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Asteroid Observations at Low Phase Angles
Icarus 155, 365–374 (2002) doi:10.1006/icar.2001.6651, available online at http://www.idealibrary.com on
Asteroid Observations at Low Phase Angles II. 5 Astraea, 75 Eurydike, 77 Frigga, 105 Artemis, 119 Althaea, 124 Alkeste, and 201 Penelope V. G. Shevchenko, I. N. Belskaya, Yu. N. Krugly, and V. G. Chiomy Astronomical Observatory of Kharkiv National University, Kharkiv, Ukraine E-mail: [email protected]
and N. M. Gaftonyuk Crimean Astrophysical Observatory, Simeiz, Crimea, Ukraine Received November 20, 2000; revised April 9, 2001
The results of photometric observations of seven main-belt asteroids with moderate surface albedos are presented. New magnitudephase dependences were obtained for these asteroids: 5 Astraea (down to a phase angle of 0.3◦ , S type), 75 Eurydike (0.1◦ , M), 77 Frigga (0.9◦ , M), 105 Artemis (0.3◦ , C), 119 Althaea (0.3◦ , S), 124 Alkeste (0.1◦ , S), and 201 Penelope (0.5◦ , M). The parameters of approximating functions and the amplitudes of the opposition effect of these asteroids were determined. The obtained data allowed us to improve values of the rotation periods for some of them: 5 Astraea (16.815 ± 0.002 h), 105 Artemis (18.56 ± 0.01 h), 119 Althaea (11.466 ± 0.001 h), and 124 Alkeste (9.907 ± 0.001 h). c 2002 Elsevier Science (USA)
Key Words: asteroids; photometry; opposition effect; rotation period; low phase angle.
in the range of the opposition effect (OE) is different for low-, moderate-, and high-albedo asteroids. The maximum amplitude of the OE occurs for the moderate-albedo S- and M-type asteroids. It is caused both by shadowing and coherent backscattering mechanisms of lightscattering processes in a regolith layer of these bodies. The region of extremely low phase angles is very important to understand the mechanisms of lightscattering. New data are needed both to improve statistics and to estimate the contribution of the different lightscattering mechanisms to the phase curves of atmosphereless bodies. The results of photometric observations at low phase angles of asteroids 5 Astraea, 75 Eurydike, 77 Frigga, 105 Artemis, 119 Althaea, 124 Alkeste, and 201 Penelope are presented in this paper. OBSERVATIONS AND RESULTS
INTRODUCTION
This work is a continuation of the observational program devoted to the investigation of the brightness behavior for asteroids of different composition types at extremely low phase angles (<1◦ ). The program has been carried out over several years at the Kharkiv Astronomical Observatory (Ukraine) in cooperation with other observatories (Shevchenko et al. 1993, 1996, 1997). The investigation of the brightness behavior at low phase angles is very important for our understanding of lightscattering properties of asteroid surfaces and for the testing of theoretical models of a regolith layer of the atmosphereless celestial bodies. According to Belskaya and Shevchenko (1999, 2000) there are only 33 asteroids that have good phase angle coverage with small errors of observation data and for which the brightness at the low phase angles was measured. The brightness behavior
The observations of the selected asteroids were carried out at the Astronomical Observatory of the Kharkiv National University (70-cm reflector) and at the Simeiz Station of the Crimean Astrophysical Observatory (60-cm and 1-m reflectors), using one-channel photoelectric photometers in 1993 and CCD cameras ST-6 in 1996–1999. The photoelectric data reduction methods were described by Shevchenko et al. (1992, 1993). CCD images were reduced using the synthetic aperture photometry package (ASTPHOT) developed at DLR by S. Mottola (Mottola et al. 1995). Almost all observations were performed in the Vband of the standard Johnson UBV system. Only 105 Artemis was observed in the Cousins R-band in the 1999 opposition. The absolute calibrations of the data were performed with standard sequences from Landolt (1992) and Lasker et al. (1988). The accuracy of absolute photometry is equal to 0.01–0.02 mag. The mean time of observations, ecliptic coordinates at the epoch
365 0019-1035/02 $35.00 c 2002 Elsevier Science (USA) All rights reserved.
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TABLE I Aspect Data and Measured Magnitudes of the Observed Asteroids UT date 1
λ2000 (◦ ) 2
β2000 (◦ ) 3
r 4
5
α (◦ ) 6
V0 (1, α) (mag) 7
1997 Aug 20.88 1997 Aug 21.91 1997 Aug 22.90 1997 Aug 29.82 1997 Sep 21.78 1997 Oct 03.65 1997 Oct 09.80
329.009 328.773 328.546 326.979 322.730 321.535 321.245
−0.970 −0.994 −1.017 −1.170 −1.595 −1.756 −1.825
5 Astraea 3.059 3.059 3.058 3.056 3.045 3.038 3.034
2.048 2.047 2.047 2.056 2.176 2.286 2.353
0.49 0.33 0.55 3.17 11.21 14.39 15.71
6.790 6.750 6.805 7.065 7.290 7.395 7.450
1996 Mar 19.82 1996 Mar 20.75 1996 Mar 21.90 1996 Mar 22.98 1996 Mar 27.88
179.711 179.921 179.819 179.575 178.477
−0.062 −0.077 −0.096 −0.114 −0.195
75 Eurydike 3.387 3.386 3.384 3.383 3.376
2.391 2.389 2.388 2.387 2.387
0.22 0.12 0.53 0.92 2.67
8.990 8.975 9.040 9.115 9.225
1997 Sep 06.04 1997 Sep 07.89 1997 Sep 13.85 1997 Sep 14.91 1997 Sep 19.94 1997 Sep 21.89 1997 Sep 29.90 1997 Oct 25.81 1997 Nov 05.77 1997 Nov 06.72
347.718 347.298 345.937 345.697 344.582 344.166 342.604 340.140 340.530 340.610
−1.065 −1.035 −0.934 −0.916 −0.825 −0.789 −0.637 −0.170 0.010 0.020
77 Frigga 2.545 2.543 2.535 2.533 2.527 2.524 2.514 2.481 2.467 2.466
1.539 1.536 1.531 1.532 1.537 1.541 1.566 1.745 1.852 1.862
1.71 0.89 2.08 2.58 4.93 5.83 9.40 18.49 20.96 21.13
8.835 8.735 8.860 8.895 9.035 9.085 9.235 9.485 9.575 9.615
1996 Sep 29.88 1996 Sep 30.88 1996 Oct 01.78 1996 Oct 03.83 1996 Oct 08.75 1996 Oct 09.80 1996 Nov 12.75 1996 Nov 14.70 1999 Apr 22.97 1999 Apr 23.94 1999 May 20.89 1999 May 21.92
9.166 8.882 8.627 8.049 6.689 6.407 0.585 0.496 264.376 264.467 263.427 263.252
0.119 −0.019 −0.144 −0.426 −1.093 −1.232 −4.908 −5.063 27.961 28.273 36.220 36.464
105 Artemis 2.549 2.551 2.552 2.556 2.564 2.566 2.618 2.621 1.955 1.955 1.957 1.957
1.548 1.550 1.552 1.556 1.573 1.577 1.872 1.897 1.216 1.210 1.088 1.085
0.84 0.34 0.12 1.14 3.55 4.06 16.90 17.38 25.56 25.39 20.46 20.31
8.730 8.575 8.590 8.740 8.915 8.920 9.450 9.470 — — — —
1998 Oct 13.79 1998 Oct 14.83 1998 Oct 20.97 1998 Oct 21.93 1998 Oct 22.85 1998 Oct 24.83 1998 Oct 25.81 1998 Oct 31.00 1998 Nov 07.73 1998 Dec 08.67 1998 Dec 09.69
30.022 29.783 28.333 28.103 27.884 27.414 27.183 25.993 24.393 21.783 21.818
−0.368 −0.418 −0.716 −0.762 −0.806 −0.900 −0.947 −1.185 −1.518 −2.487 −2.509
119 Althaea 2.375 2.375 2.376 2.377 2.377 2.377 2.377 2.379 2.381 2.392 2.392
1.386 1.384 1.381 1.381 1.382 1.384 1.385 1.397 1.428 1.683 1.694
4.09 3.56 0.50 0.33 0.66 1.64 2.13 4.75 8.49 19.62 19.87
8.610 8.565 8.265 8.230 8.290 8.405 8.470 8.590 8.735 9.010 9.015
