Lightcurves of 26 Near-Earth Asteroids

ICARUS

136, 124–153 (1998) IS985993

ARTICLE NO.

Lightcurves of 26 Near-Earth Asteroids Petr Pravec Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic E-mail: [email protected]

Marek Wolf Astronomical Institute, Charles University Prague, V Holesˇovicˇka´ch 2, CZ-18000 Praha, Czech Republic

and Lenka Sˇarounova´ Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic Received December 17, 1997; revised June 2, 1998

We present the results of our photometric observations of 26 near-Earth asteroids (NEAs) in the range of absolute magnitudes H 5 13.6–20.0 (diameters approximately 0.4–8 km). The synodic periods in the range 2.3–230 h were detected for 25 of them; 21 periods are new and in 4 cases we confirmed earlier determinations. In 20 cases the synodic periods are interpreted as being the rotation periods. Among the 5 exceptions, in two cases there remains an uncertainty whether the detected period is not half or twice that of the rotation period, and in another two cases—(3691) 1982 FT and 1997 BR—there were found large deviations of the lightcurve points from the mean curves that can be due to possible complex rotations of the small, slowly rotating asteroids. Overall, the short period end (2.3–3.3 h) of the spin rate distribution shows characteristics that are consistent with the hypothesis of their ‘‘rubble pile’’ structure, as noted by Harris (Lunar Planet. Sci. XXVII, 493–494); specifically, there is a ‘‘barrier’’ against spins faster than 2.3 h and the amplitudes of the fast rotating NEAs are smaller in comparison with the other, longer period NEAs. In the group of slow rotators (P . 12 h), the suggested presence of objects in excited rotation states must be confirmed by further observations using also different techniques. This slow rotators group may be actually more abundant than our results suggest (6 of 25 objects, i.e., 20–30%), since there is a bias against lowamplitude slow rotators in the groundbased photometric program.  1998 Academic Press Key Words: minor planets; near-Earth objects; rotations; lightcurves.

1. INTRODUCTION

From 1994 we have worked on the photometric project devoted to studies of near-Earth asteroids (NEAs) on the 124 0019-1035/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

Ondrˇejov Observatory. The primary aim of the project is to enlarge the sample of rotation periods of NEAs, to provide baseline data for their further physical studies, and to identify objects with unusual characteristics among them. In 1995–1997 several papers containing results from the project have appeared (e.g., Pravec et al. 1995, 1996, 1997a,b). These papers also describe the reasons for the NEA study and methods used in the research. The most interesting finding within the project was the identification of the possible binary nature of three NEAs—1991 VH, 1994 AW1, and (3671) Dionysus—for the last two objects in collaboration with G. Hahn and S. Mottola from DLR, Institute of Planetary Exploration, Berlin (see Pravec and Hahn 1997, Pravec et al. 1998, Mottola et al. 1997). The main bulk of the observations within the project, however, can be described just as routine work on a number of relatively normal NEAs; this paper contains results for 26 NEAs of this kind. Although most of them appear to show normal characteristics, several unusual objects were identified among them; some of them are slow rotators (rotation periods .1 day), several others are very fast rotators (periods ,3 h), and some show unusual lightcurves that may indicate peculiar shapes or rotations of those NEAs. 2. OBSERVATIONS

The CCD photometric observations of the near-Earth asteroids were made using the 0.65-m telescope of the Ondrˇejov Observatory during January 1995–November 1997. Lightcurve observations of selected NEAs were done in the Cousins R band on every observing night, with an exception for 1997 GL3 for which no filter was used. Proper observational strategy was established to optimize the use

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

of available telescope time for unambiguous determination of new periods for as many NEAs as possible but minimizing an observational bias against slow and low amplitude rotators. Once an object’s period was determined, the object’s observing priority was lowered, often resulting in skipping it from further observations and concentrating on other objects. On the other hand, for some (slowly rotating, low amplitude, or unusual lightcurve) objects, the strategy resulted in taking observations on a large number of nights until their periods were determined unambiguously. On the best nights the observations were calibrated using standard stars from Landolt (1992) and, when time constraints allowed, additional measurements in the Johnson V and Cousins I bands were made to derive color indices. The R magnitudes are calibrated with an accuracy of 0.01–0.02 mag. The observational and reduction techniques were described in Pravec et al. (1996). The observational circumstances and the mean reduced magnitudes for each but one object, each night of observation are listed in Table I. For (3691) 1982 FT, the data are listed separately in Table II due to a necessity to present its observations in a different form because of its very long period. The data in Table I are given to the nearest 10th of a day to the midtime of the observational interval. The asteroid’s geocentric right ascension and declination, ecliptic coordinates of the phase angle bisector (PAB; for its definition see, e.g., Magnusson et al. (1989), Pravec et al. (1997a)), all for the equinox J2000, the heliocentric (r) and geocentric (D) distances, the solar phase angle (a), the median of errors of points in the individual nightly lightcurve, and the mean reduced R magnitude (R(1, a), defined as the zeroth order of the Fourier fit to the lightcurve reduced to the unit geocentric and heliocentric distances and to the given phase angle; see below) are given. For uncalibrated lightcurves, values for R are not available, of course, but the same situation occurs also for the calibrated observations of the slow rotators, for which no meaningful value for R on any individual night can be given due to the impossibility to define the best Fourier fit for a fragmentary lightcurve that evolves relatively fast (on timescale not much greater than the long period). For (5143) Heracles no period was determined and we give the means of nightly measurements in brackets. 3. ANALYSIS OF THE LIGHTCURVES

