteroids with no taxonomic identification:yellow dots are asteroids with a moderate to high albedo (greater than 0.11), black ones are asteroids with low albedo, and gray dots indicate asteroids with noalbedo determination.

ejecta to orbits, which only occasionally approach Vesta. Then,

FIG. 11. Size distribution, in dependence of heliocentric distance, of numbmeaning as in Fig. 10.

KO ET AL.

From the mineralogical analysis, we do not find any com-pelling evidence for the fragmentation of a differentiatedMagnya’s parent body. Although we found a surprisingly highabundance of S- and M-type asteroids in a region that was sup-posed to be composed almost entirely of primitive bodies, thisfact per se is not convincing, since asteroids of these class arefound all throughout the main belt (Mothe-Diniz et al. 2001).The accepted model for a differentiated body implies also in alarge amount of mantle material (dunite), which, after a catas-trophic disruption, should be represented by A-type objects. Ofcourse, the lack of dunite in the asteroid belt (and in the mete-orite collections) is not a new problem, having been consideredone of the main paradoxes in the physical study of asteroids. Butwe cannot avoid considering that the lack of A-type asteroidsin the “Magnya region” is the strongest indication against thebreakup of a differentiated parent-body.

On the other hand, our current understanding of the formationof a basaltic crust precludes the possibility of a 30-km body being“the” differentiated body itself. In other words, Magnya aloneis too small to be a differentiated body, which achieved forminga basaltic crust. Therefore, if Magnya is just a piece of the crustof a larger differentiated body, where is it? We can think of twopossibilities: (1) Magnya’s parent body is still in the asteroidbelt, or (2) it has been dispersed together with its fragments.

Asteroid (4) Vesta is the only large body in the asteroid beltwith a basaltic surface. Since no other large V-type object hasbeen found near Magnya, we cannot rule out a Vesta origin forthis asteroid. But first, we should find a dynamical mechanismsuitable for transporting a fragment of Vesta’s crust to the presentlocation of Magnya. Even if the perihelion of Magnya is closeto Vesta’s orbit, its ejection from Vesta would need a very highejection velocity, which is not compatible with the large massof Vesta. Therefore, we have simulated the evolution of low-velocity ejecta from Vesta and analyzed the cumulative effect ofthe close approaches between the ejecta and Vesta. Since this as-teroid is one of the largest in the belt, we could expect that closeapproaches cause a non-negligible dispersion of the ejecta. Theinitial conditions of the simulations were taken with the ejectaat 10,000 km above the surface of Vesta and initial velocity100 m s−1 (which correspond to 374 m s−1 over Vesta’s surface,barely 10 m s−1 larger than the surface escape velocity). Prelim-inary experiments with low inclination orbits and using a sim-plified model showed many close approaches able to introducesmall changes in the ejecta semi-major axis and eccentricity(three to four close approaches to Vesta per 50 Myrs). How-ever, more realistic models showed that the planets drive the

ered asteroids in the “Magnya region.” The letters and symbols have the same

A

ORIGIN OF THE BASALTIC

a cumulative effect able to introduce important orbital variationsmay be discarded.

We should turn to the second hypothesis; i.e., there existedanother body with a basaltic crust in the outer belt that suffereda collision. The parent body and its fragments were further dis-persed in such a way that today we are unable to recognize thecorresponding family. The existence of large proto-planets orembryos in the primordial main belt has been recently proposedby several authors (Chambers and Wetherill 2001, Petit et al.2001), based on the standard accretion model in the inner SolarSystem. According to these models, most of these large embryoswere removed from the asteroid belt by close encounters and col-lisional evolution. This dynamical excitation of the asteroid beltwould have happened over a time scale of the order of 100–200 Myrs after Jupiter reached its present mass, and it wouldhave removed most of the primordial mass in the belt (>99%).The catastrophic disruption or the cratering of a large Vesta-likeobject could have been possible in this collisional scenario. Wecan think of two alternatives: (1) The breakup/cratering occurredduring the early accretion stages of the inner Solar System,and most of the resulting fragments (including the parent-body)were removed during the primordial excitation of the main belt.(2) The breakup/cratering happened by the end of the primordialexcitation event, and the fragments and parent-body were com-pletely dispersed by chaotic diffusion over the age of the SolarSystem. In any case, Magnya would just be a lucky survivor,and the no identification of a family associated to it might be anindication that the breakup/cratering of its parent-body occurreda long time ago.

Since the diffusion in the Magnya region is quite slow, we canalso imagine that the breakup occurred at a higher eccentricitythan that of Magnya’s one. It is worth noting that the region justabove Magnya (e > 0.25) is almost empty of real asteroids dueto the overlap of many higher order mean-motion resonances(see Fig. 6). If we assume that the breakup of Magnya’s parent-body occurred at this higher eccentricity region, Magnya mightbe a fragment of the crust ejected to smaller eccentricities, whichfell in a regular region where it survived until today. All otherfragments were injected in the more chaotic regions and arealready gone, or they are too small and not yet spectroscopicallyobserved.

The above scenario is also in agreement with other two piecesof observational data: the iron and HED meteorites. In the firstcase, we know that laboratory analysis of the collection of ironmeteorites indicates an origin from at least ∼70 distinct parent-bodies (Wasson 1995). This implies that at least 70 differentiatedasteroids existed which were completely disrupted and whosefragments of the metallic nuclei were injected in near-Earth or-bits. The same should have occurred for the fragments of thecrust and mantle. Then, the discovery of a crust’s fragment,Magnya, without an associated family would imply that the restof the body was transported to other parts of the belt and maybe

to the Earth. So, at least one of the parent-bodies of the ironmeteorites could be Magnya’s parent body.

STEROID 1459 MAGNYA 357

On the other hand, the HED meteorites have been tradition-ally linked to Vesta (Drake 1979, 2001) based not only on theirspectral similarity but also on the fact that no other basaltic as-teroid has been found in the main belt. Recently, subtle spectraldifferences between the HED, the Vestoids, and Vesta itself havebeen identified by Vilas et al. (2000) and Hiroi et al. (2001), in-dicating that there might exist another source of the HED. Thiswould also be in agreement with the results on the cosmic rayexposure (CRE) ages of the HED meteorites, which show twomain clusters at 21 and 38 Myr (Eugster and Michel 1995). Ithas been proven (Asphaug 1997) that the ∼450-km impact basinidentified on the southern hemisphere of Vesta (Thomas et al.1997) would have ejected a volume of material larger than themembers of Vesta family. However, Vesta’s crust alone does notseem to account for the large amount of HED material comingfrom an almost intact crust. Therefore, it would not be surpris-ing if part of these HED meteorites comes from the breakup orcratering event of Magnya’s parent body. We have shown in thispaper that dynamical routes to transport bodies from Magnya’sregion to Mars-crossing orbits do exist.

Although we are aware that we are still not able to prove thatthe origin of Magnya was the breakup of a completely differen-tiated body in the outer main belt, we believe that our currentunderstanding on the formation and collisional evolution of as-teroids indicates that this should be the correct scenario. Wehope that the problems raised and discussed in the present paperwill be an incentive other researchers to observe more asteroidsin this very interesting region and to try to develop better modelsthat account for the pieces of evidence that we have up to now ondifferentiated bodies. A sample return mission to Vesta wouldcertainly given conclusive answers to much of the problem dis-cussed in this paper.

ACKNOWLEDGMENTS

We acknowledge the technical staff of ESO for their prompt help wheneverneeded. This investigation was supported by CNPq, FAPESP, and FAPERJ.

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