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SURFACE PROPERTIES OF (6) HEBE:
A POSSIBLE PARENT BODY OF ORDINARY CHONDRITESy
F. Migliorini 1? , A. Manara 2 , F. Scaltriti 3z ,
P. Farinella 4 , A. Cellino 5 , M. Di Martino 6
1 Present address: Armagh Observatory, College Hill Armagh, BT61 9DG
Northern Ireland (UK)
e--mail: pat@star.arm.ac.uk
tel. +44--1861--522928, fax +44--1861--527174
2 Osservatorio Astronomico di Brera, I--20121 Milano (MI) Italy
e--mail: manara@brera.mi.astro.it
tel. +39--2­72320308, fax +39--2--72001600
3 Osservatorio Astronomico di Torino, I--10025 Pino Torinese (TO), Italy
e--mail: scaltriti@to.astro.it
tel. +39--11--4619012, fax +39--11--4619030
4 Dipartimento di Matematica, Universit`a di Pisa, I--56127 Pisa (PI), Italy
e--mail: paolof@dm.unipi.it
tel. +39--50--599554, fax +39--50--599524
5 Osservatorio Astronomico di Torino, 10025 Pino Torinese (TO), Italy
e­mail: cellino@to.astro.it
tel. +39--11--4619033, fax +39--11--4619030
6 Osservatorio Astronomico di Torino, 10025 Pino Torinese (TO), Italy
e­mail: dimartino@to.astro.it
tel. +39--11--4619035, fax +39--11--4619030
Manuscript pages: 18
Figures: 6
Tables: 1
y Partially based on observations carried out at the European Southern Observatory, La
Silla, Chile
z Visiting Astronomer, Complejo Astronomico El Leoncito operated under agreement be­
tween the Consejo National de Investigaciones Cientificas y Tecnicas de la Republica
Argentina and the National Universities of La Plata, Cordoba and San Juan.
1

Running title: Surface properties of (6) Hebe
Please, send communications, proofs and offprint requests to:
A. Cellino
e--mail: cellino@to.astro.it
tel : +39--11--4619035
fax : +39--11--4619030
Osservatorio Astronomico di Torino
strada Osservatorio, 20
I--10025 Pino Torinese (TO), Italy
2

Abstract
We report for the first time rotationally resolved spectroscopic obser­
vations, as well as new photometric and polarimetric measurements, of
the large S--type asteroid (6) Hebe, always at near--equatorial aspects.
We have found evidence for only minor variations in Hebe's visible re­
flectance spectrum over a rotational cycle, comparable to our measure­
ment accuracy (a few percent) and consistent with an undifferentiated
silicate assemblage on the surface. We have also confirmed previous
results of the existence of small polarization changes, but they are not
correlated with the (complex and asymmetric) photometric lightcurve
of the asteroid. A plausible interpretation of these data is that Hebe's
surface is is composed of undifferentiated materials, but presents tex­
ture, albedo and spectral changes possibly related to the occurence of
energetic cratering events. Given the comparatively large size of Hebe,
its proximity to resonance--related chaotic zones of the orbital element
space (Farinella et al. 1993, Celest. Mech. 56, 287--305 and Icarus
101, 174--187), and its assignment by Gaffey et al. (1994, Icarus 106,
573--602) to the S(IV) taxonomic subclass, our results support the idea
that this asteroid may be the source of a significant fraction of the or­
dinary chondrite meteorites.
3