The task of the lightcurve analysis was to derive the synodic rotation periods of the asteroids, to put constraints on their shapes, and to estimate their absolute magnitudes. The obtained lightcurves were corrected for light-travel times and the magnitudes were reduced to the unit geocentric and heliocentric distances. The analysis of the lightcurves follows Harris et al. (1989) in general. The principal point of the method is the fitting of a Fourier series

125

to the object’s lightcurves, which defines the lightcurve shape and the synodic period. See Pravec et al. (1996) for a description of the formalism used and details of the method. The Fourier method works with periodic data; thus we must use a special approach in a case of not fully periodic lightcurve. Generally, each observed object fell into one of the three different categories according to the character of its lightcurve; each of the categories required a different approach and application of the method. The easiest situation occurred for cases in which both the lightcurve shape and the synodic period did not change significantly during the whole observational interval (as occurred, e.g., for (3122) Florence); in these cases, the Fourier series of the highest significant order was fitted to the observational data and it gave the solution for the synodic period and supplied also its mean error. The application of the method is less straightforward in cases when the lightcurve changed during the observational interval but can be considered unchanging on shorter time intervals; in these cases, the separate composite lightcurve was constructed for each of the shorter intervals. If the separate composite lightcurves differ not too much (generally just in amplitude, like in the case of (4957) Brucemurray), a formal fit of the lower order Fourier series was done to all data and it supplied the period and its formal error. Although some systematic error may be present in these cases, we believe that it is not greater than the formal error. In the case of (2063) Bacchus, this approach was combined with another one as described in the subsection on it below. The third and most difficult situation occurred for cases in that the lighcturve shape changed on a timescale comparable to the period; in these cases (generally with period .1 day) the best fit of the Fourier series of the highest significant order was made to the composite lightcurve and it supplied the solution for the synodic period and also its formal error, but the systematic error can be relatively large and also the lightcurve shape is not well represented with the Fourier fit. In Table III and Section 4, the derived synodic periods are given together with their formal errors and also the amplitudes (A2 , or rather 2A2 that is the ‘‘peak-to-valley’’ amplitude) of the second harmonics of the best Fourier fits to the lightcurves are presented, but the reader has to remember that in several cases (commented in the text) the errors of the periods can be underestimated and the amplitudes are only approximate. In the table, also the ‘‘manually’’ measured amplitudes of the observed lightcurve extrema are given; they, although of a problematic significance in some cases (they can be very influenced by an asteroid’s local topography), allow a comparison with data given by other researchers. When a calibrated lightcurve was obtained an attempt to derive the asteroid’s mean absolute magnitude was made. The mean absolute R magnitude always corresponds

´ PRAVEC, WOLF, AND SˇAROUNOVA

126

TABLE I Geometric Circumstances and Mean Reduced Magnitudes RA Minor planet

Decl.

Date UT

h

m

8

9

LPAB (deg)

BPAB (deg)

r (AU)

D (AU)

a (deg)

Errors (mag)

R(1, a) (mag)

