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Mon. Not. R. Astron. Soc. 000,1–10 (2015) Printed 30 January 2015 (MN L
a
T
E
X style file v2.2)
The non-convex shape of (234) Barbara, the first
Barbarian ?
P. Tanga,1B. Carry,2F. Colas,2M. Delbo,1A. Matter,1,3J. Hanuˇs,1,4V. Al´ı Lagoa,1A.H. Andrei,5,9,29
M. Assafin,5M. Audejean,6,7R. Behrend,6,8J.I.B. Camargo,9A. Carbognani,10 M. Cedr´es Reyes,11 M. Conjat,12
N. Cornero,6,13 D. Coward,14 R. Crippa,6,15 E. de Ferra Fantin,11,16 M. Devog´ele,17 G. Dubos,13 E. Frappa,18 M. Gillon,17
H. Hamanowa,6,19 E. Jehin,17 A. Klotz,20 A. Kryszczy´nska ,21 J. Lecacheux,22 A. Leroy,6,23 J. Manfroid,17 F. Manzini,6,24
L. Maquet,2E. Morelle,6,25 S. Mottola,26 M. Poli´nska,21 R. Roy,6,27 M. Todd,14 F. Vachier,2C. Vera Hern´andez,11
P. Wiggins28
1Laboratoire Lagrange, UMR7293 CNRS, UNS, Observatoire de la Cˆote d’Azur, Nice, France
2IMCCE, Observatoire de Paris, UMR8028 CNRS, France 3Max Planck Institut fr Radioastronomie, Bonn, Germany 4Astronomical Institute,
Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic 5Observat´orio do Valongo/UFRJ, Brazil
6CdR & CdL Group: Lightcurves of Minor Planets and Variable Stars, Switzerland 7Observatoire de Chinon, Chinon, France
8Geneva Observatory, Switzerland 9Observat´orio Nacional/MCTI, Brazil 10Osservatorio Astronomico della regione autonoma Valle d’Aosta,
Italy 11Agrupaci´on Astron´omica de Fuerteventura, Spain 12Observatoire de Cabris, France 13Association des Utilisateurs de
D´etecteurs ´
Electroniques (AUDE), France 14Department of Imaging and Applied Physics, Curtin University of Technology, Bentley, Australia
15Osservatorio astronomico di Tradate, Italy 16Academia de ciencias e ingienerias de Lanzarote, Arrecife, Spain 17Institut d’Astrophysique,
G´eophysique et Oc´eanographie, Universit´e de Li`ege, Belgium 18 Euraster, St. Etienne, France 19Hamanowa Astronomical Observatory, Fukushima,
Japan 20CNRS, IRAP, Toulouse, France 21Astronomical Observatory Inst., Faculty of Physics, Adam Mickiewicz University, Pozna´n, Poland
22LESIA-Observatoire de Paris, CNRS, UPMC Univ. Paris 06, Univ. Paris-Diderot, Meudon, France 23 Association T60, Toulouse, France
24Stazione Astronomica di Sozzago, Italy 25Lauwin Planque, France 26 Institute of Planetary Research, German Aerospace Center, Berlin,
Germany 27Blauvac Observatory, St.-Est`eve, France 28Wiggins Observatory, Tooele, UT, USA 29SYRTE, Observatoire de Paris, France
30 January 2015
ABSTRACT
Asteroid (234) Barbara is the prototype of a category of asteroids that has been shown
to be extremely rich in refractory inclusions, the oldest material ever found in the Solar
System. It exhibits several peculiar features, most notably its polarimetric behavior.
In recent years other objects sharing the same property (collectively known as ”Bar-
barians”) have been discovered. Interferometric observations in the mid-infrared with
the ESO VLTI suggested that (234) Barbara might have a bi-lobated shape or even
a large companion satellite. We use a large set of 57 optical lightcurves acquired be-
tween 1979 and 2014, together with the timings of two stellar occultations in 2009, to
determine the rotation period, spin-vector coordinates, and 3-D shape of (234) Bar-
bara, using two different shape reconstruction algorithms. By using the lightcurves
combined to the results obtained from stellar occultations, we are able to show that
the shape of (234) Barbara exhibits large concave areas. Possible links of the shape to
the polarimetric properties and the object evolution are discussed. We also show that
VLTI data can be modeled without the presence of a satellite.
Key words: asteroid – shapes – occultations – photometry – interferometry
1 INTRODUCTION
The physical characterization of asteroids is of primary im-
portance for understanding their origin and evolution. Sim-
?Based in part on observations collected at the European Orga-
nization for Astronomical Research in the Southern Hemisphere,
Chile - program ID: 076.C-0798.
ple information such as rotation period and direction of the
spin axis have been related to evolutionary processes such
as accretion in the protoplanetary disk (Johansen & Lac-
erda 2010), impacts (Takeda & Ohtsuki 2007,2009;Marzari
et al. 2011;Holsapple & Housen 2012), thermal forces (Bot-
tke et al. 2006), internal cohesion and degree of fragmenta-
tion (Holsapple 2007), to cite a few notable examples.
