Possible Duplicities of Five Asteroids

Some evidences of possible duplicities of five asteroids are presented. A satellite of (279) Thule was convincingly detected by a stellar occultation on 2008 April 3 by Thule and also from follow-up light curve observations. The orbital period of the satellite is 3.007 or 6.014 days, and the minimum diameter is estimated to be 52 km. A satellite of (324) Bamberga was detected by secondary drops of the light curve in 2007. The rotation period of the primary is 1.22625 days, and the revolution period of the secondary is 3.00 or 6.00 days. Presumed contact duplicity of the main body of the L4 Trojan (624) Hektor was detected by a stellar occultation by Hektor on 2008 January 24. A possible satellite of (657) Gunlöd was suggested from a secondary occultation by Gunlöd on 2008 November 29. The minimum of the diameter is 7 km. A possible satellite of (739) Mandeville was suggested by stellar occultation observations on 1980 December 10.


Introduction
Since the first discovery of Dactyl, a satellite of (243) Ida, by the Galileo spacecraft in 1993, several hundreds of satellites of asteroids have been detected by various means, such as asteroidal occultations, light curve observations, radar observations, and spacecraft encounters.Discovery of a satellite of an asteroid provides a total mass of the binary system from the third law of Kepler if its evolution period and semi-major axis of the orbit are obtained.We present some evidence of the duplicities of five asteroids detected in Japan through occultation observations.

Stellar Occultation on 2008 April 3
The asteroid (279) Thule was discovered by J. Palisa in 1888.The semi-major axis of its orbit is 4.27 au, the eccentricity of the orbit is 0.01, and the revolution period is 8.83 years which is within the mean motion resonance of 4:3 with Jupiter.Asteroids with this resonance are part of a group called the Thule group.The other members of the Thule group known thus far are (185290) 2006 UB219 and (186024) 2001 QG207.Thule is a D-type asteroid [1].
The occultation of the star TYC 497200415 by (279) Thule, the first observed stellar occultation by Thule, was observed on 2008 April 3 from four sites in Japan.The event was predicted by Satō (Figure 1).The position of the occulted star is α 2000 = 13 h 31 m 32.3082 ± 0.020 s, δ 2000 = −06˚59'53".701 ± 0.022, and the brightness of the star is m v = 10.82.The assumed diameter of Thule is 127 km and the predicted extinction would be 3.7 mag for 8.6 seconds.The occultation track would go through Kanto and Chubu districts of Japan.The observation results are listed in Table 1.Three chords among four are timed by video with GPS clock, and one is visual.
Revealed occultation cross section is (126 ± 1 km) × (123 ± 7 km), the position angle of the ellipse is 80˚ ± 129˚ (Figure 2).Three chords by Yanagida Astronomical Observatory, Hideo Takashima, and Hideyoshi Karasaki are consistent with an ellipse of the primary, but the chord by Hiroyuki Tomioka is not coincident with it.This specific observation was made with GPS time-inserted video, hence the observation must be considered reliable.The extinction suggests a possible previously unknown satellite with diameter of 52 km.The following-up light curve observations of Thule was obtained after the occultation.

Light Curve Observations in 2008
A light curve observation was obtained at Hamanowa Observatory during 13 nights from 2008 April 8 to May 6.
Figure 3 shows a total combined light curve.Four instances of secondary drops are seen in the light curve.The Light curve shows at rotation period of 7 h 26 m 24 ± 1 s, peak-to-peak amplitude of 0.081 mag with secondary drops of 0.1 mag.The result is coincident with the previous result of 7.44 ± 0.05 hours [2]. Figure 4 shows the light curves of four nights with secondary drops, 2008 April 6, 15, 30, and May 3. The secondary drops suggest a satellite with revolution period of 3.007 or 6.014 days.The assumed phase of the secondary drop at the time of the stellar occultation is coincident with the hypothesis that Tomioka's extinction occurred from a satellite with a diameter of 52 km, namely, it is assumed that the possible satellite was during the partial phase of a mutual phenomenon.The second event, the occultation of HIP059807 (7.3 mag) by Bamberga, was observed from five sites in Australia on 2007 April 20 (Table 2, Figure 5).The occultation cross section shows an ellipse of (231 ± 4 km) × (211 ± 12 km), P = 106˚ ± 8˚.Hamanowa Observatory performed light curve observations just after the second event from 2007 April 23 to May 22.As a result, the amplitude is 0.084 ± 0.0030 mag during the rotation period of 29 h 27 m 27 ± 3 s (Figure 6).Light curve observations were also obtained by [4]- [6].The period is coincident with these results.

Satellite of (324) Bamberga
The light curve (Figure 6) also shows secondary drops on the three nights

Duplicity of (624) Hektor
The L4 Trojan (624) Hektor was discovered by A. Kopff in 1907.Hektor has a satellite S/2006 (624) 1 of diameter        15 km [8].The stellar occultation by (624) Hektor of TYC057700887 (10.1 mag) was observed from two sites in Japan on 2008 January 24 (Figure 12).This is the first stellar occultation observation to be observed by Hektor.Tomioka at Hitachi, Ibaraki, detected an extinction for 4.4 seconds by video with GPS clock.Uehara at Tsukuba, Ibaraki, observed two times extinction, 3.6 and 5.0 seconds, respectively, by visual (Table 3, Figure 13).His observation suggests the primary body is a close or contact binary.A possible unusual shape of the primary has been suggested by many authors [9]- [19].