1 Introduction
(6) Hebe is a very interesting asteroid from the point of view of meteoritical
science. With a size of about 200 km, it is one of the largest S--type aster­
oids, and belongs to the S(IV) subclass as defined by Gaffey et al. (1994).
This subclass is characterized by reflectance spectra indicating a silicate
surface material consistent with undifferentiated ordinary chondritic assem­
blages (although not excluding anomalous stony--irons and some primitive
achondrites meteorites); it accounts for ú 30% of all S--type asteroids and
has a significant concentration in the semimajor axis range between 2:3 and
2:6 AU, where the š 6 (secular) and 3:1 (mean motion) resonances provide
efficient transport routes from the main asteroid belt to the Earth (Farinella
et al. 1994).
Hebe's orbital elements (semimajor axis 2:42 AU, eccentricity 0:20, in­
clination 15 ffi ) place it not far from the 3:1 Kirkwood gap, and very close
to the š 6 resonance. As a consequence, fragments ejected from it can eas­
ily reach either resonance, and over a 10 6 yr time scale their eccentricities
can be pumped up to ú 0:6, corresponding to Earth--crossing orbits. As a
consequence, owing to the combination of large size and favourable location
in orbital element space, Hebe alone may account for a significant fraction
of the overall meteorite flux onto the Earth (Farinella et al. 1993a,b; Mor­
bidelli et al. 1994). An interesting possibility is that Hebe could be the
source of one of the three main groups of ordinary chondrites (OCs), which
together account for ú 80% of all meteorite falls and are believed to come
from a small number of fairly large parent asteroids (Pellas and Fi'eni 1988;
Lipschutz et al. 1989; Haack et al. 1996).
What else do we know about Hebe's physical properties? The spin pe­
riod is 7:2745 hr (Lagerkvist et al. 1987), with an uncertainty of \Sigma0:00025 hr
according to Gehrels and Taylor (1977). The period is close to the average
value for large asteroids (Binzel et al. 1989), but the lightcurve morphology
is complex, highly dependent upon aspect and phase, and has a compar­
atively small maximum amplitude (ú 0:2 mag). The asymmetric extrema
suggest the presence of some albedo variegation on the surface, consistent
with inferences from polarimetry data (Broglia et al. 1994). On the other
hand, as shown by Cellino et al. (1989), shape effects alone can also cause
complex photometric behavior, and indeed occultation data (see Magnusson
1986, p. 27) have indicated that a substantial part of Hebe's lightcurve am­
plitude is due to shape effects (it is also intriguing to recall that a possible
secondary occultation by a small satellite has been reported, see Dunham
and Maley 1977).
4

Critical to understanding Hebe's properties are spectroscopic data: sub­
stantial spectral variations for different rotational phases would provide
strong evidence for large--scale chemical/mineralogical heterogeneity of the
surface. In such a case, unless specific correlations are present (related to
the functional relationships between mineral abundances and compositions
in chondritic assemblages), the most plausible explanation would be that
during its history the asteroid has experienced intense thermal processes,
which have produced differentiated assemblages and surface mineralogical
heterogeneity (Gaffey 1984). This may be due to ancient magmatic activity
on the current surface, or to the exposure of different original stratigraphic
units within a larger, differentiated precursor body disrupted by a catas­
trophic collision; there is also the possibility that some S--type asteroids
might be partially differentiated, or only regionally melted (Taylor 1992).
The first explanation probably applies to (4) Vesta, the second one to the
two large S--type asteroids (8) Flora and (15) Eunomia (Gaffey 1984; Gaffey
and Ostro 1987; Gaffey et al. 1989). Of course, all of these interpreta­
tions would not be consistent with an ordinary chondritic composition, and
therefore would rule Hebe out as a plausible OC parent body candidate.
The available spectral data of Hebe so far have been quite limited, and
their interpretaion uncertain. While Wamsteker and Sather (1974) observed
no significant color variation, Gehrels and Taylor (1977) found a small (U--
V) change (ú 0:02 mag) during a rotational cycle, which they interpreted
as due to the presence of reddened regions on the surface. However, these
data do not rule out an undifferentiated composition for Hebe, taking into
account that, even if real, such small color variations might well be related
to a combination of space weathering and impact effects, as recently inferred
from the Galileo images of (243) Ida (Geissler et al. 1996; Chapman 1996),
spectral observations of near--Earth asteroids (Binzel et al. 1996) and lab­
oratory experiments on regolith processes (Moroz et al. 1996). In a recent
abstract, Gaffey (1996) has reported that his own 1978--79 and 1989 visible
and infrared spectroscopic observations of Hebe confirmed the existence of
small rotational spectral variations, but that they are consistent with an un­
differentiated silicate assemblage on the surface. This conclusion is at odds
with earlier ones of other researchers (e.g. Fanale et al. 1992), who argued
that S--type spectra in general cannot be reconciled with those of OCs.
Polarimetric changes over the rotational cycle have been also observed
(Broglia et al. 1994). However, they are not necessarily diagnostic of a
mineralogic surface heterogeneity, but could be caused instead by texture
and/or albedo changes on a mineralogically homogeneous surface (Dollfus
5

