Lightcurves of 7 Near-Earth Asteroids

ICARUS

124, 471–482 (1996) 0223

ARTICLE NO.

Lightcurves of 7 Near-Earth Asteroids PETR PRAVEC Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-251 65 Ondrˇejov, Czech Republic E-mail: [email protected]

LENKA SˇAROUNOVA´ Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-251 65 Ondrˇejov, Czech Republic; and Astronomical Institute, Charles University Prague, CZ-150 00 Prague 5, Sˇve´dska´ 8, Czech Republic AND

MAREK WOLF Astronomical Institute, Charles University Prague, CZ-150 00 Prague 5, Sˇve´dska´ 8, Czech Republic Received January 30, 1996; revised June 11, 1996

We present results of our CCD photometry of near-Earth asteroids (1627), (4957), (6569), 1993 UC, 1994 AH2 , 1994 CB, and 1994 LX, that we made in 1994 and 1995. Synodic rotation periods were determined for 6 of them for the first time, and we provide constraints and show a consistency of our results with the earlier spin vector determination for (1627). Among the other objects, the most interesting observations were obtained for (4957), containing information useful for future spin vector determinations; 1993 UC, that is the second fastest rotator known among asteroids (period 2.340 hr); 1994 AH2 , an object on the margin between asteroidal and cometary orbital types, with the probable rotation period of 23.95 hr; and 1994 CB, one of the smallest (est. 0.2 km) asteroids observed photometrically up to now.  1996 Academic Press, Inc.

1. INTRODUCTION

Near-Earth asteroids (NEAs) are one of the most interesting group of small bodies in the Solar System. There are several reasons for the scientific interest in NEAs: (i) they are the smallest bodies which are observable from the Earth, (ii) their origin and evolutional history represent an important source of information on the processes in the Solar System, (iii) their impacts on the Earth’s surface represent a hazard for the Earth’s biosphere. Furthermore, they can be used as a source of raw materials for future space missions. The increasing number of new discoveries of NEAs indicates a need for extensive observing programs in order to determine the fundamental physical parameters of these objects. In early 1994, we started observations within the

project of photometric follow-up of NEAs with the 0.65m CCD telescope at the Ondrˇejov Observatory (Pravec and Wolf 1994). The main scientific aim of the project is to enlarge the available sample of rotational periods of NEAs, and to provide baseline data for their further physical studies. We have constructed our observing program in such a way to provide broad-band lightcurve data for NEAs during their favorable oppositions. Priority is given to objects with no available information on their rotational states. The observations allow us to determine the synodic rotation periods, provide rough information on the shapes, and supply the first data needed for spin vector studies. Astrometric measurements of the photometrized asteroids represent an important by-product of our observations. This paper is a continuation of our previous publication on the CCD photometry of NEAs (Pravec et al. 1995). The results for seven of the objects observed from March 1994 to May 1995 are presented here. The results for other NEAs observed from Ondrˇejov within the NEA followup project and also from other stations will be published in another paper. 2. OBSERVATIONS, REDUCTION, AND ANALYSIS

The photometric observations of the selected NEAs were performed with the CCD SBIG ST-6 camera located in the primary focus of the 0.65-m reflecting telescope at the Ondrˇejov Observatory, Czech Republic. (For details on the camera see, e.g., Pravec et al. 1994.) The measurements were made primarily in the Cousins R band, occasionally with supplementary exposures in V and I bands. The expo-

471 0019-1035/96 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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sure times were chosen according to the brightness and apparent motion of the asteroid and ranged typically between 60 and 180 sec. The observations were taken while tracking the telescope at the sidereal rate. A large number of local comparison stars was present in each asteroid frame, allowing differential photometry also in non-photometric sky conditions. Calibration measurements were made on the best nights, using the fields of the standard stars by Landolt (1992). Flat fields were routinely obtained from exposures of regions of the sky taken at dusk or dawn. The photometric reduction of the series of CCD frames was performed using APHOT, a synthetic aperture photometry software developed by M. Velen and P. Pravec at the Ondrˇejov Observatory. Nightly differential lightcurves were produced with respect to an ensemble of selected local comparison stars to eliminate random errors and possible variability of individual stars. Usually at least five comparison stars were measured together with an asteroid. As a source of reference stars for the astrometric reductions, the Guide Star Catalogue (Lasker et al. 1990) was used. The observational circumstances and aspect data for the asteroids on each observing night are listed in Table I. The table gives the J2000.0 ecliptic coordinates of the phase angle bisector (PAB, that is the vector connecting the center of the asteroid and the midpoint of the great circle arc between the sub-Earth and sub-solar points; for justification of importance of the PAB see, e.g., Magnusson et al. 1989, Simonelli et al. 1995), the heliocentric and geocentric distances, the solar phase angle, the error of individual points in the lightcurve (median error or range of errors is given), and the shift of the lightcurve (reduced to the unit distances) adopted for the subsequent analysis and construction of the composite lightcurve. (While the shifts correspond basically to the phase-effect correction for the calibrated lightcurves, the relative lightcurves are shifted iteratively to minimize the sum of square residuals from the best Fourier fit (see below). The uncertainties in the calibrations are also allowed for.) The date of observation is given to the nearest tenth of a day to the midtime of the observational interval. The individual lightcurves were corrected for light-travel time and the magnitudes were reduced to unit geocentric and heliocentric distances of the asteroid. The analysis of the lightcurves was performed generally in the way described by Harris et al. (1989). The principal point of the method is a fitting of the Fourier series to the lightcurves reduced to unit distances and to the same phase angle. We represent the Fourier series in the form R(t) 5 C0 1

