Portraits of Barbarians: linking anomalous polarimetry to physical properes

Figure 6: Colored map of concave region corresponding to the main candidate crater. The color correspond to curvature. Concavities are represented in red and yellow. A measurement on the minor and major extensions of this region provide 22 15 km. The uncertainty is of the same order as the mesh resolution, i.e. around 3 km. ⇥ P. Tanga1, A. Cellino2, S. Bagnulo3 1 : Laboratoire Lagrange, Observatoire de la Côte d'Azur, Nice, France, 2 : INAF/Osservatorio Astrofisico di Torino, Italy 3. Armagh Observatory, UK 17 234 Barbara

Discovered on August 12, 1883 by C.H.F. Peters in Clinton, NY

Magnitude H 9.02

Inclinaon 15.35305 Eccentricity 0.2437485 Semimajor Axis 2.3864727

Tholen class S SMASS II class Ld

WISE AKARI IRAS Size km 53.8 47.8 43.7 Albedo 0.15 0.19 0.22

Shober et al. 1981

Paolo Tanga – Sept 23, 2013 1.5 L S 1.4

1.3

1.2

1.1 Reflectance

1

0.9

0.8 0 0.5 1 1.5 2 2.5 Wavelength (microns) Bus and Binzel (2002): L-class: similar to S, but strongly reddish <750 nm and featureless >750 nm Ld class: even redder

Paolo Tanga – Sept 23, 2013 Cellino et al., 2006

1 Ceres (G) 7 Iris (S) “The strange polarizaon of 234 Barbara” Icarus 180, 2, 565

12 Victoria (L)

Paolo Tanga – Sept 23, 2013 New findings: Gil-Huon et al. 2008 312 R. Gil-Hutton et al.: New cases of unusual polarimetric behavior in asteroids

2

1.5 172 Baucis 234 Barbara

1 236 Honoria 679 Pax 980 Anacosa 0.5

0 Pr (%)

-0.5

-1

-1.5

-2 0 5 10 15 20 25 30 35 Phase angle (deg.)

Fig. 1. Polarimetric observations of asteroids with Barbara-like polarimetric properties. Data for (172) Baucis are indicated by circles, for (234) Barbara by squares, for (236) Honoria by triangles, for (679) Pax by diamonds, and for (980) Anacostia by inverted triangles. Filled symbols indicate data taken during our present campaign. For a comparison, data for the L-class asteroid (12) Victoria are displayed by crosses, together with the corresponding fit of its phase-polarization curve. for the polarimetric parametersthatcharacterizethephase- 4. Discussion polarization curve of these objects are Pmin = 1.48 0.03% Paolo Tanga – Sept 23, 2013 | | ± at αmin = 13.6◦, h = 0.200 0.002%/◦,andα0 = 28.0◦ for Since our polarization measurements for these objects have been Baucis; and P = 1.52 ± 0.08% at α = 13.2 , h = obtained on different nights during different observing runs, and | min| ± min ◦ 0.206 0.005%/◦,andα0 = 27.3◦ for Barbara. These values they agree well with each other with reasonably small error bars, are similar± to those found for the whole group. we conclude that the observed behavior is real and represents It is possible to use these parameters to find the polarimet- new cases of asteroids exhibiting a strongly negative polarization ric albedo p applying two empirical relations linking it with h at phases larger than 20◦. or Pmin.Theserelationsareexpressedbymeansofverysimple In Table 3,welistasummaryofourcurrentknowledgeof mathematical forms: the dynamical and physical parameters for these asteroids. They are objects distributed along themainbelt,havingtypicalsizes and albedos. The only physical parameter in common is that all log p(h) = C1 log h + C2, (2) of them have similar taxonomic classes: four asteroids belong to the L-class and the other one to the K-class. These taxonomic log p(Pmin) = C3 log Pmin + C4, (3) classes were proposed by Bus & Binzel (2002)andaresubsets of the old broad S-class defined by Tholen (1989). The differ- ences between them are a change in the UV slope shortward of where C1, C2, C3,andC4 are constants. In this paper we use the set of constants proposed by Cellino et al. (1999), namely: 0.75 µmfrommoderatelysteep(K-class)toverysteep(L-class), and a subtle change in the spectral slope longward of 0.75 µm. C1 = 1.118 0.071,C2 = 1.779 0.062,C3 = 1.357 0.140, − ± − ± − ± Since their sizes do not allow them to support a developed re- and C4 = 0.858 0.030. Using these empirical relations with the polarimetric− ± parameters found previously, we obtain golith of fine particles and the only agreement in their physical properties is their similar taxonomic class, the broad negative p(h) = 0.11 0.02 and p(Pmin) = 0.09 0.01 for all the asteroids ± ± branch of their phase-polarization curves must be explained by in the group, p(h) = 0.10 0.02 and p(Pmin) = 0.08 0.01 for ± ± aphysicalpropertyoftheasteroidsurface,itscomposition,ora (172) Baucis, and p(h) = 0.10 0.02 and p(Pmin) = 0.08 0.01 for (234) Barbara. It is clear, however,± that the above albedo± val- combination of both. ues have to be taken with some care because we are applying The first clue comes from the work of Zellner et al. (1977) here the usual relations to find the albedo to objects which dis- on laboratory polarimetry of meteorites. These authors found play an unusual polarimetric behavior, and we cannot be sure a peculiarly large values of the inversion angle for the carbona- priori that these relations also hold in this case. ceous chondrites, especially for the C3 samples, reaching α0 Tentave explanaons of the polarimetric anomaly:

• “a very speculave possibility”: very large impact craters/concavies on the surface (Cellino et al. 2006)

• CO3/CV3 spinel-bearing meteorites have high negave polarizaon and inversion angles (Zellner 1977).

Spinel = MgAl2O4 oen associated to metals (Fe, Cr) à reddening of the spectrum

CO3/CV3 à relaon to K- and L-class asteroids (Burbine et al 1992, 2001, Sunshine et al 2007)

Paolo Tanga – Sept 23, 2013 The connecon to CV meteorites

Sunshine et al., 2007

fluffy w. spinel

FeO absorpon

Paolo Tanga – Sept 23, 2013 Northwest Africa group of CV3s

NWA 2086 (CV3)

NWA 2364 (CV3) Refractory inclusions up to 13% in CV3.

Most ancient materials in the Solar System ever dated: 4.568 billion yrs

Paolo Tanga – Sept 23, 2013 No meteorite samples of this kind?

