Astron. Astrophys. 354, 725-731 (2000)

3. The mass of (16) Psyche

3.1. The encounter

The close approach between (16) Psyche and (94) Aurora occurred in June 1937. During this approach, the minimal distance between both asteroids was 0.007 AU and the relative velocity of both asteroids was about 3.1 km/s. Psyche is the larger of the two asteroids. The effect of its gravitational perturbation on the orbit of Aurora was calculated by starting numerical integration from the epoch of the initial conditions (1995) back to the date of the oldest observations of this asteroid (1872), and by calculating the mass of Psyche from its diameter and an estimation of its mean density. In the different existing taxonomies of asteroids (Tholen 1989, Barucci et al. 1987, Tedesco et al. 1989), Psyche is classified as a M-type asteroid (i.e. an asteroid of dominant metallic composition). Thus, a mean density of 5 g/cm³ was assumed for this asteroid. Previously, the same value had been adopted for M-class asteroid mean density in the computation of DE planetary ephemerides (Standish et al. 1995; Standish 1998). The mean diameter of Psyche given by IRAS is 264 km, which gave an estimated mass of 2.4 10^-11 M and a corresponding maximal perturbation on the orbit of Aurora of about 6" in right ascension and 3" in declination. The maximal effect was reached for the dates of the oldest observations of Aurora (Fig. 1). Such a perturbation enabled the mass of Psyche to be determined. Reciprocally, the effect of the perturbation of (94) Aurora on the orbit of Psyche was calculated. The mean diameter of Aurora given by IRAS is 212 km. Since this asteroid belongs to a subgroup of C class, a value of 1.8 g/cm³ was assumed for its mean density (Standish et al. 1995), which gave a value of about 4.5 10^-12 M for its mass. Thus, starting backward numerical integration from the current epoch, the effect of the perturbation of Aurora on the orbit of Psyche reached a maximum of less than 2" in R.A. for the oldest observations of Psyche, in the late 1850's. This effect is of the same order than the precision of the observations of Psyche of the same epoch, which seems too faint to determine of the mass of Aurora (the attempts made to determine this mass remained unsuccessful).

Fig. 1. Effect of the gravitational perturbation of (16) Psyche on the orbit of (94) Aurora in right ascension, starting backward numerical integration at epoch JED 2450000.5 = 1995 October 10.0 TT and assuming a mass of 2.4 10-11 M for Psyche

3.2. Data

From 1872 to 1998, there are 276 available observations of (94) Aurora in the data archives of the Minor Planet Center. After elimination of 70 non astrometric observations (25%) which were provided with insufficient precision, a sample of 206 useful observations remained. Two additional observations of Aurora, made with the Bordeaux CCD meridian circle in the beginning of 1999, increased to 208 the number of observations. The O-C residuals of these data are shown in Fig. 2 in two cases, respectively without taking the perturbation of (16) Psyche on the orbit of Aurora, and with this perturbation.

Fig. 2. Top: residuals of observations of asteroid (94) Aurora with orbital elements taken in the Ephemerides of Minor Planets for 1995 (Batrakov 1994) and neglecting the perturbation of (16) Psyche; Bottom: same, taking into account the perturbation of Psyche with an assumed mass of 2.4 10-11 M

In that figure, it can be seen that the observations of Aurora are not very numerous before 1925, and that the dispersion of the residuals do not decrease significantly before the 1980's. In consequence, the observations of Aurora were separated in two groups and were selected and weighted by the iterative procedure described in Sect. 2.2. The number of selected observations for both groups and their weights after the last iteration are detailed in Table 2. It can be noted that 42% of the observations of the second group (i.e. after 1979) have been eliminated. The reason is that this group is made up of observations of very different accuracies. This can be seen in Fig. 2 in right ascension mainly, where there are after 1985 observations of poor accuracy showing scattered residuals (up to 4"), and which were eliminated during the iterations, blended with a set of observations of better quality all giving residuals close to 0.

Table 2. Characteristics of each group of observations of (94) Aurora; "initial nb" and "final nb" are respectively the number of observations before elimination by the first iteration and after the last one; "elim" and "% elim" are respectively the number and the percentage of eliminated observations; "" is the standard deviation of the residuals after the last iteration and "weight" is the final weight applied; unit weight corresponds to a mean precision of 0.5"

3.3. Results and discussion

The corrections for the mass of Psyche and for the six osculating elements of Aurora were calculated as described in Sect. 2.2. The new orbital elements of Aurora are given in Table 3, while the correlation coefficients between parameters are given in Table 4.

