ON THE AGES OF ASTEROID FAMILIES
In our works Paper I (Milani et al. 2014) and Paper II (Knežević et al. 2014) we have introduced a new methods to classify asteroids into families, applicable to an extremely large dataset of proper elements, to update continuously this classification, and to estimate the collisional ages of large families. In later works, Paper III (Spoto et al. 2015) and Paper IV (Milani et al. 2016), we have systematically applied an uniform method (an improvement of that proposed in Paper I) to estimate asteroid family collisional ages, and solved a number of problems of collisional models, including cases of complex relationship between dynamical families (identified by clustering in the proper elements space) and collisional families (formed at a single time of collision). In our latest paper (arXiv preprint), we solve several difficult cases of families for which either a collisional model had not been obtained, e.g., because it was not clear how many separate collisions were needed to form a given dynamical family, or because our method based on V-shapes (in the plane with coordinates proper semimajor axis a and inverse of diameter 1/D) did not appear to work properly.
The figure shows the chronology of the asteroid families; the grouping on the horizontal axis corresponds to fragmentation families, cratering families, young families and families with one-sided V-shape (be they cratering of fragmentation).
THE METHOD
In Paper III, we have computed the ages of 37 collisional families. The members of these collisional families belong to 34 dynamical families, including 30 of those with more than 250 members. Moreover, we have computed uncertainties based on a well defined error model.
The computation of the family ages can be performed by using the V-shape plots in the proper a - 1/D plane. The key idea is to compute the diameter D from the absolute magnitude, assuming a common geometric albedo. The geometric albedo is the average value of the known WISE albedos for the asteroids in the family. Then we use the least squares method to fit the data with two straight lines, one for the low proper a (IN side) and the other for the high proper a (OUT side), with an outlier rejection procedure.
The method we use to convert the inverse slopes from the V-shape fit into family ages consists in finding a Yarkovsky calibration, which is the value of the Yarkovsky driven secular drift da/dt for an hypothetical family member of size D = 1 km and with spin axis obliquity 0° for the OUT side and 180° for the IN side. Since the inverse slope is the change accumulated over the family age by a family member with unit 1/D, the age is this change divided by the Yarkovsky calibration.
It is a fact that the V-shape method, when applied without the prejudice that each dynamical family (found as density contrast in the space of proper elements) must correspond to one and only one collisional family (a single originating collision, with a single age), results in many case with two ages.
In some cases a W-shape is actually visible , and all 4 sides are used in the fit for slopes (see the V-shape of 569 Misa, or the case of 847 Agnia with the 3395 Jitka subfamily). In other cases some of the sides are either partially or totally obliterated by the superposition of the substructure.
The OUT side of the family of 15 Eunomia at higher a corresponds to a much younger age that the IN side at lower a, thus the difference in age is statistically very significant (see the table of the slopes for the ratio of the inverse slopes). Nevertheless, only 2 slopes have been fit, although the OUT one is based essentially only on data points with proper a>2.67 au. For 2.62 < a < 2.67 it would be possible to fit a third slope which can be interpreted as the OUT slope for the family with older age, and would be consistent with the age from the IN slope. The fourth side of the W, the IN side for the younger family, is obliterated by the superposition of the two V-shapes.
MAIN RESULTS
Among the first 34 dynamical families for which we have computed the ages in Paper III, we find:
- 3 cases in which a dynamical family corresponds to at least 2 collisional ones: 4 Vesta, (15) Eunomia, and 1521 Seinajoki.
- 2 examples of two separate dynamical families together forming a single V-shape: 101955 Harig and 19466 Darcydiegel , 163 Erigone and 5026 Martes. In these cases we use the definition of family joint.
- 2 cases of families containing a conspicuous subfamily, with a sharp number density contrast, such that it is possible to measure the slope of a distinct V-shape for the subfamily, thus the age of the secondary collision: the subfamily 3395 Jitka of 847 Agnia and 15124 2000 EZ39 of 569 Misa.
