Palomar-Leiden Research Articles

Subaru Main Belt Asteroid Survey (SMBAS)—Size and color distributions of small main-belt asteroids

Since February, 2001, we have been conducting a series of survey observations to investigate the physical property of very small Main Belt Asteroids (sub-km MBAs) using the Subaru prime-focus camera (Suprime-Cam) attached to the 8.2 m Subaru telescope. We call our surveys “SMBAS: Subaru Main-Belt Asteroids Survey”. This paper presents the results of the second SMBAS (SMBAS-II) which was performed in October 2001. In SMBAS-II, a ∼ 4.0 deg 2 sky area near the opposition and near the ecliptic was surveyed with the R- and B-bands. We detected 1838 moving objects up to R ∼ 25 mag . In SMBAS-II, we could not determine the exact orbits of the objects, because of the short observational arc of only ∼ 40 min . Instead, we statistically estimated the semi-major axis ( a) of each moving object from its apparent sky-motion vector assuming its circular orbit and then, we used the a's to select MBAs and to estimate their absolute magnitudes ( H). The limiting magnitude of SMBAS-II for MBAs was R ∼ 24.2 mag. It corresponds to H ∼ 20 mag at the outer edge of main belt. Thus, assuming their mean albedos, down to D ∼ 0.3 km of S-type asteroids and 0.6 km of C-type asteroids were detected in SMBAS-II. We found that the slopes ( b) of the cumulative size distribution (CSD) (i.e. N ( > D ) ∝ D - b , D: diameter) for sub-km MBAs ranging from 0.6 to 1 km in diameter is 1.29 ± 0.02 . Our b value (1.29) is much shallower than those ( ∼ 1.8) of the Palomer Leiden Survey (PLS) [van Houten, C.J., van Houten, G.I., Herget, P., Gehrels, T., 1970. The Palomar-Leiden survey of faint minor planets. Astr. Astrophys. Suppl. 2, 339–448] and Spacewatch surveys [Jedicke, R., Metcalfe, T.S., 1998. The orbital and absolute magnitude distributions of main belt asteroids. Icarus 131, 245–260.] for larger asteroids ( D > 5 km) and almost consistent with that (1.3) of SDSS [Ivezić, Ž., Tabachnik, S., Rafikov, R., Lupton, R.H., Quinn, T., Hammergren, M., Eyer, L., Chu, J., Armstrong, J.C., Fan, X., Finlator, K., Geballe, T.R., Gunn, J.E., Hennessy, G.S., Knapp, G.R., Leggett, S.K., Munn, J.A., Pier, J.R., Rockosi, C.M., Schneider, D.P., Strauss, M.A., Yanny, B., Brinkmann, J., Csabai, I., Hindsley, R.B., Kent, S., Lamb, D.Q., Margon, B., McKay, T.A., Smith, J.A., Waddel, P., York, D.G. (for the SDSS Collaboration), 2001. Solar system objects observed in the Sloan Digital Sky Survey commissioning data. Astron. J. 122, 2749–2784] for MBAs with 0.4 km < D < 5 km. This means that the number of sub-km MBAs is much more depleted than the result extrapolated from the size distribution for larger asteroids. This shallow slope of sub-km MBAs has been obtained from our first SMBAS (SMBAS-I) ( b = 1.19 ± 0.02 ) which was carried out in February 2001 [Yoshida, F., Nakamura, T., Watanabe, J., Kinoshita, D., Yamamoto, N., Fuse, T., 2003. Size and spatial distributions of sub-km main-belt asteroids. Publ. Astron. Soc. Jpn. 55, 701–715]. We examined taxonomic distribution of sub-km MBAs. Although we could not exactly distinguish S-type and C-type asteroids only using the R and B-magnitude, we divided SMBAS-II MBAs into two groups: S-like asteroids (rocky) and C-like asteroids (carbonaceous). The heliocentric distribution of S-like MBAs was almost flat throughout the entire main belt, while that of C-like MBAs shows an asymmetric distribution, namely, the number of C-like asteroids increases with the heliocentric distance. The number ratio of S- and C-like MBAs with D > 0.6 km was 1:1 in the inner belt (2.0 AU < a < 2.6 AU), 1:2.3 in the middle belt (2.6 AU < a < 3.0 AU), and 1:4 in the outer belt (3.0 AU < a < 3.5 AU), respectively. For the entire main belt, the ratio was 1:2.3.