O C cos 2fnP (t 2 t ) m

n

n 51

2fn (t 2 t0 ), 1 Sn sin P

0

(1)

where R is the computed reduced magnitude at time t, C0 is the mean reduced magnitude, Cn and Sn are the Fourier coefficients of the nth order, P is the period, and t0 is the zero-point time (epoch). The best fit is achieved by minimizing the sum of squares of residuals of the computed magnitudes from the measured ones (reduced to the unit distances and the same phase angle). The standard errors (S.E.) of the Fourier coefficients are obtained using the formula given by Harris et al. (1989). We also compute the equivalent set of parameters, amplitudes (An ) and arguments ( fn ), defined by the formulas An 5 ÏC 2n 1 S 2n , for n 5 1 to m, cos fn 5

Cn Sn , sin fn 5 , for n 5 1 to m. An An

(2) (3)

The maximum order (m) of the fitted Fourier series is chosen according to the significance F-test, in the way described, e.g., in the paper by Magnusson et al. (1995). In all but one case, the orders used are significant at the level of 0.5%, thus they contain some information about the lightcurve shape. (The exception is the 5th order of the Fourier series fitted to the lightcurve of 1993 UC. The reason for its inclusion is that the 6th order is still significant and provides a clearly better fit.) 3. RESULTS AND DISCUSSION

The main results of the observations are summarized in Table II. There are given the synodic rotation periods, amplitudes (or their ranges), and absolute magnitudes in the H 2 G magnitude system (Bowell et al. 1989). The errors of the amplitudes are not presented here, but they are between ,0.01 and 0.05 mag for individual cases. The absolute magnitudes were derived in heterogeneous ways, and they represent a supplementary information to the main results on rotations of the NEAs. The parameters (i.e., epochs, periods, Fourier coefficients, their standard errors, amplitudes, and arguments) of the best fit Fourier series to the reduced lightcurves are given in Table IV. In the following, the results for individual objects are discussed. (1627) Ivar This Amor-type S-class asteroid (Tholen 1989) was observed photometrically in 1985 (Hahn et al. 1989) and 1990 (Chernova et al. 1995). The observations from 1985 have revealed the synodic rotation period of 4.7957–4.7996 hr. Velichko and Lupishko (see Hahn et al. 1989) have obtained the preliminary solution for Ivar’s pole of rotation of (Lp , Bp ) 5 (3308, 1208) (ecliptic coordinates, equinox 1950.0) and the sidereal period of 4.7952 hr from the 1985 data. (They also obtained a less

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TABLE I Observational Circumstances and Aspect Data Date UT

LPAB [deg]

BPAB [deg]

r [AU]

D [AU]

a [deg]

Errors [mag]

Shifts in c.l.

(1627)

1995 Feb. 24.0 28.1 Mar. 2.1 7.1 8.1 9.0

186.4 186.8 187.0 187.4 187.5 187.5

18.1 18.5 18.6 19.1 19.2 19.2

2.009 1.991 1.981 1.958 1.953 1.949

1.161 1.113 1.091 1.037 1.027 1.018

19.2 17.8 17.0 14.9 14.5 14.1

0.012 0.018 0.011–0.015 0.012 0.013 0.015–0.020

20.044 10.014 10.010 10.027 10.065 rel.