et al. 1989). Finally, we recall that the radar albedo of Hebe, as reported by
Ostro et al. (1991, Table 2 and Fig. 4), is quite typical for large main--belt
asteroids, and does not suggest a high abundance of metals on its surface.
Given the potential importance of Hebe as an OC parent body and the
ongoing debate on this issue, we were motivated to carry out a dedicated
campaign of spectroscopic observations of Hebe, in order to assess in some
detail whether and/or which spectral changes appear for different rotational
phases, and whether Hebe may stand as a plausible OC parent body. We
have also performed new photometric and polarimetric measurements of this
asteroid, also at epochs when it was visible at a near­equatorial aspect. The
remainder of this paper is organized as follows: in Sec. 2 we will report on
our spectroscopic and photopolarimetric observation techniques. Sec. 3 will
be devoted to the description of the results and the interpretations of these
observations. Finally, in Sec. 4 we will discuss the implications of these data
for Hebe's putative genetic relationship with OCs.
2 Observations and data reduction
2.1 Viewing geometry and rotational phasing
For practical reasons, spectroscopic and photopolarimetric observations were
carried out during different observation runs, as described below. Since our
goal was to detect possible spatial mineralogic variations, an essential re­
quirement was a near--equatorial view of the asteroid during all the obser­
vations. ?From the pole coordinates of (6) Hebe reported by Magnusson
(1989), the aspect angle (between the rotation axis and the direction of the
Earth) at the times of the observations can be derived easily. Taking into
account the existing uncertainty in the polar coordinates, for the spectro­
scopic run we have found that the aspect angle was in the interval between
about 68 ffi and 84 ffi ; for the photopolarimetric observations, the correspond­
ing interval was from about 79 ffi to 89 ffi . Thus the viewing geometry of Hebe
has always been favorable to detect possible changes phased with the rota­
tional cycle, and the similar aspect angles at the epochs of different sets of
observations implies that there was no large difference in surface covering,
and makes it unlikely that some surface feature has shown up in one set and
not in the other.
The uncertainty in Hebe's spin period, as quoted in Sec. 1, translates into
an uncertaintly of about 20 minutes (0:05 cycles) in the relative rotational
phasing over the 15 months interval between the photopolarimetric and the
spectroscopic observations. Thus we have been able to plot our data using,
6

to a good accuracy, self--consistent relative phases.
2.2 Spectroscopy
Observations were performed at ESO--La Silla on September 14--18, 1995,
with the 1.52--m spectroscopic telescope equipped with a Boller and Chivens
instrument. The CCD has 2048\Theta2048 pixels, windowed at about 300\Theta2048.
The grating used was ruled at 225 gr/mm, so the dispersion in the first order
was of about 330 š A/mm. The CCD has a 15 ¯m square pixel, yielding a
dispersion of 4.7 š A/pixel in the wavelength direction. The useful spectral
range is from about 4800 š A to 9400 š A, the instrumental FWHM being
9.8 š A. Unfortunately, at the long wavelenght end (beyond 9000 š A), a strong
atmospheric absorption due to OH \Gamma degrades the signal--to--noise ratio of
the images, making the spectrum of poorer quality. This is annoying, since
in this spectral region variations due to mineralogical heterogeneity are likely
to show up.
The slit was 2 to 5 arcsec wide, aligned in the East--West direction. The
slit width was much larger than the seeing conditions (typically about 1
arcsec), in order to minimize the possibility of losing the signal due to errors
in pointing and guiding the target. An optical camera was used for target
acquisition and guiding. The asteroid was very bright (m v ú 8:5), and as
a consequence it was quite difficult to center the asteroid image in the slit,
due to the large amount of scattered light, resulting into a sizeable image in
the camera screen. The target was confirmed by noting its motion relative
to fixed stars. The observational circumstances are listed in detail in Table
1.
In addition to the rotational spectra of Hebe, solar analog stars HD
20630, HD 1835, HD 144585 and 64 Hyades, flat fields, bias images, and
lamp spectra (He--Ar) were taken during each night using the same instru­
mentation setup. Spectra were reduced with the Image Redution and Anal­
ysis Facility (IRAF) package, installed on a SUN--OS workstation at the
Brera Observatory, according to the standard procedure described in Di
Martino et al. (1995). This includes subtraction of the bias level, flattening
of the data, elimination of the cosmic rays, subtraction of the sky, wave­
length two--dimensional calibration, transformation from a two--dimensional
spectrum to a uni--dimensional one, extinction correction and division by
the solar analog (Hardorp 1978). Finally, each spectrum was normalized to
asteroid/star flux at 7000 š A.
7

