EDP Sciences
Free Access
Issue
A&A
Volume 508, Number 3, December IV 2009
Page(s) 1503 - 1507
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/200912741
Published online 08 October 2009

A&A 508, 1503-1507 (2009)

Photometry and models of selected main belt asteroids

VII. 350 Ornamenta, 771 Libera, and 984 Gretia[*],[*]

A. Marciniak1 - T. Micha\lowski1 - R. Hirsch1 - R. Behrend2 - L. Bernasconi3 - P. Descamps4 - F. Colas4 - K. Sobkowiak1 - K. Kaminski1 - A. Kryszczynska1 - T. Kwiatkowski1 - M. Polinska1 - R. Rudawska1 - S. Fauvaud5,6 - G. Santacana6 - A. Bruno7 - M. Fauvaud5 - J.-P. Teng-Chuen-Yu8 - A. Peyrot8

1 - Astronomical Observatory, Adam Mickiewicz University, S\loneczna 36, 60-286 Poznan, Poland
2 - Geneva Observatory, 1290 Sauverny, Switzerland
3 - Les Engarouines Observatory, 84570 Mallemort-du-Comtat, France
4 - IMCCE - Paris Observatory - UMR 8028 CNRS, 77 av. Denfert-Rochereau, 75014 Paris, France
5 - Observatoire du Bois de Bardon, 16110 Taponnat, France
6 - Association T60, 14 avenue Edouard Belin, 31400 Toulouse, France
7 - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
8 - Makes Observatory, 18 rue G. Bizet - Les Makes, 97421 La Rivière, France

Received 22 June 2009 / Accepted 14 September 2009

Abstract
We analyze photometric observations of the three main-belt asteroids 350 Ornamenta, 771 Libera, and 984 Gretia, conducted over a twelve-year interval. Our data and those of other authors allow us to determine pole and shape models using the lightcurve inversion technique. In all three cases, a single pole solution was obtained without any significant mirror solution:
Ornamenta - P = 9.180 414 h, $\lambda_{\rm p} = 184\hbox{$^\circ$ }$, $\beta_{\rm p} = -29\hbox{$^\circ$ }$
Libera - P = 5.890 423 h, $\lambda_{\rm p} = 64\hbox{$^\circ$ }$, $\beta_{\rm p} = -78\hbox{$^\circ$ }$
Gretia - P = 5.778 025 h, $\lambda_{\rm p} = 245\hbox{$^\circ$ }$, $\beta_{\rm p} = +52\hbox{$^\circ$ }$.
This analysis and the development of asteroid models increase the set of asteroids with known spin and shape parameters, which consists of only around 100 objects.

Key words: techniques: photometric - minor planets, asteroids

1 Introduction

There is a constant need for new physical models of asteroids as strong advances continue to search for a statistically significant conclusions about the Solar System's history. Reliable information about these objects' spin axis orientations and shapes can be useful to investigations such as those of YORP effect detection and modelling (Kaasalainen et al. 2007; Lowry et al. 2007; Durech et al. 2008).

Lightcurves of more than 3800 asteroids have already been published (as April 2009 release of the Asteroid Lightcurve Database[*] lists). It is important to collect all the available data of one object to construct a model on possibly biggest dataset. Lightcurves collected at a wide range of phase angles are an invaluable source of information about object's shape. A unique model can usually only be obtained when data for at least five apparitions of one main-belt asteroid are available. Here, amateur astronomers provide substantial help, by observing many objects during subsequent apparitions.

This is the seventh paper in the series in which we combine data from either the Asteroid Photometric Catalogue (Lagerkvist et al. 2001) or directly from the authors themselves, including our own photometric observations conducted since 1997 at the Borowiec Observatory. The aim is to create asteroid models using the lightcurve inversion method.

The three models presented in this work will be added to two databases[*][*].

