Revised albedos of Trojan asteroids (911) Agamemnon and (4709) Ennomos



CCD-photometry was performed for two Jupiter Trojan asteroids (911) Agamemnon and (4709) Ennomos for which the diameters were obtained from occultation events. New data on rotation periods, lightcurve amplitudes, color indices, magnitude–phase slopes, and absolute magnitudes were obtained for these asteroids. We have used the diameters from occultations (166 and 99 km) and new data on absolute magnitudes at the instant occultation (7.95 and 8.85 mag) to revise their albedos to 0.042 (911 Agamemnon) and 0.052 (4709 Ennomos).


The surfaces of large Trojan asteroids (with D > 50 km) have typically very dark geometrical albedos (Tedesco et al. 2002; Fernandez et al. 2003; Grav et al. 2011; Usui et al. 2011). Of all the measured large Trojans, the asteroid (4709) Ennomos was found to have an exceptionally high albedo. Fernandez et al. (2003) obtained geometric albedos of 0.18 and 0.13 based on thermal data for this asteroid, assuming beaming parameters of 0.76 and 0.94, respectively. To explain these relatively high geometric albedo values, they speculate that an impact event may have uncovered a subsurface layer of pristine ice, thus raising the albedo. Others authors (Tedesco et al. 2002; Grav et al. 2011; Usui et al. 2011) also obtained high albedos for this asteroid (see Table 2) as compared with the average albedo for large Trojans.

It is well known that asteroid albedos derived from observations in the thermal infrared wavelengths are very sensitive to uncertainties in the assumed absolute magnitude. Usually, asteroid magnitudes in the visible and infrared wavelengths are obtained at times widely separated from the thermal measurements, and rotational and/or aspect variations of the brightness are not taken into account (Tedesco et al. 2002; Grav et al. 2011; Usui et al. 2011). In contrast with other authors, however, Fernandez et al. (2003) carried out simultaneous observations in the visual and infrared wavelengths. As the observations were conducted at nonzero phase angles, they used an HG phase function (Bowell et al. 1989), with a slope parameter G = 0.05 to obtain estimates for the absolute magnitudes of the observed asteroids. However, Shevchenko et al. (2012) have recently shown that using the HG function for the Trojan asteroids results in systematic errors in their absolute magnitude determination. Phase functions of all Trojans measured so far show a linear behavior down to subdegree phase angles, and this cannot be simulated by the form of the HG functions. Furthermore, uncertainties in absolute magnitude can substantially affect albedo determinations. To investigate this sensitivity, we have performed new CCD observations of two Trojans, namely (911) Agamemnon and (4709) Ennomos. We chose these objects because albedos from both thermal data and from occultation events are available. As shown by Shevchenko and Tedesco (2006), albedos from occultation diameters and absolute magnitudes taken at the time of occultation are more precise and more accurate and can be used for the calibration of albedos obtained using polarimetric and radiometric methods. The main goals of this work are thus to determine the absolute magnitudes of these asteroids at the time of the occultation events and to revise the estimates of their albedos.

Observations and Results

Photometric observations of the selected asteroids were carried out in the 2010–2012 time frame at the Chuguevskaya Station of the Astronomical Institute of Kharkiv National University (70 cm reflector) using the IMG 47-10 CCD-camera. The CCD observation and data reduction methods are explained in Krugly et al. (2002) and Shevchenko et al. (2012). The CCD-image data were reduced with the synthetic aperture photometry package (ASTPHOT) developed at the DLR by S. Mottola (Mottola et al. 1995). The observations were obtained mainly in the R band of the standard Johnson-Cousins photometric system. The absolute calibrations of the comparison stars were performed with standard star sequences from Landolt (1992) and Skiff (2007). The accuracy of absolute photometry is in the range of ±0.02–0.03 mag.

Aspect data of the observed asteroids are given in Table 1. The columns are the date of observation, distance from the asteroid to the Sun (in AU), distance from the asteroid to the Earth (in AU), phase angle, ecliptic coordinates at epoch 2000.0, and the magnitude V0(α) and R0(α) in the V and R spectral bands corrected for distances from the Earth and the Sun and reduced to the primary maximum of the asteroid lightcurve, and errors in V0(α) and R0(α).