(4957)

1994 Oct. 3.1 12.0 13.1 Dec. 1.1 1995 Jan. 3.9

69.1 73.4 73.9 82.7 80.7

130.1 126.5 126.1 20.9 218.2

1.291 1.312 1.315 1.453 1.558

0.803 0.747 0.740 0.489 0.674

50.8 49.1 48.8 14.1 24.4

0.04–0.045 0.04–0.045 0.03–0.04 0.015 0.03

rel. rel. rel. rel. rel.

(6569)

1995 Apr. 29.9 May 1.9 3.0 28.0

202.5 203.1 203.4 212.4

140.2 140.1 140.0 136.3

1.430 1.424 1.421 1.356

0.649 0.646 0.645 0.622

38.6 39.0 39.3 44.7

0.07–0.12 0.05–0.10 0.05–0.09 0.06–0.11

rel. 10.036 10.025 20.165

1993 UC

1994 Mar. 31.0 Apr. 2.9 7.1 8.9

164.1 171.1 178.6 181.2

143.9 143.4 142.5 142.1

1.018 1.043 1.080 1.096

0.181 0.208 0.249 0.268

78.8 72.4 65.2 62.6

0.015 0.009–0.010 0.015 0.012

0.000 rel. rel. rel.

1994 AH2

1994 June 15.0 20.0 21.0 July 4.0

264.3 269.3 270.0 276.2

146.8 138.9 137.5 124.4

1.048 1.102 1.112 1.254

0.174 0.192 0.197 0.295

74.5 59.0 56.3 32.2

0.025 0.010–0.015 0.015 0.013

rel. rel. rel. rel.

1994 CB

1994 Aug. 4.0 4.9 5.9

312.7 312.8 312.8

12.5 14.7 16.8

1.078 1.080 1.082

0.0637 0.0663 0.0696

5.1 8.3 12.0

0.04–0.07 0.04–0.07 0.05–0.08

rel. 0.000 rel.

1994 LX

1995 May 3.9 22.9 24.9 26.0

154.3 175.9 178.0 179.1

151.7 151.0 150.6 150.5

1.124 1.230 1.241 1.246

0.864 0.933 0.941 0.945

59.2 53.7 53.2 52.9

0.04–0.08 0.05–0.06 0.05–0.07 0.05–0.09

rel. 20.012 10.008 rel.

Minor planet

probable solution of (1508, 1108).) Magnusson (see Hahn et al. 1989) has obtained pole solutions that differ from those by Velichko and Lupishko by 208 to 408—(3208, 1408) and (1108, 1208)—and the sidereal period of 4.7989 hr. Later, Lupishko and Velichko (1990) reworked their analysis; while their newer poles have not changed significantly, they obtained the new solution for the sidereal period of 4.79888 and 4.80025 hr for the two pole solutions, respectively. The radar observations (Ostro et al. 1990) made during a close approach in July 1985 have revealed an elongated shape with estimated dimensions of the convex hull of Ivar’s pole-on silhouette of approximately 2.0 : 1. The maximum breadth of the pole-on silhouette was estimated Dmax 5 11.5 6 0.8 km, assuming the asteroid-centered declination of the radar of d 5 508. The dimensional constraints from the radar observations seem compatible with the infrared-radiometric diameter, that is within 10% of 9 km (Veeder et al. 1989).

We observed (1627) Ivar on 6 nights from 1995 Feb 24.0 to March 9.0. The asteroid was visible at the solar phase angles within a few degrees of 178 and approaching opposition. The direction of PAB changed by 1.588 in 13 days, that means a synodic period was very close to the sidereal period (see below). The PAB direction differed by P308 from the PAB direction in mid-May 1990 when Chernova et al. observed Ivar at the phase angles of 248 to 328, but it was within 108 of 1808 (i.e., the opposite direction) from one in September–October 1985 when Hahn et al. observed it at similar phase angles of about 218. We have analyzed our observations of (1627) Ivar and found the synodic rotation period Psyn 5 (4.79515 6 0.00014) hr. This result was obtained assuming the linear phase dependence of 0.020 mag/deg, that is close to the values of (0.022 6 0.001) and (0.024 6 0.002) determined by Hahn et al. and Chernova et al., respectively. (An even smaller value would fit our data better, but the differences of a few thousandths of a mag/deg can be due to uncer-

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TABLE II Main Results Minor planet (1627) (4957) (6569) 1993 UC 1994 AH2 1994 CB 1994 LX

Synodic period [hr]