- 2 cases in which the parent body is an interloper in his dynamical families: we are going to speak of the family 1272 Gefion instead of 93 Minerva, and of the family 1521 Seinajoki instead of 293 Brasilia. Both are obtained by removing the interlopers selected because of the albedo data, and the namesake is the lowest numbered after removing the interlopers
LIST OF DYNAMICAL FAMILIES INCLUDING MULTIOPPOSITION ASTEROIDS
In Paper IV we present a new and larger classification, upgraded by using a proper elements catalog with more than 500.000 asteroids, numbered and multi-oppositions.
- We simplify the classification, by decreasing the number of families: indeed, 7 small/tiny families (with less than 100 members) and 2 medium families (173 and 19466) have been merged with larger ones. 1 tiny family (less than 30 members) has been removed because its lack of growth suggests that it should be a statical fluke.
- The increase in family members is an important improvement.
- We have been able to compute 6 new ages. 3 fragmentations: (221) Eos, 1040 Klumpkea, and 1303 Luthera , 1 young: 302 Clarissa, and 2 one-sided: 650 Amalasuntha and 752 Sulamitis .
RESONANT, ERODED AND FOSSIL ASTEROID FAMILIES
We attempt to give a collisional model to a number of families for which the same attempt had previously failed. Most of these families were either locked in resonances or anyway significantly affected by resonances, both mean motion and secular. To estimate an age for the family required in each of these resonant cases we apply a specific calibration for the Yarkovsky effect, which in principle could be different in each case.
- In the Hilda region the Yarkovsky effect results in a secular change in eccentricity, thus the V-shape technique had to be applied in the (e,1/D) plane. We find family (1911) Schubart with a good age determination, and family (153) Hilda of the eroded type.
- For the Trojans we presents a new classification which identifies a number of families by using synthetic proper elements and a full HCM method. Numerical calibration have shown that the Yarkovsky perturbations are ineffective in determining secular changes in all proper elements. Thus all Trojan families are fossil families, frozen with the original field of relative velocities. We find no way to estimate the ages of the families.
- Of the 25 families with more than 1000 members, we have computed at least one age for all but 490, which has a too recent age, already known and unsuitable for out method. Of the 19 families with 300 < N < 1000 members, excluding 778 which has a too recent age, already known, there is only one case left without age, namely 179. On the 24 families with 100 < N < 300 we have computed 6 ages, the others we believe could only give low reliability results.
TABLES, V-SHAPES AND HISTOGRAMS
The numerical data with the computation of ages are collected in the tables. Tables and Figures are partitioned into sections for families of type fragmentation, of type cratering, of type young and with one side only.TABLES
Fit region: family
number and name, explanation of the choice, minimum value
of proper a, minimum value of the diameter
selected for the inner and the outer
side. xls
and pdf format.
Fit region: family
number and name, explanation of the choice, minimum value
of proper e, minimum value of the diameter
selected for the inner and the outer
side. xls
and pdf format.
Family albedos: family number and name, albedo of the parent body with standard deviation and code of reference, maximum and minimum value for computing mean, mean and standard deviation of the albedo. xls and pdf format.
Slopes of the
V-shapes: family number and name, side, slope
(S), inverse slope (1/S), standard deviation of the
inverse slope, ration OUT/IN of 1/S, and standard
deviation of the
ratio. xls
and pdf format.
Slopes of the
V-shapes for the families in the 3/2 resonance:
family number and name, side, slope (S) in
the (e,1/D) plane, inverse slope (1/S), standard
deviation of the inverse slope, ration OUT/IN of 1/S, and
standard deviation of the
ratio. xls
and pdf format.
Data for the Yarkovsky calibration: family number and name, proper semimajor axis a and eccentricity e for the inner and outer side, 1-A, density value at 1 km, taxonomic type, a flag with values m (measured), a (assumed) and g (guessed), and the relative standard deviation of the calibration. xls and pdf format.
Age estimation:
family number and name, da/dt, age estimation,
uncertainty of the age due to the fit, uncertainty of the
age due to the calibration, and total uncertainty of the
age estimation. xls
and pdf format.
Age estimation for
the families in the 3/2 resonance: family number and
name, de/dt, age estimation, uncertainty of the
age due to the fit, uncertainty of the age due to the
calibration, and total uncertainty of the age
estimation. xls
and pdf format.