CAIs type B FTA CAIs

Radiave transfer model by Sunshine et al 2008. 30% of fluffy-type (unaltered) CAIs are required…

(Note: visual poron poorly modeled)

Paolo Tanga – Sept 23, 2013 1232 DELBO ET AL. Vol. 694

3 1.2 data (a) Data NEATM NEATM (b) STM STM 2.5 FRM 1 FRM Uniform Disk Disk 2 0.8 NEATM

0.6 STM 1.5 flux (Jy)

The Astrophysical Journal,694:1228–1236,2009April11 doi:10.1088/0004-637X/694/2/1228

Calibrated visibility More on 234 Barbara 0.4 C 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A. ! 0.2 The Astrophysical JournalFRM ,694:1228–1236,2009April10.5 doi:10.1088/0004-637X/694/2/1228 C 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A. ! FIRST0 VLTI-MIDI DIRECT DETERMINATIONS0 OF ASTEROID SIZES∗ 3.5e+06 4e+06 4.5e+06 5e+06 8 9 10 11 12 13 14 -1 B/λ (rad ) wavelength (microns) M. Delbo1,2,S.Ligori3,A.Matter4,A.Cellino5,andJ.Berthier6 Figure 2. (a) Observed1 interferometric visibility data for (951) Gaspra, and the corresponding best fit by means of a uniform disk model. The NEATM, STM, and FRM curves are the predictedUNS, interferometric CNRS, Observatoire visibility derived de la from Coteˆ the d’Azur, three thermal BP model4229 06304solutions Nice obtained cedex from 04, the France measured infrared fluxes in the range between 8 2 andINAF-Osservatorio 13 µm (measured visibilities Astronomico were not di used Torino in the Strada thermal Osservatorio models fits).FIRST (b) 20, The 10025 measured VLTI-MIDI Pino thermal Torinese, infrared Torino, fluxes at DIRECT Italy; [email protected] wavelengths, DETERMINATIONS and the corresponding OF ASTEROID SIZES∗ best-fit solutions3 INAF-Osservatorio by means of the three Astronomico thermal models di Torino described Strada in the Osservatorio text. 20, 10025 Pino Torinese, Torino, Italy MIDI@VLTI, 8-13 4 UNS, Observatoireµm (in Nov. 2005) de la Coteˆ d’Azur, BP 4229 06304 Nice cedex 04, France 5 No. 2, 20091,2 MIDI-VLTI3 OBSERVATIONS OF ASTEROIDS4 5 1235 6 INAF-Osservatorio Astronomico di Torino Strada OsservatorioM. 20,16 10025 Delbo Pino Torinese,,S.Ligori Torino, Italy ,A.Matter ,A.Cellino ,andJ.Berthier 0.3 6 1 data this object (Cellino et al. 2006). The above properties are most Institut de Mecanique Celeste (IMCCE)data 77 av. Denfert Rochereau,UNS, 75014 CNRS, Paris, Observatoire France de laNEATM Coteˆ d’Azur, BP 4229 06304 Nice cedex 04, France NEATM (b) 100 STM likely due to an unusual surface composition of this object, as (a)Received 2008 August 26; accepted2 2008 December 16;14 published 2009 March 24 N INAF-OsservatorioSTM Astronomico di Torino StradaFRM Osservatorioalso suggested by 20, its unusual 10025 taxonomic Pino classification. Torinese, We have Torino, Italy; [email protected] 0.25 FRM here a very interesting example of an object which seems to Uniform Disk 3 12 exhibit clear evidence of a complex history, and this makes it Binary INAF-Osservatorio Astronomico di Torino Strada Osservatorio 20, 10025 Pino Torinese, Torino, Italy ABSTRACT 50 ahigh-prioritytargetforfurtherobservationsandtheoretical 4 investigations. 0.2 STM 10 UNS, Observatoire de la Coteˆ d’Azur, BP 4229 06304 Nice cedex 04, France We have obtained the first successful interferometric measurements5 of asteroid sizes and shapesSecondary by means of the INAF-Osservatorio Astronomico di Torino StradaWe Osservatoriothank the staff and the 20, Science 10025 Archive Operation Pino Torinese, of Torino, Italy 8 0 E the European Southern Observatory (ESO), and in particular Very Large Telescope0.15 Interferometer-Mid-Infrared Interferometric Instrument6 km (VLTI-MIDI). The VLTI can spa-

flux (Jy) Institut de Mecanique Celeste (IMCCE)Markus 77 av. Wittkowski. Denfert The comments Rochereau, and suggestions 75014 from an Paris, France tially resolve asteroids in a range of sizes and heliocentric distances that6 are not accessible to otherPrimary techniques suchanonymous referee are gratefully acknowledged. The work of Received 2008 August 26; accepted 2008M.D.B. December has been supported 16; by the published European Space 2009 Agency March 24