Amplitude

Ha

Remark

6 6 6 6 6 6 6

0.43 0.14–0.38 0.98 0.10 .0.27 $0.90 0.32–0.39

13.17 6 0.04 b (15.0)c 16.2 d 15.0e (16.5) f 21.4 6 0.2 g 15.3 e

Consistent with pole at (3308, 1208) Synodic period variation detected

4.79515 2.8921 5.9588 2.3398 23.949 8.676 2.74064

0.00014 0.0001 0.0003 0.0003 0.004 0.010 0.00014

Most plausible period solution

The values of H 5 HV were derived from the zero-order coefficients (C0 ) of the Fourier fits to the R lightcurves (see Table IV), corrected for measured (V 2 R)s, unless otherwise specified. b The H value for (1627) was derived assuming G 5 0.65 and V 2 R 5 0.48 (from Hahn et al. 1989). The error was computed from errors of calibrations of our lightcurves and the uncertainty of G of 0.04 given by Hahn et al. c From MPC 23852. d The H for (6569) was computed using the value of G 5 20.05 6 0.05 derived from the observation in the range of phase angles from 39.08 to 44.78. (See text for discussion.) e For 1993 UC and 1994 LX, H values were derived assuming G 5 0.15 and V 2 R 5 0.45. f From MPC 26422. g The error accounts for an uncertainty due to the use of assumed value of G 5 0.15 for determination of H for 1994 CB. a

tainties in absolute calibrations.) The determined period is not sensitive to the uncertainty in the linear phase coefficient. The composite lightcurve reduced to the phase angle of 17.08 is shown in Fig. 1, together with the best fit 6th order

Fourier series to the best four lightcurves of 1995 Feb 24.0, Mar 2.1, 7.1, and 8.1. The amplitude of the lightcurve is 0.43, with most of the signal in the second order, as expected for the highly elongated body if not observed pole-on.

FIG. 1. Composite lightcurve of (1627) Ivar. Curve is the best fit 6th order Fourier series.

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TABLE III Comparison of the Lightcurves of (1627) Ivar Obtained at Comparable Solar Phase Angles Aspect for pole Observation interval 1985 1985 1990 1995

Sept. 14–27 Oct. 16 May 11–24 Feb. 24–Mar. 9

Solar phase [deg] 18–24 20 24–32 14–19

LPAB BPAB eq. 2000.0 [deg] [deg] 5 11 216 187

216 215 117 19

The motion of PAB causes a priori uncertainty of the difference between the synodic (Psyn ) and the sidereal (Psid ) periods of rotation. It is given by the formula D P 5 g PAB P 2syn ,

(4)

where DP is the maximum possible difference between the periods (i.e., uPsid 2 Psyn u # DP), and g PAB is the angular velocity of the PAB. In the case of our observations of (1627) Ivar, DP 5 0.00032 hr. This means that the sidereal period is in the range from 4.7944 to 4.7959 hr. (The uncertainty (33 the error) of the synodic period is also accounted

Lightcurve amplitude

(3308, 1208) [deg]

(1508, 1108) [deg]

0.57 0.62 1.12 0.43

49 53 106 134

145 140 64 36

for.) This is in agreement with the preliminary result for the sidereal period determined by Velichko and Lupishko, but it rules out their later result, as well as the result by Magnusson (see above). We can compare our composite lightcurve with those observed in 1985 and 1990. For the comparison we select just those lightcurves that were obtained at solar phase angles less than P308, i.e., in September and October 1985 and May 1990 (see Table III). The other lightcurves were obtained at large phase angles and the lightcurve’s amplitude can increase due to the phase effect, as observed, e.g., in June 1990 (see Chernova et al. 1995).

FIG. 2. Composite lightcurves of (4957) Brucemurray obtained on (a) 1994 Oct 3.1 (rhombs), 12.0 (plus marks) and 13.1 (crosses); (b) 1994 Dec 1.1; (c) 1995 Jan 3.9. Curves are the best fit Fourier series up to the (a) 5th, (b) and (c) 4th orders. Magnitude scale is relative, shifts of the lightcurves are arbitrary.