Possible Satellite of (657) Gunlöd
(657) Gunlöd was discovered by A. Kopff in 1908.The planet is a main belt asteroid with a revolution period of 4.22 years.The stellar occultation of UCAC2 43078953 (12.0 mag) by (657) Gunlöd was observed from three sites in Japan (Table 4, Figure 14) on 2008 November 29.Hiroyuki Tomioka at Hitachi, Ibaraki, detected a 3.5 second extinction by video with GPS clock.Akira Yaeza at Hitachi, Ibaraki, also observed a 4.6 seconds visual extinction.
Two chords are coincident with a circle with a cross section of a diameter 45 ± 5 km compared with the assumed diameter of 42 km.These extinctions were caused by the primary.On the other hand, a short extinction of for 0.7 second was detected at Hamanowa Observatory by video with GPS clock located about 100 km north of the occultation track of the primary (Figure 15).Compared with the predicted extinction of 2.9 mag for 4.4

Possible Satellite of (739) Mandeville
(739) Mandeville was discovered by J. H. Metcalf in 1913.The planet is a main belt asteroid with a revolution period of 4.53 years.The stellar occultation of PPM177093 = HIP052360 (9.4 mag) by (739) Mandeville was observed from two sites in Japan on 1980 December 10 (Table 5, Figure 16).The event was the first ever successfully observed asteroid occultation from Japan.Miyoshi Ida at Ohmi-hachiman, Shiga, observed an extinction for five or six second visually with 6.5 cm telescope, but he failed to record his voice, as a result the time and duration of the event are uncertain.The extinction corresponds to a chord from 69 to 83 km.On the other hands, Toshio Hirose at Yaita, Tochigi, visually observed an extinction of 2.1 seconds also with 6.5 cm telescope.The extinction corresponds to a chord of 29 km.Both Ida and Hirose are experienced lunar occultation

Figure 2 .
Figure 2. Result of the occultation of TYC 497200415 by (279) Thule on 2008 April 3.An ellipse of (126 ± 1 km) × (123 ± 7 km) is fitted for the primary, and a circle of a diameter of 52 km is fitted for the satellite.

Figure 3 .
Figure 3. Composed light curve of (279) Thule from 2008 April 3 to May 6 at Hamanowa Astronomical Observatory.The main light curve is consistent with a period of 7.44 ± 0.05 hoursand a peak-to-peak amplitude of 0.081 mag.In addition to the main light curve, secondary drops are shown on four nights (April 6, 15, 30, and May 3).

Figure 4 .
Figure 4. Detailed features of the light curves of (279) Thule on 2008 April 6, 15, 30, and May 3.Each figure shows a secondary drop on the main light curve.The period of the secondary drops is 3.007 or 6.014 days.

( 324 )
Bamberga was discovered by J. Palisa in 1892.The planet is a main belt asteroid with a revolution period of 4.4 years.The first stellar occultation by (324) Bamberga was observed from the USA, Japan and China on 1987 December 8.The occultation cross section showed a diameter of 227.6 ± 1.8 km[3].

Figure 5 .
Figure 5. Occultation track and locations of the black circles observers of the occultation of HIP 059807 by (324) Bamberga on 2007 April 20.The black circles (#3 -7) are sites where the occultation was successfully timed and the crosses (#1, 2) are sites where no occultation occurred.

Figure 6 .
Figure 6.Composed light curve of (324) Bamberga from 2007 April 23 to May 22.The primary period is 1.2274 ± 0.0008 days.In addition to the primary period, secondary drops are shown on 2007 April 28, May 4 and 7.

Figure 7 .
Figure 7. Expanded light curve of (324) Bamberga from 2007 April 23 to May 9.The short period sine curve (blue line) is 1.2274 days, and the long period sine curve (red line) is 2.96 days.The secondary drops on 2007 April 23, May 4 and 7 do not fall on the short period sine curve but are coinsident with the bottom of the long period sine curve.

Figure 12 .
Figure 12.Occultation track and locations of observers of the occultation of TYC 057700817 by (624) Hektor on 2008 January 24.The black circles indicate sites where occultations were successfully timed.

Figure 13 .
Figure 13.Result of the occultation of TYC 057700887 by (624) Hektor on 2008 January 24.Two extinctions were visually observed at #2 site.Since the main body is assumed to be a contact binary, two contact ellipses of (280 × 130 km) and (181 × 141 km) are fitted.

Figure 14 .
Figure 14.Occultation track and location of observers of the occultation of UCAC2 43078953 by (657) Gunl ōd on 2008 November 29.The black circles indicate location where occultations were successfully timed.Sites #2 and 3 are where the star was occulted by the primary, and site #1 is where the occultation was by a possible satellite.

Figure 15 .
Figure 15.Result of the occultation of UCAC2 43078953 by (657) Gunlōd on 2008 November 29.Chord #1 and #2 are from timed video and #3 is from a visual timing.

Figure 16 .
Figure 16.Occultation track and locations of observers of the occultation of HIP 052360 by (739) Mandeville on 1980 December 10.The black circle #3 is visual timing site, and #8 is an occultation from a site where no timing was observed.Crosses (#1, 2, 5) indicate sites where no occultation took place and points (#6, 7, 9) sites where clouds obscured any observation.

Figure 17 .
Figure 17.Result of the occultation of HIP 052360 by (739) Mandeville on 1980 December 10.Locations #3 and #8 are where visual occultation were timed but those times are inaccurate.But location #5 between them was no occultation.