1997 July 28.9 Aug. 5.0 6.0 28.0

22 21 21 21

09 58 57 24

18 18 17 13

12 02 57 25

327.5 328.5 328.7 330.6

18.3 18.6 18.6 17.9

1.341 1.367 1.371 1.453

0.409 0.416 0.418 0.481

31.6 27.1 26.4 19.0

0.014 0.02 0.012 0.017

16.28

1996 Mar. 26.1 28.0 Apr. 1.0 7.0 7.9 15.9 16.9 17.9

19 17 15 13 13 12 12 12

21 59 10 20 11 31 29 26

64 65 58 35 31 12 10 9

42 54 07 03 57 29 52 23

187.4 188.4 189.2 190.3 190.5 193.1 193.5 193.9

51.5 47.0 36.4 21.3 19.5 8.2 7.3 6.4

0.989 1.001 1.025 1.061 1.067 1.113 1.118 1.124

0.076 0.072 0.068 0.079 0.082 0.122 0.128 0.134

94.5 85.8 65.8 39.2 36.1 25.0 24.9 24.9

0.019 0.014 0.010 0.007 0.008 0.006 0.007 0.008

20.34 19.96 19.12 18.28 18.13 17.88 17.87 17.87

1997 Aug. 31.0 Sept. 2.0 3.0 4.0 6.1 9.0 12.0

1 1 1 1 1 1 1

41 38 37 36 32 27 19

14 13 12 11 9 6 2

53 20 30 36 34 22 33

8.2 8.2 8.2 8.1 7.9 7.5 6.7

2.7 1.9 1.4 1.0 0.0 21.6 23.2

1.195 1.195 1.194 1.194 1.193 1.191 1.187

0.267 0.256 0.250 0.244 0.233 0.218 0.205

41.2 39.0 37.8 36.6 33.9 29.9 25.4

0.015 0.010 0.02 0.015 0.02 0.015 0.013

17.43 17.36 17.30 17.27 17.19 17.03 16.88

1996 July 15.0 17.0 20.0 22.0 27.0 1997 Mar. 8.0

22 22 22 22 23 9

15 24 40 52 32 22

8 7 5 3 22 36

40 31 19 28 59 07

319.3 321.0 323.7 325.7 331.1 142.5

11.5 10.2 7.9 6.0 0.0 14.4

1.183 1.173 1.156 1.145 1.119 1.600

0.234 0.217 0.194 0.179 0.147 0.709

40.3 40.2 40.3 40.5 42.5 23.7

0.012 0.012 0.014 0.008 0.010 0.02

16.43 16.41 16.43 16.44

1996 Oct. 3.1 4.1 Nov. 23.1 Dec. 22.0 1997 Jan. 27.1 Feb. 2.0

8 8 10 10 9 9

56 59 36 41 38 23

40 40 34 34 35 34

37 29 42 28 08 39

99.2 99.9 126.1 132.9 132.9 132.5

24.3 24.3 21.9 19.6 14.8 13.8

1.266 1.271 1.569 1.736 1.925 1.954

1.249 1.249 1.158 1.028 0.974 0.994

46.9 46.7 38.9 29.6 10.7 9.2

0.04 0.035 0.04 0.025 0.03 0.02

1995 Jan. 4.8 1997 Nov. 1.1 2.1

0 8 8

47 28 32

11 27 26

33 04 48

47.5 98.5 99.1

5.0 6.8 6.7

1.094 1.321 1.308

0.458 0.777 0.755

63.9 48.4 49.0

0.025 0.03 0.035

1995 Aug. 3.0 4.0 5.0 6.0 7.0 16.9 17.9 18.9 20.0 23.0 23.9 25.9 28.8 29.9

21 21 21 21 21 20 20 20 20 20 20 20 20 20

23 20 18 16 14 52 49 47 45 38 36 32 26 23

17 17 16 15 15 6 5 5 3 1 0 21 24 25

52 13 34 52 09 59 59 02 59 02 08 53 47 53

323.5 323.2 323.0 322.7 322.4 319.4 319.1 318.8 318.5 317.5 317.2 316.7 315.8 315.5

22.9 22.5 22.1 21.7 21.3 16.7 16.2 15.6 15.1 13.4 12.9 11.8 10.1 9.5

1.737 1.734 1.732 1.729 1.727 1.701 1.699 1.696 1.693 1.685 1.682 1.676 1.668 1.664

0.812 0.804 0.796 0.788 0.781 0.727 0.723 0.721 0.718 0.714 0.713 0.714 0.717 0.719

20.3 19.7 19.2 18.6 18.1 14.2 14.1 14.1 14.2 14.9 15.3 16.2 18.0 18.7

0.03 0.05 0.03 0.03 0.04 0.03 0.04 0.07 0.03 0.06 0.03 0.05 0.02 0.03

(1943) Anteros

(2063) Bacchus

(2100) Ra-Shalom

(3103) Eger

a

(3122) Florence

15.16

(3200) Phaethon

(3752) Camillo a a a a a a a a a a a a a a

127

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

TABLE I—Continued RA Minor planet

Decl. 9

LPAB (deg)

BPAB (deg)

r (AU)

D (AU)

a (deg)

Errors (mag)

