New Clusters for highly inclined Main Belt AsteroidsSergio FogliaOsservatorio Astronomico Serafino Zani, LumezzaneF. Bisleri 11, I-20148 Milano, Italy andGianluca MasiUniversity of Tor Vergata, Roma, ItalyMadonna de Loco 47, I-03023 Ceccano FR, ItalyAbstract:This paper describes the search of new, high-inclination clusters in the main belt asteroid population, using the D-criterion. We find three possible new clusters: (31) Euphrosyne; (702) Alauda and(945) Barcelona. We provide simple ephemerides for the next oppositions in the time interval 2004-2008, in order to motivate physical observations of these objects, to check their reliability as families.IntroductionThanks to the availability of Synthetic proper elements (Knezevic and Milani, 2000) it was possible to apply the D-criterion (Lindblad and Southworth, 1994) to find new clusters in the highly inclined main belt asteroid population. Synthetic proper elements (Knezevic and Milani, 2000) have better accuracy respect to the previously available ones by more than a factor 3; in terms of the relative velocities at breakup this means that the typical accuracy is the order of ~5 m/s. Analytical proper elements were usually involved in asteroid families identification but they are computed with the limitation of (sin i) < 0.3 so we do not have any family for orbital inclination greater than 17.5. Figures 1 to 3 give the distributions of minor planets in the Main Belt having (sin I) greater than 0.3. Figure 1: Main Belt asteroids: (a, sin i) distribution with (sin i) > 0.3 Figure 2: Main Belt asteroids: (a, e) distribution with (sin i) > 0.3 Figure 3: Main Belt asteroids: (e, sin i) distribution with (sin i) > 0.3 Phocaea region is clearly visible in the inner part of the Main Belt, with proper elements 2.2 < a < 2.5 AU and sin i > 0.3. Condensation of objects should not necessarily be interpreted as a family, with a common origin from a single parent body; it might be instead a stability island, which means that the group might be separated from the other asteroids by gaps resulting from the destabilizing effect of some resonances.Identification MethodThe D-criterion method for identifying dynamical families was introduced by Lindblad and Southworth (1971) and modified by Lindblad (1994) and may be written in the following form: (1) where m and n represent two orbits to be compared, e and i are eccentricity and inclination and q = a · (1 - e) the perihelion distance, a is the semi-major axis; D is a generalised distance in proper elements space: D=0 thus indicates two orbits identical in proper (q, e, i) space. The D-criterion search method may be described as a cluster analysis program based on a neighbour linking technique. The program computes a distance D(m,n) for all possible pairs in proper elements space; if for a given pair the discriminant D(m,n) is less than a priori stipulated distance Ds the program accepts these two orbits as neighbours, i.e. as belonging to a cluster. A problem in any cluster analysis based on the neighbour searching technique is how to specify the rejection level, i.e. the appropriate cut-off distance Ds. The rejection level Ds = 0.011 was adopted and to study the statistical significance of the obtained clusters several rejection levels were adopted and the robustness factor R is defined as follow: (2) where N0.011 is the number of members in a given family at the adopted rejection level Ds = 0.011 and N0.009 is the number of members in the same family at the next stricter rejection level Ds = 0.009. R is a degree of persistance or stability of a family to changes in the rejection level.ResultsFound clusters are shown in figures 4 to 6 with the (a, sin i), (a, e) and (e, sin i) distributions; numbers is the catalogue number of the first member of clusters. * (2) Pallas family (a ~2.771 AU, e ~0.281, sin i ~0.548, i ~33.2) is well known and it was found by Hirayama and using proper elements computed by semianalytic method (Lemaitre, Morbidelli, 1994); finally it was confirmed by Bus with spectroscopic observation. * (480) Hansa family (a ~2.644 AU, e ~0.009, sin i ~0.375, i ~22.1) is proposed by Hergenrother , Larson and Spahr (1996) and also by Knezevic and Milani (2000) but no results are currently available. For the first time we suggest the following clusters: * (31) Euphrosyne cluster (a ~3.155 AU, e ~0.208, sin i ~0.447, i ~26.5) * (702) Alauda cluster (a ~3.194 AU, e ~0.021, sin i ~0.369, i ~21.7) * (945) Barcelona cluster (a ~2.637 AU, e ~0.251, sin i ~0.513, i ~30.8) Figure 4: Main Belt asteroids: (a, sin i) distribution with (sin i) > 0.3 Figure 5: Main Belt asteroids: (a, e) distribution with (sin i) > 0.3 Figure 6: Main Belt asteroids: (e, sin i) distribution with (sin i) > 0.3 Table 1 shows the obtained results, where MPC is the catalogue number of the minor planet representative of cluster; N0.050, N0.020, N0.011 and N0.009 give the number of members in a given family at the adopted rejection levels Ds = 0.050,0.020, 0.011, 0.009 respectively; R is the robustness factor, a is the proper semi-major axis, e is the proper eccentricity, sin i is the sine of the proper inclination, i is the proper inclination. Table 2 shows the catalogue number of members of found clusters respect to the different rejection level Ds. Table 1: obtained clusters Table 2: members of obtained clustersSpectroscopic campaign: from clusters to families?The first step in the process leading to the discovery of a family consist in identifying it as a statistically significant clustering of objects in the space of proper elements. The second step is to compare the physical properties of the supposed members with what is known about the outcomes of catastrophic impacts, and with the mineralogical properties of asteroidal bodies. As a first step we call these groups of asteroids "clusters"; the term "families" should be used only when both the statistical and physical definitions are coincident. In order to investigate the physical properties of these objects, we have calculated basic ephemeredes for the incoming oppositions, lying in the time interval 2004-2008. Table 3 reports the current knowledge about physical parameters of involved minor planets, MPC is the catalogue number, family is the suggested cluster, taxonomy class from Tholen and SMASSII, absolute magnitude, diameter, albedo and photometric parameters are reported. Table 3: physical parameters of involved minor planets(31) Euphrosyne cluster (a ~3.155 AU, e ~0.208, sin i ~0.447, i ~26.5)Figure 7 shows orbit and position at 2005 Jan 1of members of this cluster with the major planets from Mercury to Jupiter. Table 4 gives the observational's opportunities of members fro the years 2004-2008: MPC is the catalogue number, Year Mo Day is the opposition date, Phase is the phase angle (Sun-asteroid-Earth), RA is the J2000.0 Right Ascension in hours, Dec is the J2000.0 Declination in degrees, Mag is the visual magnitude. Figure 7: orbits of (31) Euphrosyne cluster Table 4: observational's opportunities of (31) Euphrosyne cluster(480) Hansa family (a ~2.644 AU, e ~0.009, sin i ~0.375, i ~22.1)Figure 8 shows orbit and position at 2005 Jan 1of members of this cluster with the major planets from Mercury to Jupiter. Table 5 gives the observational's opportunities of members fro the years 2004-2008: MPC is the catalogue number, Year Mo Day is the opposition date, Phase is the phase angle (Sun-asteroid-Earth), RA is the J2000.0 Right Ascension in hours, Dec is the J2000.0 Declination in degrees, Mag is the visual magnitude. Figure 8: orbits of (480) Hansa family Table 5: observational's opportunities of (480) Hansa family(702) Alauda cluster (a ~3.194 AU, e ~0.021, sin i ~0.369, i ~21.7)Figure 9 shows orbit and position at 2005 Jan 1of members of this cluster with the major planets from Mercury to Jupiter. Table 6 gives the observational's opportunities of members fro the years 2004-2008: MPC is the catalogue number, Year Mo Day is the opposition date, Phase is the phase angle (Sun-asteroid-Earth), RA is the J2000.0 Right Ascension in hours, Dec is the J2000.0 Declination in degrees, Mag is the visual magnitude. Figure 9: orbits of (702) Alauda cluster Table 6: observational's opportunities of (702) Alauda cluster(945) Barcelona cluster (a ~2.637 AU, e ~0.251, sin i ~0.513, i ~30.8)Figure 10 shows orbit and position at 2005 Jan 1of members of this cluster with the major planets from Mercury to Jupiter. Table 7 gives the observational's opportunities of members fro the years 2004-2008: MPC is the catalogue number, Year Mo Day is the opposition date, Phase is the phase angle (Sun-asteroid-Earth), RA is the J2000.0 Right Ascension in hours, Dec is the J2000.0 Declination in degrees, Mag is the visual magnitude. Figure 10: orbits of (945) Barcelona cluster Table 7: observational's opportunities of (945) Barcelona clusterBibliographyBendjoya Ph., Zappalà V. Asteroid Family Identification 2002, Asteroids III Binzel R. P., Physical studies of Hirayama families: recent results and future prospects Seventy-Five Years of Hirayama Families ASP Conference Series, vol. 63, 1994 Y. Kozai, R. P. Binzel and T. Hirayama eds. Bottke W. F., Vokrouhlicky D., Broz M., Nesvorny D., Morbidelli A. Dynamical Spreading of Asteroid Families via the Yarkowsky Effect 2001, Science vol. 294, 1693 Bus S. J., Binzel R. P., Phase II of Small Main-Belt Asteroid Spectroscopic Survey - A Feature-Based Taxonomy 2002, Icaurs 158, 146-177 Cellino A., Bus S. J., Doressoundiram A., Lazzaro D. Spectroscopic properieties of asteroid families 2002, Asteroids III Cellino A. Asteroid families 2003, CD VI, Cannes Chapman C. R., Paolicchi P., Zappalá V., Binzel R. P., Bell J. F. Asteroid families: physical properties and evolution 1989, in Binzel R. P., Gehrels T., Matthews M. S. Ed., Asteroids II, 387-415 Unviersity of Arizona Press Farinella P., Davis D. R., Cellino A., Zappalà V., From asteroid clusters to families: a proposal for new nomenclature Asteroids, Comets, Meteors 1991, 165-166 Lunar and Planetary Institute, Houston, 1992 Farinella P., Davis D. R., Marzari F. Asteroid families, old and young Completing the inventory of solar system ASP conference series, vol. 107, 1996 Rettig T. W., Hahn J. M. ed. Farinella P., How many families are there and how old are they? Seventy-Five Years of Hirayama Families ASP Conference Series, vol. 63, 1994 Y. Kozai, R. P. Binzel and T. Hirayama eds. Foglia S., Minor Planet Software 2003, http://www.uai.it/sez_ast/ Gradie J. C., Chapman C. R., Williams J. G. Families of minor planets 1979, in Gehrels T.Ed., Asteroids, 359-390 Unviersity of Arizona Press Hergenrother C. W., Larson S. M., Spahr T. B., The Hansa family: a new high inclination asteroid family 1996, Bulletin of the American Astronomical Society, vol. 28, 1097 Kozai Y. The dynamical evolution of the Hirayama family 1979, in Gehrels T.Ed., Asteroids, 334-357 Unviersity of Arizona Press Knezevic Z., Milani A., Asteroid proper elements: the big picture 1993, Asteroid Comets Meteors, 143-158 Knezevic Z., Milani A., Synthetic proper elements for outer main belt asteroids 2000, Knezevic Z., Milani A., Proper elements catalogs and asteroid families 2003, Astronomy & Astrophysics Knezevic Z., Milani A., The determination of asteroid proper elements 2003, Asteroids III Jopek T. J., Froeschlé Cl. A stream search among 502 TV meteor orbits. An objective approach Astron. Astrophys. 320, 631-641 (1997) Lemaitre A., Morbidelli A., proper elements for highly inclined asteroidal orbits Celestial Mechanics and Dynamical Astronomy, no. 60, 29-56, 1994 Lindblad B. A., a study of asteroid dynamical families Seventy-Five Years of Hirayama Families ASP Conference Series, vol. 63, 1994 Y. Kozai, R. P. Binzel and T. Hirayama eds. Lindblad B. A., the statistical significance of small asteroid dynamical families Seventy-Five Years of Hirayama Families ASP Conference Series, vol. 63, 1994 Y. Kozai, R. P. Binzel and T. Hirayama eds. Morbidelli A., Zappalá V., Moons M., Cellino A., Gonzi R. Asteroid families close to mean motion resonances: dynamical effect and physical implications 1995, Icarus 188, 132-154 Morbidelli A., Nesvorny D., Bottke W. F., Michel P., Vokrouhlicky D., Tanga P. The shallow magnitude distribution of asteroid families CDS VI, 2003, Cannes Roig F., Nesvorny D., Ferraz-Mello S. Asteroids in the 2:1 resonance with Jupiter: dynamics and size distribution 2002, Mon. Not. R.Astron.Soc., 335, 417-431 Valsecchi G. B., Carusi A., Knezevic Z., Kresak L., Williams J. G. Isentification of asteroid dynamical families 1989, in Binzel R. P., Gehrels T., Matthews M. S. Ed., Asteroids II, 368-385 Unviersity of Arizona Press Zappalà V., Cellino A., Farinella P., Hierarchical Clustering: how to identify asteroid families and assess their reliability ACM 1990 Zappalà V., Cellino A., Farinella P., Knezevic Z. Asteroid Families. I. Identification by Hierarchical Clustering and Reliability Assessment The Astronomical Journal, vol. 100, no. 6, 2030 (1990) Zappalà V., Cellino A., Dell'Oro A., Paolicchi P. Physical and dynamical properties of asteroid families Asteroids III Zappalà V., Cellino A., asteroid families 1993, Asteroid Comets Meteors, 395-414 Family Data Set Catalog File PDS Catalog File http://pdssbn.astro.umd.edu/