Asteroid (234) Barbara exhibits peculiar features, such
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2015 RAS
2P. Tanga et al.
as an anomalous polarimetric behavior (Cellino et al. 2006),
a possible very irregular shape, a suspected large companion
(Delbo et al. 2009), a long rotation period (Schober 1981),
as detailed in Sect. 2. Polarimetry and near-infrared spec-
troscopy suggest that (234) Barbara and other similar aster-
oids could be composed by high fraction of the most ancient
solids formed in the Solar System, the Ca-Al-rich Inclusions
(CAI, see Sunshine et al. 2008).
These properties motivated a focused study of this tar-
get, given the substantial lack of other physical data. Here
we address in particular the determination of the shape and
the infirmation of the binary hypothesis. We proceeded by
setting up a long and intense campaign of photometric ob-
servations, complemented with two stellar occultations.
Traditional lightcurve inversion (e.g., Kaasalainen &
Torppa 2001;Kaasalainen et al. 2001), retrieving complex
shapes described by several parameters, converge to a unique
solution only under the hypothesis of convexity of the shape.
In the specific case of (234) Barbara, an imposed convexity
could hide the evidence of a bi-lobated structure, responsible
of the suspected presence of a satellite (Delbo et al. 2009).
Given the limitations of photometry when taken alone,
we also apply the inversion algorithm KOALA (Carry et al.
2010;Kaasalainen 2011), which can use data coming from
different sources for deriving a consistent, unique model of
an asteroid. Its main applications have concerned the joint
inversion of photometry, disk-resolved imaging and stellar
occultations. We illustrate in the following the results that
we obtained on the asteroid (234) Barbara by this approach.
Our efforts were focused on an observation campaign in
the period 2008-2011 (plus some additional data in 2014),
involving both time-series photometry and stellar occulta-
tions, whose results are presented in Sect. 3.1 and 3.2. We
were able to invert both photometric and occultation data
for deriving a 3-D shape model, as described in Sect. 4. We
use this model to validate the interferometric observations
at VLTI presented by Delbo et al. (2009), and eventually
discuss the implications of our results.
2 PECULIARITIES OF (234) BARBARA
Barbara is an asteroid belonging to the inner Main Belt, clas-
sified for a long time as a S type (Tedesco et al. 1989). Its
slow rotation (about 26.5 hours) was discovered by Schober
(1981). A detailed, dedicated, physical characterization for
this object was not attempted in the past, with the excep-
tion of spectroscopy. Owing to a slight excess in reflectance
in the red part of the spectrum with respect to the core of
the S class, followed by a flat plateau in the near-infrared,
Barbara was classified Ld in the Bus & Binzel (2002) tax-
onomy. From thermal radiometry with IRAS, a diameter of
44 ±1 km was derived (Tedesco et al. 2002) corresponding
to a geometric albedo pv= 0.22 ±0.01 (assuming an absolute
magnitude of H= 9.02). Other available size determinations
involve AKARI (47.8±0.68 km) and the Wide Infrared Sur-
vey Explorer (WISE). WISE yielded two measurements, but
one of them is clearly discrepant. We discuss this issue in de-
tail and provide a new, coherent diameter determination, in
Sect.4.
Cellino et al. (2006) pointed out that this asteroid has
an unusual polarimetric behavior. The degree of linear po-
larization of sunlight scattered by asteroid surfaces exhibits
a variation as a function of the illumination conditions, de-
scribed by means of the phase angle, namely the angle be-
tween the directions to the Sun and to the observer, as
seen from the asteroid. In particular, the morphology of the
phase-polarization curve has some general properties which,
apart from some differences related mainly to the geometric
albedo of the surface, tend to be shared by all known aster-
oids. The case of (234) Barbara is different, as it exhibits
a “negative polarization branch” wider than usual, with an
“inversion angle” around 30◦, a much larger value with re-
spect to the ∼20◦displayed by other objects (for details see
Cellino et al. 2006). We recall here that the negative polar-
ization corresponds to a polarization plane parallel to the
scattering plane.
A very similar phase-polarization curve was found later
on for other L, Ld and K-type asteroids (Gil-Hutton et al.
2008;Masiero & Cellino 2009), collectively known as “Bar-
barians” from the first discovered. Data concerning the as-
teroid (21) Lutetia seems to indicate also a peculiar polariza-
tion, but with a lower inversion angle (Belskaya et al. 2010)
intermediate between regular asteroids and Barbarians.
Several hypothesis have been formulated in the past for
explaining the high fraction of negative polarization. In par-
ticular, the role of coherent backscattering (Muinonen et al.