Calibrated visibility 0.1 as adaptive optics and radar. We have observed, as a typical bench mark, the-50 asteroid (951) Gaspra, visited in the(ESA). This research was partially carried out while M.D.B. 4 was a Henri Poincare´ Fellow at the Observatoire de la Coteˆ past by the Galileo space probe, and we derive a size inNEATM good agreement with the groundProj. baseline truth coming from the Disk d’Azur. The Henri PoincareFellowshipisfundedbytheCNRS-´ 0.05 in situ measurements by the Galileo mission. Moreover, we have also2 observed the asteroid (234) Barbara, knownINSU, the Conseil Gen´ eral´ des Alpes-Maritimes, and the Rotary ABSTRACTInternational—District 1730. This work has been partially FRM -100 to exhibit unusual polarimetric properties, and we found evidence of a potential binary nature. In particular, ourfunded through the project PRIN INAF 2007 no. 6. M.D.B. 0 0 -100 -50 0 50 100 thanks O. Chesneau, D. Loreggia, L. Saba, and M. Zio for data are best fit by3.5e+06 a system4e+06 of two4.5e+06 bodiesWe of5e+06 have 37 and5.5e+06 obtained 21 km6e+06 in diameter, the first8 separated successful9 by a10 center-to-center interferometric11 12 distance13 measurementsvaluable of 14 comments and discussions, of and asteroid D. Licchelli for having sizes and shapes by means of the -1 km 24 km (projected along the directionB/λ of(rad the) baseline at the epoch of our observations).wavelength (microns) made at disposal the set of lightcurves of (951) Gaspra obtained Figure 6. Sketch of the binary model for the asteroid (234) Barbara resulting quasi-simultaneously to the MIDI observations. ∼ Figure 3. Same as Figure 2,butfor(234)Barbara.In(Very Largea), in addition Telescope to the interferometric Interferometer-Mid-Infraredfrom visibility VLTI-MIDI predicted observations. by The a uniform most external disk circle model represents and the to width the Interferometric thermal model Instrument (VLTI-MIDI). The VLTI can spa- of the 10 µm beam of the UT telescopes in which the source must be solutions, the best-fit interferometric visibility of the binary model (see the text) is also plotted. Note how the latter model produces a clearly muchbetterfittothe positioned in order to provide an interferometric signal measurable by MIDI. REFERENCES observations than the others. tially resolve asteroids inThe a secondary range component of of the systemsizes Paolo Tanga – Sept 23, 2013 can be anywhere and within heliocentric the two dashed distances that are not accessible to other techniques such Key words: infrared: solar system – minor planets, asteroids – techniques:lines perpendicular interferometric to the interferometer projected baseline. Cellino, A., Belskaya, I. N., Bendjoya, P., di Martino, M., Gil-Hutton, R., as adaptive optics and radar. We have observed, as a typicalMuinonen, K., bench& Tedesco, E. F. 2006, mark,Icarus, 180, 565 the asteroid (951) Gaspra, visited in the Barbara was brighter, the MIA mask was used without problems Inable the to next distinguish section, between we the possibility describe that (234)how Barbara asteroidCellino, physical A., Dell’Oro, A., & Tedesco, E. F. 2009, P&SS, 57, 173 past by the Galileo spaceis a probe,single object having and a bi-lobated we derive shape, or it is actuallya sizeCellino, in A., good Gil-Hutton, R., agreement Di Martino, M., Bendjoya, Ph., with Belskaya, I. the N., & ground truth coming from the to extract the fringes and the photometric images. parameters were derived from MIDI measurements. Tedesco, E. F. 2005, Icarus, 179, 304 adetachedorcontactbinarysystem.Furtherinterferometric Suppression of the sky background, which is the predom- Conrad, A. R., et al. 2007, Icarus, 191, 616 in situ measurementsshapes and byobservations sizes the Galileofor using a sample different4. mission. projected RESULTS of kilometer- baselines Moreover, coupled and with subkilometer-Cohen, we M., Walker, have R. G., Carter, also B., Hammersley, observed P., Kidger, M., & Noguchi, the asteroid (234) Barbara, known inant1. INTRODUCTION flux contribution in the N band, is an issue. Sky back- optical lightcurve measurements are required to test the different K. 1999, AJ,117,1864 sized objects.possible This alternatives. technique, however, is mostly limitedDelbo, M. 2004, to the Freie Universitaet Berlin, Digitale Dissertation. online at ground generates a DC offset of theto whole exhibit spectrum. unusual This DC polarimetricAsteroidIn order sizes to compare were properties, thederived size offrom (234) Barbara the and application derived we from found of thehttp://www.diss.fu-berlin.de/2004/289/indexe.html models evidence of a potential binary nature. In particular, our population of NEAs, which can experience closeDelbo, encounters M., Dell’Oro, A., Harris, A. W., Mottola, S., & Mueller, M. 2007, Icarus, The study of thecomponent physics of creates asteroids a fringe is artifact crucial at to zero constrain OPD (optical path describedthe geometric in Section binary model2 to MIDIand those measurements. obtained from thermal First of190, all, 236 the difference between the two beams)data when areEWS best calculates fit the by a systemmodeling, of we two compare bodies the diameters of of the 37 spheres and with 21Delb kmo,´ M., & inHarris, diameter, A. W. 2002, Meteorit. Planet. separated Sci., 37, 1929 by a center-to-center distance of models of formation, growth and physical properties of the with ourSTM, planet.equivalent the FRM, This area, D is.Thetotalsurfaceofthebinarymodelvaries and due the to NEATM the fact were that fit the to intensity the measuredDelbo, M., Harris,of the A. W., Binzel, R. P., Pravec, P., & Davies, J. K. 2003, Icarus, Fourier transform of the measured signal24 dispersed km (projected along wave-radar echo alonginfrared decreasesfrom thefluxes 1420 direction30I kmwith(λ2)only,toobtaineffectivediameters.Flux,correspondingtothefullyseparatedcase, the fourth of the power baseline of the distance. at166, the116 epoch of our observations). planetesimals that accreted into the inner solar system planets. to 1370 30± km2 when the center-to-center distance of the two Delbo, M., & Tanga, P. 2009, Planet. Space Sci., 57, 259 lengths on the detector, in order to estimate∼ the fringe position. data and thermal± models’ best-fit continua for (951)Delbo, Gaspra M., et al. 2006, Icarus, 181, 618 Most asteroids are too small to allow a direct determina- To summarize,disks is 29 km. the These vast values majority correspond to D ofof 43 asteroid1kmand sizes,Gil-Hutton, due R., Mesa, to V., Cellino, A., Bendjoya, P., Penaloza,˜ L., & Lovos, F. If the source is weak and so is the signal within the fringe, the and (234)42 1km,respectively,andtheylieinbetweentheNEATM Barbara are plotted in Figures ±2 and 3,respectively. 1 their small apparent± angular extension and orbital location2008, A&A, 482, in 309 tion of their fundamentalartifact at physical zero OPD properties, may be considered including as thesizes, real fringe by The geometricand the STM sizevisible estimates. albedos were calculated from theGlindemann, derived A., et al. 2003, Ap&SS, 286, 35 2 Harris, A. W. 1998, Icarus, 131, 291 shapes, and masses.EWS.According As our sources to current are weak expectations, andKey the fringe words: in tracking the wasinfrared: notthe Mainsizes, solar Belt, utilizing remain systemH values beyond – from minor the the range Minor planets, of Planet measurability Center, asteroidsHarris, namely A. W. using 2006, – in Proc. techniques: IAU Symp. 229, Asteroids, Comets, interferometric Meteors, ed. 6. CONCLUSIONS L. Daniela, M. Sylvio Ferraz, & F. J. Angel (Cambridge: Cambridge Univ. next decade, the Gaiaperformed mission around of the the European zero OPD, we Space used Agency an option of EWScurrentH techniques.11.46 for As (951) a consequence, Gaspra and H nearly9.02 for all (234) of the Barbara.Press), available449 (dAve) to remove the DC background component of the signal Table= 4Wereports have obtainedD and thep firstobtained direct measurements from= the of asteroid applicationHarris, of A. W., the & Lagerros, J. S. V. 2002, in Asteroids III, ed. W. F. Bottke, A. will provide accurate mass determinations for about 100 of the informationsizes we from have ground today based interferometryV about asteroid in the thermal sizes infrared comesCellino, from R. P. Paolicchi, the & P. Binzel (Tucson, AZ: Univ. of Arizona Press), by subtracting the mean of all pixels in the spectrum from each thermalusing models the MIDI and of the the ESO corresponding VLTI. Our observations angular of (951) extension205 of the largest main belt asteroidsindividual (MBAs) pixel. and will be able to directly results of indirectGaspra convincingly methods show ofthat MIDI size observations determination. can spatially Harris, A. W., & Young, J. W. 1983, Icarus, 54, 59 bodyresolve at the asteroids time asof small our as VLTI12 km observation. in the Main Belt An with uncertaintyKaasalainen, of M., Torppa, J., & Muinonen, K. 2001, Icarus,153,37 measure the sizes ofMoreover, all MBAs at larger the end than of the 30 data km reduction ( 1000 process ob- of MIA,The0.5 most mag widely (see Cellino adopted et al.