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Updated Feb. 3, 2012


In February 2012, the binary asteroid (22) Kalliope will reach one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, will be aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. Such a favorable configuration occurs every 5 years.

OA Kalliope image

Fig. 1: Views of Kalliope from it 3D topographic shape model.

A dedicated international campaign of photometric observations, based on amateur-professional collaboration, is organized and coordinated by the IMCCE in order to catch several of these events. This is the second campaign of such kind, the first one occuring in 2007 (Descamps et al, 2008). Due to the fast-evolving aspect of the system, as seen by an Earth observer, the season of mutual events lasts barely one month. Mutual eclipses will take place mainly in February 2012. Due to the positive declination of Kalliope (+34°), northern hemisphere telescopes are favoured. The brightness of Kalliope (mv = 11 and geocentric distance of about 2UA) will permit photometric observations with a small aperture telescope.

We have refined orbital model of the satellite (F.Vachier et al 2012) obtained by our new genetic-based algorithm. Theses results provide an orbital solution accurate within 15 mas on the satellite position relative to the primary. The figure show some recorded chords during the 2006 occultation in Japan, and at this date, the couple Kalliope-Linus has the most precisely estimated mutual orbit of all known binary asteroids. We use this orbit to calculate mutual phenomena between the satellite and its primary.

2006 Occultation in Japan

Fig. 2: Predicted position of Linus (upper right blue cross) compared with the adjusted chords of Linus stellar occultation, see Descamps et al. (2008): dx = 9 km = -7 mas, dy = 3.6 km = 3 mas.

Anomalous attenuation events were predicted to last about 2 hours with detectable amplitude ranging from 0.03 to 0.07 magnitudes. Among all large binary systems known so far, the secondary-to-primary size ratio of the Kalliope system is the highest with a value estimated to 0.2 which is considered as the lower photometric detection limit of a binary system (Pravec et al., 2006). The decrease in luminosity depends on the irregular shape of Kalliope. We estimated that a photometric accuracy of about -0.02mag is required to highlight such small photometrical variations. The eclipse can be detected only if reference "healthy" lightcurves have been recorded the day before or/and the day after the phenomenon.

Photometric observations of mutual eclipses will enable us to further improve our knowledge of physical and orbital properties of this amazing binary system. The mutual events observations provide a unique opportunity to get anew measurement of the very size of Kalliope which mainly governs the duration of an event.

Prediction of events

Animated Eclipse

Fig. 3: Synthetic lightcurve of an eclipse by Linus on March, 2 2012.
The shadow of Linus cast on the surface of Kalliope removes a tiny fraction
of the reflected solar light giving a slight decrease in collected light of
the whole system from a ground-based telescope.

The table 1 gives the list of events.

The drop in flux during the events will be small, and quite dependent on the primary shape and the orbit solution. Nevertheless, thanks to the brightness of 22 Kalliope (mv = 11), it should be possible to detect this variation and get valuable information about the size ratio and the shape of the secondary. Our calculations show that the brightness variation for the integrated flux will reach at most 0.07 mag. Very precise photometric capabilities and data-processing are necessary to get magnitude accuracy better than 0.005.

The figure 2 shows two synthetic lightcurves of Kalliope during an event. In both cases a global attenuation can be seen, indicative of the additional dimming of the sunlight reflected by the asteroid. The shape and the intensity of the attenuation will depend on the shapes and size ratio of the components as well as on the illumination and viewing geometries of the system at the time of the event.

The following table lists all observable events. The columns display the following predicted parameters:

  • Date: the date of the event
  • Event: the type of event: 'O' = occultation, 'E' = eclipse, '1' = Kalliope, '2' = Linus
  • Begin: the hour of the beginning of the event
  • End: the hour of the ending of the event
  • Δt: the duration of the event
  • Δmag: the drop in flux
  • View: the icons allow one to download an MPEG animation and the predicted lightcurve of the event (Postscript format)
The timing accuracy of the events is of the order of a few minutes.

2012-02-04 1E2 08h11m 10h04m 01:53 0.0057 16.54
2012-02-06 2E1 03h05m 05h15m 02:10 0.0175 16.96
2012-02-07 1E2 22h23m 00h06m 01:43 0.0217 17.37
2012-02-09 2E1 17h26m 19h20m 01:54 0.0172 17.76
2012-02-11 1E2 12h10m 14h47m 02:37 0.0446 18.12
2012-02-13 2E1 07h16m 09h57m 02:41 0.0281 18.47
2012-02-15 1E2 02h31m 05h25m 01:54 0.0440 18.80
2012-02-16 2E1 21h44m 00h38m 02:54 0.0547 19.10
2012-02-18 1E2 16h36m 19h14m 02:38 0.0491 19.39
2012-02-20 2E1 11h40m 14h29m 02:49 0.0447 19.65
2012-02-22 1E2 06h55m 09h43m 02:48 0.0511 19.90
2012-02-24 2E1 02h12m 04h57m 02:45 0.0567 20.13
2012-02-25 1E2 21h26m 23h48m 02:22 0.0453 20.34
2012-02-27 2E1 16h06m 18h52m 02:46 0.0462 20.53
2012-02-29 1E2 11h22m 13h58m 02:36 0.0441 20.70
2012-03-02 2E1 06h50m 09h11m 02:21 0.0639 20.86
2012-03-04 1E2 02h07m 04h01m 01:54 0.0307 20.99



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