1996 Sep 12.92 1996 Sep 29.83 1996 Sep 30.88 1996 Oct 01.85 1996 Oct 03.80 1996 Oct 08.73 1996 Oct 09.80 1996 Nov 12.74
11.931 8.213 7.969 7.744 7.293 6.175 5.939 1.244
0.345 0.052 0.034 0.017 −0.018 −0.104 −0.122 −0.617
124 Alkeste 2.699 2.712 2.713 2.714 2.715 2.719 2.719 2.743
1.738 1.711 1.712 1.713 1.716 1.729 1.732 1.995
7.84 0.45 0.02 0.45 1.33 3.51 3.97 15.90
8.563 8.120 8.030 8.110 8.215 8.375 8.430 8.813
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TABLE I—Continued λ2000 (◦ ) 2
UT date 1
β2000 (◦ ) 3
r 4
5
α (◦ ) 6
V0 (1, α) (mag) 7
1.225 1.221 1.192 1.186 1.182 1.182 1.182 1.182 1.183 1.239 1.275 1.389 1.464
9.91 9.45 4.85 3.28 1.14 0.47 0.75 1.16 1.73 11.33 14.09 19.56 21.78
8.829 8.761 8.596 8.508 8.310 8.237 8.270 8.316 8.370 8.833 8.909 9.094 9.140
201 Penelope 1993 Aug 06.00 1993 Aug 06.95 1993 Aug 15.95 1993 Aug 18.90 1993 Aug 22.98 1993 Aug 24.88 1993 Aug 25.96 1993 Aug 26.84 1993 Aug 27.95 1993 Sep 15.72 1993 Sep 21.87 1993 Oct 06.73 1993 Oct 14.70
335.455 335.302 333.638 333.028 332.157 331.747 331.513 331.324 331.085 327.610 326.880 326.289 326.682
2.093 2.045 1.553 1.380 1.136 1.020 0.953 0.899 0.831 −0.307 −0.649 −1.369 −1.690
2.199 2.198 2.195 2.194 2.193 2.193 2.192 2.192 2.192 2.191 2.191 2.194 2.196
2000.0, distances to the Sun and the Earth in astronomical units, phase angle, and magnitude reduced to the lightcurve maximum of the observed asteroids are listed in Table I. Some main physical characteristics (taxonomic type, albedo, diameter, and the adopted values of H and G parameters) of the observed asteroids are presented in Table II. Table III contains the results of observations: determined rotation periods, lightcurve amplitudes, and calculated parameters of the magnitude-phase dependences. V0 is the V magnitude at zero phase, a is the parameter describing the amplitude of opposition brightening, and b is the coefficient for the linear part of the phase curve. All parameters were calculated using an empirical three-parametric function for an approximation of the magnitude-phase dependences (Shevchenko 1996, 1997). The determined values of the H and G parameters calculated according to Bowell et al. (1989) are also given in Table III.
magnitude-phase dependence has been obtained for this asteroid. Taylor (1978) used a linear phase coefficient βv = 0.014 mag/◦ computed using data collected during several oppositions. This value is very small and atypical for S-type asteroids (see Shevchenko and Lupishko 1998). Different values for the parameter G were obtained by Lagerkvist and Williams (1987) (G = 0.18), Lagerkvist et al. (1989) (G = 0.34), Lagerkvist et al. (1992) (G = 0.26) and Piironen et al. (1997) (G = 0.34). In all these cases it was calculated using the data obtained with the Carlsberg Meridian Circle. Our observations were carried out during August–October 1997 for seven nights in the range of phase angles 0.33–15.7◦ . The composite lightcurve with period 16.815 ± 0.002 h, determined by our data, is shown in Fig. 1. The lightcurve has amplitude 0.16 mag for this opposition. The phase dependence of brightness is shown in Fig. 2. The dashed and solid lines 5 Astraea. The rotation period of this asteroid (P = 16.806 h) are approximations using H and G (Bowell et al. 1989) and was determined by Chang and Chang (1962) for the first time Shevchenko’s (1996, 1997) functions, respectively. Parameters in the 1962 opposition. Later many photometric observations of these functions are listed in Table III. The value we obtained were performed by different authors (see Taylor 1978, of the parameter G is similar to those determined by Lagerkvist Weidenschilling et al. 1990, Harris et al. 1999, etc.), but no et al. (1989) and by Piironen et al. (1997). The value of parameter a is the same as the mean for S-type asteroids, whereas the parameter b differs from the mean value for this kind of asterTABLE II oids (Shevchenko 1997). The amplitude of the OE determined Physical Characteristics of the Observed Asteroids according to Belskaya and Shevchenko (1999, 2000) is equal to a b b c c 0.35, which is typical for S-type asteroids. Asteroid Type Albedo Diameter H G 5 Astraea 75 Eurydike 77 Frigga 105 Artemis 119 Althaea 124 Alkeste 201 Penelope a
S M M C S S M
Tholen (1989). Tedesco and Veeder (1992). c Tedesco (1989). b
0.23 0.15 0.14 0.047 0.23 0.17 0.16
119.1 55.7 69.3 119.1 57.3 76.4 68.4
7.24 9.02 8.57 8.89 8.61 8.13 8.48
0.67 0.25 0.26 0.29 0.57 0.31 0.14
75 Eurydike. Two groups of observers obtained lightcurves of this asteroid in 1980. First observations were performed by Zappal`a et al. (1983) in October 1980 for two nights. They determined a rotation period of 8.92 h, but they stated that the period could be wrong. Harris and Young (1989) also carried out observations of 75 Eurydike during this opposition for six nights in November. They obtained a period of 5.357 ± 0.003 h and a magnitude-phase curve with H and G parameters of 8.98 ± 0.01 and 0.23 ± 0.02, respectively. Our observations were performed
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TABLE III Rotation Periods, Amplitudes, and Parameters of Photometric Approximating Functions of the Observed Asteroids Asteroid
Period (h)
Ampl. (mag)
V0 (mag)
a
b
H (mag)
G
5 Astraea 75 Eurydike 77 Frigga 105 Artemis 119 Althaea 124 Alkeste 201 Penelope
16.815 ± 0.002 5.360 ± 0.003 8.999 ± 0.001 18.560 ± 0.010 11.466 ± 0.001 9.907 ± 0.001 3.7474 ± 0.0001
0.16 0.15 0.20 0.05 0.30 0.12 0.34
7.09 ± 0.03 9.25 ± 0.01 8.92 ± 0.02 8.85 ± 0.03 8.58 ± 0.02 8.35 ± 0.02 8.53 ± 0.02
0.46 ± 0.05 0.32 ± 0.02 0.36 ± 0.04 0.32 ± 0.05 0.50 ± 0.03 0.35 ± 0.04 0.47 ± 0.05
0.024 ± 0.002 0.033 ± 0.001 0.033 ± 0.001 0.036 ± 0.002 0.023 ± 0.001 0.031 ± 0.002 0.029 ± 0.001
6.74 ± 0.02 8.97 ± 0.01 8.64 ± 0.01 8.58 ± 0.02 8.24 ± 0.02 8.06 ± 0.01 8.20 ± 0.01
0.31 ± 0.03 0.23 ± 0.01 0.22 ± 0.01 0.18 ± 0.03 0.32 ± 0.03 0.25 ± 0.02 0.26 ± 0.01
in March 1996 and only the region of the OE was comprised (see Table I). The composite lightcurve with rotation period 5.360 ± 0.003 h determined by our data is shown in Fig. 3. This period is very similar to that determined by Harris and Young (1989). Maximum amplitude of the lightcurve is 0.15 mag. The phase curve is presented in Fig. 4. The data of Harris and Young (1989) were shifted 0.04 mag to our data to calculate parameters of approximating functions for opposition in 1996 (see Table III). The amplitude of the OE is equal to 0.25. 77 Frigga. Harris and Young (1989) were the first who determined the rotation period (8.9985 ± 0.002 h) of this asteroid. They observed 77 Frigga for eight nights in November 1980 and obtained a magnitude–phase curve in the phase angle range of 2.5◦ –16.3◦ with parameters H = 8.52 ± 0.06 and G = 0.16 ± 0.01, and a linear phase coefficient β = 0.034 mag/◦ .