2 Photometry of three main-belt asteroids

Asteroid 350 Ornamenta, 771 Libera, and 984 Gretia were observed photometrically during 67 nights spanning twelve years. The majority of observations were made at the Borowiec Station of the Poznan Astronomical Observatory in Poland equipped with the 40-cm Newtonian telescope. A description of both the equipment and the reduction procedure can be found in the first paper of the present series (Micha\lowski et al. 2004).

Table 1 (online only) provides aspect data for all of the observing runs. After the date of observation, given as the mid-time of the lightcurve, the distances from the object to either the Sun or the Earth in AU are given. In the fourth column, we indicate the Sun-asteroid-Earth phase angle, and the other two columns show the J2000 ecliptic coordinates of a given object at a specific time. The next two columns show the number of points in a single lightcurve and, where available, the standard deviation in the relative brightnesses of one comparison star relative to another star, usually the brightest ones in the image. This provides information about the quality of the given lightcurve. The last column indicates the observatory code.

Table 2:   Asteroid parameters.

Table 2 contains the physical and orbital parameters of all three asteroids. There are objects' IRAS diameters, albedos, and taxonomic types, as well as the semi-major axes, eccentricities, and their orbit inclinations[*][*].

Our original observations are presented in the form of composite lightcurves, one for each of the apparitions (Figs. 1-16, online only). The composites were created from the single relative lightcurves by means of a vertical shift with a fixed synodic period, to obtain the smallest possible scatter. Different symbols denote different observing runs. The vertical scale, which is the same for all the lightcurves of a given object, is the relative magnitude, while the horizontal scale represents the phase of rotation. This composition is being made to obtain a first approximation of the rotation period, that is needed by the inversion procedure. Since we apply no corrections, the lightcurve's changes in shape and amplitude within one apparition are clearly visible in the composites.

2.1 350 Ornamenta

The first lightcurve of Ornamenta was presented in Schober et al. (1993). The lightcurve was compiled from data of five observing runs in December 1991 using a period $9.17 \pm 0.01$ h. The lightcurve amplitude was 0.20 mag and the colour indices were determined to be $B - V = 0.71 \pm 0.01$ mag and $U - B = 0.41 \pm 0.02$ mag. Shevchenko & Tedesco (2006) improved this asteroid's albedo and diameter determinations using data from stellar occultations, to 0.0679 and 99.5 km from the values 0.057 and 118 km known previously from IRAS.

Our observations of Ornamenta spanned five appatitions: 1999, 2004, 2005, 2007, and 2008/2009. It was a difficult, long-period object for the short observing runs possible in April or May, so it was not until the last apparition that, mainly because of an almost 8-h lightcurve, we were able to identify synodic period of rotation of $9.178 \pm 0.001$ h. It confirmed the first determination by Schober et al. (1993). The composite lightcurves shown in Figs. 1 to 5 (online only) were created using that period. Ornamenta exhibited very unusual, asymmetric lightcurves, with three maxima in some apparitions and a long, flat minimum in another. The amplitudes ranged from 0.13 mag to 0.25 mag.

2.2 771 Libera

In 1984, Binzel (1987) obtained three poorly sampled lightcurves of the asteroid 771 Libera, which had an amplitude of 0.53 mag, and combined them to form a single curve with a period of $5.92 \pm 0.01$ h. Next, Libera was observed by Warner (2000) during two nearby nights in September 1999, which resulted in a dense composite with $5.892 \pm 0.002$ h period and a 0.57 mag amplitude. One minimum was about 0.1 mag brighter than another.

We observed this minor planet during four apparitions in the years: 1999, 2005, 2006, and 2008/2009. The lightcurves within each of the apparitions were combined with a period $5.890 \pm 0.001$ h (Figs. 6 to 9, online only), similar to the value given by Warner (2000). The lightcurves were always of rather high amplitude, from 0.39 mag to 0.48 mag, and changed little between apparitions.

Table 3:   Spin models.