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The lightcurves from Sept.–Oct. 1985 and Feb.–Mar. 1995, that were taken almost exactly in the opposite directions (of PAB), have similar amplitudes. The smaller amplitude observed in Feb.–Mar. 1995 is consistent with the aspect closer to the pole derived by Velichko and Lupishko (see the 6th column in Table III) and slightly smaller phase angles, than those in Sept.–Oct. 1985. The lightcurve observed in May 1990 has a large amplitude. That is, again, compatible with the nearly equator-on position of the PAB for the Velichko and Lupishko’s pole of (3308, 1208), while it can be due in part also to the moderate phase angles of the observations. A modeling of the phase effect is needed to judge if the 1990 lightcurve is consistent with the pole-on axis-ratio of approximately 2.0 : 1 derived from the radar observations. The solution for the pole of (3308, 1208) and the sidereal period of 4.7952 hr is in agreement with our observations also considering the fact, that the PAB was moving almost exactly in the direction of the pole during 1995 Feb. 24 to Mar. 9. This means that the sidereal period must be within the estimated uncertainties of the observed synodic period of (4.79515 6 0.00014) hr—this is exactly the case of Velichko and Lupishko’s preliminary result of Psid 5 4.7952 hr. (4957) Brucemurray This high-inclination (i 5 358) Amor asteroid was observed on 5 nights from 1994 Oct. 3.1 to 1995 Jan. 3.9. Using the lightcurve data, we have determined the mean synodic rotation period Psyn 5 (2.8921 6 0.0001) hr during the covered interval. Three composite lightcurves constructed using this period are presented in Fig. 2. The lightcurve amplitude has changed significantly during the observational interval—it was 0.38 mag during 1994 Oct. 12.0–13.1 at solar phase angle of 49.0 deg, 0.14 mag on 1994 Dec. 1.1 at 14.1 deg, and 0.17 mag on 1995 Jan. 3.9 at 24.3 deg. The analysis reveals that the only significantly detected changes in the shape of the lightcurve of (4957) are in the 1st and 2nd Fourier orders. The lightcurve’s amplitude is correlated with the solar phase angle, although there may be also present an effect of changing aspect— direction of the asteroid’s PAB has changed by 458 from 1994 Oct. 12.0 to 1995 Jan. 3.9. The lightcurve was asymmetric on each observing night. There are two features present in all the nightly lightcurves: (i) intervals between different lightcurve maxima are different from Psyn /2 by 0.06Psyn , and (ii) there is present a continuously decreasing or constant part of the lightcurve with duration of 0.30Psyn . The two persistent features may be related to a real shape irregularity of the asteroid and also allow the different lightcurve extrema in different nightly lightcurves to be easily resolved. The synodic rotation period varied during the observa-

tional interval. The period analysis of the data of (4957) was started with 3 nightly lightcurves obtained on 1994 Oct. 3.1, 12.0, and 13.1. The resulted synodic period was (2.8920 6 0.0003) hr. Using this result, considering the maximum a priori uncertainty in the synodic period due to the motion of PAB of 0.0006 hr and using the observed asymmetry of lightcurve shape as a check, we have linked all the nightly lightcurves with the mean synodic rotation period of Psyn 5 (2.8921 6 0.0001) hr. Variations in the 2nd order Fourier arguments (A2 ) of individual nightly lightcurves were used for estimation of the period. A formal use of the method based on the best Fourier fit to all the lightcurves yields the mean synodic period of (2.89206 6 0.00005) hr, but a systematic error may be present there due to the changes of the lightcurve’s shape, thus we adopt the greater error. In Fig. 2, it is apparent that the extrema of the individual nightly lightcurves occur at different rotational phases when plotted using the mean synodic period. Analyzing the lightcurves in the intervals 1994 Oct. 3.1–Dec. 1.1 and 1994 Dec. 1.1–1995 Jan. 3.9, we have obtained the synodic periods of (2.89220 6 0.00011) hr and (2.89187 6 0.00011) hr for these two intervals, respectively. Thus, a change of the synodic period is marginally detected. This indicates that there is information in the lightcurves that can be used for a spin vector determination in the future. (6569) 1993 MO This Amor-type object was observed on 4 nights from 1995 Apr. 29.9 to May 28.0. We have determined a synodic rotation period Psyn 5 (5.9588 6 0.0003) hr from the lightcurve data. The composite lightcurve reduced to solar phase of 40.08 is presented in Fig. 3. The amplitude of the lightcurve is 0.98 mag at the solar phase angle of about 408. No significant change of the lightcurve shape was detected during the covered interval. Color indices of (6569) measured on 1995 May 3.0 were V 2 R 5 0.45 6 0.03 and R 2 I 5 0.41 6 0.03. The period search was done for different assumed values of the slope parameter G. The best fit was achieved for G 5 20.05 6 0.05. However, this result must be considered of limited significance, since it is based on a narrow interval of solar phases from 39.08 to 44.78 covered from 1995 May 1.9 to 28.0. Assuming that the value G 5 20.05 is valid for the whole interval of solar phases from 08 to 458, we obtain the mean absolute V magnitude of H 5 16.2. But, if the phase dependence of the mean V magnitude for this asteroid cannot be described by the H 2 G relation (Bowell et al. 1989) with G 5 20.05 down to the zero solar phase angle, the error of the above determined value for H can be as large as 1 magnitude. The Fourier analysis of the lightcurve data has revealed