FIG. 1. Composite lightcurve of 5 Astraea. Zero phase at UT 1997 Aug 22.7886 corrected for light time. Comp. period: 16,815 h. The UT date and V magnitude shift are defined as follows: , 1997 Aug 20.88, 0.040; , 1997 Aug 21.91, 0.000; , 1997 Aug 22.40, 0.055; , 1997 Aug 29.82, 0.315; , 1997 Sep 21.78, 0.540; +, 1997 Oct 3.65, 0.645; ×, 1997 Oct 09.80, 0.700.
Subsequently, Lagerkvist and Rickman (1982) performed observations of Frigga for eight nights in March 1982 in a range of the low phase angles spanning from 0.15◦ to 2.72◦ . They determined the parameters V (0) = 8.58 and Q = 0.03 (see Bowell and Lumme 1979) of the magnitude–phase relation. Values of the parameter G were also obtained by Tedesco (1989) (see Table II) and by Piironen et al. (1997) (0.13). Several single lightcurves were obtained by other observers (see, e.g., Zappal`a et al. 1983, Hainaut-Rouelle et al. 1995, and Lagerkvist et al. 1995). We observed 77 Frigga for 10 nights in September–November 1997 (see Table I). The composite lightcurve with a rotation period 8.999 h determined by our data is shown in Fig. 5. Our period is the same as determined by Harris and Young (1989). The phase dependence of brightness is shown in Fig. 6. The data of Lagerkvist and Rickman (1982) were added to our data. Their data were reduced using a formalism by Bowell and Lumme (1979) and were shifted 0.04 mag to our data. The values of
FIG. 2. Magnitude–phase dependence of 5 Astraea. - - -, HG function; —, Shevchenko (1997).
ASTEROIDS AT LOW PHASE ANGLES
FIG. 3. Composite lightcurve of 75 Eurydike. Zero phase at UT 1996 Mar 19.7493 corrected for light time. Comp. period: 5.360 h. UT date and V magnitude shift are defined as follows: , 1996 Mar 19.82, −0.050; , 1996 Mar 20.75, −0.065; , 1996 Mar 21.90, 0.0; , 1996 Mar 22.98, 0.075; , 1996 Mar 27.88, 0.185.
parameters of approximating functions are presented in Table III. The amplitude of the OE is equal to 0.24.
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FIG. 5. Composite lightcurve of 77 Frigga. Zero phase at UT 1996 Sep 14.7913 corrected for light time. Comp. period: 8.999 UT date and V magnitude shift are defined as follows: 0, 1997 Sep 06.04, −0.060; , 1997 Sep 07.89, −0.160; , 1997 Sep 13.85, −0.035; , 1997 Sep 14.91, 0.000; , 1997 Sep 19.94, 0.140; +, 1997 Sep 21.89, 0.190; ×, 1997 Sep 29.90, 0.340; , 1997 Oct 25.81, 0.590; , 1997 Nov 12.75, 0.680; , 1997 Nov 14.70, 0.720.
105 Artemis. Photometric observations of this asteroid were performed during two oppositions: 1977 (Tedesco 1979) and 1980 (Debehogne et al. 1982, Schober and Schroll 1986, Schober et al. 1994). The rotation period (P = 16.84 h) was
determined for the first time by Schober et al. (1994). We observed 105 Artemis for two apparitions: for eight nights in September–November 1996 and for four nights in April–May 1999 (see Table I). The rotation period determined by Schober et al. (1994) does not fit our data. We found a new rotation period P = 18.56 ± 0.01 h. This period fits also other data but
FIG. 4. Magnitude–phase dependence of 75 Eurydike. - - -, HG function; —, Shevchenko (1997); , Harris and Young (1989); , this work.
FIG. 6. Magnitude–phase dependence of 77 Frigga. - - -, HG function; —, Shevchenko (1997); , Lagerkvist and Rickman (1982); , this work.
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FIG. 7. Composite lightcurves of 105 Artemis in 1996. Zero phase at UT 1996 Oct 1.6799 corrected for light time. Comp. period: 18.56 h. UT date and V magnitude shift are defined as follows: , 1996 Sep 29.88, 0.140; , 1996 Sep 30.88, −0.015; , 1996 Oct 01, 0.000; , 1996 Oct 03.83, 0.150; , 1996 Oct 08.75, 0.325; , 1996 Oct 09.80, 0.330; +, 1996 Nov 12.75, 0.860; ×, 1996 Nov 14.70, 0.860.
new observations are needed to define more accurately the period. The composite lightcurves obtained using this period are shown in Figs. 7 and 8. The lightcurves show only one pair of extrema with amplitudes equal to 0.05 mag in 1996 and 0.10 mag in 1999. The phase curve is shown in Fig. 9. Our values
FIG. 8. Composite lightcurves of 105 Artemis in 1999. Zero phase at UT 1999 Apr 22.9072 corrected for light time. Comp. period: 18.56 h. UT date and R magnitude shift are as follows: , 1999 Apr 22.18, 0.000; , 1999 Apr 20.88, −0.005; , 1999 May 20.88, rel −12.295; , 1999 May 20.88, rel −12.295.
FIG. 9. Magnitude–phase dependence of 105 Artemis. - - -, HG function; —, Shevchenko (1997).
of H and G parameters (see Table III) are different from those obtained by Tedesco (1989). The values of the parameters of the approximating functions (Table III) and the amplitude of the OE (0.24) are different from mean values for C-type asteroids. 119 Althaea. The first observations of this asteroid were performed in 1984 by Weidenschilling et al. (1990) for 4.5 h, which supposed that the rotation period is longer than 12 h. Later Gil Hutton (1990) observed 119 Althaea for three nights in July 1989. He determined a period P = 11.484 ± 0.010 h. Our observations were carried out during October–December 1998 for 11 nights (see Table I). Figure 10 shows the composite lightcurve obtained with the rotation period P = 11.466 ± 0.001 h. This period was determined using lightcurves in a wider time interval and it is more accurate. The amplitude of the lightcurve for this opposition is 0.30 mag. The phase curve of 119 Althaea in the phase angle range 0.3◦ –19.9◦ is presented in Fig. 11. The values of the parameters of the approximating functions are listed in Table III. Previously, the parameters H and G were determined by Tedesco (1989) (see Table II) and by Piironen et al. (1997) (H = 8.36, G = 0.17). Our values of the parameters differ from previous ones, but on the basis of the length of our observations we consider our data more reliable. The value of parameter a is the same as that for S-type asteroids but the values of the parameters b and G differ from mean values of S-type (Shevchenko and Lupishko 1998). The amplitude of the OE (0.36) is typical for S-type asteroids. 124 Alkeste. There are photometric observations of this asteroid only for two apparitions. First observations were carried out by Harris and Young (1983) for four nights in October– November 1979. They determined the rotation period (P = 9.921 h), and lightcurve amplitude (A = 0.15 mag). They also
ASTEROIDS AT LOW PHASE ANGLES
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FIG. 10. Composite lightcurve of 119 Althaea. Zero phase at UT 1998 Oct 21.8109 corrected for light time. Comp. period: 11.466 h. UT date and V magnitude shift are as follows: , 1998 Oct 13.79, 0.380; , 1998 Oct 14.83, 0.335; , 1998 Oct 20.0, 0.035; , 1998 Oct 21.93, 0.0; , 1998 Oct 22.85, 0.060; +, 1998 Oct 24.83, 0.175; ×, 1998 Oct 25.81, 0.240; , 1998 Oct 31.00 0.360; , 1998 Nov 07.73, 0.505; , 1998 Dec 08.67, 0.780; , 1998 Dec 09.69, 0.785.
FIG. 12. Composite lightcurve of 124 Alkeste. Zero phase at UT 1996 Sep 30.7729 corrected for light time. Comp. period: 9.907 h. UT date and V magnitude shift are as follows: , 1996 Sep 12.92, 0.533; , 1996 Sep 29.83, 0.090; , 1996 Sep 30.88, 0.0; , 1996 Oct 01.85, 0.080; , 1996 Oct 03.80, 0.185; +, 1996 Oct 08.73, 0.345; ×, 1996 Oct 09.80, 0.400; , 1996 Nov 12.94, 0.783.
calculated H and G parameters (H = 8.11, G = 0.20). Using the data by Harris and Young (1983), Lagerkvist and Magnusson (1990) computed H and G parameters equal to 8.12 and 0.18, respectively. Hainaut-Rouelle et al. (1995) performed observations of 124 Alkeste for two nights in July 1991. They obtained lightcurves with amplitude 0.10 mag. Our observations were carried out during September– November 1996 for eight nights (see Table I). The phase an-
gle range spans from 0.02◦ to 16◦ . The composite lightcurve with the rotation period P = 9.907 ± 0.001 h and amplitude 0.12 mag is shown in Fig. 12. Our value of the rotation period differs a little from that obtained by Harris and Young (1983). The magnitude–phase dependence of 124 Alkeste is shown in Fig. 13. The parameters of the approximating functions are listed in Table III. The parameter G is different from that obtained by
FIG. 11. Magnitude–phase dependence of 119 Althaea. - - -, HG function; —, Shevchenko (1997).