2.3 Photopolarimetry
Simultaneous photometric and polarimetric observations of 6 Hebe were car­
ried out on three consecutive nights (June 5 to 7, 1994). We used the Torino
photopolarimeter attached at the 2.15­m telescope of Complejo Astronomico
El Leoncito (Argentina).
A full description of the instrument functioning can be found in Piirola
(1988) and Scaltriti et al. (1989). Here we recall that the photopolarimeter
allows the observer to perform linear and circular polarization measurements
(by means of –=2 and –=4 plates), simultaneously in the five bands UBVRI.
The ordinary and extraordinary beams produced by a calcite plate are al­
ternately recorded by means of a rotating chopper. Dichroic filters, which
reflect a desired spectral interval and transmit the other wavelengths, se­
lect the incoming beam according to the standard colour bands UBVRI.
In the dewar, cooled down to \Gamma30 ffi C, five separate photomultipliers (three
HAMAMATSU--type, for VRI, and two EMI--type, for UB) allow one to
gather the signal of the object separately.
The principle of operation of the photopolarimeter is that the polariza­
tion due to the sky--background is directly eliminated; this has been found
to be especially valuable in the observation of faint stars and when there is
moonlight. In principle, if a considerable amount of background radiation
is composed of scattered light, it can be highly polarized and small relative
changes in the sky background could give rise to large errors in the measured
polarization. Our photopolarimeter was especially designed to minimize this
undesirable effect.
The counts obtained by the equipment allow the observer to get the po­
larization parameters (amount of polarization, P and position angle, P.A.)
and the photometry of the object, in the five bands UBVRI. Both for pho­
tometric and polarimetric curves, phases were computed according to the
reference epoch (corresponding to the epoch of our first observation) JD
2449509.45, assuming a period of 7 h :2745. As explained in Sec. 2.1, this was
consistent with the phasing of our spectroscopic observations, as reported
below.
Unfortunately, the sky conditions during the three observing nights were
not generally good, so that we were not able to get a full--cycle coverage
of the photometric lightcurve. However, the operational principle of the
equipment allows one to obtain fairly good--quality polarimetric curves even
when veiling or spread clouds are present in the sky. Thus, the overall quality
of the polarimetric and photometric data reported below was not seriously
degraded by the sky conditions, thanks also to the brightness of the object.
8

A technical problem on the power supply of channel R prevented us from
obtaining data at that wavelength. Therefore, we got results in the UBVI
bands only.
3 Results
3.1 Spectroscopy
In order to obtain a single low--noise reflectance spectrum of Hebe (Fig. 1),
we have taken the average of all of our spectra. The procedure of adopting
four different solar analog stars (see Sec. 2.2) allowed us to reduce the pos­
sible errors due to a calibration based on just one solar analog. Morover,
spectra were taken on six different nights, minimizing uncertainties in the
data due to variable sky conditions.
The averaged reflectance spectrum shown in Fig. 1 can be compared with
those available in the published literature. In particular we have compared
our data to those obtained in the framework of the ECAS survey (Zellner
et al. 1985) and to the spectrum published by Xu et al. (1995). In both
cases, the agreement is very good (see Fig. 1 for the comparison with the
ECAS data points). Our spectral range does not allow us to detect all the
features typical of the S taxonomic type (e.g., the band at 2.2 ¯m); on the
other hand, the position of the olivine--pyroxene band near 9000 š A closely
matches that corresponding to the S(IV) subclass, as defined by Gaffey et
al. (1994).
In order to look for rotational spectral variations, we grouped our data
into bins of 0:1 width in rotational phase, and averaged the spectra available
in each bin. As shown in Figs. 2 and 3, no differences exceeding a few percent
have been detected, comparable to the noise in the data, and therefore no
evidence is present for a large--scale spectral heterogeneity of Hebe's surface.
However, several spectra shown in Fig. 2 deviate in a consistent fashion
above or below the averaged spectrum of Fig. 1 over a significant range
of wavelengths; this is confirmed by the ratioed spectra plotted in Fig. 3.
For example, the intensity of the 0:9 ¯m feature (in the ú 0:8 to 0:92 ¯m
wavelenght interval) is about 3% stronger than the average at phase 0:8,
slightly less strong at phase 0:7, and about 2% weaker at phases 0:2 and
0:3 (that is, on the other side of the asteroid), whereas intermediate phases
show ratios closer to 1. On the othr hand, the small--wavelength portions of
the spectra (between 0:5 and 0:7 ¯m) indicate that Hebe is somewhat more
blue than average at phases 0:8--0:9, and more red at phases 0:2--0:4. These
changes are of the same order of magnitude as the U--V color variations
9

