A 3-D Shape Model of (704) Interamnia from Its Occultations and Lightcurves

Isao Satō, Marc Buie, Paul D. Maley, Hiromi Hamanowa, Akira Tsuchikawa, David W. Dunham

Astronomical Society of Japan, Yamagata, Japan.
Hamanowa Astronomical Observatory, Fukushima, Japan.
International Occultation Timing Association, Greenbelt, USA.
International Occultation Timing Association, Houston, USA.
Southwest Research Institute, Boulder, USA.
Yanagida Astronomical Observatory, Ishikawa, Japan.

DOI: 10.4236/ijaa.2014.41010                

Abstract

A 3-D shape model of the sixth largest of the main belt asteroids, (704) Interamnia, is presented. The model is reproduced from its two stellar occultation observations and six lightcurves between 1969 and 2011. The first stellar occultation was the occultation of TYC 234500183 on 1996 December 17 observed from 13 sites in the USA. An elliptical cross section of (344.6 ± 9.6 km) × (306.2 ± 9.1 km), for position angle P = 73.4 ± 12.5° was fitted. The lightcurve around the occultation shows that the peak-to-peak amplitude was 0.04 mag. and the occultation phase was just before the minimum. The second stellar occultation was the occultation of HIP 036189 on 2003 March 23 observed from 39 sites in Japan and Hawaii. An elliptical cross section of (349.8 ± 0.9 km) × (303.7 ± 1.7 km), for position angle P = 86.0 ± 1.1° was fitted. A companion of 8.5 mag. of the occulted star was discovered whose separation is 12 ± 2 mas (milli-arcseconds), P = 148 ± 11°. A combined analysis of rotational lightcurves and occultation chords can return more information than can be obtained with either technique alone. From follow-up photometric observations of the asteroid between 2003 and 2011, its rotation period is determined to be 8.728967167 ± 0.00000007 hours, which is accurate enough to fix the rotation phases at other occultation events. The derived north pole is λ₂₀₀₀ = 259 ± 8°, β₂₀₀₀ = -50 ± 5° (retrograde rotation); the lengths of the three principal axes are 2a = 361.8 ± 2.8 km, 2b = 324.4 ± 5.0 km, 2c = 297.3 ± 3.5 km, and the mean diameter is D = 326.8 ± 3.0 km. Supposing the mass of Interamnia as (3.5 ± 0.9) × 10^-11 solar masses, the density is then ρ = 3.8 ± 1.0 g·cm^-3.

Keywords

Asteroids; Occultations; Lightcurve

1. Introduction

A stellar occultation by an asteroid offers a unique opportunity to obtain information on the accurate size and shape of the occulting asteroid as well as about possible duplicity of the occulted star. The first attempt to predict this kind of event was made by G. E. Taylor [1] . The first reported visual observation was the the occultation of BD by (3) Juno at Malmö, Sweden on February 19, 1958 [2] . The first successful photoelectric observation was obtained at Uttar Pradesh State Observatory, India during the occultation of BD by (2) Pallas on October 2, 1961 [2] [3] . Since then, over 2000 events have been observed.

A successful asteroid occultation observation gives a cross section of the occulting asteroid. Follow-up photometric observation around the occultation observation gives a rotation phase at the time of occultation and an amplitude of its lightcurve. This information is significant in order to determine a pole and 3-D shape of the asteroid.

The first follow-up photometric observations were performed at the occasion of the occultation of AG by (375) Ursula in 1982 [4] . Satō et al. (2000) obtained concrete expression of the constraint on the pole and the 3-D shape for the Trojan (1437) Diomedes from an occultation cross section and follow-up photometry in 1997 [5] . Although a strong constraint on the pole direction and the 3-D shape of Diomedes were obtained from these observations, they were not determined uniquely.

Now, we have two occultation cross sections with enough chords for the 1996 December 17 and 2003 March 23 events and lightcurves of (704) Interamnia. This paper shows an instance of unique determination of a pole and an ellipsoidal model of an asteroid by combination of its occultations and photometric observations.

2. Occultation Observations

(704) Interamnia was discovered by Vincenzo Cerulli in 1910. It has an assumed diameter of 317 km [6] , and is the sixth largest among the main belt asteroids. It is classified by Tholen (1984) as an F-type asteroid [7] . Hiroi observed Interamnia’s spectrum to be a good match to that of a specific carbonaceous chondrite meteorite [8] . De Angelis (1995) and Michalowski (1995) showed approximate pole positions [9] [10] .

Stellar occultations by Interamnia have been observed 11 times as of 2012 (Table 1). Six events among them were observed at only one site. We can obtain valid cross sections of Interamnia with enough chords from only the 1996 and the 2003 events as is discussed in the following subsections. Some other events are available for checking the derived model.

2.1. 1996 December 17 Event

The occultation of (TYC 234500183, ,) by (704) Interamnia on 1996 December 17 was initially predicted by D. W. Dunham and E. Goffin in 1996 besed on a computerized search. In an effort to refine the location of the occultation track, transit circle measurements of the star (11 nights) and the asteroid (21 nights) were made at the U.S. Naval Observatory Flagstaff Station by R. Stone. The predicted occultation track is indicated by dashed lines in Figure 1.

Based on this prediction, observing teams were deployed by Lowell Observatory and the University of Arizona [11] [12] , and also by independent observers to some other locations. A total of 19 teams were involved. The event was observed at 13 sites among them. Their locations, instuments, and observation results are listed in Table 2. The occultation cross section is shown in Figure 2. The observed occultation track was shifted to the north compared with the prediction. As a result, about of the cross section is covered by the observation chords. Residuals of visual observations are large compared with video, CCD, and photoelectric observations. Among the visual observations, the site #12 near the southern limit reported a blink but it is not coincident with the photoelectric observation at the site #13. So this observation is assumed to be inaccurate and the observation is omitted from the reduction. An ellipse of whose posi

Table 1 . List of observed stellar occultations by (704) interamnia.

Figure 1. Local map of the occultation track and the locations of the observers in the USA for the 1996 December 17 event. The time is in UT. The observer numbers correspond to Table 2. indicates an occulted site (#1-13), and × indicates a no occultation site (#14-19). Solid lines indicate the actual occultation track, and dashed lines indicates the predicted occultation track.

Conflicts of Interest

The authors declare no conflicts of interest.

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