FIG. 13. Magnitude–phase dependence of 124 Alkeste. - - -, HG function; —, Shevchenko (1997).
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FIG. 14. Composite lightcurve of 201 Penelope. Zero phase at UT 1993 Aug 25.8787 corrected for light time. Comp. period: 3.7474 h. UT date and V magnitude shift are as follows: , 1993 Aug 06.00, 0.505; , 1993 Aug 06.95, 0.455; , 1993 Aug 15.95, 0.330; , 1993 Aug 18.90, 0.250; , 1993 Aug 22.98, 0.035; +, 1993 Aug 24.88, −0.030; ×, 1993 Aug 25.96, 0.0; , 1993 Aug 26.84, 0.046; , 1993 Aug 27.95, 0.105; , 1993 Sep 15.72, 0.530; , 1993 Sep 21.87, 0.610; , 1993 Oct 06.73, 0.795; 1993 Oct 14.70, 0.84.
Harris and Young (1983), Lagerkvist and Magnusson (1990), and Tedesco (1989) (see Table II). The amplitude of the OE (0.26) is also different from mean values for S-type asteroids.
The rotation period P = 3.7474 h of this asteroid was determined by Lagerkvist et al. (1981) for the first time using photometric observations of the 1980 apparition. The photometric observations were carried out also by Surdej et al. (1983) and Harris and Young (1989) during this opposition. The phase angles of these observations span from 2.1◦ to 17.5◦ . Using the observations of Lagerkvist et al. (1981) and Surdej et al. (1983), as well as their own observations, Harris and Young (1989) computed the H and G parameters (8.54, 0.17) of the phase curve, while Lagerkvist and Magnusson (1990) obtained H = 8.55 and G = 0.20. Several lightcurves were obtained by different authors (Di Martino et al. 1987; Pfleiderer et al. 1987; Weidenschilling et al. 1987, 1990) during other oppositions of 201 Penelope. Our observations were performed in August–October 1993 for 13 nights. The composite lightcurve is shown in Fig. 14. The lightcurve amplitude changed with phase angle. It can be seen in Fig. 15 for the second minimum, which was observed for a wider range of phase angles. Zappal`a et al. (1990) found that the amplitude at zero phase was A(0) = 0.50 ± 0.01 and the slope parameter m = 0.0102 ± 0.0012 during the 1980 opposition. In our case the amplitude A(0) is equal to 0.34 ± 0.01 and the slope parameter m = 0.0132 ± 0.0005. The differences between the parameters may be due to the different aspect angles of the observations. The phase dependence of brightness is plotted in Fig. 16. The values of the parameters of the approximating functions are presented in Table III. Our parameters H and G differ from those obtained by other authors. The parameters b, a and the amplitude of the OE (0.38) are typical for M-type asteroids.
201 Penelope. This is an LASPA-asteroid (large-amplitude, small-period asteroid), an elongated asteroid with fast rotation.
FIG. 15.
Amplitude–phase dependence of 201 Penelope.
FIG. 16. Magnitude–phase dependence of 201 Penelope. - - -, HG functions; —, Shevchenko (1997).
ASTEROIDS AT LOW PHASE ANGLES
CONCLUSION
As a result of a series of photometric observations we obtained the magnitude–phase relations for seven asteroids. It is still one more addition to the available set of tasteroids for which the brightness behavior has been measured both in the region of the OE (including very low phase angles) and the linear part of phase curve. We have determined more accurate values of the absolute magnitudes H and V0 and other parameters of the approximating functions. The values of the absolute magnitudes can be used for more accurate estimation of albedos and/or diameters of these asteroids. We obtained the amplitudes of the OE for the observed asteroids, which are in general the same as the mean or near to the mean for their types. Small differences in the OE amplitudes of some asteroids from the mean can be due to their individual surface features. We determined the lightcurve amplitudes of the observed asteroids and improved values of the rotation periods for some of them: 5 Astraea, 105 Artemis, 119 Althaea, and 124 Alkeste. The amplitude of the lightcurve of 201 Penelope increases with increasing phase angle and the slope parameter in this opposition is larger then that determined by Zappal`a et al. (1990). It should be pointed out that interest in the investigations of OE atmosphereless bodies has grown due to space missions (see Buratti et al. 1996, Helfenstein et al. 1998, etc.). We will continue our program and will concentrate our efforts on the study of the brightness behavior at low phase angles for distant asteroids (Hilda’s group, Trojans, and Centaurs). These asteroids have a very low surface albedo and the brightness behavior has not been studied enough. The magnitude–phase curves of such asteroids can form by shadow mechanism only and the opposition effect can be absent for them. ACKNOWLEDGMENTS This work was carried out thanks to the financial support of the Ukrainian Ministry of Education and Science (Grant 2.4/314). The authors are grateful to the DLR Institute of Planetary Exploration (Berlin, Germany) for the provision of the CCD camera and the image reduction software.
REFERENCES Belskaya, I. N., and V. G. Shevchenko 1999. Albedo dependence of asteroid opposition effect. Lunar Planet. Sci. 30, 1374. [Abstract] Belskaya, I. N., and V. G. Shevchenko 2000. Opposition effect of asteroids. Icarus 146, 490–499. Bowell, E., and K. Lumme 1979. Colorimetry and magnitudes of asteroids. In Asteroids (T. Gehrels, Ed.), pp. 132–169. Univ. of Arizona Press, Tucson. Bowell, E., B. Hapke, D. Domingue, K. Lumme, J. Peltoniemi, and A. W. Harris 1989. Application of photometric models to asteroids. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 524–556. Univ. of Arizona Press, Tucson. Buratti, B. J., J. H. Hillier, and M. Wang 1996. The lunar opposition surge: Observations by Clementine. Icarus 124, 490–499. Chang, Y. C., and C.-S. Chang 1962. Photometric investigation of seven variable asteroids. Acta Astron. Sin. 10, 101–111.
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Piironen, J., P. Magnusson, C.-I. Lagerkvist, I. P. Williams, M. E. Buontempo, and L. V. Morrison 1997. Physical studies of asteroids. XXXI. Asteroid photometric observations with the Carlsberg Automatic Meridian Circle. Astron. Astrophys. Suppl. Ser. 121, 489–497. Schober, H. J., and A. Schroll 1986. 105 Artemis—A new puzzle among asteroids? In Asteroids, Comets, Meteors II. (C.-I. Lagerkvist, B. A. Lindblad, M. Lundstedt, and H. Rickman, Eds.), pp. 75–76. Univ. of Uppsala Press, Uppsala, Sweden. Schober, H. J., A. Erikson, G. Hahn, C.-I. Lagerkvist, R. Albrecht, W. Ornig, A. Schroll, and M. Stadler 1994. Physical studies of asteroids. XXVIII. Lightcurves and photoelectric photometry of the asteroids 2, 14, 51, 105, 181, 238, 258, 369, 377, 416, 487, 626, 679, 1048 and 2183. Astron. Astrophys. Suppl. Ser. 105, 281–300. Shevchenko, V. G. 1996. Analysis of the asteroid phase dependences of brightness. Lunar Planet. Sci. 27, 1193–1194. [Abstract] Shevchenko, V. G. 1997. Analysis of the asteroid phase dependences of brightness. Astron. Vest. 31, 246–251. Shevchenko, V. G., and D. F. Lupishko 1998. Optical properties of asteroids from photometric data. Astron. Vest. 32, 250–263. [Sol. Syst. Res. (Engl. transl.) 32, 220–232.] Shevchenko, V. G., I. N. Belskaya, V. G. Chiomy, J. Piironen, A. Erikson, G. Neukum, and R. Mohamed 1997. Asteroid observations at low phase angles. I. 50 Virginia, 91 Aegina and 102 Miriam. Planet. Space Sci. 45, 1615– 1623. Shevchenko, V. G., V. G. Chiomy, A. V. Kalashnikov, Yu. N. Krugly, R. A. Mohamed, and F. P. Velichko 1996. Magnitude-phase dependences for three asteroids. Astron. Astrophys. Suppl. Ser. 115, 475–479. Shevchenko, V. G., V. G. Chiomij, Yu. N. Krugly, D. F. Lupishko, R. A. Mohamed, F. P. Velichko, T. Michalowski, V. V. Avramchuk, and A. N. Dovgopol 1992. Photometry of seventeen asteroids. Icarus 100, 295–306. Shevchenko, V. G., Yu. N. Krugly, D. F. Lupishko, A. W. Harris, and G. P.