Table 1. Aspect data and measured magnitudes of the observed asteroids.
UT Date dayλ2000 degβ2000 degr auΔ auα degV0 (1,α) magσR0 (1,α) magσ
(911) Agamemnon 
2012 03 10.82114.45914.3415.0854.4789.458.3300.0157.9700.011
2012 03 24.85114.34313.3335.0924.67310.658.3470.0157.9870.011
2012 04 29.83116.92310.9625.1085.23211.107.8860.015
2012 05 01.82117.16910.8465.1095.26311.028.2630.0177.9030.015
(4709) Ennomos 
2010 07 04.96314.05025.5405.1104.2867.289.0220.0158.6280.012
2010 07 08.90313.62325.8125.1104.2596.848.8450.0188.4650.014
2010 07 12.92313.14826.0685.1104.2376.41
2010 07 13.91313.02626.1285.1104.2316.31
2010 07 17.91312.51426.3525.1104.2145.928.7800.0158.4000.012
2010 08 02.89310.26726.9685.1094.1845.17
2011 07 07.94353.96627.9365.1034.68410.878.9180.0188.5180.015
2011 07 29.90353.52129.6385.1034.4389.248.8480.0188.4380.015
2011 08 27.82350.54731.1055.1044.2426.498.7380.0128.3480.010
2011 09 18.79347.33431.1585.1054.2266.008.6900.0188.3000.015
2011 10 07.80344.83230.3795.1064.3117.408.7770.0188.3770.015

Our observations are mainly presented as composite lightcurves, which have been constructed according to the procedures described by Harris and Lupishko (1989) and Magnusson and Lagerkvist (1990). The data are composited with the period shown in the figures. Data from each night, denoted by different symbols in the figures, were shifted along the magnitude axis to obtain the best fit. The values of these shifts are displayed in the figures.

The main physical parameters of the observed asteroids are listed in Table 2. They include composition type, diameters and albedos from the literature (with corresponding references), calculated absolute magnitudes, revised albedos, rotation periods, amplitudes, and BVR colors from our observations.

Table 2. Physical parameters of observed asteroids.
 (911) Agamemnon(4709) EnnomosReferences
TypeDTholen (1989)
H (mag)7.798.28Fernandez et al. (2003)
Albedo (0.76)0.051 ± 0.0040.180 ± 0.020Fernandez et al. (2003)
Diameter (km) (0.76)163.4 ± 3.670.4 ± 3.4Fernandez et al. (2003)
Albedo (0.94)0.036 ± 0.0030.129 ± 0.015Fernandez et al. (2003)
Diameter (km) (0.94)195.2 ± 4.483.4 ± 4.2Fernandez et al. (2003)
H (mag)7.898.90Tedesco et al. (2002)
IRAS albedo0.044 ± 0.0020.074 ± 0.009Tedesco et al. (2002)
IRAS diameter (km)166.7 ± 3.980.8 ± 4.3Tedesco et al. (2002)
H (mag)7.898.90Usui et al. (2011)
AKARI albedo0.037 ± 0.0010.078 ± 0.005Usui et al. (2011)
AKARI diameter (km)185.3 ± 3.480.0 ± 2.2Usui et al. (2011)
H (mag)7.898.60Grav et al. (2011)
WISE albedo0.060 ± 0.0120.091 ± 0.024Grav et al. (2011)
WISE diameter (km)143.8 ± 4.583.8 ± 7.4Grav et al. (2011)
Vocc(1,0) (mag)7.95 ± 0.088.85 ± 0.08This work
Occult. albedo0.042 ± 0.0050.052 ± 0.008This work
Occult. diameter (km)166 ± 299 ± 5IOTA
P (h)6.585 ± 0.00412.2696 ± 0.0005This work
Max. ampl., mag0.05 ± 0.020.45 ± 0.02This work
B-V, mag0.71 ± 0.03This work
V-R, mag0.36 ± 0.020.39 ± 0.02This work

(4709) Ennomos

This asteroid was previously observed photometrically in 1990 by Mottola et al. (2011), who determined its rotation period to be equal to 12.275 h, and later in 2003 by Reuillard et al. (2010), and in 2011 by French et al. (2012). French et al. (2012) reported a rotation period of 11.12 h.

Our CCD observations were carried out during the 2010 and 2011 apparitions. We have obtained lightcurves in two standard VR bands and color indices in BVR bands, and we have determined a new estimate of the rotation period to be 12.2696 ± 0.0005 h. This value is very close to the period obtained by Mottola et al. (2011), 12.275 h, but is different from the period obtained by French et al. (2012), 11.12 h. We note, however, that the French et al. observations are consistent with our period, assuming 39 rotation cycles between their two nights of observations, rather than 43 as they assumed. Figures 1a and 1b show the composite lightcurves of (4709) Ennomos for oppositions in 2010 and 2011, respectively. The shape of the lightcurves varies slightly between apparitions; however, the maximum amplitude is the same and is equal to 0.45 ± 0.02 mag. The lightcurves in all three observed oppositions (1990, 2010, and 2011) show similar shapes with only minor differences in maximum amplitude, suggesting that the pole direction is very close to perpendicular to the ecliptic plane.

