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New Clusters for highly inclined Main Belt Asteroids Sergio Foglia Osservatorio Astronomico Serafino Zani, Lumezzane F. Bisleri 11, I-20148 Milano, Italy and Gianluca Masi University of Tor Vergata, Roma, Italy Madonna de Loco 47, I-03023 Ceccano FR, Italy
Abstract: 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. Introduction Thanks 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 Method The 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. Results Found 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 clusters Spectroscopic 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. 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