Asteroid Trails in Hubble Space TelescopeWFPC2 Images: First Results

Careful examination of 28,460 selected Wide Field and Planetary Camera 2 (WFPC2) long exposures from 1994, 1995, and early 1996 has revealed trails of 96 distinct moving objects. They have been reported to the International Astronomical Union's (IAU) Minor Planet Center for their asteroid database and a few have been identified with known asteroids and used to update their orbits. Most of the objects are new, as they are too faint to show up on ground-based surveys.The trails often show a characteristic curvature due to the parallax induced by HST's orbital motion during the exposures. Using ephemerides for HST, the distance to each object can be directly determined from the parallax contribution to the trail shapes. Based on these distances, constraints on the orbits, and photometry of the trails (16 <V< 24), most of the moving objects appear to be small, main-belt asteroids a few km in diameter. A few are known objects—three are potential Mars crossers. Modern wide-field CCD surveys detect asteroids nearly as faint as these (V< 21), but the corresponding absolute magnitudes are uncertain unless their orbits have been established.The detected objects span the absolute magnitude range 13.6 <H< 19.3 (His the symbol for absolute magnitude, not H-band). Statistics of the detections imply a reservoir of (3.1 ± 0.6) × 105such asteroids within 25° of the ecliptic. We find that the slope of the cumulative distribution of absolute magnitudes follows a power law N ∝ H0.2to N ∝ H0.3over this absolute magnitude range in the three distance ranges defined by the Palomar–Leiden survey. These are significantly shallower slopes than those inferred by the Palomar–Leiden survey or extrapolated from population studies of larger asteroids.

Asteroid families—An initial search

A sample of both numbered and faint Palomar-Leiden Survey (PLS) asteroids was searched for clusters in three-dimensional proper element (semimajor axis, eccentricity, sine inclination) space. These clusters, selected by stereo examination, were then filtered objectively by requiring that their Poisson probability of chance occurence be small (log P < −3.5). One-hundred four clusters were accepted as families. These families have populations from 4 to 102 members, with a median of 8 members. Well-populated families in uncrowded regions are the most certain. The Themis, Eos, and Koronis families are obvious; major families include Eunomia and Alexandra. Families are interpreted as generated by impact. The Eos and Koronis families are examples of total breakups and the Themis family is a partial breakup with all or most of the material excavated from one side of the parent body. Themis and other one-sided, partial breakups are recognizable when one large object (sometimes several) is present at one edge (in proper element space) of a family; when the proportion of ejected material is small these are more appropriately called large cratering events. Such cratering events are found with 2 Pallas, 4 Vesta, 8 Flora, 14 Irene, and 20 Massalia. Some material from Flora has been ejected into Mars crossing orbits. Structure is common in the well-populated families—the Eos and Koronis families have densely populated cores with additional material extending out from one side, Themis has a dense core attended by clumps, and Alexandra has an embedded disk. The better sampled families are discussed in terms of their geometry and taxonomy. A selection of the other families are discussed using the available proper element and physical properties data. Some families are very rich in faint PLS members and there is evidence that families do not all have the same size distribution. Many families would benefit from the discovery of additional objects and improved sampling of physical properties.

The second Palomar-Leiden Trojan survey

The 1973 Trojan survey of a region close to the preceding Lagrangian point is discussed in this paper. This region consists of four overlapping fields and one field for the photometric calibration, centered on Selected Area 68. Orbital elements of most of the 1504 asteroids found have been published in the Minor Planet Circulars. Among these are 5 Hungaria-type asteroids, 12 of the Hilda type and 55 Trojans. The accuracy of the orbits is somewhat lower than in the Palomar-Leiden survey of 1960, because of the shorter arc in the present investigation. A discussion of the degree of completeness of this material shows that the (photographic) magnitude interval 19.5–20.0 is only 50% complete; to obtain completeness down to magnitude 20.0 the number of found Trojans brighter than this limit has to be increased by 9. In combination with the surveys of 1960 and 1965 an improved distribution of the number of Trojans as a function of distance to the preceding Lagrangian point (L4) has been constructed. A preliminary discussion, including the result on L5, yields a value of 2.0 for the ratio of Trojans around L4 and L5, along the ecliptic. The L5 Trojans appear to be deficient in orbits of small inclination. Taking this into account we find this ratio again to be 2.0 for the total Trojan clouds around L4 and L5. Possibly, however, high-inclination Trojans were systematically overlooked in this survey. If this would be true, the ratio N(L4)/ N(L5) is increased to 2.3. The uncertainty of these numbers can be estimated to be ±0.5.