1989;Shkuratov et al. 1994) was invoked, normally associ-
ated to high albedos producing narrow and strong opposi-
tion peaks in the phase-brightness curve. Another possibility
is single particle scattering (Mu˜noz et al. 2000;Shkuratov
et al. 2002) on refractory inclusions. In fact, among mete-
orites, some carbonaceous chondrites (type CV3 and CO3)
produce the highest negative polarization, which could be
related to the abundance of fine-grained Ca-Al refractory
inclusions (CAI) (Zellner et al. 1977). Burbine et al. (1992)
suggested that (980) Anacostia, another object having po-
larimetric properties similar to (234) Barbara, could be a
spinel-rich body with a mineralogy similar to CO3/CV3 me-
teorites. The reason of the negative polarization should then
be related to the fine-grained structures of white spinel in-
clusions surrounded by a dark matrix (Burbine et al. 1992).
Sunshine et al. (2008) reached similar conclusions for Bar-
bara itself by comparing its visible and IR spectra to lab-
oratory spectra of CAI materials. Surprisingly, a satisfac-
tory match can be reached only when the fraction of spinel-
bearing CAIs is very high (up to 30% for explaining the
spectral features observed). If this finding were true, the
Barbarians should have formed in a nebula rich of refractory
materials, and would be among the most ancient asteroids
formed. No sample with high percentages of CAI is present
in the current meteorite collections.
If mineralogy is the culprit for the polarization anomaly,
it is then not surprising that all Barbarians belong to a sim-
ilar spectral class. At first sight, it is unclear why not all
other L, Ld, and K asteroids (and more in general the whole
S-complex) do not share similar polarization properties. For
example the L-type (12) Victoria has a usual polarization
with inversion angle ∼20◦. However, if the near-IR spectrum
is considered, all Barbarians belong to the same L class as
defined by DeMeo et al. (2009).
Cellino et al. (2006) suggested that anomalous polar-
ization could be due to large-scale concavities responsible
of introducing a distribution of scattering and incidence an-
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2015 RAS, MNRAS 000,1–10
The non-convex shape of (234) Barbara, the first Barbarian 3
gles different from those of a regular, convex surface. This
conjecture has never been proven to play a role, essentially
due to the lack of measurements at high phase angles of ob-
jects known to have large concave features. Also, theoretical
models do not seem to explore explicitly this possibility.
Asteroid (234) Barbara was one of the targets chosen for the
first interferometric observations of asteroids by the Very
Large Telescope Interferometer (VLTI), using the MID-
infrared Interferometer (MIDI, Leinert et al. 2003). This in-
strument can reach an angular resolution in the range 20-200
mas, depending on the choice of the baseline. It can thus be
used to measure the apparent size of asteroids, by modeling
the visibility of the interferometric fringes, independently
from other common methods, such as thermal infrared ra-
diometry. It can also be used to detect and study the orbit
of multiple asteroid systems. VLTI-MIDI observations, ob-
tained in November 2005, yielded an average diameter of
44.6 ±0.3 km. These observations and their processing are
extensively described in Delbo et al. (2009). Their main re-
sult, obtained by modeling the VLTI visibility function, is
the detection of a signature of duplicity of the source. In fact,
they show that a fit with a single object cannot reproduce
the data. A satisfactory fit requires a second component.
The resulting system, composed by two uniform disks ∼37
and ∼21 km in diameter, could be interpreted either as a
single object of irregular shape, or as a binary close to the
alignment with the line of sight. This model is reproduced
for ease of comparison in Fig. 6.
The unambiguous hints of a binary or bi–lobated body
has been an additional motivation for our focused study of
(234) Barbara. We stress here that we don’t use VLTI data
in the shape determination process described below (a rather
difficult task to the very different nature of such data). Con-
versely, we will test our derived shape against the VLTI ob-
servations.
Very recently, by observing the polarization properties
of the members of the high-inclination dynamical family of
the L-type (729) Watsonia, Cellino et al. (2014) discovered
that it is composed by Barbarians. This fact seems to indi-
cate that the Barbarian character is intrinsic to bulk prop-
erties of the body, not only to some surface effects. In fact, if
the anomalous polarization was limited to a surface process,
the parent body shattering and the subsequent fragment
mixing, would strongly dilute the polarimetric signature of
the original surface on the family members.
3 OBSERVATIONS
3.1 Photometric campaign
We obtained R-band photometry of Barbara starting in
June 2008. The most recent observations that we use in
our data reduction have been acquired in February 2014.
Given the long rotation period, a single site is highly inef-
ficient in covering a full rotation. We thus put at contribu-
tion many observers and telescopes, at widely different lon-
gitudes. Thanks to this considerable, shared effort we were
able to provide an adequate coverage of the brightness vari-
ations.
In Table 1we list the different photometric data sets
that we used for this study. A sample lightcurve is pre-
sented in Fig. 1. This result is the composite of 13 observing
Figure 1. Lightcurve obtained in June 2008 over 13 days by
M. Conjat (from the main OCA site) and P. Tanga (Tourrette-
Levens, private facility), folded on the rotation period of 26.474 h.