reported by Gehrels and Taylor (1977, Fig. 28, top) and appear to have also
the same rotational phasing, based on the comparison of lightcurves. These
small spectral variations can be intepreted as due to different degrees of space
weathering on Hebe's surface, possibly related to large--scale ejecta blankets
resulting from relatively recent and energetic cratering events, similar to
those observed in the Galileo spacecraft images of (243) Ida (see discussion
in Chapman 1996), or to subtle mineralogic variations, consistent with an
undifferentiated silicate assemblage (as concluded by Gaffey 1996). In either
case, our spectral data are consistent with a genetic relationship between
Hebe and OCs.
3.2 Photometry
Our lightcurves are shown in Fig. 4; most but not all of the rotational cycle
was covered. The general trend is in agreement with previous results (e.g.,
Lagerkvist et al. 1987). In spite of the partial coverage of the lightcurve,
three maxima (at ú 0:1, 0:3, 0:6 phases) and three minima (ú 0:18, 0:45,
0:9 phases) can be distinguished in the lightcurve.
Owing to the unfavourable sky conditions we were not able to perform
a transformation to the standard UBVRI system; the \Deltam's given in Fig. 4
refer to a frequently observed nearby star which differed from night to night.
As for accuracy, typical errors are of the order of 0:02--0:03 magnitudes (or
twice as large for the rotational phases between 0.8 and 1.0, covered during
the worst night).
These (limited) data confirm that Hebe's photometric variations have a
relatively small amplitude, but a complex behavior. As remarked in Sec. 1,
such behavior in principle may be associated both with a globally irregular
(non--ellipsoidal) shape, and with large--scale albedo variegation of the sur­
face (related for instance to impact shock--darkening processes of chondritic
materials, as suggested by Britt and Pieters 1991). Moreover, the different
shapes and amplitudes of the lightcurves at different wavelengths suggest
the existence of color variations, in agreement with the conclusions reported
in Sec. 3.1. Note that for most known processes occurring on asteroid sur­
faces (grain size alteration, melting and crystallization), albedo variations
are accompanied by spectral changes (Fanale et al. 1992, Moroz et al. 1996).
3.3 Polarimetry
It is well known that asteroids, like other atmosphereless solar system bod­
ies, show a well defined variation of polarization as a function of the Sun--
10