∼2009 technique), affecting todetermine the uncertaintyLebofsky, asteroid L. on A., et al. 1986, Icarus, 68, 239 ∼ excellent accuracy. This is suggested by the comparison of our Leinert, C., et al. 2003, Ap&SS, 286, 73 jects) (Mouret et al.the2007 calculated; Mignard visibilities et al. 2007 turned). At out present, to be quite how- noisy. Sincesizes isthe thermal derivedVLTI results albedo,infrared with the was shape radiometry modelassumed obtained on by(see the means adopted of Harris in situ value &Loreggia, Lagerros of D.,the Delbo,shapes M., Gai, M., and Lattanzi, M. sizes G., Ligori, S.,for Saba, aL., sample of kilometer- and subkilometer- we do not request high spectral resolution we modified1. the INTRODUCTIONλ imaging observations during the flyby of the Galileo mission. Wittkowski, M., & Cellino, A. 2008, in Eso Astrophysics Symp., The Power ever, the most important source of progress in this field is related 2002,andreferencestherein).ThismethodisbasedonthefactabsoluteOur observations magnitude suggestH (from that the the second MPC). target, (234) Barbara, of Optical/IRsized Interferometry: objects. Recent Scientific Results This and 2nd Generation, technique, however, is mostly limited to the binning (the default value is 3 pixels for each spectral channel) Weis then a potential computed binary system. interferometric However, further visibilities investigation corresponding(Berlin: Springer), 565 to the increasing rate of discovery of binary systems. These dis- that the infrared flux I(λ)carriesinformationaboutthesizeMarchis, F., Descamps, P., Baek, M., Harris, A. W., Kaasalainen, M., Berthier, to 8 pixels for the calculation of the visibilities. to theare obtained required to NEATM, fully prove this STM, hypothesis and and FRM to derive solutions the (byJ., Hestroffer, usingpopulation D., & Vachier, F. 2008, Icarus, 196, of 97 NEAs, which can experience close encounters The study of the physicsof the of source. asteroidsgeometric In parameters particular, is of crucial the systemI(λ (in)isproportionaltothearea particular, to constrain the separation Mignard, F., et al. 2007, Earth Moon Planets, 101, 97 coveries have been made possible by adaptive optics imaging at of the two components, which might also be in contact). We Mouret, S., Hestroffer, D., & Mignard, F. 2007, A&A, 472, 1017 several large telescopes, radar—particularlymodels suited of for formation, the study growthof the asteroid andnote that physicalvisible a binary to nature the of properties (234) observer. Barbara is However, not surprising of theI(Muinonen,λ)depends K., Piironen,with J., Shkuratov, our Y. planet. G., Ovcharenko, A., This & Clark, B. E. is due to the fact that the intensity of the given the slow rotation period of this object obtained in the 2002, in Asteroids III, ed. W. F. Bottke, A. Cellino, R. P. Paolicchi, & P. also upon the temperature distribution on the asteroidBinzel surface. (Tucson, AZ: Univ. of Arizona Press), 123 of near-Earth objects (NEAs)—and opticalplanetesimals lightcurve observa- that accreted into thepast from inner lightcurve solar observations. system A binary nature, planets. however, Mueller, M. 2007,radar Freie Universitaet echo Berlin, Digitaledecreases Dissertation, online with at the fourth power of the distance. can not explain per se the unusual polarimetric properties of http://www.diss.fu-berlin.de/2007/471/indexe.html tions. Binary asteroids are extremely important to derive the Different models of asteroid thermal infrared emission (the so-To summarize, the vast majority of asteroid sizes, due to mass of the system; the sizes and shapesMost of the components asteroids are are toocalled small asteroid to thermal allow models; a direct see Section determina-2,Harris&Lagerros 1 then needed to estimate average densities,tion which of their in turn fundamental provide 2002 physical;Delbo&Harris properties,2002,andreferencestherein)areusedto including sizes, their small apparent angular extension and orbital location in crucial information about the internalshapes, structure and of the masses. bodies. 2 Accordingestimate the to surface current temperature expectations, distribution in allowing the onethe to Main Belt, remain beyond the range of measurability using Unfortunately, asteroid sizes are generallynext decade, not measurable the Gaia by missionderive D offrom the measurements European of SpaceI(λ). The Agency asteroid’s geometriccurrent techniques. As a consequence, nearly all of the available means of direct imaging. Improvements in the performances of visible albedo, pV ,canthenbeobtainedfromEquation(1) modern adaptive optics systems are currentlywill provide making significant accurate masswhich determinations represents the fundamental for about relation 100 linking of the the effectiveinformation we have today about asteroid sizes comes from the progress, but this is forcedly limitedlargest to size measurements main belt asteroids of diameter, (MBAs)D (in and km), will the albedo, be able and to the directly absolute magnituderesults of indirect methods of size determination. the largest MBAa, and very close approaching NEAs (Conrad H (the magnitude in the V band that would be measured byThe most widely adopted technique to determine asteroid et al. 2007). Radar has been proven tomeasure be a powerful the tool sizes to infer of allobserving MBAs larger the object than at 1 AU 30 distance km ( from1000 both ob- the Sun and the jects) (Mouret et al. 2007observer,; Mignard and et at zeroal. 2007 phase). angle): At present,∼ how- sizes is thermal infrared radiometry (see Harris & Lagerros ever, the most important source of progress in this field is related 2002,andreferencestherein).Thismethodisbasedonthefact ∗ Based on data obtained at the Very Large Telescope Interferometer (VLTI) log pV 6.247 2logD 0.4H. (1) of the European Southern Observatory (ESO):to program the increasing ID 076.C-0798. rate of discovery of binary= systems.− These− dis- that the infrared flux I(λ)carriesinformationaboutthesize 1 Only for the largest hundred main belt asteroidscoveries their sizes have can be been directly madeWe possible note that by the adaptive value of opticspV is perimaging se a very at importantof the source. In particular, I(λ)isproportionaltothearea measured with present-day adaptive optics systems at 10 m class telescopes physical parameter, because it is a function of the composition, (Conrad et al. 2007). several large telescopes, radar—particularlytexture, and roughness of suited an asteroid’s for the surface. study Polarimetricof the asteroid visible to the observer. However, I(λ)depends 2 At the time of writing, only 15 multiple main belt asteroids had their components resolved, allowing determinationof of their near-Earth orbits and thus objects of the (NEAs)—andobservations can optical also be lightcurve used to estimate observa- the value ofalsopV upon the temperature distribution on the asteroid surface. masses of the systems (Marchis et al. 2008). tions. Binary asteroids are(Muinonen extremely et al. 2002 important; Cellino to et al. derive2005)fromempirical the Different models of asteroid thermal infrared emission (the so- mass of the system; the1228 sizes and shapes of the components are called asteroid thermal models; see Section 2,Harris&Lagerros then needed to estimate average densities, which in turn provide 2002;Delbo&Harris2002,andreferencestherein)areusedto crucial information about the internal structure of the bodies. estimate the surface temperature distribution allowing one to Unfortunately, asteroid sizes are generally not measurable by derive D from measurements of I(λ). The asteroid’s geometric means of direct imaging. Improvements in the performances of visible albedo, pV ,canthenbeobtainedfromEquation(1) modern adaptive optics systems are currently making significant which represents the fundamental relation linking the effective progress, but this is forcedly limited to size measurements of diameter, D (in km), the albedo, and the absolute magnitude the largest MBAa, and very close approaching NEAs (Conrad H (the magnitude in the V band that would be measured by et al. 2007). Radar has been proven to be a powerful tool to infer observing the object at 1 AU distance from both the Sun and the observer, and at zero phase angle):