2.3 984 Gretia

Van Houten (1962) analyzed old photographic plates from the thirties, on which asteroids were recorded, that had exposure times of half an hour each. In the case of Gretia, this resulted in 3 sparse lightcurves, from three nights in August 1931. The derived period was 5.76 h and the amplitude was about 0.4 mag. However, the brightness measurements, as the author remarked, might have been affected by errors.

Other researchers to observe Gretia included, over 50 years later, Di Martino et al. (1984). Observed on three nearby nights in September 1983, Gretia exhibited a 0.63 mag variations and its lightcurves were combined to produce one with a $5.781 \pm 0.002$ h period.

Piironen et al. (1994) observed this object during two nights in January 1985, at a small phase angle. They confirmed the previous period determinations ( $P = 5.781 \pm 0.005$ h) and in addition found a small (0.03 mag) colour variation during its rotation. The lightcurve appeared to be regular, and to have a 0.6 mag variation. An average colour index of B - V = 0.89 mag, and data about albedo (Table 2) suggested that this object was S-type of a very high albedo.

In July and August 1997, Riccioli et al. (2001) obtained four very sparsely sampled data points and combined them to produce a curve with a $5.560 \pm 0.018$ h period. The resulting lightcurve had an amplitude of about 0.8 mag and looked asymmetric. The B - V colour index was $0.95 \pm 0.03$ mag.

\begin{figure}
\par\includegraphics[width=18cm,clip]{12741f17.eps}
\end{figure} Figure 17:

Observed lightcurves (points) superimposed on the lightcurves created by a model (curves) at the same epochs for 350 Ornamenta.

Open with DEXTER

Blanco et al. (2000), using data from three apparitions and the AM-method, obtained the first pole determinations of this object to be: $\lambda_{\rm p} = 46\hbox{$^\circ$ }\pm 2\hbox{$^\circ$ }$, $\beta_{\rm p} = 47\hbox{$^\circ$ }\pm 1\hbox{$^\circ$ }$, and $\lambda_{\rm p} = 228\hbox{$^\circ$ }\pm 9\hbox{$^\circ$ }$, $\beta_{\rm p} = -12\hbox{$^\circ$ }\pm 9\hbox{$^\circ$ }$. The axes ratios were a/b = 2.25, and b/c = 1.00.

Finally, during four nights in February 2003, Gandolfi et al. (2009) observed Gretia obtaining very high quality lightcurves with each of the extrema having a different level and an amplitude $0.66\pm 0.02$ mag, from which the period was found to be $5.780 \pm 0.001$ h. All of the published lightcurve data, apart from the last set, was used in our modelling of this object.

We added seven apparitions (1997, 1999, 2002, 2005, 2006, 2007/2008, and 2009) to the existing set of observations. The composite lightcurves are shown in Figs. 10 to 16 (online only) and were created using the period $5.778 \pm 0.001$ h and are regular with large amplitudes, ranging from 0.50 mag to 0.78 mag.

3 Pole and shape results

For the asteroid modelling, we use the lightcurve inversion method described in Kaasalainen & Torppa (2001) and Kaasalainen et al. (2001). The method allows us to determine both the pole and period solutions and recover a detailed convex shape model. As a result, the model can reproduce almost all the lightcurve details down to the noise level. Good longitude and phase angle coverage are an advantage in the datasets.

In Table 3, the parameters of the three models are presented. The first column contains the sidereal period with its uncertainty. The next four columns present the pole solution (J2000 ecliptic longitude $\lambda_{\rm p}$ and latitude $\beta_{\rm p}$), which has no significant mirror solution. For each of the pole coordinates, a separate error analysis was performed, because errors in this method can only be estimated from the resulting parameter space (see Torppa et al. 2003; Kaasalainen & Durech 2007 for more details). As a rule, the pole longitudes are badly constrained for ``high'' pole latitudes (far from the ecliptic plane), while for other latitudes they can be quite precise, even down to $\pm$1 degree. The next three columns of Table 3 contain the observing span in years, and the number of all apparitions and lightcurves used in the modelling. In the two last columns, the method used (``L'' for lightcurve inversion) is indicated and its reference. Only for 984 Gretia has the pole solution been previously reported, but proved to be wrong (predicting too low amplitudes), as new data was gathered.