LIGHTCURVES OF 7 NEAR-EARTH ASTEROIDS

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FIG. 3. Composite lightcurve of (6569) 1993 MO. Curve is the best fit 4th order Fourier series.

two additional periods, which could explain the observed lightcurves. They are 5.9295 hr and 6.7276 hr. However, they require the presence of large variations of the lightcurve shape and the least-squares fit of the Fourier series with those periods leave too large residuals. Thus, we believe that the period of 5.9588 hr is the real synodic rotation period of the asteroid and the other two are artifacts due to poor lightcurve quality and coverage. 1993 UC This Apollo asteroid made an aproach to 0.13 AU to the Earth on 1994 Mar. 20, five months after discovery. It was the closest approach of this object for several tens of years. We observed it on 4 nights from 1994 Mar. 31.0 to Apr. 8.9. From the data, we have determined a synodic rotation period of Psyn 5 (2.3398 6 0.0003) hr. This is the second shortest rotation period detected among asteroids up to now—only (1566) Icarus, an Apollo-type object, has a shorter period of 2.273 hr. A composite lightcurve of 1993 UC reduced to the phase angle of 78.88 is shown in Fig. 4. It has an amplitude of 0.10 mag. No change of the lightcurve shape was detected during the covered interval, while the direction of PAB changed by 138 and solar phase angle decreased from 78.88 to 62.68.

1994 AH2 Similar to 1993 UC, this Apollo-type object made a close approach to 0.17 AU to the Earth on 1994 June 11, five months after discovery. The Tisserand invariant of its orbit is 3.03, i.e., close to the limit dividing asteroidal and cometary orbits (Weissman et al. 1989). Thus, 1994 AH2 is of particular interest, since it may be a member of the population of inactive cometary nuclei among near-Earth asteroids. (The existence of a sizeable population of asteroidal objects in comet-like orbits among near-Earth asteroids is indicated by an analysis of the orbital distribution of NEAs (P. Pravec, in preparation).) We observed this asteroid on 4 nights from 1994 June 15.0 to July 4.0. A reduction of the observations revealed an increasing branch and a maximum of the lightcurve with similar shape detected on each night. Assuming a regular double-extrema character of the lightcurve, a plausible solution for the synodic rotation period is Psyn 5 (23.949 6 0.004) hr. (See Fig. 5 for a fractional composite lightcurve constructed using this period.) A period of half a day is not compatible with the slow variation of brightness in the observed part of the lightcurve, unless the lightcurve has just one maximum. A period of 2 days is not formally excluded, but it suggets a lightcurve with a large amplitude and the same shape for the two lightcurve maxima, that

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FIG. 4. Composite lightcurve of 1993 UC. Curve is the best fit 6th order Fourier series.

FIG. 5. Composite lightcurve of 1994 AH2 . Less than 20% of the full rotation cycle is covered.

LIGHTCURVES OF 7 NEAR-EARTH ASTEROIDS

are half-cycle apart. The period close to 1 day seems to be the most plausible solution. 1994 AH2 will be observable again in June 1998 in conditions similar to those in 1994. Then coordinated observations from a few stations spread in longitude can confirm the obtained period that is close to 24 hr. The lightcurve amplitude is expected to be similar to that observed in June 1994, which was greater than 0.27 magnitude (at the phase angle of P588). However, it is possible that the small slowly rotating asteroid (est. diameter 2 km) is in an excited rotation state. (See Harris 1994 and the discussion for 1994 CB below.) The observations during the next apparition should be carefully made to detect any deviation from the principal-axis rotation. 1994 CB This asteroid revolves in a low-eccentricity (0.145) orbit with semi-major axis of 1.15 AU, just slightly larger than the Earth’s orbit. (Rabinowitz et al. (1993) propose the existence of a belt of small, Earth-approaching asteroids in similar orbits.) It has an effective diameter of 0.24 km (assuming the geometric albedo of 0.08), thus being one of the smallest asteroids with lightcurve observations available up to now. 1994 CB made a close approach of 0.06 AU from the Earth on 1994 July 30, six months after discovery. It was the closest approach of this object for many tens of years. We observed it on three consecutive nights of 1994 Aug. 4.0, 4.9, and 5.9. An analysis has revealed a synodic rotation period of Psyn 5 (8.676 6 0.010) hr. The amplitude of the composite lightcurve, shown in Fig. 6 (reduced to the solar phase of 8.78), is 0.90 magnitude (or greater, as a part of the lightcurve was not covered) at the phase angle of 5.18, indicating an elongated shape with an equatorial axis-ratio greater than 2 : 1. V 2 R of 0.44 6 0.04 was measured on 1994 Aug. 4.9. Using the calibrated observations made on that night and assuming G 5 0.15, the absolute V magnitude of the asteroid is H 5 21.0 and 21.9, for the maximum and minimum of brightness, respectively. Errors of these estimates of absolute magnitudes depend on the assumption of a G value, but are probably #0.2 magnitude. Formally, two other periods of 7.20 hr and 10.80 hr can also explain the observed lightcurves. But, composite lightcurves constructed with these periods are very unusual—there are large asymmetries between widths of different brightness maxima, that in combination with the large amplitude observed at the small phase angle would mean an unusual shape of the body. Moreover, the two periods are equal to 0.3 and 0.45 days; i.e., they are commensurable with the Earth’s rotation period and seem to be an artifact of observations made around local midnight during the short summer nights. The period of (8.676 6 0.010) hr gives the best match of the data and provides a