Figure 1.

a) Composite lightcurve of (4709) Ennomos in 2010. The magnitude values correspond to the phase angle α = 5.9° (Jul 17). b) Composite and modeled lightcurves of (4709) Ennomos in 2011. The magnitude values correspond to the phase angle α = 6° (Sep 18). The arrow indicates the occultation time on Aug 11, 2011.

We have obtained the magnitude–phase relation (Fig. 2) in the range of phase angles from 6 to 11 deg. Unfortunately, smaller phase angles are rarely observable because the asteroid's orbit is highly inclined (= 25 deg) to the ecliptic plane. Linear phase coefficients in the V and R bands are found to be 0.043 ± 0.004 and 0.041 ± 0.003 mag deg−1, respectively. These measured values are consistent with values measured for other Trojans (Shevchenko et al. 2012). Previous work has shown that the value of the phase coefficient correlates with the asteroid surface albedo (e.g., Belskaya and Shevchenko 2000). The measured value of Ennomos' phase coefficient is typical for low-albedo surfaces. In Fig. 2, we present the HG-function fit to the data to illustrate the way such fits overestimate the absolute magnitude in comparison with the linear fit. We find a 95% confidence level for the linear fit.

Figure 2.

Magnitude–phase dependence for (4709) Ennomos in 2011. The magnitude scale corresponds to the lightcurve primary maximum.

The asteroid aspect we observed in 2011 is only 20 deg different in longitude and 5 deg different in latitude from the aspect observed by Fernandez et al. (2003). We used Fernandez's visual measurements and linear fit with our phase coefficient (and assumed zero nonlinear opposition behavior) to come up with a revised absolute magnitude. The difference between our absolute magnitude (V(1,0) = 8.58 mag) and that of Fernandez et al. (2003) is equal to 0.29 mag. As shown by Harris and Harris (1997), an inaccurate determination of absolute magnitude propagates to an inaccurate albedo value. Using the equation from Harris and Harris (1997), we obtained revised albedos of 0.14 and 0.10 for the beaming parameters 0.76 and 0.94, respectively. These albedos are lower than those obtained by Fernandez et al. (2003), but higher than the values presented in Tedesco et al. (2002), Grav et al. (2011), and Usui et al. (2011) (see Table 2).

On 11 August 2011, Ennomos occulted a star. This event was observed by several groups of observers from the Euraster team. The size profile projection was determined to be 108 × 91 km ( Our lightcurve observations allow us to very precisely identify the timing of the occultation (see the arrow in Fig. 2b). The instant of occultation falls near the minimum of the lightcurve. Using our magnitude and linear phase coefficient, we obtain an absolute magnitude at the instant of occultation equal to 8.85 ± 0.08 mag (at the 95% confidence level). With this value and the equivalent diameter (108 × 91 km) from the occultation event, we obtain an albedo of 0.052 ± 0.008 for Ennomos.

(911) Agamemnon

The first photometric observations of this asteroid were performed by Dunlap and Gehrels (1969), who estimated a rotation period in the range of 6–10 h. Binzel and Sauter (1992) obtained only six points on the lightcurve during 3.5 h of observations in the B band, so they were not able to determine the period. A rotation period of 6.592 ± 0.004 h was found by Stephens (2009). Mottola et al. (2011) and French et al. (2012) confirmed this value. According to our observations, the rotation period is equal to 6.585 ± 0.004 h. The composite lightcurve with this period is presented in Fig. 3. The measured rotation period is largely consistent with the previously obtained values.

Figure 3.

Composite lightcurve of (911) Agamemnon. The magnitude values correspond to the phase angle α = 9.45º (March 10).