\begin{figure}
\par\includegraphics[width=17cm]{12741f18.eps}
\end{figure} Figure 18:

Shape model of 350 Ornamenta, shown at equatorial viewing and illumination geometry, with rotational phases $90\hbox {$^\circ $ }$ apart (two pictures on the left), and the pole-on view on the right.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=18cm,clip]{12741f19.eps}
\end{figure} Figure 19:

Observed versus modelled lightcurves for 771 Libera.

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\begin{figure}
\par\includegraphics[width=17cm]{12741f20.eps}
\end{figure} Figure 20:

Shape model of 771 Libera.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=18cm,clip]{12741f21.eps}
\end{figure} Figure 21:

Observed versus modelled lightcurves for 984 Gretia.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=17cm]{12741f22.eps}
\end{figure} Figure 22:

Shape model of 984 Gretia.

Open with DEXTER

To show how the model lightcurves reproduce the observed ones, in Figs. 17, 19 and 21 we present three example observing runs for each asteroid (dots) compared to the fits produced by the model (lines). Data on the aspect angles of the Earth and the Sun ($\phi$ and $\phi_0$), and phase angle $\alpha$ are also given.

3.1 350 Ornamenta

We constructed the model of 350 Ornamenta using 37 lightcurves from 6 apparitions (in the years 1991, 1999, 2004, 2005, 2007, and 2008/2009). The number of lightcurves is high, but individual observing runs were usually short compared to Ornamenta's over a 9-h period of rotation. The apparitions were well spread along the asteroid's orbit. The irregular shape model is shown in Fig. 18, and the lightcurves generated by this model, compared to observations, are in Fig. 17.

Apart from the highly accurate pole solution presented in Table 3, we obtained a second solution, at $\lambda_{\rm p} = 40\hbox{$^\circ$ }\pm 30\hbox{$^\circ$ }$ and $\beta_{\rm p} = -81 \pm 5\hbox{$^\circ$ }$, with larger errors. This is a mirror solution, but because of Ornamenta's high orbital inclination, in ecliptic coordinates, it differs profoundly from the first one. However, this solution, although having marginally acceptable deviations, provided far poorer fits in two last apparitions than the first solution. Therefore, it can almost certainly be rejected.

3.2 771 Libera

Libera was an object that allowed us to obtain a unique model from only a small number of lightcurves. We constructed a final model basing on 20 lightcurves from 5 apparitions (1984, 1999, 2005, 2006, and 2008/2009), but the model solution was clearly distinctive among other solutions even when created from a smaller dataset. What is more, there is only one, unambiguous pole solution, probably because of a large $\vert\beta_{\rm p}\vert$ value (Table 3).

As expected, the object has an elongated shape (Fig. 20), producing large amplitude lightcurves, shown in Fig. 19. Although the spin axis is almost perpendicular to the ecliptic plane, the amplitudes vary visibly, probably because of Libera's high orbital inclination, as for the main-belt object. The small, round feature in the shape model is probably real, maybe a crater, because it is present in all the shape solutions, regardless of the input parameters or the dataset size.

3.3 984 Gretia

Gretia is an unusual asteroid, whose photometric observations span almost 80 years. This caused the step in the period scan to be very small, and one single period (5.778 025 h) was identified with unprecedented clarity in the periodogram.

The model was obtained using 28 lightcurves from 10 apparitions (1931, 1983, 1985, 1997, 1999, 2002, 2005, 2006, 2007/2008, and 2009). The pole solution in Table 3 was the only one that provided satisfactory fits and realistic shape models, although a second solution at $\lambda_{\rm p} = 110\hbox{$^\circ$ }\pm 20\hbox{$^\circ$ }$ and $\beta_{\rm p} = +79 \pm 5\hbox{$^\circ$ }$ was also found.