Palomar-Leiden minor planets: Proper elements, frequency distributions, belt boundaries, and family memberships

Proper elements have been calculated for 1227 higher accuracy orbits from the Palomar-Leiden Survey of faint minor planets. Tabulations are given for the special orbits: Earth and deep Mars crossers, Trojans, Hildas, and one 2:1 librator. The frequency distributions of the proper semimajor axis, eccentricity, sine inclination, longitudes of perihelion and node plus their rates, and the closest distances of approach to Mars and Jupiter are displayed as histograms and discussed. The distribution of the closest approach distance to Mars drops off sharply near zero while that for Jupiter vanishes near 1.1 AU. Mars and Jupiter have apparently caused these boundaries and the asteroid belt must have been larger early in the history of the solar system. 3.5% of the sample can impact Mars. Most of these potential impactors are shallow crossers which require occasional fortuitous alignments of the secular terms to intersect Mars' orbit so that long lifetimes result and moderate populations remain. As these fortuitous alignments occur with near simultaneity for many, but not all, asteroids the shallow crossers in the observed size range will episodically bombard Mars. Proper elements have been used to recognize families and 49% of the sample of minor planets fall into these families. The proper elements and family assignments are tabulated.

The Palomar-Leiden survey of faint minor planets: Conclusion

The results are given of a revision and small extension of the Palomar-Leiden Survey of minor planets. The majority of the class 4 orbits in the original Survey have been rederived using positions measured from the second plate of each blink pair, and in some cases the orbits could be raised to class 1 quality by the identification of observations in the second month. By using the concept of “e- assumed orbits,” meaningful—if not always accurate—orbits are given for the cases that previously had to be rejected. The extension to the Survey consists of 170 new objects found in the field used for photometric calibration purposes. The total number of orbits in the Survey is 2403, and a tabulation is given of the 1198 orbits that supplement or amend those in the original Survey. A listing is included of the identifications of Palomar-Leiden objects with minor planets observed at other oppositions.

10. A Statistical Investigation of Asteroid Families: Preliminary Results

The correct identification of asteroid families is a prerequisite for understanding their nature, their orbital evolution and their physical origin. For this reason, a statistical investigation of asteroid families has been carried out, using a new clustering technique developed by A. I. Gavrishin. Proper elements for 2764 asteroids (1810 numbered and 954 Palomar-Leiden-Survey (PLS) asteroids) have been computed. Using these data, the Gavrishin method gives only ten significant classes. Five of them are coincident with the Hirayama families 1, 2, 3, 5, and the Flora group, that cannot be univocally subdivided. The PLS families are recognized. Furthermore many small-sized families reported by several authors lose their statistical relevance.

Minor planets and comets in libration about the 2:1 resonance with Jupiter

view Abstract Citations (30) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Minor planets and comets in libration about the 2:1 resonance with Jupiter. Franklin, F. A. ; Marsden, B. G. ; Williams, J. G. ; Bardwell, C. M. Abstract We examine the orbits of minor planets in a search for objects librating about the 2:1 mean-motion resonance with Jupiter. Some 30 candidates are found among the Palomar-Leiden Survey and other unnumbered minor planets. Although almost all the orbits are very uncertain, there does seem to be an indication that librators of low orbital eccentricity do exist, contrary to the hypothesis by Giffen. We also tabulate data describing 12 comets that are temporarily librating about the 2:1 resonance. Finally, we present a discussion of what are apparently 'apocentric' librations. This type of libration, of which we find seven representatives among the numbered minor planets, can occur only for sufficiently small eccentricity. For such bodies, the role of Jupiter's eccentricity is vital; it is associated with a continuing alternation between apocentric libration and an oscillation of the line of apsides. Publication: The Astronomical Journal Pub Date: September 1975 DOI: 10.1086/111806 Bibcode: 1975AJ.....80..729F Keywords: Asteroids; Comets; Jupiter (Planet); Librational Motion; Orbital Elements; Planetary Orbits; Circular Orbits; Eccentric Orbits; Resonance; Saturn (Planet); Tables (Data); Lunar and Planetary Exploration full text sources ADS |