∗ Based on data obtained at the Very Large Telescope Interferometer (VLTI) log pV 6.247 2logD 0.4H. (1) of the European Southern Observatory (ESO): program ID 076.C-0798. = − − 1 Only for the largest hundred main belt asteroids their sizes can be directly We note that the value of pV is per se a very important measured with present-day adaptive optics systems at 10 m class telescopes physical parameter, because it is a function of the composition, (Conrad et al. 2007). texture, and roughness of an asteroid’s surface. Polarimetric 2 At the time of writing, only 15 multiple main belt asteroids had their components resolved, allowing determination of their orbits and thus of the observations can also be used to estimate the value of pV masses of the systems (Marchis et al. 2008). (Muinonen et al. 2002; Cellino et al. 2005)fromempirical

1228 Predicted stellar occultaon events :

2009 October 5 Canary Islands star V = 7.2 2009 November 21 Florida star V = 6.5

Paolo Tanga – Sept 23, 2013 Paolo Tanga – Sept 23, 2013 Paolo Tanga – Sept 23, 2013 Photometry campaign • From 2008 to 2011 • 19 teams

Figure 1: A lightcurve obtained by M. Conjat and P. Tanga on June 2008 over 13 days. The curve is folded on the rotation period of the object. [I’m on it]

Figure 2: Lightcurve segments used for the determination of shape and pole by KOALA. The grey dots correspond to the observed brightness, while the curves are computed fromPaolo Tanga – Sept 23, 2013 the model presented in ??. [I am in favor of NOT showing this figure, but instead a table with RMS for each epoch... to be discussed.] [I think that a single full light curve immediately gives a visual of how irregular the shape of this body is. In my view, it is not mandatory, but it o↵ers a ”traditional” comparison to other light curves, available for any object in general.]

1 The high realibility of the asteroid ephemeris was a precious information 2 for planning the deployment of the observers around the path of the second 3 event. Several astronomers in the United States gathered in Florida and few 4 others in central Europe at the other extreme of the path. The noticeable 5 e↵ort of deployment of several automated stations by single observers was 6 successfull, and several occultation chords were thus observed (Table 2). 7 Data reduction of the occultation on Oct. 2, 2009 event results in the 8 strong hint of an elongated, oval shape (Fig. 3), with possible irregular fea- 9 tures. The observed chords on November 21, 2009 consistently draw an over- 10 all triangular shape, with a large and pronounced concavity in the South, 11 along with hints of other smaller concavities. Both occultations provide an 12 average size consistent with the results obtained by interferometry (Sect. 3.3). 13 Other occultation events by Barbara were observed later on. We neglect

7 Shape determinaon by B. Carry (IMCCE, Paris) Simultaneous inversion of light curves and occultaon data (KOALA)

!

Figure 3: Plot on the plane of the sky of the occultation chords reported in Tables 1 and 2. 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.

two stellar occultations and the 55 lightcurves Paolo Tanga – Sept 23, 2013 described in Sect. 3. 1 The 3-D shape modeling of Barbara turned out to be a real challenge. 2 Owing to the slow rotation of Barbara, each lightcurve covered a small frac- 3 tion its period only (less than 20% on average). Moreover, a large degree of 4 non-convexity was required to properly describe the large concavity visible 5 in the stellar occultation from November 2009 (Fig. 3), with direct measure- 6 ments of the shape available for two geometries only. 7 Considering the amount and the high quality of the timings for the stellar 8 occultation of 2009 November 21, we chose to use the profile drawn by the 9 chords as if it was obtained by disk-resolved imaging. This assumption was 10 required to model the large concavity revealed by the southern interrupted 11 chord. The algorithm otherwise failed to render this chord. Although this 12 use of stellar occultation chords is not fully adequate, the number of positive 13

10 Curvature map

Figure 6: Colored map of concave region corresponding to the main candidate crater. The color correspond to curvature. Concavities are represented in red and yellow. A measurement on the minor and major extensions of this region provide 22 15 km. The uncertainty is of the same order as the mesh resolution, i.e. around 3 km. ⇥ Paolo Tanga – Sept 23, 2013

17 Davis et al. 2002 (Asteroids III)

Paolo Tanga – Sept 23, 2013 Other barbarians, more mystery…

Paolo Tanga – Sept 23, 2013 Where the Barbarians (could) hide?

Pax

L, Ld and K

0.30 Watsonia family 0.28 0.26 Barbara & Baucis 0.35 0.24 0.22 0.3 0.20

0.18 0.25 0.16 sin(i) 0.14 0.2 0.12 0.10 0.15 0.08 0.06 0.04 0.1 0.02 Henan group 0.00 0.05 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 a (AU) Albedo (WISE)

Paolo Tanga – Sept 23, 2013 729 Watsonia: chief of the 1st Barbarian family?

• Observaons close to “ordinary” inv. angle < 20° – Negave polarizaon à barbarian

312 R. Gil-Hutton et al.: New cases of unusual polarimetric behavior in asteroids • Approach: 2 1.5

– FORS2 @ VLT in polarimetric mode 1 – between April and September 2013 0.5

0 Pr (%)

-0.5

-1

-1.5

-2 0 5 10 15 20 25 30 35 Phase angle (deg.)