Table 3. New orbital elements of (94) Aurora, and standard deviations, at epoch JED 2450000.5 = 1995 October 10.0 TT

Table 4. Correlation coefficients for initial position and velocity of (94) Aurora, and mass of (16) Psyche

The value obtained for the mass of Psyche is M. This value is three times smaller than expected. Indeed, using the IRAS value for the mean diameter of Psyche, which is km, the mean density found for this asteroid is g/cm³. However, Psyche is classified in the M-type asteroids, because its spectral characteristics are similar to those of metallic meteorites (McCord & Gaffey 1974, Chapman et al. 1975, Zellner & Gradie 1976, Bowell et al. 1978). Unlike asteroids belonging to other classes for which mass determinations gave in most cases a mean density about 2 g/cm³, the mean density of M-class asteroids is expected to be much larger (Standish 1998). Thus, our value of the density of Psyche is two or three times smaller than expected.

Several reasons can explain this fact. First, the standard deviation on the value obtained for the mass is rather high, and it is known that the real uncertainty is often greater than the formal uncertainty. During the iterations, where the selection of the observations of Aurora as well as the weights applied on them varied, the result for the mass of Psyche oscillated between and M. Thus, the maximal value obtained is 15% higher than the upper bound given by the final result, but it is still half the expected value.

Additional uncertainty on the result is caused by the perturbation of (10) Hygiea on the orbit of Aurora (Table 1). The value M found by Scholl et al. (1987) for the mass of Hygiea was used in this work. Although the uncertainty of this mass is high, it must be noted that this value gives a mean density of 2.3 g/cm³ for Hygiea, which seems quite normal for a C-class asteroid (Fig. 5). As an example, it is about the same density as (1) Ceres'. In order to see how the uncertainty on the mass of Hygiea influences the determination of the mass of Psyche, two computations of the latter were performed using different values for the mass of Hygiea, which correspond to quite extreme values of the mean density of this asteroid (Table 5). The result obtained for the mass of Psyche is respectively 7.2 and M. Again, we stay in the same range of uncertainty as before, and, since the values of the mass of Hygiea were chosen as extreme, the effect of the uncertainty of this mass can be believed to be smaller than that.

Table 5. Variation of the mass found for Psyche with respect to the value used for the mass of Hygiea

For the previous reasons, the result for the mass of Psyche must be regarded as a first indication of what the actual value of this mass could be. Other close encounters between Psyche and other asteroids would be very useful for improving this result. We have made searches in this direction, but the encounters found were not close enough to enable the mass of Psyche to be determined. Further investigations should also be made about asteroids which may have induced additional gravitational perturbations on the orbit of (94) Aurora. The perturbations of the 7 largest asteroids (Table 1) are already taken into account in the standard procedure, but non negligible additional perturbations on the orbit of Aurora induced by other large asteroids could result in biases in the value found for the mass of Psyche.

The reasons evoked before give only a partial answer to the problem. Another reason that can explain why the mass of Psyche is smaller than expected is the fact that this asteroid is not spherical but is believed to have the shape of a triaxial ellipsoid (Morando & Lindegren 1989). In such conditions, the volume of Psyche calculated from its mean diameter given by IRAS may be easily erroneous. We did not find in literature additional measurements of the dimensions of Psyche obtained from star occultations (e.g. Vasta & Manek 1998). Such measurements would be very helpful for improving the accuracy of the volume of this asteroid. Nevertheless, old determinations of the diameter of Psyche, made by radiometric or polarimetric techniques, are available and led to values about 250 km (e.g. Gaffey & McCord 1978). It must be noted that, if an uncertainty of 10% on the IRAS value of the diameter is assumed (which is not so much), a upper bound of 3.2 g/cm³ is obtained for the mean density of this asteroid (when using the formal uncertainty on the mass). An uncertainty of 20% on the mean diameter would give a upper bound of 4.6 g/cm³. For this reason, a better knowledge of the actual size of Psyche is essential.

The last reason which can explain a mean density smaller than expected is obviously the fact that the actual composition of Psyche may be different from what is believed.

© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000
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