Before we acquired data for the last apparition, the resulting shape models tended to be non-physical (too large along the axis of rotation), and varied a lot in otherwise similar solutions. However, with these data, the shape model stabilized itself. The colour variation observed by Piironen et al. (1994) was not confirmed, because the sole combination of the pole and shape model reproduces the observed lightcurve features well, even though the observations were made in various filters. The model fit is shown in Fig. 21, and the shape model for the best pole solution is given in Fig. 22.

4 Conclusions and future plans

Including also this paper, we have published models of 21 main-belt asteroids (Micha\lowski et al. 2004, 2005, 2006; Marciniak et al. 2007, 2008, 2009). Many of these objects were found to be irregularly shaped bodies that would be impossible to model properly with classical EAM methods, which assume that the asteroids have smooth, ellipsoidal shapes. We are preparing a paper that will combine the results from the lightcurve inversion asteroid modelling. In the meantime, the continual gathering of new data to increase the database of asteroids with known spin and shape parameters is our long-term aim. This database will be especially valuable when the first asteroids models based on Gaia mission data become available. There will then be a need for a large sample of common objects modelled in both ways, to check the accuracy of models obtained basing on sparsely sampled photometric measurements performed by Gaia, compared to traditional, dense photometry.

Acknowledgements
Borowiec observations were reduced with the CCLRS STARLINK package. This work was partially supported by grant No. N N203 302535 from the Polish Ministry of Science and Higher Education. This paper uses observations made at the South African Astronomical Observatory (SAAO). The lightcurve inversion code was created by Mikko Kaasalainen and modified by Josef Durech, and is available at http://astro.troja.mff.cuni.cz/projects/asteroids3D.

References

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Online Material

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg1.eps}
\end{figure} Figure 1:

Composite lightcurve of 350 Ornamenta in 1999.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg2.eps}
\end{figure} Figure 2:

Composite lightcurve of 350 Ornamenta in 2004.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg3.eps}
\end{figure} Figure 3:

Composite lightcurve of 350 Ornamenta in 2005.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg4.eps}
\end{figure} Figure 4:

Lightcurve of 350 Ornamenta in 2007.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg5.eps}
\end{figure} Figure 5:

Composite lightcurve of 350 Ornamenta in 2008/2009.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg6.eps}
\end{figure} Figure 6:

Composite lightcurve of 771 Libera in 1999.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg7.eps}
\end{figure} Figure 7:

Composite lightcurve of 771 Libera in 2005.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg8.eps}
\end{figure} Figure 8:

Composite lightcurve of 771 Libera in 2006.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg9.eps}
\end{figure} Figure 9:

Composite lightcurve of 771 Libera in 2008/2009.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f10.eps}
\end{figure} Figure 10:

Lightcurve of 984 Gretia in 1997.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f11.eps}
\end{figure} Figure 11:

Composite lightcurve of 984 Gretia in 1999.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f12.eps}
\end{figure} Figure 12:

Composite lightcurve of 984 Gretia in 2002.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f13.eps}
\end{figure} Figure 13:

Lightcurve of 984 Gretia in 2005.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f14.eps}
\end{figure} Figure 14:

Composite lightcurve of 984 Gretia in 2006.

Open with DEXTER

\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f15.eps}
\end{figure} Figure 15:

Composite lightcurve of 984 Gretia in 2007/2008.

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\begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f16.eps}
\end{figure} Figure 16:

Composite lightcurve of 984 Gretia in 2009.

Open with DEXTER

Table 1:   Aspect data.