Each color represents a different observing session. As the observ-
ing sites were in the same geographic area, several nights were
needed to cover the entire rotation. The curve qualitatively repre-
sent the amplitude and shape of the brightness variation, hinting
to an irregular body.
sessions spanning ∼6 weeks, from two sites very close in
longitude. Over this time, the object changes its geometry,
relative to the Sun and to the observer, thus introducing
potentially complex variations that are not linked to the ob-
ject rotation alone. In particular, phase angle variations can
rapidly change shadowing effects. For this reason the folded
lightcurve has just an indicative value. From a qualitative
point of view, it is however interesting to note that the am-
plitude is rather large and the variation complex.
We can judge the long-term photometric coverage by
considering the ranges of ecliptic heliocentric longitudes cor-
responding to the three apparitions over which the asteroid
was observed. We thus obtain ∼357◦in September 1997,
260◦in June 2008, 160◦-180◦in the period November 2010 -
April 2011, and 120◦in February 2014. The distribution over
different values in ecliptic longitude favors the coverage of
the largest possible range of aspects angle allowed by the
pole obliquity.
3.2 Stellar occultations
Two stellar occultations by (234) Barbara were successfully
observed by our team and collaborators, on October 5, 2009
and only a few weeks later, on November 21, 2009. Both
target stars had a magnitude V<8, which greatly facili-
tated the use of portable instruments and the deployment
of several stations.
The first event took place on the Atlantic Ocean, with a
predicted path passing on Canary Islands and central Africa.
An expedition from France installed portable observing sta-
tions on the islands of Fuerteventura and Lanzarote (south-
ern tip). Local amateur astronomers contributed with equip-
ment at further sites, and logistic support. Good weather
granted nearly optimal conditions and several chords of the
occultation were recorded (see Table 2). The positive re-
sult showed that the prediction was very accurate, the real
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4P. Tanga et al.
Table 1. Photometric observing runs used to derive the shape of (234) Barbara. The full table is available among the online resources.
Legend: ℵ: 0.32 m Observatoire du Chinon (France): M. Audejean. [: 0.40 m, Hamanowa Astronomical Observatory (Japan): H. & H.
Hamanowa. : 0.4 m Observatoire de la Cˆote d’Azur (France): M. Conjat; and 0.2 m Specola Tourrette Levens: P. Tanga. ]: From
Schober (1981).
Session start (yyyy-mm-dd hh:mm) Duration (min.) N obs. Notes
1979 09 13 05:11 262 138 ]
1979 09 14 01:54 455 212 ]
1979 09 15 02:06 437 64 ]
2008 06 18 20:56 226 51
2008 06 19 20:46 236 41
2008 06 20 20:58 279 34
2008 06 21 20:41 313 52
2008 06 22 20:45 291 41
2008 06 23 20:35 216 34
2008 06 25 20:41 283 50
2008 06 26 20:45 256 46
2008 06 27 21:21 182 41
2008 06 28 21:18 157 36
2009 11 18 23:21 22 51 =
2009 11 24 23:16 121 25 ℵ
2009 11 25 22:55 160 13 ℵ
2009 11 25 12:41 206 17 [
...
Complete table available in the online resources.
shadow being shifted southward relatively to predictions by
∼10 km only.
The high reliability of the asteroid positional ephemeris
was a precious information for planning the deployment of
the observers around the path of the following event. Several
astronomers in the United States gathered in Florida and
few others in central Europe at the oriental extreme of the
path. The noticeable effort for the deployment of several
automated stations by single observers was successful, thus
securing a dense set of occultation chords (Table 3). For
both events the entire data set is available, for example, at
PDS1(Dunham et al. 2011).
Data reduction of the occultation on October 5, 2009
event results in the strong hint of an elongated, oval shape
(Fig. 2), with possible irregular features. The observed
chords on November 21, 2009 consistently draw an overall
triangular shape, with a large and pronounced concavity at
the South limb, and hints of other minor concavities (Fig. 2).
Both occultations provide an average size consistent with the
results obtained at VLTI (Sect. 4).
Other occultation events by Barbara were observed
later on. We neglect here the results obtained on December
14, 2009 in the USA, given that only 3 chords are available
(Dunham et al. 2011). Also, positive observations of the oc-
cultation on January 17, 2010, obtained in Japan, have not
been used as the faintness of the target star (V=12.0) pre-
vented accurate timings.
None of the observed occultations presents secondary
events linked to the presence of possible satellites in prox-
imity of the primary body.