asteroid--Earth phase angle ff; the corresponding curve is often used e.g.
to infer the albedo (see e.g. Lupishko and Mohamed 1996). In particu­
lar, polarization is usually expressed through the P r parameter, that is the
ratio I ? \GammaI k
I ?+I k
, I ? and I k being the intensities of the reflected light polarized
perpendicular and parallel to the Earth--Sun--asteroid scattering plane, re­
spectively. The relationship between the coefficient of linear polarization P
(which is the quantity directly obtained from the observations) and P r is
simply P r = P \Delta cos (2`), where ` is the angle between the position angle
P.A. of the observed polarized radiation, and the plane perpendicular to the
plane of scattering.
Fig. 5 shows the coefficient of linear polarization P (in percent) and the
corresponding polarization angle P.A. plotted versus rotational phase. In
making these plots, polarimetric data were grouped in bins of 0.1 in rota­
tional phase, and averaged in each bin. A simple first--order Fourier fitting
of the P vs. rotational phase curve is also shown, and gives a satisfactory
fit to the data.
The amplitude of the P curves decreases from the U to the I band.
Especially in the U, B and V bands, the positions of the extrema of the
curve are quite close to each other. On the other hand, except for the U
band, the P.A. curves do not show any well defined pattern, and there is
no clear correlation between the trends observed in different colors. In the
U band, where a definite trend is visible, the positions of the maximum
and the minimum do not coincide with the corresponding positions in the
P curve. All these findings are consistent with previous observations of
Broglia et al. (1994). It is interesting to note that the trends apparent in
the polarimetric and photometric lightcurves are different, and there is no
clear correlation between them. We will discuss the possible interpretation
of these observations below.
As for P r vs. ff curve, we recall that for asteroids it always shows a
well defined behavior, with the presence of a negative branch of polariza­
tion, whose origin has not been fully understood yet (see Muinonen 1994
and references therein). Fig. 6 shows our observed values of P r vs. ff (our
observations were performed at ff = 12 ffi :5), together with other P r measure­
ments reported in the literature for Hebe (Zellner and Gradie 1976). In this
figure, nightly averages of P r for each of our three observing nights have
been plotted for each color with different symbols. Our values agree very
well with the general trend indicated by previous observations. This can
be considered as further confirmation of the accuracy of our polarimetric
measurements.
11

We note that the lack of a correlation between the polarimetric and pho­
tometric lightcurves as shown in Figs. 4 and 5 is quite unusual for asteroids.
For instance, in the well--known case of (4) Vesta a clear correlation be­
tween the photometric and polarimetric behaviours is present, and has been
used to unequivocally derive the correct rotation period of the asteroid (see
e.g. Dollfus et al. 1989, and references therein). Such a correlation has been
generally explained as diagnostic of large--scale albedo variegation of the sur­
face. In particular, since Vesta's polarimetric variation is roughly sinusoidal
over a rotational cycle, the presence of a hemispheric albedo asymmetry has
been proposed as a plausible explanation for both the polarimetric and the
photometric lightcurves, and has been used to derive the orientation of the
spin axis as well as the polar flattening of this sizeable asteroid (Cellino et
al. 1987). In the case of Hebe the polarimetric behaviour is generally similar
to that of Vesta, but the photometric lightcurve is much more peculiar.
There are two possible explanations for Hebe's behaviour. First, we may
interpret the lack of correlation between photometric and polarimetric data
as suggesting that the polarimetric variation in this case is due to large--scale
changes in the surface texture, rather than to significant albedo features. We
stress that a detailed theoretical understanding of the relationship between
polarimetric behaviour and microscopic surface texture is still lacking for
atmosphereless solar system bodies, so for the time being we cannot test this
possibility in a quantitative way. Alternatively, large--scale albedo patterns
resulting in significant polarization changes may be present, without playing
an important role in molding the lightcurve morphology, in which global
shape effects would be predominant. Although Hebe's size (almost 200 km
in diameter) implies that it is not likely to be an irregularly shaped fragment
from a larger parent asteroid (as is the case for most smaller asteroids,
see Catullo et al. 1984, Davis et al. 1989), its relatively small lightcurve
amplitude does not require large deviations from an axisymmetric shape,
especially if surface features such as craters or ridges produce complex (and
variable) shadowing effects.
Despite these interpretation problems, our work shows that in the ab­
sence of close--up spacecraft observations, unravelling the main physical and
mineralogic properties of asteroid surfaces requires the simultaneous con­
siderations of data from several different observing techniques. Rotation­
ally resolved data are especially important when the detection of strong,
large--scale heterogeneity is a crucial test for inferences about the asteroid's
thermal history. In the case of Hebe, we have not carried out rotationally
resolved spectral measurements at infrared wavelengths, which could have
12