479

fairly symmetric composite lightcurve. We believe that this is the true synodic rotation period of the asteroid. The rotation of 1994 CB is slow enough to be in an excited rotation state. According to the formula for estimation of the damping time scale of the excited rotation by Harris (1994), the P0.2-km asteroid with the period of 8.68 hr is expected to be damped down to the principalaxis rotation on the time scale on order of 1 billion years, much longer than its collisional survival time. Our observations show no evidence for complex rotation, however; more extensive observations could detect changes in the lightcurve due to precessional motion. 1994 LX This high-inclination (i 5 378) Apollo asteroid was observed on 4 nights from 1995 May 3.9 to 26.0. We found a synodic rotation period of Psyn 5 (2.74064 6 0.00014) hr. A composite lightcurve reduced to the solar phase angle of 53.58 is shown in Fig. 7. The amplitude was about 0.32 at the phase angle of 538. The best fit 4th order Fourier series to the nightly lightcurves of 1995 May 22.9, 24.9, and 26.0 is shown in Fig. 7. The shape of the lightcurve of 1995 May 3.9 is different from that of 1995 May 22.9–26.0. The significant change is in the amplitude of the first Fourier order, which was greater by (0.09 6 0.02) at May 3.9 than those of May 22.9–26.0. (Here we mention the difference in the peakto-peak amplitude, i.e., twice the A1 values from Table IV.) This can be partly due to the greater solar phase of 598 at 1995 May 3.9, but also an effect of changing aspect may be present, since the PAB direction has changed by 158 during the observing interval. A period of 2.5930 hr can also explain the observed brightness variations. But this leaves significantly larger scatter in the composite lightcurve, than that with the period of 2.74064 hr, requiring some night-to-night variations in lightcurve shape. So we believe that the synodic rotation period mentioned above is the true one, and the other is an artifact of the low-accuracy observations in short latespring nights. 4. CONCLUSIONS AND SUMMARY OF RESULTS

The observations of 7 near-Earth asteroids in 1994 and 1995 have revealed synodic rotation periods for 6 of them for the first time, and provided important constraints for the spin vector solution of (1627) Ivar. The detected periods are between 2.34 and 24 hr, i.e., in the range observed for other near-Earth objects. No observations of longerperiod rotators are presented here, since they are being prepared for publication in another paper. In the case of (1627) Ivar, our observations are in agreement with the pole solution of (Lp , Bp ) 5 (3308, 1208) by Velichko and Lupishko (see Hahn et al.

480

´ , AND WOLF PRAVEC, SˇAROUNOVA

FIG. 6. Composite lightcurve of 1994 CB.

FIG. 7. Composite lightcurve of 1994 LX. Curve is the best fit 4th order Fourier series to the lightcurves of 1995 May 22.9, 24.9, and 26.0.