4 SHAPE AND SPIN DETERMINATION OF
(234) BARBARA
As the occultations indicate the clear presence of concav-
ities and the lightcurve is rather irregular, a simultaneous
inversion by KOALA of photometry and occultation data
1http://sbn.psi.edu/pds/resource/occ.html
East-West (km)
North-south (km)
-50
-30
-10
10
30 12009-10-05 03:52
1s
CCD,Video
Negative
Visual
Duration-only
-30 -10 10 30 50 70 90
-50
-30
-10
10
30 22009-11-21 03:23
5s
Figure 2. Plot on the plane of the sky of the occultation chords
reported in Tables 2and 3. The different line formats distinguish
among positive observations (CCD, Video), negative ones, visual
timings, and duration measurements. The profile of (234) Barbara
at the epoch of each occultation, as derived by the shape model
presented in this article, is represented by the black contours.
appeared necessary (see Kaasalainen 2011;Carry et al. 2010,
2012, for a description of the algorithm). For a further con-
sistency check we also ran the usual lightcurve-only inversion
(e.g., Kaasalainen & Torppa 2001;Kaasalainen et al. 2001)
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The non-convex shape of (234) Barbara, the first Barbarian 5
Table 2. Observers and chords for the occultation of HIP32822 (V=7.77), on 2009 October 5. The UT columns contain the epochs
associated to each chord. In the “Event” column, the flags can be: M = missed, no occultation observed; D = disappearance; and R
= reappearance. Uncertainties on timing in seconds at the 3-σlevel are provided. Some observers were capable of deploying multiple
stations, so their name appear more than once.
# Observer and site UT Event 3σUT Event 3σ
1 Vachier, Morro del Jable, Spain M M
2 Vachier, Costa Calma, Spain M M
3 Lecacheux, Gran Tarajal, Spain M M
4 Maquet, Tuineje, Spain M M
5 Lecacheux, Antigua, Spain 04 10 22.02 D 0.03 04 10 24.50 R 0.03
6 Maquet/de Ferra/Cedr´es, Tefia, Spain 04 10 22.25 D 0.02 04 10 25.11 R 0.02
7 Colas/Vera, La Oliva, Spain 04 10 22.44 D 0.02 04 10 25.21 R 0.02
8 Colas, Corralejo, Spain 04 10 23.50 D 0.15 04 10 24.96 R 0.15
9 Tanga, Playa Blanca, Spain M M
Table 3. Similar as Table 2, for the occultation of the star HIP34106 (V=7.5), on 2009 November 21.
# Observer and site UT Event 3σUT Event 3σ
1 Harris, Deltona, FL, USA M M
2 Dunham, Okahumpka, FL, USA M M
3 Dunham, Center Hill, FL, USA M M
4 Venable, Webster, FL, USA M M
5 Venable, Tarrytown, FL, USA M M
6 Venable, Tarrytown, FL, USA 03 38 34.27 D 0.03 03 38 35.62 R 0.03
7 Dunham, Groveland, FL, USA 03 38 32.77 D 0.10 03 38 34.21 R 0.10
8 Maley, Clermont, FL, USA 03 38 32.18 D 0.05 03 38 36.01 R 0.05
9 Fernandez/N Lust, Orlando, FL, USA 03 38 26.70 D 0.50 03 38 30.60 R 0.50
10 Dunham, Green Pond, FL, USA 03 38 32.63 D 0.02 03 38 38.37 R 0.02
11 Maley, Polk City, FL, USA 03 38 32.82 D 0.02 03 38 39.16 R 0.02
12 Turcani, Christmas, FL, USA 03 38 27.30 D 0.10 03 38 34.50 R 0.10
13 Bredner, Germany 03 18 12.40 D – 03 18 18.70 R –
14 Maley, Polk City, FL, USA 03 38 33.90 D 0.10 03 38 41.50 R 0.02
15 Maley, Polk City, FL, USA 03 38 34.52 D 0.02 03 38 42.79 R 0.02
16 Povenmire, Deer Park, FL, USA 03 38 28.30 D 0.30 03 38 37.50 R 0.30
17 Denzau, Panker, Germany 03 18 02.68 D – 03 18 10.64 R –
18 Maley, Polk City, FL, USA 03 38 34.61 D 0.02 03 38 43.85 R 0.02
19 Iverson, Harmony, FL, USA 03 38 30.95 D 0.02 03 38 40.23 R 0.02
20 Coles, Harmony, FL, USA 03 38 30.73 D 0.03 03 38 40.01 R 0.03
21 Degenhardt, Deer Park, FL, USA 03 38 29.61 D 0.02 03 38 38.77 R 0.02
22 Degenhardt, Deer Park, FL, USA 03 38 36.26 D 0.02 03 38 38.79 R 0.02
23 Degenhardt, Deer Park, FL, USA 03 38 29.96 D 0.02 03 38 33.96 R 0.02
24 Degenhardt, Deer Park, FL, USA 03 38 31.70 D 0.10 03 38 33.50 R 0.02
25 Degenhardt, Deer Park, FL, USA 03 38 32.23 D 0.02 03 38 33.16 R 0.02
26 Degenhardt, Deer Park, FL, USA 03 38 33.27 D 0.02 03 38 33.40 R 0.02
27 Degenhardt, Deer Park, FL, USA M M
28 Bulder, Buinerveen, The Netherlands M M
to retrieve a convex model, the close envelope of the concave
shape.