Chernova 1993. Lightcurves and phase relations of asteroid 55 Pandora. Astron. Vest. 27, 75–80. Surdej, J., R. Louis, N. Cramer, F. Rufener, C. Waelkens, R. Barbier, and P. V. Birch 1983. Photoelectric lightcurves and rotation period of the minor planet 201 Penelope. Astron. Astrophys. Suppl. Ser. 54, 371–378. Taylor, R. C. 1978. Minor planet and related objects. XXIV. Photometric observations for (5) Astraea. Astron. J. 83, 201–204. Tedesco, E. F. 1979. A Photometric Investigation of the Colors, Shapes and Spin Rates of Hirayama Family Asteroids. Ph.D. Dissertation, New Mexico State University. Tedesco, E. F. 1989. Asteroid magnitudes, UBV colors, and IRAS albedos and diameters. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.) pp. 1090–1138. Univ. of Arizona Press, Tucson. Tedesco, E. F., and G. J. Veeder 1992. IMPS albedos and diameters catalog. In Infrared Astronomical Satellite Minor Planet Survey Catalog (E. F. Tedesco, Ed.), pp. 243–285. Phillips Laboratory Techn. Rep. PL-TR-92-2049, Hanscom Air Force Base, MA. Tholen, D. J. 1989. Asteroid taxonomic classification. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 1139–1150. Univ. of Arizona Press, Tucson. Weidenschilling, S. J., C. R. Chapman, D. R. Davis, R. Greenberg, D. H. Levy, and S. Vail 1987. Photometric geodesy of main-belt asteroids. I. Lightcurves of 26 large, rapid rotators. Icarus 70, 191–245. Weidenschilling, S. J., C. R. Chapman, D. R. Davis, R. Greenberg, D. H. Levy, R. P. Binzel, S. M. Vail, and M. Magee 1990. Photometric geodesy of mainbelt asteroids. III. Additional lightcurves. Icarus 86, 402–407. Zappal`a, V., F. Scaltriti, and M. Di Martino 1983. Photoelectric photometry of 21 asteroids. Icarus 56, 325–344. Zappal`a, V., A. Cellino, A. M. Barucci, M. Fulchgnoni, and D. F. Lupishko 1990. An analysis of the amplitude-phase relationship among asteroids. Astron. Astrophys. 231, 548–560.
Asteroid Observations at Low Phase Angles II. 5 Astraea, 75 Eurydike, 77 Frigga, 105 Artemis, 119 Althaea, 124 Alkeste, and 201 Penelope V. G. Shevchenko, I. N. Belskaya, Yu. N. Krugly, and V. G. Chiomy Astronomical Observatory of Kharkiv National University, Kharkiv, Ukraine E-mail: [email protected]
and N. M. Gaftonyuk Crimean Astrophysical Observatory, Simeiz, Crimea, Ukraine Received November 20, 2000; revised April 9, 2001
The results of photometric observations of seven main-belt asteroids with moderate surface albedos are presented. New magnitudephase dependences were obtained for these asteroids: 5 Astraea (down to a phase angle of 0.3◦ , S type), 75 Eurydike (0.1◦ , M), 77 Frigga (0.9◦ , M), 105 Artemis (0.3◦ , C), 119 Althaea (0.3◦ , S), 124 Alkeste (0.1◦ , S), and 201 Penelope (0.5◦ , M). The parameters of approximating functions and the amplitudes of the opposition effect of these asteroids were determined. The obtained data allowed us to improve values of the rotation periods for some of them: 5 Astraea (16.815 ± 0.002 h), 105 Artemis (18.56 ± 0.01 h), 119 Althaea (11.466 ± 0.001 h), and 124 Alkeste (9.907 ± 0.001 h). c 2002 Elsevier Science (USA)
Key Words: asteroids; photometry; opposition effect; rotation period; low phase angle.
in the range of the opposition effect (OE) is different for low-, moderate-, and high-albedo asteroids. The maximum amplitude of the OE occurs for the moderate-albedo S- and M-type asteroids. It is caused both by shadowing and coherent backscattering mechanisms of lightscattering processes in a regolith layer of these bodies. The region of extremely low phase angles is very important to understand the mechanisms of lightscattering. New data are needed both to improve statistics and to estimate the contribution of the different lightscattering mechanisms to the phase curves of atmosphereless bodies. The results of photometric observations at low phase angles of asteroids 5 Astraea, 75 Eurydike, 77 Frigga, 105 Artemis, 119 Althaea, 124 Alkeste, and 201 Penelope are presented in this paper. OBSERVATIONS AND RESULTS
INTRODUCTION
This work is a continuation of the observational program devoted to the investigation of the brightness behavior for asteroids of different composition types at extremely low phase angles (<1◦ ). The program has been carried out over several years at the Kharkiv Astronomical Observatory (Ukraine) in cooperation with other observatories (Shevchenko et al. 1993, 1996, 1997). The investigation of the brightness behavior at low phase angles is very important for our understanding of lightscattering properties of asteroid surfaces and for the testing of theoretical models of a regolith layer of the atmosphereless celestial bodies. According to Belskaya and Shevchenko (1999, 2000) there are only 33 asteroids that have good phase angle coverage with small errors of observation data and for which the brightness at the low phase angles was measured. The brightness behavior
The observations of the selected asteroids were carried out at the Astronomical Observatory of the Kharkiv National University (70-cm reflector) and at the Simeiz Station of the Crimean Astrophysical Observatory (60-cm and 1-m reflectors), using one-channel photoelectric photometers in 1993 and CCD cameras ST-6 in 1996–1999. The photoelectric data reduction methods were described by Shevchenko et al. (1992, 1993). CCD images were reduced using the synthetic aperture photometry package (ASTPHOT) developed at DLR by S. Mottola (Mottola et al. 1995). Almost all observations were performed in the Vband of the standard Johnson UBV system. Only 105 Artemis was observed in the Cousins R-band in the 1999 opposition. The absolute calibrations of the data were performed with standard sequences from Landolt (1992) and Lasker et al. (1988). The accuracy of absolute photometry is equal to 0.01–0.02 mag. The mean time of observations, ecliptic coordinates at the epoch
365 0019-1035/02 $35.00 c 2002 Elsevier Science (USA) All rights reserved.