481

LIGHTCURVES OF 7 NEAR-EARTH ASTEROIDS

TABLE IV Fourier Coefficients of the Best Fit Fourier Series to the Lightcurves of (1627) Ivar, (4957) Brucemurray, (6569) 1993 MO, 1993 UC, and 1994 LX Minor planet (1627)

(4957)

Interval

Epoch JD

Period [hr]

S.E.

n

Cn

Sn

An

fn

1995 Feb. 24.0–Mar. 8.1

2449780.5

4.79515

0.0011

0 1 2 3 4 5 6

13.1291 0.0040 20.1253 0.0072 20.0063 0.0014 20.0001

20.0252 20.1611 0.0143 0.0200 20.0065 0.0029

0.0256 0.2041 0.0160 0.0210 0.0067 0.0029

279.0 232.1 63.3 107.5 282.0 92.1

0 1 2 3 4 5 0 1 2 3 4 0 1 2 3 4

1.8435 20.0764 20.0011 0.0089 20.0092 0.0068 2.2231 0.0016 20.0170 20.0132 0.0052 2.5203 20.0287 0.0042 20.0076 20.0105

0.0157 0.1219 0.0055 20.0214 0.0138

0.0780 0.1219 0.0105 0.0233 0.0154

168.4 90.5 31.9 246.7 63.7

20.0131 0.0529 0.0061 20.0116

0.0132 0.0556 0.0142 0.0127

276.9 107.8 155.2 294.0

0.0247 0.0529 0.0221 20.0134

0.0378 0.0531 0.0234 0.0170

139.2 85.5 109.1 231.7

0 1 2 3 4

17.8227 0.0243 20.1700 0.0321 20.0916

20.0330 0.3695 20.0281 20.0371

0.0410 0.4067 0.0426 0.0989

306.4 114.7 318.8 202.0

0 1 2 3 4 5 6

17.3298 0.0030 0.0136 20.0076 0.0037 20.0005 0.0027

0.0159 20.0294 0.0059 0.0040 20.0010 0.0025

0.0162 0.0324 0.0097 0.0054 0.0011 0.0037

79.2 294.8 142.3 46.7 243.1 42.4

0 1 2 3 4 0 1 2 3 4

16.7703 0.0467 20.1132 0.0434 20.0111 16.7741 0.0162 20.1203 0.0245 20.0219

0.0439 20.0163 0.0154 0.0253

0.0641 0.1144 0.0461 0.00276

43.2 188.2 19.5 113.6

20.0061 20.0347 20.0059 0.0072

0.0173 0.1252 0.0252 0.0231

339.3 196.1 346.6 161.9

1994 Oct. 12.0–13.1

1994 Dec. 1.1

1995 Jan. 3.9

(6569)

1993 UC

1994 LX

1995 May 1.9–28.0

1994 Mar. 31.0–Apr. 8.9

1995 May 3.9

1995 May 22.9–26.0

2449680.5

2449680.5

2449680.5

2449840.3

2449447.5

2449860.5

2449860.5

2.89210

2.89210

2.89210

5.95884

2.33976

2.74064

2.74064

1989), confirming their sidereal period determination of 4.7952 hr. In any case, our observations constrain the sidereal period between 4.7944 and 4.7959 hr. The observations of (4957) Brucemurray have revealed significant changes of lightcurve shape and marginally detected a variation of synodic period. This can be used for a spin vector and

0.0035

0.0023

0.0044

0.0095

0.0012

0.0067

0.0066

shape determination in future. The lightcurve of (6569) 1993 MO indicates that it is an elongated object, with the equatorial axis-ratio very approximately 2 : 1. Observations on different aspects and smaller solar phases are needed to put better constraints on its shape. 1993 UC is the second fastest rotator known among asteroids—we have detected

´ , AND WOLF PRAVEC, SˇAROUNOVA

482

the period of 2.3398 hr. That makes this object of particular interest due to its placement on the tail of the rotational frequency distribution. (See, e.g., Binzel et al. 1989, McFadden et al. 1989.) 1994 AH2 is a relatively slow rotator with the most plausible period of 23.95 hr. This finding, together with the fact that its orbit is on the margin between asteroidal and cometary ones, makes the object an important target for observations during its next apparition in June 1998. For 1994 CB, one of the smallest asteroids (est. diameter 0.2 km) observed photometrically up to now, we have obtained a period of 8.68 hr and found it to be an elongated body with an equatorial axis-ratio .2 : 1. For 1994 LX, the synodic rotation period of 2.7406 hr was found. The observational data will be included in the Asteroid Photometric Catalogue Data Base (Magnusson et al. 1994), which is available by anonymous ftp at address ftp.astro.uu.se and on the World Wide Web at http://www.astro.uu.se/planet/apc.html. ACKNOWLEDGMENTS This work has been supported by the Grant Agency of the Czech Republic, Grant No. 205-95-1498, and by the ESO C&EE Programme, Grant No. A-02-069. We gratefully acknowledge the assistance of Michal Varady, Petr Ba´rta, and Toma´sˇ Hudecˇek during some of our CCD observations.

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