In running the pure photometric inversion, we decided
to include sparse photometry to better constrain rotation
period and spin vector coordinates, to compensate the short
coverage of lightcurves induced by the long rotation period
of Barbara. The whole procedure is described in detail in
(Hanuˇs et al. 2013). In our case we selected 182 and 124 pho-
tometric measurements coming from the USNO–Flagstaff
station (IAU code 689) and the Catalina Sky Survey (IAU
code 703, Larson et al. 2003), respectively, that were added
to our collection of 57 dense lightcurves. We started by
searching for optimum sidereal rotation period, by using
the period scan software, available on DAMIT2(ˇ
Durech
et al. 2010), on the combined data set of lightcurves and
sparse photometry (Fig. 3). Starting from the best-fit pe-
riod of 26.4744 h, we then explored the possible locations of
the spin-vector coordinates. We ran a full exploration of the
2http://astro.troja.mff.cuni.cz/projects/asteroids3D/
Table 4. Shape and spin vectors for (234) Barbara. In the bot-
tom section, the overall shape parameters (axis ratios of the best-
fitting ellipsoid) are listed.
Parameter light-curve only KOALA Unit
Period 24.4744 ±0.0001 24.4744 ±0.0001 h
Pole (λ,β) (156,-46) (144,-38) deg.
DV46.3 ±5 km
a/b 1.12 1.11
b/c 1.59 1.14
ecliptic J2000 celestial sphere (λ,β) by keeping the period
fixed. For each position of the spin axis we computed the
residuals of the model-derived brigthness, with respect to
the photometric measurements. The resulting map of resid-
uals is shown in Fig. 4. The resulting pole coordinates and
rotation periods are in Table 4.
At negative latitudes, several minima in the residual
map appear. The two deepest ones (around λ∼150◦and
290◦) are both candidates for the spin axis direction. The
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6P. Tanga et al.
26.00 26.05 26.10 26.15 26.20 26.25 26.30 26.35 26.40 26.45 26.50 26.55 26.60 26.65 26.70 26.75 26.80 26.85 26.90 26.95 27.00
Sidereal period (h)
0.046
0.048
0.050
0.052
0.054
0.056
0.058
RMS residuals
Figure 3. The RMS deviation of the photometry relative to the convex model, against sidereal rotation period.
0 90 180 270 3600
-90
-60
-30
0
30
60
90
0
ECJ2000 Longitude (o)
ECJ2000 Latitude (o)
8.7 9.8 10.8 11.9 13.0 14.0
RMS
Figure 4. The RMS deviation of the photometry relative to the
convex model, obtained by exploring the whole space of pole co-
ordinates. In the plot, the ecliptic longitude λis on the horizontal
axis, and the ecliptic latitude βon the vertical. Red and black
values visualize the position of the minima.
fact that the solution is not unique clearly illustrates the
challenge of the inversion process, despite the large number
of lightcurves available. This is most probably due to the
rather slow rotation. In such conditions, all the lightcurves
embrace only very limited portion of the entire rotation (less
than 20% on average).
As the convex solution is not perfectly constrained, the
computation of a shape without the convexity constraint
(i.e., with concavities) might appear as an academic exer-
cise. However, the concavities explored by the occultations
are well constrained by the accuracy and the consistency
of the timings, in particular for the event of November 21,
2009. For this reason, it seemed appropriate to attempt an
inversion by KOALA, including both occultations and pho-
tometry. In the process, KOALA adapts the concavities to
the occultations, but will also tend to create other less-
constrained concavities to better reproduce the photometry.
For this reason the result should not be taken at face value.
Nevertheless we expect the shape to be approximately con-
sistent with the possible VLTI detection of a very elongated
or bi-lobated objects (see further below).
Considering the amount and the high quality of the tim-
ings for the stellar occultation of 2009 November 21, we
chose to use the profile drawn by the chords as if it was
obtained by disk-resolved imaging. This assumption was re-
quired to model the large concavity revealed by the inter-
rupted chords at the South limb. We consider that this ap-
proach is fully justified and does not introduce a significant
bias, since the number of positive chords available allowed a
profile sampling with a resolution close to that obtained in
disk-resolved imaging.
We thus ran KOALA to determine the best-fit period,
spin, and 3-D shape to the lightcurves and stellar occul-
tations, using the period and two spin locations determined
above. We then checked the two solutions against the overall
outline obtained from the MIDI-VLTI observations in 2005.
The solution with a spin axis lying close to ECJ2000 (144◦,
-38◦) provided a good match to the geometry derived from
interferometric fitting (see Fig. 6and Delbo et al. 2009). The
resulting shape is shown in Fig. 5.
The resulting comparison has to be interpreted by tak-
ing into account the orientation of the VLTI baseline, es-
sentially aligned along the direction of a protruding region
in the NE direction. Clearly, this protrusion is the most
relevant irregularity found by KOALA and can be related
to the “secondary” body revealed by VLTI observations. It
also happens to be well constrained by the occultation data.