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TABLE I Aspect Data and Measured Magnitudes of the Observed Asteroids UT date 1
λ2000 (◦ ) 2
β2000 (◦ ) 3
r 4
5
α (◦ ) 6
V0 (1, α) (mag) 7
1997 Aug 20.88 1997 Aug 21.91 1997 Aug 22.90 1997 Aug 29.82 1997 Sep 21.78 1997 Oct 03.65 1997 Oct 09.80
329.009 328.773 328.546 326.979 322.730 321.535 321.245
−0.970 −0.994 −1.017 −1.170 −1.595 −1.756 −1.825
5 Astraea 3.059 3.059 3.058 3.056 3.045 3.038 3.034
2.048 2.047 2.047 2.056 2.176 2.286 2.353
0.49 0.33 0.55 3.17 11.21 14.39 15.71
6.790 6.750 6.805 7.065 7.290 7.395 7.450
1996 Mar 19.82 1996 Mar 20.75 1996 Mar 21.90 1996 Mar 22.98 1996 Mar 27.88
179.711 179.921 179.819 179.575 178.477
−0.062 −0.077 −0.096 −0.114 −0.195
75 Eurydike 3.387 3.386 3.384 3.383 3.376
2.391 2.389 2.388 2.387 2.387
0.22 0.12 0.53 0.92 2.67
8.990 8.975 9.040 9.115 9.225
1997 Sep 06.04 1997 Sep 07.89 1997 Sep 13.85 1997 Sep 14.91 1997 Sep 19.94 1997 Sep 21.89 1997 Sep 29.90 1997 Oct 25.81 1997 Nov 05.77 1997 Nov 06.72
347.718 347.298 345.937 345.697 344.582 344.166 342.604 340.140 340.530 340.610
−1.065 −1.035 −0.934 −0.916 −0.825 −0.789 −0.637 −0.170 0.010 0.020
77 Frigga 2.545 2.543 2.535 2.533 2.527 2.524 2.514 2.481 2.467 2.466
1.539 1.536 1.531 1.532 1.537 1.541 1.566 1.745 1.852 1.862
1.71 0.89 2.08 2.58 4.93 5.83 9.40 18.49 20.96 21.13
8.835 8.735 8.860 8.895 9.035 9.085 9.235 9.485 9.575 9.615
1996 Sep 29.88 1996 Sep 30.88 1996 Oct 01.78 1996 Oct 03.83 1996 Oct 08.75 1996 Oct 09.80 1996 Nov 12.75 1996 Nov 14.70 1999 Apr 22.97 1999 Apr 23.94 1999 May 20.89 1999 May 21.92
9.166 8.882 8.627 8.049 6.689 6.407 0.585 0.496 264.376 264.467 263.427 263.252
0.119 −0.019 −0.144 −0.426 −1.093 −1.232 −4.908 −5.063 27.961 28.273 36.220 36.464
105 Artemis 2.549 2.551 2.552 2.556 2.564 2.566 2.618 2.621 1.955 1.955 1.957 1.957
1.548 1.550 1.552 1.556 1.573 1.577 1.872 1.897 1.216 1.210 1.088 1.085
0.84 0.34 0.12 1.14 3.55 4.06 16.90 17.38 25.56 25.39 20.46 20.31
8.730 8.575 8.590 8.740 8.915 8.920 9.450 9.470 — — — —
1998 Oct 13.79 1998 Oct 14.83 1998 Oct 20.97 1998 Oct 21.93 1998 Oct 22.85 1998 Oct 24.83 1998 Oct 25.81 1998 Oct 31.00 1998 Nov 07.73 1998 Dec 08.67 1998 Dec 09.69
30.022 29.783 28.333 28.103 27.884 27.414 27.183 25.993 24.393 21.783 21.818
−0.368 −0.418 −0.716 −0.762 −0.806 −0.900 −0.947 −1.185 −1.518 −2.487 −2.509
119 Althaea 2.375 2.375 2.376 2.377 2.377 2.377 2.377 2.379 2.381 2.392 2.392
1.386 1.384 1.381 1.381 1.382 1.384 1.385 1.397 1.428 1.683 1.694
4.09 3.56 0.50 0.33 0.66 1.64 2.13 4.75 8.49 19.62 19.87
8.610 8.565 8.265 8.230 8.290 8.405 8.470 8.590 8.735 9.010 9.015
1996 Sep 12.92 1996 Sep 29.83 1996 Sep 30.88 1996 Oct 01.85 1996 Oct 03.80 1996 Oct 08.73 1996 Oct 09.80 1996 Nov 12.74
11.931 8.213 7.969 7.744 7.293 6.175 5.939 1.244
0.345 0.052 0.034 0.017 −0.018 −0.104 −0.122 −0.617
124 Alkeste 2.699 2.712 2.713 2.714 2.715 2.719 2.719 2.743
1.738 1.711 1.712 1.713 1.716 1.729 1.732 1.995
7.84 0.45 0.02 0.45 1.33 3.51 3.97 15.90
8.563 8.120 8.030 8.110 8.215 8.375 8.430 8.813
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TABLE I—Continued λ2000 (◦ ) 2
UT date 1
β2000 (◦ ) 3
r 4
5
α (◦ ) 6
V0 (1, α) (mag) 7
1.225 1.221 1.192 1.186 1.182 1.182 1.182 1.182 1.183 1.239 1.275 1.389 1.464
9.91 9.45 4.85 3.28 1.14 0.47 0.75 1.16 1.73 11.33 14.09 19.56 21.78
8.829 8.761 8.596 8.508 8.310 8.237 8.270 8.316 8.370 8.833 8.909 9.094 9.140
201 Penelope 1993 Aug 06.00 1993 Aug 06.95 1993 Aug 15.95 1993 Aug 18.90 1993 Aug 22.98 1993 Aug 24.88 1993 Aug 25.96 1993 Aug 26.84 1993 Aug 27.95 1993 Sep 15.72 1993 Sep 21.87 1993 Oct 06.73 1993 Oct 14.70
335.455 335.302 333.638 333.028 332.157 331.747 331.513 331.324 331.085 327.610 326.880 326.289 326.682
2.093 2.045 1.553 1.380 1.136 1.020 0.953 0.899 0.831 −0.307 −0.649 −1.369 −1.690
2.199 2.198 2.195 2.194 2.193 2.193 2.192 2.192 2.192 2.191 2.191 2.194 2.196
2000.0, distances to the Sun and the Earth in astronomical units, phase angle, and magnitude reduced to the lightcurve maximum of the observed asteroids are listed in Table I. Some main physical characteristics (taxonomic type, albedo, diameter, and the adopted values of H and G parameters) of the observed asteroids are presented in Table II. Table III contains the results of observations: determined rotation periods, lightcurve amplitudes, and calculated parameters of the magnitude-phase dependences. V0 is the V magnitude at zero phase, a is the parameter describing the amplitude of opposition brightening, and b is the coefficient for the linear part of the phase curve. All parameters were calculated using an empirical three-parametric function for an approximation of the magnitude-phase dependences (Shevchenko 1996, 1997). The determined values of the H and G parameters calculated according to Bowell et al. (1989) are also given in Table III.
magnitude-phase dependence has been obtained for this asteroid. Taylor (1978) used a linear phase coefficient βv = 0.014 mag/◦ computed using data collected during several oppositions. This value is very small and atypical for S-type asteroids (see Shevchenko and Lupishko 1998). Different values for the parameter G were obtained by Lagerkvist and Williams (1987) (G = 0.18), Lagerkvist et al. (1989) (G = 0.34), Lagerkvist et al. (1992) (G = 0.26) and Piironen et al. (1997) (G = 0.34). In all these cases it was calculated using the data obtained with the Carlsberg Meridian Circle. Our observations were carried out during August–October 1997 for seven nights in the range of phase angles 0.33–15.7◦ . The composite lightcurve with period 16.815 ± 0.002 h, determined by our data, is shown in Fig. 1. The lightcurve has amplitude 0.16 mag for this opposition. The phase dependence of brightness is shown in Fig. 2. The dashed and solid lines 5 Astraea. The rotation period of this asteroid (P = 16.806 h) are approximations using H and G (Bowell et al. 1989) and was determined by Chang and Chang (1962) for the first time Shevchenko’s (1996, 1997) functions, respectively. Parameters in the 1962 opposition. Later many photometric observations of these functions are listed in Table III. The value we obtained were performed by different authors (see Taylor 1978, of the parameter G is similar to those determined by Lagerkvist Weidenschilling et al. 1990, Harris et al. 1999, etc.), but no et al. (1989) and by Piironen et al. (1997). The value of parameter a is the same as the mean for S-type asteroids, whereas the parameter b differs from the mean value for this kind of asterTABLE II oids (Shevchenko 1997). The amplitude of the OE determined Physical Characteristics of the Observed Asteroids according to Belskaya and Shevchenko (1999, 2000) is equal to a b b c c 0.35, which is typical for S-type asteroids. Asteroid Type Albedo Diameter H G 5 Astraea 75 Eurydike 77 Frigga 105 Artemis 119 Althaea 124 Alkeste 201 Penelope a
S M M C S S M