On the fragmentation of asteroids

AbstractMembers of each family or stream of asteroids represent fragments of a single collision of two parent asteroids. Therefore the mass distribution for family members is at the same time the distribution for such fragments. For 4 families with large numbers of known members the mass distribution can be approximated by an inverse power low withs≈ 1.7–2.0. The comparison of distributions for big and small members of these 4 families shows that the Palomar-Leiden Survey of faint asteroids contain about 1/60 of their true number which is thus of about 120000. About 1/3 of families contain from 1 to 4 big asteroids more than 10 times more massive than the remaining. Among 49 asteroids revealed to be of variable brightness, 18 are members of asteroid families and 17 of the latter are their biggest members.

The Palomar-Leiden Survey

The Palomar-Leiden survey (PLS) was set up as an extension to fainter magnitudes of the McDonald survey. The latter is, therefore, the more important survey as far as asteroid statistics are concerned. The main result of the PLS is that no clearcut differences exist between the fainter asteroids found in this survey and the numbered asteroids in the distribution functions of eccentricity, inclination, and semimajor axis and that the statistical relations found in the McDonald survey have a continuous extension in the PLS material. I would, therefore, propose not to summarize the results of the PLS, which would appear to be a tedious job, but to give here some new results that should properly have been included in the publication, but, for reasons of pressures to publish as soon as possible, were not.

Asteroid Masses and Densities

Before 1966, when Hertz (1966) published his first direct determination of the mass of Vesta, all our knowledge on asteroid masses was based on estimates. The masses of the first four minor planets resulted from the measured diameters by Barnard (1900) (see the paper by Dollfus in this volume) and from estimated mean densities. The diameters of the smaller objects were derived from their brightness and an estimate of their reflectivity (usually the reflectivity of the Moon was adopted). In 1901, Bauschinger and Neugebauer (1901) derived a value for the total mass of the first 458 asteroids. All the diameters were computed from the brightness with an assumed value for the reflectivity. The diameter of Ceres found in this way is very close to Barnard’s (1900) value. The mean density of the 458 asteroids was put equal to that of Earth, and their total mass resulted as 3 X 10-9 solar mass. Stracke (1942) used the same method with an increased material, but the addition of more than 1000 faint asteroids did not bring a significant change in the estimate of the total mass. The report on the McDonald asteroid survey (Kuiper et al., 1958) does not contain another estimate of the total mass of the asteroid ring, but it points to the possibility of a very rapid increase in the number of asteroids with decreasing absolute brightness. If this increase is strong enough, each interval of 1 mag in absolute magnitude can contribute the same amount to the total mass. In the range of magnitudes covered by the Palomar-Leiden survey (PLS) (van Houten et al., 1970), there are no indications for such a strong increase.

Orbital Selection Effects in the Palomar-Leiden Asteroid Survey

The selection effects appearing in the list of minor planet orbits based on the Palomar-Leiden survey are discussed. In addition to purely geometrical effects produced by the limitation of the survey in time and position, the arrangement of orbits by perturbations plays an important role. Some apparent differences from the orbits of brighter asteroids can be easily explained. As an example of the operation of the selection effects, it is shown that the asteroidal Jetstream believed to exist within the Nysa family is spurious.

Proper Elements, Families, and Belt Boundaries

Families of asteroids were first found by Hirayama (1918, 1923, 1928). More recently Brouwer (1951) and Arnold (1969) have extended greatly the number of families known from the cataloged asteroids. The Palomar-Leiden survey (PLS) (van Houten et al., 1970), which mainly covered very faint, uncataloged objects, found several more families.Except for the work of Hirayama (1918), which used osculating elements, all of the above studies looked for clusterings of the semimajor axis a, the proper eccentricities é, and proper inclinations í. The calculation of proper elements involves using a theory of secular perturbations to remove the long-period, large-amplitude disturbances of the major planets. The theory used Up to now (Brouwer and van Woerkom, 1950; Brouwer and Clemence, 1961) involved a low-order expansion in the eccentricities and inclinations. There is now a theory available (Williams, 1969) that will accurately handle much higher eccentricities and inclinations than before.