provided additional constraints on the nature of its surface variegation. The
recently reported observational results of Gaffey (1996) appear to confirm
the main results of our work.
4 Conclusions
The main finding from this work is that Hebe's visible reflectance spectrum
shows only minor variations over the course of the asteroid's rotation, and
that these variations do not require that differentiated materials are exposed
on the surface. In this respect, Hebe appears to be different from other large
S--type asteroids such as (8) Flora and (15) Eunomia, whose rotationally
resolved spectra show clear variations, which do not appear to be consistent
with undifferentiated (ordinary chondritic) assemblages (Gaffey et al. 1989).
Although photometric and polarimetric data suggest that the surface of
Hebe is optically heterogeneous, probably due to changes in the microscopic
surface texture and/or albedo, this may be due to a variety of processes
related to impact events. We thus propose our most plausible interpretation
of the data:
(i) Hebe's surface is composed of an undifferentiated mineral assemblage;
(ii) since its formation, the surface has undergone a number of energetic im­
pact cratering events, causing some changes in its large--scale albedo/pola­
rization properties, and possibly minor spectral variations related to the
exposure of ``fresh'' (i.e., unaffected by space weathering processes) subsur­
face material.
According to this interpretation, Hebe can be considered as a plausible
parent body for OCs. Following Farinella et al. (1993a), we speculate that
a substantial fraction of these meteorites may have been generated by large
impact craters on this asteroid. This is consistent with a simple order--of--
magnitude estimate. If we consider craters formed by projectile asteroids
? 1 km in diameter, the average frequency of these events for a target as
big as Hebe can be estimated at one every 2 \Theta 10 7 yr (assuming an intrinsic
collision probability of 2:8 \Theta 10 \Gamma18 km \Gamma2 yr \Gamma1 and a projectile population
of about 2 \Theta 10 6 ; see Farinella and Davis 1992, 1994). This is comparable
with the typical cosmic--ray exposure (CRE) ages of ordinary chondrites
--- H chondrites in particular display a strong CRE peak at about 8 Myr
(Anders 1964, Marti and Graf 1992), which may well correspond to the last
such cratering event; the evidence for different orbital pathways followed
by different subgroups of these H chondrites (Graf and Marti 1995) may
13

be explained by the availability of both the š 6 and the 3:1 resonant routes
near Hebe. Larger impact events have also occurred on Hebe, of course,
but may have been separated on average by longer time intervals; since the
dynamical/collisional lifetime of fragments injected into the š 6 resonance is
at most of the order of 10 8 yr (Morbidelli et al. 1994; Bottke et al. 1995), it
is unlikely that current meteorite falls record such larger and rarer impacts.
If we assume that the mass ejected from Hebe's craters is typically some
900 times that of the projectile, consistent with Holsapple's (1993) scaling
of crater dimensions for rocky surfaces in the gravity regime and a mean
impact velocity of 6:6 km/s (Farinella and Davis 1992), we get an ejecta
production rate of ú 6 \Theta 10 7 kg/yr. Conservatively assuming that: (i)
only ú 10% of this material is injected into the resonances and reaches an
Earth--crossing orbit (according to the results of Farinella et al. 1993b and
Morbidelli et al. 1994); (ii) ú 10% of the latter material has meteorite--
like sizes (smaller than a few meters; a plausible estimate for crater ejecta);
and (iii) another factor of ú 10 is lost during the transfer process due to
collisional disruption, impact with other planets and the Sun, or ejection
from the solar system (this is consistent with the typical exposure ages of
ordinary chondrites, which are about a factor 10 shorter than the Earth--
impact lifetimes of Earth--crossing bodies), we eventually get an Earth influx
of some 6 \Theta 10 4 kg/yr. This is about 20% of the overall meteorite influx as
estimated (in order of magnitude) by Halliday et al. (1984) and Wetherill
(1985).
Of course this kind of comparison has only a semi--quantitative value, but
is important to show how different kinds of arguments and data can be linked
together in a self--consistent scenario. Impact cratering models, meteoritic
evidence, the observational results reported in this paper and the facts that
Hebe is the largest S(IV) object and lies very close to the resonant chaotic
zones (see Sec. 1), all point to the conclusion that this asteroid should be
considered as one of the most promising candidate OC parent bodies, and
should become the target of further observational efforts.
5 Acknowledgements
We are grateful to R.P. Binzel for making his spectrum of (6) Hebe available
to us. Constructive reviews by M. Gaffey and B. Clark have led to substan­
tial improvements with respect to a previous version of the paper. This
work has received partial financial support from the Italian Space Agency
(ASI), the Italian Ministry for University and Scientific Research (MURST)
14