Fig. 1. Polarimetric observations of asteroids with Barbara-like polarimetric properties. Data for (172) Baucis are indicated by circles, for (234) Barbara by squares, for (236) Honoria by triangles, for (679) Pax by diamonds, and for (980) Anacostia by inverted triangles. Filled symbols indicate data taken during our present campaign. For a comparison, data for the L-class asteroid (12) Victoria are displayed by crosses, together with the corresponding fit of its phase-polarization curve.

for the polarimetric parametersthatcharacterizethephase- 4. Discussion polarization curve of these objects are P = 1.48 0.03% | min| ± at αmin = 13.6◦, h = 0.200 0.002%/◦,andα0 = 28.0◦ for Since our polarization measurements for these objects have been Baucis; and P = 1.52 ± 0.08% at α = 13.2 , h = obtained on different nights during different observing runs, and | min| ± min ◦ 0.206 0.005%/◦,andα0 = 27.3◦ for Barbara. These values they agree well with each other with reasonably small error bars, are similar± to those found for the whole group. we conclude that the observed behavior is real and represents It is possible to use these parameters to find the polarimet- new cases of asteroids exhibiting a strongly negative polarization ric albedo p applying two empirical relations linking it with h at phases larger than 20◦. or Pmin.Theserelationsareexpressedbymeansofverysimple In Table 3,welistasummaryofourcurrentknowledgeof mathematical forms: the dynamical andPaolo Tanga – Sept 23, 2013 physical parameters for these asteroids. They are objects distributed along themainbelt,havingtypicalsizes and albedos. The only physical parameter in common is that all log p(h) = C1 log h + C2, (2) of them have similar taxonomic classes: four asteroids belong to the L-class and the other one to the K-class. These taxonomic log p(Pmin) = C3 log Pmin + C4, (3) classes were proposed by Bus & Binzel (2002)andaresubsets of the old broad S-class defined by Tholen (1989). The differ- ences between them are a change in the UV slope shortward of where C1, C2, C3,andC4 are constants. In this paper we use the set of constants proposed by Cellino et al. (1999), namely: 0.75 µmfrommoderatelysteep(K-class)toverysteep(L-class), and a subtle change in the spectral slope longward of 0.75 µm. C1 = 1.118 0.071,C2 = 1.779 0.062,C3 = 1.357 0.140, − ± − ± − ± Since their sizes do not allow them to support a developed re- and C4 = 0.858 0.030. Using these empirical relations with the polarimetric− ± parameters found previously, we obtain golith of fine particles and the only agreement in their physical properties is their similar taxonomic class, the broad negative p(h) = 0.11 0.02 and p(Pmin) = 0.09 0.01 for all the asteroids ± ± branch of their phase-polarization curves must be explained by in the group, p(h) = 0.10 0.02 and p(Pmin) = 0.08 0.01 for ± ± aphysicalpropertyoftheasteroidsurface,itscomposition,ora (172) Baucis, and p(h) = 0.10 0.02 and p(Pmin) = 0.08 0.01 for (234) Barbara. It is clear, however,± that the above albedo± val- combination of both. ues have to be taken with some care because we are applying The first clue comes from the work of Zellner et al. (1977) here the usual relations to find the albedo to objects which dis- on laboratory polarimetry of meteorites. These authors found play an unusual polarimetric behavior, and we cannot be sure a peculiarly large values of the inversion angle for the carbona- priori that these relations also hold in this case. ceous chondrites, especially for the C3 samples, reaching α0 A successful hunt for Barbarians in the Watsonia family 3

Table 1. Polarimetry of 9 asteroids of the Watsonia family in the special Bessell R band. PQ and PU are the reduced Stokes parameters measured in a reference system such that PQ is the flux perpendicular to the plane Sun-Object-Earth (the scattering plane) minus the flux parallel to that plane, divided by the sum of the two fluxes. It is therefore identical to the Pr parameter usually adopted in asteroid polarimetry.Polarimetry of Watsonia family members – results 1

Date Time (UT) Exp Object Phase angle PQ PU (yyyy mm dd) (hh:mm) (sec) (DEG) (%) (%)

2013 07 05 23:41 480 5492 18.79 1.14 0.10 0.05 0.10 − ± ± 7 new Barbarians 2013 07 29 01:44 960 18.31 1.01 0.09 0.00 0.09 over 9 observed targets! − ± ± 2013 06 03 09:40 2000 42365 23.30 0.83 0.15 0.06 0.15 − ± − ± 2013 08 03 09:08 960 18.55 1.73 0.12 0.06 0.12 − ± − ± 2013 07 12 23:50 960 56233 17.83 1.07 0.16 0.09 0.16 − ± − ± 2013 08 05 01:03 2200 19.31 1.09 0.12 0.07 0.12 − ± − ± 2013 07 30 00:38 2000 106059 18.30 1.06 0.30 0.15 0.31 − ± − ± 2013 08 04 01:09 4000 18.82 0.94 0.14 0.00 0.14 − ± ± 2013 08 28 01:24 4800 19.64 0.84 0.20 0.09 0.20 − ± − ± 2013 07 06 01:33 1400 106061 20.21 0.94 0.11 0.06 0.11 − ± ± 2013 08 09 02:46 4000 23.97 0.57 0.12 0.05 0.12 − ± − ± 2013 07 06 02:05 960 144854 21.30 0.81 0.12 0.13 0.12 − ± ± 2013 08 05 02:06 4000 24.19 0.15 0.12 0.13 0.13 − ± − ± 2013 07 07 02:40 3440 247356 19.97 0.10 0.15 0.33 0.15 ± − ± 2013 08 13 06:28 4000 236408 18.31 0.97 0.15 0.22 0.15 − ± ± 2013 04 17 08:58 4800 320971 23.78 0.11 0.31 0.06 0.31 ± − ± 2013 06 03 07:08 3440 20.53 0.03 0.22 0.06 0.21 − ± − ±

Paolo Tanga – Sept 23, 2013 possibly also Aquitania, which is fairly close to them in the tories. Even a negative result would be very interesting. If space of proper elements, were issued from the disruption of no other members of the Watsonia family were found to a common parent body exhibiting the rare properties which be Barbarians, the peculiar composition properties of (729) produce the Barbarian polarization phenomenon, it is natu- Watsonia, (387) Aquitania and (980) Anacostia would prove ral to expect that also the other, still not observed members to be not responsible of the polarimetric behaviour char- of this same family, should be found to be Barbarians. acterizing the Barbarians. In this scenario, other physical mechanisms would have to be identified to explain the po- For this reason, we submitted a successful proposal to larimetric behaviour, and no evidence that Barbarians must carry out polarimetric observations of a sample of members be necessarily primitive and very old would remain. of the Watsonia family using one of the ESO VLT 8-m tele- scopes. The results of the observations have now been fully collected, and are presented in this paper. 2THEOBSERVATIONS Before giving the results of our polarimetric measure- ments, let us summarize what we could aprioriexpect to be Please, Stefano, take care of this Section, by adding the possible results of our investigation. If the above expec- everything that is missing and should be mentioned tations to be able to find new Barbarians in the Watsonia Our program of polarimetric observations aimed at family were proven to be correct, we would have at disposal identifying new Barbarians was very simple. At small phase a much larger sample of Barbarians to be further studied angles ( 20degr), all asteroids exhibit negative polariza- ! by means of dedicated photometric and spectroscopic cam- tion, whereas at phase angles > 20◦ (approximately), nearly paigns. As a by-product, we would get also a proof of the all asteroids exhibit positive polarization. By contrast, at true collisional origin of the Watsonia family. This is impor- phase angle 20◦, Barbarians still exhibit a relatively high " tant, because the identification of dynamical families based degree of negative polarization, of the order of 1%. Polar- on the distribution of orbital proper elements is always sub- ization turns to positive only at phase-angle 28 30◦. ! ÷ ject to some kind of statistical uncertainty, and independent Therefore, to identify Barbarians it is sufficient to carry out evidence coming from physical properties of the members simple polarization measurements at phase angles around are important to confirm proper element-based inferences. 17◦ or slightly above, in order to establish whether the mea- If the members of the Watsonia family were found to be sured polarization plane is found to be parallel or perpen- Barbarians, we would conclude that these objects originate dicular to the scattering plane. from the collisional disruption of a common parent body, Our target list includes nine objects that were found to and the Barbarian behaviour depends most likely on sur- be members of the Watsonia family according to the analy- face composition rather than on individual collisional his- sis carried out by (Novakovi´cet al. 2011). These objects are c 2002 RAS, MNRAS 000,1–?? " Polarimetry of Watsonia family members – results 2

12 Victoria

234 Barbara

Paolo Tanga – Sept 23, 2013 Other anomalies?