Tholen (1989). Tedesco and Veeder (1992). c Tedesco (1989). b
0.23 0.15 0.14 0.047 0.23 0.17 0.16
119.1 55.7 69.3 119.1 57.3 76.4 68.4
7.24 9.02 8.57 8.89 8.61 8.13 8.48
0.67 0.25 0.26 0.29 0.57 0.31 0.14
75 Eurydike. Two groups of observers obtained lightcurves of this asteroid in 1980. First observations were performed by Zappal`a et al. (1983) in October 1980 for two nights. They determined a rotation period of 8.92 h, but they stated that the period could be wrong. Harris and Young (1989) also carried out observations of 75 Eurydike during this opposition for six nights in November. They obtained a period of 5.357 ± 0.003 h and a magnitude-phase curve with H and G parameters of 8.98 ± 0.01 and 0.23 ± 0.02, respectively. Our observations were performed
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TABLE III Rotation Periods, Amplitudes, and Parameters of Photometric Approximating Functions of the Observed Asteroids Asteroid
Period (h)
Ampl. (mag)
V0 (mag)
a
b
H (mag)
G
5 Astraea 75 Eurydike 77 Frigga 105 Artemis 119 Althaea 124 Alkeste 201 Penelope
16.815 ± 0.002 5.360 ± 0.003 8.999 ± 0.001 18.560 ± 0.010 11.466 ± 0.001 9.907 ± 0.001 3.7474 ± 0.0001
0.16 0.15 0.20 0.05 0.30 0.12 0.34
7.09 ± 0.03 9.25 ± 0.01 8.92 ± 0.02 8.85 ± 0.03 8.58 ± 0.02 8.35 ± 0.02 8.53 ± 0.02
0.46 ± 0.05 0.32 ± 0.02 0.36 ± 0.04 0.32 ± 0.05 0.50 ± 0.03 0.35 ± 0.04 0.47 ± 0.05
0.024 ± 0.002 0.033 ± 0.001 0.033 ± 0.001 0.036 ± 0.002 0.023 ± 0.001 0.031 ± 0.002 0.029 ± 0.001
6.74 ± 0.02 8.97 ± 0.01 8.64 ± 0.01 8.58 ± 0.02 8.24 ± 0.02 8.06 ± 0.01 8.20 ± 0.01
0.31 ± 0.03 0.23 ± 0.01 0.22 ± 0.01 0.18 ± 0.03 0.32 ± 0.03 0.25 ± 0.02 0.26 ± 0.01
in March 1996 and only the region of the OE was comprised (see Table I). The composite lightcurve with rotation period 5.360 ± 0.003 h determined by our data is shown in Fig. 3. This period is very similar to that determined by Harris and Young (1989). Maximum amplitude of the lightcurve is 0.15 mag. The phase curve is presented in Fig. 4. The data of Harris and Young (1989) were shifted 0.04 mag to our data to calculate parameters of approximating functions for opposition in 1996 (see Table III). The amplitude of the OE is equal to 0.25. 77 Frigga. Harris and Young (1989) were the first who determined the rotation period (8.9985 ± 0.002 h) of this asteroid. They observed 77 Frigga for eight nights in November 1980 and obtained a magnitude–phase curve in the phase angle range of 2.5◦ –16.3◦ with parameters H = 8.52 ± 0.06 and G = 0.16 ± 0.01, and a linear phase coefficient β = 0.034 mag/◦ .
FIG. 1. Composite lightcurve of 5 Astraea. Zero phase at UT 1997 Aug 22.7886 corrected for light time. Comp. period: 16,815 h. The UT date and V magnitude shift are defined as follows: , 1997 Aug 20.88, 0.040; , 1997 Aug 21.91, 0.000; , 1997 Aug 22.40, 0.055; , 1997 Aug 29.82, 0.315; , 1997 Sep 21.78, 0.540; +, 1997 Oct 3.65, 0.645; ×, 1997 Oct 09.80, 0.700.
Subsequently, Lagerkvist and Rickman (1982) performed observations of Frigga for eight nights in March 1982 in a range of the low phase angles spanning from 0.15◦ to 2.72◦ . They determined the parameters V (0) = 8.58 and Q = 0.03 (see Bowell and Lumme 1979) of the magnitude–phase relation. Values of the parameter G were also obtained by Tedesco (1989) (see Table II) and by Piironen et al. (1997) (0.13). Several single lightcurves were obtained by other observers (see, e.g., Zappal`a et al. 1983, Hainaut-Rouelle et al. 1995, and Lagerkvist et al. 1995). We observed 77 Frigga for 10 nights in September–November 1997 (see Table I). The composite lightcurve with a rotation period 8.999 h determined by our data is shown in Fig. 5. Our period is the same as determined by Harris and Young (1989). The phase dependence of brightness is shown in Fig. 6. The data of Lagerkvist and Rickman (1982) were added to our data. Their data were reduced using a formalism by Bowell and Lumme (1979) and were shifted 0.04 mag to our data. The values of
FIG. 2. Magnitude–phase dependence of 5 Astraea. - - -, HG function; —, Shevchenko (1997).
ASTEROIDS AT LOW PHASE ANGLES
FIG. 3. Composite lightcurve of 75 Eurydike. Zero phase at UT 1996 Mar 19.7493 corrected for light time. Comp. period: 5.360 h. UT date and V magnitude shift are defined as follows: , 1996 Mar 19.82, −0.050; , 1996 Mar 20.75, −0.065; , 1996 Mar 21.90, 0.0; , 1996 Mar 22.98, 0.075; , 1996 Mar 27.88, 0.185.
parameters of approximating functions are presented in Table III. The amplitude of the OE is equal to 0.24.
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FIG. 5. Composite lightcurve of 77 Frigga. Zero phase at UT 1996 Sep 14.7913 corrected for light time. Comp. period: 8.999 UT date and V magnitude shift are defined as follows: 0, 1997 Sep 06.04, −0.060; , 1997 Sep 07.89, −0.160; , 1997 Sep 13.85, −0.035; , 1997 Sep 14.91, 0.000; , 1997 Sep 19.94, 0.140; +, 1997 Sep 21.89, 0.190; ×, 1997 Sep 29.90, 0.340; , 1997 Oct 25.81, 0.590; , 1997 Nov 12.75, 0.680; , 1997 Nov 14.70, 0.720.
105 Artemis. Photometric observations of this asteroid were performed during two oppositions: 1977 (Tedesco 1979) and 1980 (Debehogne et al. 1982, Schober and Schroll 1986, Schober et al. 1994). The rotation period (P = 16.84 h) was
determined for the first time by Schober et al. (1994). We observed 105 Artemis for two apparitions: for eight nights in September–November 1996 and for four nights in April–May 1999 (see Table I). The rotation period determined by Schober et al. (1994) does not fit our data. We found a new rotation period P = 18.56 ± 0.01 h. This period fits also other data but
FIG. 4. Magnitude–phase dependence of 75 Eurydike. - - -, HG function; —, Shevchenko (1997); , Harris and Young (1989); , this work.
FIG. 6. Magnitude–phase dependence of 77 Frigga. - - -, HG function; —, Shevchenko (1997); , Lagerkvist and Rickman (1982); , this work.
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FIG. 7. Composite lightcurves of 105 Artemis in 1996. Zero phase at UT 1996 Oct 1.6799 corrected for light time. Comp. period: 18.56 h. UT date and V magnitude shift are defined as follows: , 1996 Sep 29.88, 0.140; , 1996 Sep 30.88, −0.015; , 1996 Oct 01, 0.000; , 1996 Oct 03.83, 0.150; , 1996 Oct 08.75, 0.325; , 1996 Oct 09.80, 0.330; +, 1996 Nov 12.75, 0.860; ×, 1996 Nov 14.70, 0.860.
new observations are needed to define more accurately the period. The composite lightcurves obtained using this period are shown in Figs. 7 and 8. The lightcurves show only one pair of extrema with amplitudes equal to 0.05 mag in 1996 and 0.10 mag in 1999. The phase curve is shown in Fig. 9. Our values
FIG. 8. Composite lightcurves of 105 Artemis in 1999. Zero phase at UT 1999 Apr 22.9072 corrected for light time. Comp. period: 18.56 h. UT date and R magnitude shift are as follows: , 1999 Apr 22.18, 0.000; , 1999 Apr 20.88, −0.005; , 1999 May 20.88, rel −12.295; , 1999 May 20.88, rel −12.295.