On 19 January 2012, a stellar occultation event by this asteroid was successfully observed by the International Occultation Timing Association ( observations/Results/). A size profile projection of 190.6 × 143.8 km has been determined. The rotational phase at which the occultation occurred is marked on our composite lightcurve (see Fig. 3). Note, however, that the uncertainty in the rotation phase at the time of occultation is quite large due to insufficient knowledge of Agamemnon's rotation period. As the lightcurve amplitude is small (0.05 ± 0.02 mag), it is safe to use an average magnitude for the albedo estimate. The largest amplitude observed by previous observers was 0.29 magnitude in November of 1997 (Mottola et al. 2011). As this is more than five times greater amplitude than we observed in 2012, we can infer that the current observations were made at a nearly pole-on aspect; hence, the pole must lie within 20 deg or so of 115 (295) longitude and 15 (−15) latitude. The Mottola et al. observations were taken at an aspect about 80 deg of longitude away, fully consistent with a near-equatorial aspect at that time. It can further be noted that the elongation of the occultation profile, a/b = 1.31, is exactly what we would expect for a near-polar profile of an object with an equatorial-aspect lightcurve amplitude of approximately 0.3 magnitude. To determine the absolute magnitude at the time of the instant of occultation, we used the mean linear phase coefficient for Trojans (0.043 mag/deg) and assumed zero nonlinear opposition behavior (Shevchenko et al. 2012). We obtained a value for the absolute magnitude equal to 7.95 ± 0.08 mag. Using this value and the equivalent diameter of 166 km from the occultation, we obtain an albedo of 0.042 ± 0.005.

We have also recalculated the absolute magnitude of (911) Agamemnon using the observations by Fernandez et al. (2003) and a linear phase function and find V(1,0) = 8.10 mag. Using an equation from Harris and Harris (1997) that relates the newly revised and previous albedos, we obtain albedo values of 0.039 and 0.028 for Agamemnon, corresponding to the two beaming parameters 0.76 and 0.94, respectively. These albedos are lower than those obtained from occultation by Fernandez et al. (2003) and Grav et al. (2011), and close to the values found by Tedesco et al. (2002) and Usui et al. (2011).


The albedo of (4709) Ennomos derived from the occultation substantially differs from the albedo from the thermal data obtained by Fernandez et al. (2003). If the V magnitude in Fernandez et al. (2003) is correct, then they performed observations of Ennomos near the lightcurve primary maximum. One of the possible explanations for the differences between occultation and thermal albedo is the assumption of the bright albedo spot seen in the lightcurve maximum. We have modeled the shape of the Ennomos lightcurve using a triaxial ellipsoid with a bright spot on the surface. The dashed line in Fig. 1b is the best model fit to the observed lightcurve. The best fit has been obtained with an ellipsoid with axial ratios 1.3:1.1:1 for which the bright spot with the albedo of 0.25 occupies about 10% of the surface area. Yang and Jewitt (2007) performed spectral observations of this object in the near-infrared range for three nights and did not find any spectral changes. The precision of the rotation period is insufficient for a determination of the subobserver longitude during the spectral measurements. To search for a possible albedo dichotomy on Ennomos, one would need to carry out measurements at the lightcurve maxima and minima. On the other hand, the asymmetry of the Ennomos lightcurve can also be accounted for by its shape alone (see Kaasalainen and Torppa 2001). All other data obtained from thermal observations indicate a low albedo surface (Tedesco et al. 2002; Grav et al. 2011; Usui et al. 2011). At present, we do not have enough data to definitely resolve the question of whether or not there is an albedo dichotomy on Ennomos's surface.

The recalculated albedo of (911) Agamemnon from the thermal data obtained by Fernandez et al. (2003) is different from the occultation albedo found in this work. These differences can be reconciled if we assume that the beaming parameter is less than 0.76 for Agamemnon.


We carried out photometrical observations and obtained new estimates for the absolute magnitudes for two Jupiter Trojans: (911) Agamemnon and (4709) Ennomos. Using occultation diameters, we determined revised albedo values for these asteroids. The values we obtain are very low and typical of other Trojans. Our simple model of the shape of Ennomos does not preclude the possible presence of a bright albedo spot on its surface. New observational data (especially spectral) are needed to answer definitely whether a bright spot really exists. We suggest that the albedos we calculate from the occultations can be used to calibrate the accuracy of physical properties derived from thermal infrared observations of Trojans.


The June 2006 observations on a 0.7 m telescope were carried out with a CCD camera obtained thanks to INTAS grant Ref. No 03-70-567. This research was partly supported by the Ukrainian Ministry of Education and Science. We thank the reviewers, Alan W. Harris and Stefano Mottola, for their constructive reviews that helped to improve the paper, and we thank Beth Ellen Clark for editing assistance.

Editorial Handling

Dr. Michael Zolensky