Footnotes

... Gretia[*]
Composite lightcurves (Figs. 1-16), and aspect data (Table 1) are only available in electronic form at http://www.aanda.org
... [*]
Photometric data are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/508/1503
... Database[*]
http://www.minorplanetobserver.com/astlc/LightcurveParameters.htm
... databases[*]
A regularly updated database of all published asteroids' spin parameters obtained with various techiques is available at our website:
http://www.astro.amu.edu.pl/Science/Asteroids/ (Kryszczynska et al. 2007).
...[*]
Models from lightcurve inversion are collected at: http://astro.troja.mff.cuni.cz/projects/asteroids3D
... inclinations[*]
Data for this physical properties (except for 350 Ornamenta) come from The Small Bodies Node of the NASA Planetary Data System http://pdssbn.astro.umd.edu/), where the diameters and albedos are from the IRAS Minor Planet Survey (Tedesco et al. 2004), and the taxonomic classifications are given after Tholen (1989).
...[*]
The data on orbital parameters come from the Minor Planet Center database available at: ftp://cfa-ftp.harvard.edu/pub/MPCORB/MPCORB.DAT
Copyright ESO 2009

All Tables

Table 2:   Asteroid parameters.

Table 3:   Spin models.

Table 1:   Aspect data.

All Figures

  \begin{figure}
\par\includegraphics[width=18cm,clip]{12741f17.eps}
\end{figure} Figure 17:

Observed lightcurves (points) superimposed on the lightcurves created by a model (curves) at the same epochs for 350 Ornamenta.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=17cm]{12741f18.eps}
\end{figure} Figure 18:

Shape model of 350 Ornamenta, shown at equatorial viewing and illumination geometry, with rotational phases $90\hbox {$^\circ $ }$ apart (two pictures on the left), and the pole-on view on the right.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=18cm,clip]{12741f19.eps}
\end{figure} Figure 19:

Observed versus modelled lightcurves for 771 Libera.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=17cm]{12741f20.eps}
\end{figure} Figure 20:

Shape model of 771 Libera.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=18cm,clip]{12741f21.eps}
\end{figure} Figure 21:

Observed versus modelled lightcurves for 984 Gretia.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=17cm]{12741f22.eps}
\end{figure} Figure 22:

Shape model of 984 Gretia.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg1.eps}
\end{figure} Figure 1:

Composite lightcurve of 350 Ornamenta in 1999.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg2.eps}
\end{figure} Figure 2:

Composite lightcurve of 350 Ornamenta in 2004.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg3.eps}
\end{figure} Figure 3:

Composite lightcurve of 350 Ornamenta in 2005.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg4.eps}
\end{figure} Figure 4:

Lightcurve of 350 Ornamenta in 2007.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg5.eps}
\end{figure} Figure 5:

Composite lightcurve of 350 Ornamenta in 2008/2009.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg6.eps}
\end{figure} Figure 6:

Composite lightcurve of 771 Libera in 1999.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg7.eps}
\end{figure} Figure 7:

Composite lightcurve of 771 Libera in 2005.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg8.eps}
\end{figure} Figure 8:

Composite lightcurve of 771 Libera in 2006.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741fg9.eps}
\end{figure} Figure 9:

Composite lightcurve of 771 Libera in 2008/2009.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f10.eps}
\end{figure} Figure 10:

Lightcurve of 984 Gretia in 1997.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f11.eps}
\end{figure} Figure 11:

Composite lightcurve of 984 Gretia in 1999.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f12.eps}
\end{figure} Figure 12:

Composite lightcurve of 984 Gretia in 2002.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f13.eps}
\end{figure} Figure 13:

Lightcurve of 984 Gretia in 2005.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f14.eps}
\end{figure} Figure 14:

Composite lightcurve of 984 Gretia in 2006.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f15.eps}
\end{figure} Figure 15:

Composite lightcurve of 984 Gretia in 2007/2008.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12741f16.eps}
\end{figure} Figure 16:

Composite lightcurve of 984 Gretia in 2009.

Open with DEXTER
In the text


Copyright ESO 2009

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