FIG. 9. Magnitude–phase dependence of 105 Artemis. - - -, HG function; —, Shevchenko (1997).
of H and G parameters (see Table III) are different from those obtained by Tedesco (1989). The values of the parameters of the approximating functions (Table III) and the amplitude of the OE (0.24) are different from mean values for C-type asteroids. 119 Althaea. The first observations of this asteroid were performed in 1984 by Weidenschilling et al. (1990) for 4.5 h, which supposed that the rotation period is longer than 12 h. Later Gil Hutton (1990) observed 119 Althaea for three nights in July 1989. He determined a period P = 11.484 ± 0.010 h. Our observations were carried out during October–December 1998 for 11 nights (see Table I). Figure 10 shows the composite lightcurve obtained with the rotation period P = 11.466 ± 0.001 h. This period was determined using lightcurves in a wider time interval and it is more accurate. The amplitude of the lightcurve for this opposition is 0.30 mag. The phase curve of 119 Althaea in the phase angle range 0.3◦ –19.9◦ is presented in Fig. 11. The values of the parameters of the approximating functions are listed in Table III. Previously, the parameters H and G were determined by Tedesco (1989) (see Table II) and by Piironen et al. (1997) (H = 8.36, G = 0.17). Our values of the parameters differ from previous ones, but on the basis of the length of our observations we consider our data more reliable. The value of parameter a is the same as that for S-type asteroids but the values of the parameters b and G differ from mean values of S-type (Shevchenko and Lupishko 1998). The amplitude of the OE (0.36) is typical for S-type asteroids. 124 Alkeste. There are photometric observations of this asteroid only for two apparitions. First observations were carried out by Harris and Young (1983) for four nights in October– November 1979. They determined the rotation period (P = 9.921 h), and lightcurve amplitude (A = 0.15 mag). They also
ASTEROIDS AT LOW PHASE ANGLES
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FIG. 10. Composite lightcurve of 119 Althaea. Zero phase at UT 1998 Oct 21.8109 corrected for light time. Comp. period: 11.466 h. UT date and V magnitude shift are as follows: , 1998 Oct 13.79, 0.380; , 1998 Oct 14.83, 0.335; , 1998 Oct 20.0, 0.035; , 1998 Oct 21.93, 0.0; , 1998 Oct 22.85, 0.060; +, 1998 Oct 24.83, 0.175; ×, 1998 Oct 25.81, 0.240; , 1998 Oct 31.00 0.360; , 1998 Nov 07.73, 0.505; , 1998 Dec 08.67, 0.780; , 1998 Dec 09.69, 0.785.
FIG. 12. Composite lightcurve of 124 Alkeste. Zero phase at UT 1996 Sep 30.7729 corrected for light time. Comp. period: 9.907 h. UT date and V magnitude shift are as follows: , 1996 Sep 12.92, 0.533; , 1996 Sep 29.83, 0.090; , 1996 Sep 30.88, 0.0; , 1996 Oct 01.85, 0.080; , 1996 Oct 03.80, 0.185; +, 1996 Oct 08.73, 0.345; ×, 1996 Oct 09.80, 0.400; , 1996 Nov 12.94, 0.783.
calculated H and G parameters (H = 8.11, G = 0.20). Using the data by Harris and Young (1983), Lagerkvist and Magnusson (1990) computed H and G parameters equal to 8.12 and 0.18, respectively. Hainaut-Rouelle et al. (1995) performed observations of 124 Alkeste for two nights in July 1991. They obtained lightcurves with amplitude 0.10 mag. Our observations were carried out during September– November 1996 for eight nights (see Table I). The phase an-
gle range spans from 0.02◦ to 16◦ . The composite lightcurve with the rotation period P = 9.907 ± 0.001 h and amplitude 0.12 mag is shown in Fig. 12. Our value of the rotation period differs a little from that obtained by Harris and Young (1983). The magnitude–phase dependence of 124 Alkeste is shown in Fig. 13. The parameters of the approximating functions are listed in Table III. The parameter G is different from that obtained by
FIG. 11. Magnitude–phase dependence of 119 Althaea. - - -, HG function; —, Shevchenko (1997).
FIG. 13. Magnitude–phase dependence of 124 Alkeste. - - -, HG function; —, Shevchenko (1997).
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FIG. 14. Composite lightcurve of 201 Penelope. Zero phase at UT 1993 Aug 25.8787 corrected for light time. Comp. period: 3.7474 h. UT date and V magnitude shift are as follows: , 1993 Aug 06.00, 0.505; , 1993 Aug 06.95, 0.455; , 1993 Aug 15.95, 0.330; , 1993 Aug 18.90, 0.250; , 1993 Aug 22.98, 0.035; +, 1993 Aug 24.88, −0.030; ×, 1993 Aug 25.96, 0.0; , 1993 Aug 26.84, 0.046; , 1993 Aug 27.95, 0.105; , 1993 Sep 15.72, 0.530; , 1993 Sep 21.87, 0.610; , 1993 Oct 06.73, 0.795; 1993 Oct 14.70, 0.84.
Harris and Young (1983), Lagerkvist and Magnusson (1990), and Tedesco (1989) (see Table II). The amplitude of the OE (0.26) is also different from mean values for S-type asteroids.
The rotation period P = 3.7474 h of this asteroid was determined by Lagerkvist et al. (1981) for the first time using photometric observations of the 1980 apparition. The photometric observations were carried out also by Surdej et al. (1983) and Harris and Young (1989) during this opposition. The phase angles of these observations span from 2.1◦ to 17.5◦ . Using the observations of Lagerkvist et al. (1981) and Surdej et al. (1983), as well as their own observations, Harris and Young (1989) computed the H and G parameters (8.54, 0.17) of the phase curve, while Lagerkvist and Magnusson (1990) obtained H = 8.55 and G = 0.20. Several lightcurves were obtained by different authors (Di Martino et al. 1987; Pfleiderer et al. 1987; Weidenschilling et al. 1987, 1990) during other oppositions of 201 Penelope. Our observations were performed in August–October 1993 for 13 nights. The composite lightcurve is shown in Fig. 14. The lightcurve amplitude changed with phase angle. It can be seen in Fig. 15 for the second minimum, which was observed for a wider range of phase angles. Zappal`a et al. (1990) found that the amplitude at zero phase was A(0) = 0.50 ± 0.01 and the slope parameter m = 0.0102 ± 0.0012 during the 1980 opposition. In our case the amplitude A(0) is equal to 0.34 ± 0.01 and the slope parameter m = 0.0132 ± 0.0005. The differences between the parameters may be due to the different aspect angles of the observations. The phase dependence of brightness is plotted in Fig. 16. The values of the parameters of the approximating functions are presented in Table III. Our parameters H and G differ from those obtained by other authors. The parameters b, a and the amplitude of the OE (0.38) are typical for M-type asteroids.
201 Penelope. This is an LASPA-asteroid (large-amplitude, small-period asteroid), an elongated asteroid with fast rotation.
FIG. 15.
Amplitude–phase dependence of 201 Penelope.
FIG. 16. Magnitude–phase dependence of 201 Penelope. - - -, HG functions; —, Shevchenko (1997).
ASTEROIDS AT LOW PHASE ANGLES
CONCLUSION
As a result of a series of photometric observations we obtained the magnitude–phase relations for seven asteroids. It is still one more addition to the available set of tasteroids for which the brightness behavior has been measured both in the region of the OE (including very low phase angles) and the linear part of phase curve. We have determined more accurate values of the absolute magnitudes H and V0 and other parameters of the approximating functions. The values of the absolute magnitudes can be used for more accurate estimation of albedos and/or diameters of these asteroids. We obtained the amplitudes of the OE for the observed asteroids, which are in general the same as the mean or near to the mean for their types. Small differences in the OE amplitudes of some asteroids from the mean can be due to their individual surface features. We determined the lightcurve amplitudes of the observed asteroids and improved values of the rotation periods for some of them: 5 Astraea, 105 Artemis, 119 Althaea, and 124 Alkeste. The amplitude of the lightcurve of 201 Penelope increases with increasing phase angle and the slope parameter in this opposition is larger then that determined by Zappal`a et al. (1990). It should be pointed out that interest in the investigations of OE atmosphereless bodies has grown due to space missions (see Buratti et al. 1996, Helfenstein et al. 1998, etc.). We will continue our program and will concentrate our efforts on the study of the brightness behavior at low phase angles for distant asteroids (Hilda’s group, Trojans, and Centaurs). These asteroids have a very low surface albedo and the brightness behavior has not been studied enough. The magnitude–phase curves of such asteroids can form by shadow mechanism only and the opposition effect can be absent for them. ACKNOWLEDGMENTS This work was carried out thanks to the financial support of the Ukrainian Ministry of Education and Science (Grant 2.4/314). The authors are grateful to the DLR Institute of Planetary Exploration (Berlin, Germany) for the provision of the CCD camera and the image reduction software.
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