and the European Union Human Capital and Mobility Programme (contract
number CHRX­CT94­0445).
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Figure Captions
Figure 1. Averaged spectrum of Hebe, obtained by combining many differ­
ent spectra calibrated with different solar analogs. It matches very well the
spectrum published by Xu et al. (1995). The dots with error bars (normal­
ized to 5500 š A) correspond to data taken in the framework of the eight­color
survey (ECAS) of Zellner et al. (1985).
Figure 2. Rotationally resolved spectra of Hebe. Spectra obtained at differ­
ent rotational phases were binned at intervals of 0:1 cycles (36 ffi ), and then
averaged and vertically offset for clarity. The dashed curves correspond to
the average spectrum of Fig. 1, after filtering out the small--scale wiggles
due to observational noise.
Figure 3. Ratios between the averaged spectrum of Hebe (Fig. 1) and the
spectra taken at different phases (Fig. 2), as specified by the labels on the
right side. The curves have been vertically offset for clarity.
Figure 4. Photometric lightcurves of Hebe in U, B, V, and I colors. The
data were collected during three different nights, on June 5, 6, and 7, 1994,
at El Leoncito Observatory (Argentina).
Figure 5. Polarimetric lightcurves of Hebe in U, B, V, I colours. Left: the
coefficient of linear polarization P (in percent) vs. rotational phase, and a
first--order Fourier fit. Right: the P.A. polarization angle (in degrees) vs.
rotational phase. Data collected at El Leoncito Observatory (Argentina) on
June 5, 6, and 7, 1994.
Figure 6: Nightly averages of P r vs. Sun--asteroid--Earth phase angle for
our UBVI polarimetric observations of Hebe (full symbols). Open symbols
correspond to the data reported by Zellner and Gradie (1976).
20

Table 1: Spectroscopic observations of (6) Hebe. The rotational phase has
been estimated from a period of 7 h :274 (Lagerkvist et al. 1988).
Day UT Slit Airmass Phase
14/09/95 05h33m 2'' 1.23 0.000
17/09/95 06h27m 5'' 1.10 0.022
16/09/95 08h42m 2'' 1.12 0.032
14/09/95 06h26m 2'' 1.12 0.121
18/09/95 05h18m 5'' 1.23 0.163
16/09/95 09h43m 2'' 1.26 0.172
17/09/95 07h34m 5'' 1.07 0.176
19/09/95 03h32m 5'' 1.80 0.220
17/09/95 07h54m 5'' 1.07 0.221
14/09/95 07h17m 2'' 1.08 0.229
15/09/95 05h04m 2'' 1.32 0.233
15/09/95 05h08m 2'' 1.30 0.242
17/09/95 08h45m 5'' 1.13 0.338
19/09/95 04h31m 5'' 1.39 0.355
14/09/95 08h14m 2'' 1.09 0.360
18/09/95 06h47m 5'' 1.08 0.367
16/09/95 03h50m 2'' 1.75 0.363
16/09/95 04h03m 2'' 1.64 0.393
15/09/95 06h26m 2'' 1.11 0.421
18/09/95 07h18m 5'' 1.07 0.438
19/09/95 05h15m 5'' 1.22 0.456
17/09/95 09h39m 5'' 1.26 0.462
16/09/95 05h17m 2'' 1.26 0.562
15/09/95 07h35m 2'' 1.07 0.579
14/09/95 09h46m 2'' 1.25 0.580
18/09/95 08h23m 5'' 1.10 0.587
17/09/95 03h22m 5'' 2.02 0.598
19/09/95 06h20m 5'' 1.10 0.605
19/09/95 06h56m 5'' 1.07 0.687
16/09/95 06h19m 2'' 1.12 0.704
18/09/95 09h26m 5'' 1.23 0.732
15/09/95 08h59m 2'' 1.14 0.771
17/09/95 04h38m 5'' 1.39 0.772
18/09/95 09h47m 5'' 1.30 0.780
19/09/95 07h54m 5'' 1.08 0.820
17/09/95 05h06m 5'' 1.28 0.836
16/09/95 07h23m 2'' 1.07 0.851
15/09/95 09h52m 2'' 1.28 0.893
19/09/95 08h58m 5'' 1.16 0.967
18/09/95 04h04m 5'' 1.57 0.994
21