Opposition effect of Trojan asteroids
Highlights
► We have obtained detailed magnitude–phase relations for three Jupiter Trojans. ► The magnitude–phase relations are linear down to phase angle of 0.1–0.2°. ► We have not revealed any noticeable opposition brightening for the V and R bands. ► Such behavior is inherent for dark surfaces where single scattering plays main role.
Introduction
The majority of atmosphereless celestial bodies show the brightness opposition effect (OE). For asteroids, the opposition effect was first discovered for (20) Massalia as pronounced nonlinear increase in brightness close to opposition (Gehrels, 1956). At present magnitude–phase relations with good phase angle coverage and good accuracy were measured for less than 100 asteroids. All good-quality phase curves show a linear behavior in the phase angle range 5–25° with a slope correlating with asteroid albedo (e.g., Belskaya and Shevchenko, 2000). The phase slope increases when surface albedo decreases assuming that shadowing (both mutual shadowing among particles and shadowing due to surface roughness) is the main mechanism responsible for the phase angle behavior in this phase range (e.g., Muinonen et al., 2002). At smaller phase angles (<5°) a nonlinear increase of 0.1–0.4 mag is typically observed. An opposition surge is usually explained by the coherent backscattering enhancement which is more effective for high albedo surfaces (e.g., Muinonen et al., 2002).
The OE amplitudes defined as an increase in magnitude at close to zero phase angle relative to the extrapolation of the linear part were found to be smallest for low albedo asteroids (Belskaya and Shevchenko, 2000). Moreover, a few low-albedo asteroids had not revealed a nonlinear increase in brightness (Harris and Young, 1989, Harris et al., 1992, Piironen et al., 1994, Shevchenko et al., 1996, Shevchenko et al., 2008). French (1987) pointed out a possible absence of the opposition surge for the Trojan Asteroid (1173) Anchises. These asteroids belong mainly to the P-type spectral class, which are believed to contain the most primitive objects in the asteroid belt.
Initial purpose of our new observations was to check whether opposition effect is inherent for a D-type asteroid. For observations we chose the Trojan Asteroid (588) Achilles and initiated a wide observational program joined efforts of several observatories to obtain detailed magnitude–phase dependence with maximal possible phase angle coverage. Preliminary results of these observations showing an absence of opposition surge down to phase angle of 0.1° were presented at 40th Lunar and Planetary Science Conference (Shevchenko et al., 2009). Independently, phase curve observations of nine Trojans, including (588) Achilles, were carried out by Schaefer et al. (2010). They obtained phase dependences not corrected for asteroid rotation with a diversity of phase slopes, including negative values. Based on these data Schaefer et al. (2010) have concluded that surface properties of Trojans are significantly different from main-belt asteroids, and thus strongly support the idea that Trojans were captured from the outer Solar System (see Schaefer et al., 2010).
In this paper we present photometric observations of three Trojans, namely (588) Achilles, (884) Priamus, and (1143) Odysseus, which allows us to obtain high quality phase curves of these objects and show their similarity to low albedo asteroids.
Section snippets
Observations
Our CCD-observations of Jupiter Trojan asteroids were carried out in 2007, 2008 and 2010. To decrease an influence of weather conditions and to obtain comprehensive data on the asteroid magnitude–phase dependence we performed coordinated observations from four observatories, namely Kharkiv Observatory (KhO) with the 70-cm reflector, Simeiz Observatory (SO) with the 1-m reflector, Rozhen Observatory (RO) with the 2-m reflector, and Maidanak Observatory (MO) with the 1.5-m reflector. The method
Discussion
Photometric observations of three Trojans in the V and R bands reveal that the observed asteroids do not show a nonlinear opposition brightening down to angles of ∼0.1°. Table 2 contains a summary of their properties based on new data and also published data on diameter, albedo, taxonomy, and rotational lightcurve amplitude.
All three asteroids are of the same taxonomic type and have rather similar albedos and diameters. The range of their rotational lightcurve amplitudes are also comparable,
Conclusions
As a result of our long-term observations we have determined the rotation periods and have obtained the detailed magnitude–phase relations in two (or three) spectral bands for three Jupiter Trojans, namely (588) Achilles, (884) Priamus, and (1143) Odysseus. The magnitude phase dependences of these asteroids are found to be linear down to phase angles of 0.1–0.2°. We have not revealed any noticeable opposition brightening in either the V or in the R spectral bands.
The observed Trojans have
Acknowledgments
Observations at 0.7-m telescope were carried out with the CCD camera obtained thanks to INTAS Grant (Ref. No 03-70-567). We are grateful to G. Borisov, A.L. Marshalkina, and I.A. Tereschenko for their help in observations. The research was partially supported by the Bulgarian National Science Fund under Contract DO 02-85 and a bilateral agreement between Bulgarian Academy of Sciences and Kharkiv Karazin National University. INB has been supported by a Marie Curie Fellowship of the European
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