In fact, it appears close to the main concavity observed in
November 2009 (and pointing downward in Fig. 2).
The 3-D model of Barbara derived here is made of
512 triangular facets3and is scaled to absolute dimensions
thanks to the contribution of stellar occultations. The mesh
volume of our model is equivalent to a sphere having a di-
ameter of 45.9 km.
These size measurements should be compared to the
thermal diameter derived by AKARI (47.8±0.68 km) and
IRAS (43.7±1 km). WISE derived 53.80±1.12 km in the
fully cryogenic phase (Masiero et al. 2011) and 45.29±1.33
km during the 3-band cryogenic/post-cryogenic operation
(Masiero et al. 2012). The first of the WISE measurements
is clearly discrepant from all the other measurements. This
3The model is available on DAMIT
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2015 RAS, MNRAS 000,1–10
The non-convex shape of (234) Barbara, the first Barbarian 7
!
Y
X
Z
X
X
X
T
Y
Y
Y
Z
Z
Z
Figure 5. Four different projections of (234) Barbara. The two panels at the top have the South axis pointing upward. At bottom left,
the South polar view is presented. At bottom right, a view at an intermediate aspect angle, strongly enhancing the visibility of concave
areas. The z axis is parallel to the spin axis.
discrepancy is due to the assumption made in Masiero et al.
(2011) that the 4.6-µm albedos are equal to the 3.4-µm albe-
dos, which biases the relative contributions of thermal flux
and reflected sunlight in the WISE 4.6-µm data. By fitting
the NEATM to the fully cryogenic, purely thermal WISE
bands (12 and 22 µm), we obtained a thermal diameter of
46 ±7 km (for details on our particular data selection crite-
ria and procedure see Al´ı-Lagoa et al. 2013, and references
therein). Since the average of the four accepted values (45.7
km) is just 200 m less than our volume-equivalent diameter
(0.4% relative difference), we consider that our model size
is in excellent agreement with the thermal diameters.
Unfortunately, the sole published mass estimate (Fienga
et al. 2010) is very poorly constrained (0.44 ±1.45 ×1018 kg)
and cannot be used to derive the density or to draw any con-
clusion on the internal structure.
5 DISCUSSION
As suggested by stellar occultation and VLTI data, the
shape of (234) Barbara is highly irregular with the presence
of large concavities.
At all apparitions, the brightness variations seems to
have approximately a similar amplitude, despite the change
in aspect angle. This is probably to be ascribed to the ubiq-
uitous irregularities - present for all illumination and obser-
vation directions.
The derived shape, when rotated at an orientation cor-
responding to the VLTI observations, suggests an interpre-
tation of the interferometric signal as the presence of a big
prominence oriented along the baseline. Our results thus
show that the VLTI observations can be explained with-
out the presence of a large satellite. Stellar occultations also
failed to show the presence of such a companion. Of course,
this evidence cannot exclude that small satellites might be
orbiting (234) Barbara (a few km in size), but they have no
signatures in the available data.
Concerning the origin of the object and its collisional
history, the absence of an identified family around (234) Bar-
bara makes any interpretation loosely constrained.
A first possibility is that (234) Barbara is in fact the
assemblage of two bodies of different sizes, resulting in a bi-
lobated object. This interpretation could be consistent with
the prominence revealed by VLTI. However, with the current
limitations on the shape resolution and in absence of other
constraints, this scenario remains rather speculative.
Another common factor of reshaping and excavation
are, of course, non-disruptive impacts. In this case, we can
reasonably assume that the convex hull of the shape of Bar-
bara could represent the minimum volume that the original
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2015 RAS, MNRAS 000,1–10
8P. Tanga et al.
-100 -50 0 50 100
-100
-50
0
50
100
km
N
E
Proj. baseline
Figure 6. Comparison of the binary model of Barbara derived
by Delbo et al. (2009) in blue lines with the KOALA shape model
(black contour) at the time of VLTI observations. The irregular
shape of Barbara mislead the interpretation, by mimicking the
signal of a binary system projected on the VLTI baseline. As
spatial resolution is missing in the direction perpendicular to the
baseline, the dashed lines enclose possible locations for a satellite
compatible with the VLTI signal.
body had, before being excavated by impacts. If no ejecta
fall back is considered, we find an excavated volume 6.8%
of the convex hull, representing 3.7×1012 m3. Since some
fall-back probably occurred, the dislocation of the material
could have been much more important.
According to Davis et al. (2002, Fig. 6), the probability
that a 50-km object is a re-accumulated rubble-pile ranges
from 45 to 70%.