Paolo Tanga – Sept 23, 2013 Light curves - Rotaon periods

729 Watsonia 0.3

0.25

0.2

0.15

0.1

0.05

0

−0.05 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

New period = 25.19 h …! Photometry by: C2PU + M. Devogele, J. Surdej (OCA Nice + Liege) P. Hickson, Cerro Tololo, Chile A. Marciniak, T. Michalowski, Poznan F. Pilcher, NM, USA M. Todd, Australia

Paolo Tanga – Sept 23, 2013 Rotaon periods – all “lazy” rotators?

30 Ld 28 K 26 L 24 All

22

20

18

16

14 PERIOD / hour 12

10

8

6

4

2 0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 MAGH

Paolo Tanga – Sept 23, 2013 518 T. Takeda, K. Ohtsuki / Icarus 202 (2009) 514–524

Icarus 202 (2009) 514–524

Contents lists available at ScienceDirect

Despinning aggregates by collisions Icarus

www.elsevier.com/locate/icarus Icarus 202 (2009) 514–524

Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids. II. Effects of initial rotation and spin-down through disruptive collisionsContents lists available at ScienceDirect

a, b Takaaki Takeda ∗,KeijiOhtsuki

a National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Fig. 3. Time seriesb of a simulation of an impact that resulted in despinning of a target asteroid (! 0.8, C 3). Results are shown looking down onto the plane of the impact Laboratory for Atmospheric and Space Physics, University of Colorado, 392 UCB, Boulder, CO 80309-0392,= ˜ = USA (from (a) to (d)). The initial size of the target is shown as a gray circle in each panel for comparison. The impactor–target mass ratio is µ 1/63, and the impact velocity = 3v . The internal density of the constituent particles is 3.64g/cm3, and the bulk density of the aggregate is about 2.5 g/cm3. Through the collision, about 40% of the ∼ grav Icarus total mass isarticle lost and the rotation info rate is about 40% decreased. Inabstract the last panel, the size of particles is exaggerated for clarity.

Article history: Expanding on our previous N-body simulation of impacts between initially non-rotating rubble-pile Received 26 December 2008 objects [Takeda, T., Ohtsuki, K., 2007. Icarus 189, 256–273], we examine effects of initial rotation of targets Revised 26 February 2009 on mass dispersal and change of spin rates. Numerical results show that the collisional energy needed to Accepted 1 March 2009 www.elsevier.com/locate/icarusdisrupt a rubble-pile object is not sensitive to initial rotation of the target, in most of the parameter range Available online 5 March 2009 studied in our simulations. We find that initial rotation of targets is slowed down through disruptive Keywords: impacts for a wide range of parameters. The spin-down is caused by escape of high-velocity ejecta and Asteroids, rotation asymmetric re-accumulation of fragments. When these effects are significant, rotation is slowed down Collisional physics even when the angular momentum added by an impactor is in the same direction as the initial rotation Impact processes of the target. Spin-down is most efficient when the impact occurs in the equatorial plane of the target, because in this case most of the ejected fragments originate from the equatorial region of the target and a significant amount of angular momentum can be easily removed. In the case of impacts from directions inclined relative to the target’s equatorial plane, spin-down still occurs with reduced degree, unless impacts occur onto the pole region from the vertical direction. Our results suggest that such spin-down through disruptive impacts may have played an important role in spin evolution of asteroids through collisions in the gravity-dominated regime. Mass dispersal and angular momentum transfer during 2009 Elsevier Inc. collisions All rights reserved. between rubble-pile asteroids. II.1. Effects Introduction of initial rotationsmall asteroids which and experienced a spin-downrecent break-up event and through have not had long enough time for spin evolution due to the YORP The average rotation period of asteroids in the main-belt is effect (Yoshida et al., 2004; Nesvorný et al., 2006b). Thus, clarify- disruptive collisions about 6 hours, and their rotation rates and obliquities would pro- ing the effect of collisions on asteroid rotation is still important. Fig. 4. Rotationvide rate us of the with largest useful remnant information after head-on about impacts, their as dynamical a function of evolution its mass fraction toMany the total earlier mass. Themodels trajectory on asteroid of the impactor rotation before attempted collision lies to inexplain the z 0 plane,and and history the impactor (Harris, collides 1979; onto Binzel the target’s et al., equatorial 1989; plane.Davis Panels et al., (a) 1989; and (b) showthe results fact that for µ the1/ mean63 and spin 1/255, rate respectively. of asteroids Filled has and a open minimum symbols value = . = represent resultsPravec with et different al., 2002 initial). rotation Recent rates studies of the targetshow (4 that6 and thermal 2.6 rev/day, torques respectively).at Small diameter and largeD symbols100 km. represent Despinning results withdue differentto cratering total numbersimpacts onto of particles used in simulation (4096 and 16384, respectively). Squares and circles represents hard targets (C 3or6,! 0.8and0.2, respectively), while upward and produced by the reflection and re-emission of sunlight from an ˜ = ≈ = a, downwardb triangles represents soft targets (C 0.75 or 1.5, ! 0.8and0.2, respectively). The dashedarotatingasteroidandasymmetricescapeoffragmentsproposed lines show the fits to the results for each initial rotation rate. ˜ Takaaki Takeda ∗,KeijiOhtsuki asteroid’s surface (the Yarkovsky–O’Keefe–Radzievskii–Paddack= = ef- by Dobrovolskis and Burns (1984) was shown to be ineffective fect or YORP effect) are likely to have played a major role in the as compared to the effect of catastrophic collisions Paolo Tanga – Sept 23, 2013 (Davis et al., of b). Filledlong-term and open spin symbols evolution represent of small results asteroids of simulations with diameter with less thanparameters. This is because the final rotation of the remnant de- a 1989). A similar mechanism of despinning in catastrophic collisions different values40 km of (e.g.,! andRubincam,C. 2000; Bottke et al., 2002; Vokrouhlickpendsý onwas the also degree proposed of bydisruptionCellino et as al. well (1990) as,andacollisionalsimula- the amount and National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka,˜ Tokyo 181-8588, Japan b In the caseet al., of 2003 retrograde). Direct collisions, detections the of therotation change of inthe the largest rotation rateorigin oftion the demonstrated escaping fragments the possibility (whether that they the originate above minimum from the of the Laboratory for Atmospheric and Space Physics,remnant University isof slowed small of asteroids down Colorado, as by compared the YORP 392 to effect the UCB, target’s have Boulder, also initial been ro- reported COimpactor 80309-0392,mean or from spin therate USA target, may be and explained which by part such of thean effect target (Farinella they et (Kaasalainen et al., 2007; Lowry et al., 2007; Taylor et al., 2007; tation regardless of the values of the parameters, ! and C.On originateal., from), 1992). which However, depends these on previous these parameters. works on collisional The efficiency despinning Kitazato et al., 2007). However, collisions likely determined˜ rota- the other hand, results for prograde collisions depend on these of angularare momentum based on a simple transfer collision from the model, impactor where to interactions the remnant between tional states of larger asteroids (e.g., Love and Ahrens, 1997)and fragments or their reaccumulation processes were not modeled ac- probably had a significant effect on current rotational states of curately. Love and Ahrens (1997) performed smoothed particle hydro- article info abstract dynamics (SPH) simulations to examine the effect of catastrophic * Corresponding author. Fax: +81 422 34 3835. E-mail addresses: [email protected] (T. Takeda), [email protected] impacts on the rotation of gravitating asteroids. They found that (K. Ohtsuki). the fraction of a projectile’s orbital angular momentum that is re- Article history: 0019-1035/$Expanding – see front matter  2009 on Elsevier our Inc. All rights previous reserved. N-body simulation of impacts between initially non-rotating rubble-pile doi:10.1016/j.icarus.2009.03.001 Received 26 December 2008 objects [Takeda, T., Ohtsuki, K., 2007. Icarus 189, 256–273], we examine effects of initial rotation of targets Revised 26 February 2009 on mass dispersal and change of spin rates. Numerical results show that the collisional energy needed to Accepted 1 March 2009 disrupt a rubble-pile object is not sensitive to initial rotation of the target, in most of the parameter range Available online 5 March 2009 studied in our simulations. We find that initial rotation of targets is slowed down through disruptive Keywords: impacts for a wide range of parameters. The spin-down is caused by escape of high-velocity ejecta and Asteroids, rotation asymmetric re-accumulation of fragments. When these effects are significant, rotation is slowed down Collisional physics even when the angular momentum added by an impactor is in the same direction as the initial rotation Impact processes of the target. Spin-down is most efficient when the impact occurs in the equatorial plane of the target, because in this case most of the ejected fragments originate from the equatorial region of the target and a significant amount of angular momentum can be easily removed. In the case of impacts from directions inclined relative to the target’s equatorial plane, spin-down still occurs with reduced degree, unless impacts occur onto the pole region from the vertical direction. Our results suggest that such spin-down through disruptive impacts may have played an important role in spin evolution of asteroids through collisions in the gravity-dominated regime.  2009 Elsevier Inc. All rights reserved.

1. Introduction small asteroids which experienced a recent break-up event and have not had long enough time for spin evolution due to the YORP The average rotation period of asteroids in the main-belt is effect (Yoshida et al., 2004; Nesvorný et al., 2006b). Thus, clarify- about 6 hours, and their rotation rates and obliquities would pro- ing the effect of collisions on asteroid rotation is still important. vide us with useful information about their dynamical evolution Many earlier models on asteroid rotation attempted to explain and history (Harris, 1979; Binzel et al., 1989; Davis et al., 1989; the fact that the mean spin rate of asteroids has a minimum value Pravec et al., 2002). Recent studies show that thermal torques at diameter D 100 km. Despinning due to cratering impacts onto ≈ produced by the reflection and re-emission of sunlight from an arotatingasteroidandasymmetricescapeoffragmentsproposed asteroid’s surface (the Yarkovsky–O’Keefe–Radzievskii–Paddack ef- by Dobrovolskis and Burns (1984) was shown to be ineffective fect or YORP effect) are likely to have played a major role in the as compared to the effect of catastrophic collisions (Davis et al., long-term spin evolution of small asteroids with diameter less than 1989). A similar mechanism of despinning in catastrophic collisions 40 km (e.g., Rubincam, 2000; Bottke et al., 2002; Vokrouhlický was also proposed by Cellino et al. (1990),andacollisionalsimula- et al., 2003). Direct detections of the change in the rotation rate tion demonstrated the possibility that the above minimum of the of small asteroids by the YORP effect have also been reported mean spin rate may be explained by such an effect (Farinella et (Kaasalainen et al., 2007; Lowry et al., 2007; Taylor et al., 2007; al., 1992). However, these previous works on collisional despinning Kitazato et al., 2007). However, collisions likely determined rota- are based on a simple collision model, where interactions between tional states of larger asteroids (e.g., Love and Ahrens, 1997)and fragments or their reaccumulation processes were not modeled ac- probably had a significant effect on current rotational states of curately. Love and Ahrens (1997) performed smoothed particle hydro- dynamics (SPH) simulations to examine the effect of catastrophic * Corresponding author. Fax: +81 422 34 3835. E-mail addresses: [email protected] (T. Takeda), [email protected] impacts on the rotation of gravitating asteroids. They found that (K. Ohtsuki). the fraction of a projectile’s orbital angular momentum that is re-

0019-1035/$ – see front matter  2009 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2009.03.001 The puzzle: pung the pieces together • Over 20 among L, Ld types observed by polarimetry today: – 14 are certainly Barbarians + 1 uncertain – 4 are not + 1 uncertain (spectral type ambiguies possible with S and K types; 1 K-type Barbarian: Pax)

• 234 Barbara: a very irregular body – Large craters ~20 km in diameter? à rubble pile structure?

• Possible role of collisions – Excavaon of concavies in 234 Barbara – Angular momentum reducon • L-Ld types: lazy rotators? To be confirmed by more data – Creaon of families • Shared polarimetric properes inside the family of Watsonia (Cellino et al. 2013, MNRAS)

• CAI-extreme composion in L, Ld types? – The highest concentraon of the oldest Solar System material – 30% CAI composion...? Not found on Earth – Not enrely sasfactory spectral fit in the visual range

Paolo Tanga – Sept 23, 2013 Tentave conclusions / open quesons

• The Watsonia family, an important evidence: – Barbarian “state" is “genecally” transmied à It is not just a surface property

• The oldest Solar System objects that accreted? – Oldest material known, in high concentraon – Fragmented and de-spinned over me?

• Composions AND concavies both needed to explain spectra + polarizaon?

Paolo Tanga – Sept 23, 2013 The End

Paolo Tanga – Sept 23, 2013