The possibility of a rubble-pile structure is probably
strengthened by the relatively slow rotation period of (234)
Barbara. The role of non-destructive impacts on the evo-
lution of rotation periods of relatively large asteroids has
been the subject of several studies in the past. It has been
suggested that collisions could diminish the angular momen-
tum on average, carried away by escaping fragments, both
in the case of craterization events (Dobrovolskis & Burns
1984, “angular momentum drain”) and in shattering impacts
(Cellino et al. 1990, “angular momentum splash”). This last
mechanism was invoked to explain the fact that asteroids
smaller than ∼100 km have shorter average rotation peri-
ods than larger ones (Farinella et al. 1992). More recently,
detailed numerical simulations of impacts on rubble-pile as-
teroids (Takeda & Ohtsuki 2007,2009) have shown that spin
down is in fact a common consequence of impact events. If
this was the case for (234) Barbara, we can suggest that one
or more impacts subtracted angular momentum from an ini-
tially much larger body. Internal fragmentation during the
process would then be a natural outcome of the collisional
sequence that slowed down rotation and excavated the large
concavities. A long history of collisional de-spinning and the
ancient age of the material seem to suggest a self-consistent
scenario, supporting the idea that Barbarians might be very
old objects.
The data that we have at our disposal do not show the
evidence of a Barbara family, suggesting that the impact
events could be very old, and the hypothetical family is now
indistinguishable from the background. Future spectroscopic
surveys could permit the detection of an anomalous concen-
trations of L/Ld-type asteroids in the corresponding region
of the orbital elements space.
6 CONCLUSIONS
Stellar occultations, coupled to photometry, are a powerful
tool to characterize bodies that present concave features.
They were seminal in obtaining the shape of (234) Barbara,
appearing to be very irregular and dominated by large con-
cavities. One of these concavities is particularly extended
and well sampled by our occultations.
The non-convex model that we present can still be im-
proved and confirmed by more extensive observing cam-
paigns, however it appears to explain the observations pre-
viously obtained at VLTI. The sky projection of the largest
prominence present on the object is aligned to the VLTI
baseline at the epoch of observation, mimicking the signa-
ture of a bi-lobated object.
Even if apparently our results seem to support the direct
relation of concavities to polarization properties (Cellino
et al. 2006), this is valid only in the empirical sense, as it
has no theoretical ground at present. In principle it might
be possible that the presence of concavities is related to po-
larimetry only in an indirect sense. For example, the colli-
sional excavation could have changed the composition or the
texture of the surface, by exposing layers that remain oth-
erwise hidden, or by redistributing/ejecting a layer of sur-
face regolith. On the other hand, as the “barbarians” share
common spectral properties, we cannot exclude that their
peculiar polarimetry is essentially due to their bulk compo-
sition. The recent discovery of several Barbarians inside the
Watsonia family seems to corroborate this hypothesis, as it
implies the transmission by direct heritage of the Barbarian
properties from the parent body to family members (Cellino
et al. 2014).
We underline the role played in this work by a large col-
laboration of amateur and professional astronomers, both in
obtaining an adequate photometric coverage and in securing
the positive results of the two occultations that have allowed
us to constrain the concavities. The long rotation period,
and its commensurability to the duration of Earth’s day is
an obstacle to an efficient coverage of the object rotation.
A network of observers at different longitudes constitute
a clear advantage that we will try to exploit in future photo-
metric campaigns devoted to barbarian asteroids. Obtaining
more shapes of the Barbarians, polarimetric measurements
and near-infrared spectra to confirm the presence of spinel-
rich inclusions is required to better understand such objects
that could represent a rare sample of CAI-rich Solar Sys-
tem bodies, dating back to the first phases of Solar System
formation.
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2015 RAS, MNRAS 000,1–10
The non-convex shape of (234) Barbara, the first Barbarian 9
ACKNOWLEDGMENTS
This research used the Miriade VO tool developed at IM-
CCE (Berthier et al. 2008) and MP3C at OCA (Delbo’ and
Tanga, http://mp3c.oca.eu/). We acknowledge the financial
support of the occultation activity carried on by OCA mem-
bers, from the BQR program of the Observatoire de la Cˆote
d’Azur, the Action Specifique Gaia, and the Programme Na-
tionale de Plan´etologie. The work of JH was carried under
the contract 11-BS56-008 (SHOCKS) of the French Agence
National de la Recherche (ANR). We thank the develop-
ers and maintainers of Meshlab and VO Topcat software.
TRAPPIST is a project funded by the Belgian Fund for Sci-
entific Research (Fonds de la Recherche Scientifique, F.R.S
FNRS) under grant FRFC 2.5.594.09.F, with the partici-
pation of the Swiss National Science Fundation (SNF). E.
Jehin and M. Gillon are FNRS Research Associates, J. Man-
froid is Research Director FNRS. A. Matter acknowledges
financial support from the Centre National d’Etudes Spa-
tiales (CNES). We thank all the members of “Agrupaci´on
Astron´omica de Fuerteventura” for the coordination of the
observations and the “Cabildo de Fuerteventura” for the lo-
gistic support in Tef´ıa observatory. Also, S. Degenhart is
acknowledged for the organization of the campaign in the
U.S.A. that yielded the second occultation profile presented
in this paper.
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