9 9 8 8 8 7 6 5 4 4

28 11 54 36 18 04 44 26 46 25

250.6 250.4 250.2 250.0 249.8 248.9 248.7 247.9 247.5 247.3

22.4 22.1 21.8 21.6 21.3 20.1 19.9 18.7 18.2 17.9

1.268 1.279 1.290 1.301 1.312 1.356 1.367 1.409 1.430 1.441

0.396 0.399 0.403 0.407 0.411 0.429 0.435 0.457 0.470 0.477

41.7 40.2 38.8 37.4 35.9 30.5 29.2 24.5 22.3 21.3

0.03 0.025 0.03 0.025 0.02 0.02 0.025 0.04 0.04 0.04

35 58

27 29

44 15

90.8 92.1

4.8 223.0

1.422 1.586

0.716 0.671

40.3 20.1

0.02 0.03

16.27

22 22 22 22

18 16 14 12

25 25 25 26

41 49 57 05

330.5 330.3 330.1 330.0

3.6 3.6 3.6 3.7

2.227 2.235 2.243 2.250

1.239 1.243 1.247 1.252

7.8 7.2 6.6 5.9

0.03 0.03 0.03 0.035

[14.17] [14.15] [14.13] [14.11]

1997 Mar. 5.9 9.9 10.8 Apr. 7.9 8.9

9 9 9 9 9

31 27 26 09 09

24 23 23 2 3

19 27 14 59 11

150.5 150.3 150.3 150.5 150.6

214.5 214.2 214.1 211.1 210.9

2.408 2.383 2.377 2.199 2.193

1.476 1.468 1.467 1.523 1.527

10.3 11.9 12.3 23.3 23.6

0.04 0.07 0.05 0.06 0.05

1996 Feb. 25.0 26.1 27.0 Mar. 16.0

11 11 11 12

52 55 56 13

24 26 27 37

58 19 18 01

162.2 162.6 163.0 170.6

12.2 13.0 13.6 20.4

1.095 1.099 1.102 1.173

0.115 0.119 0.123 0.211

22.5 23.0 23.5 29.9

0.02 0.015 0.02 0.025

18.82 18.80 18.82 19.02

1996 Oct. 14.9 16.0 Nov. 4.9 22.8 Dec. 3.7 4.8

0 0 23 22 22 22

12 10 21 47 31 29

22 22 21 17 15 15

48 47 08 59 48 34

15.9 16.0 17.8 21.8 25.6 26.0

12.5 12.7 14.9 16.4 17.3 17.4

1.358 1.349 1.203 1.081 1.016 1.010

0.380 0.374 0.286 0.230 0.195 0.191

15.8 16.6 37.4 60.4 75.4 77.0

0.025 0.025 0.016 0.03 0.02 0.025

17.42 17.37 17.92 18.59 19.24 19.26

1996 Dec. 28.9 1997 Jan. 13.9 15.9 16.9

5 5 5 5

18 19 20 20

3 12 13 13

09 20 15 42

86.2 91.9 92.7 93.1

212.5 27.2 26.7 26.4

1.283 1.354 1.363 1.368

0.326 0.427 0.442 0.450

20.3 24.9 25.7 26.0

0.015 0.018 0.016 0.027

a

1997 Jan. 26.8 Feb. 1.2 1.8 2.8

0 22 22 22

00 36 29 19

39 49 50 51

44 56 27 11

78.2 90.8 92.2 94.7

29.9 46.1 47.3 49.1

0.965 0.948 0.946 0.943

0.091 0.138 0.144 0.154

99.8 101.8 101.7 101.6

0.035 0.03 0.025 0.025

1996 Aug. 7.0 9.0 10.0 19.0 22.0 23.0 24.0 1997 Mar. 5.1 9.1 10.1

23 23 23 0 1 1 1 12 12 12

16 25 29 34 09 23 39 40 35 33

59 58 58 52 45 42 37 35 42 44

22 58 42 11 39 14 50 01 46 26

344.6 346.3 347.1 356.5 0.8 2.5 4.2 169.2 167.7 167.4

37.6 36.5 35.9 27.5 21.8 19.2 15.9 21.3 25.2 26.0

1.086 1.080 1.078 1.054 1.046 1.043 1.041 1.196 1.205 1.208

0.251 0.229 0.218 0.123 0.093 0.084 0.075 0.244 0.268 0.274

66.9 67.2 67.3 67.0 65.9 65.4 64.8 29.6 33.3 34.3

0.035 0.04 0.04 0.03 0.02 0.025 0.02 0.025 0.015 0.025

Date UT

h

m

1997 May 2.0 3.0 4.0 5.0 6.0 10.0 11.0 15.0 17.0 18.0

18 17 17 17 17 17 17 17 17 17

04 59 55 51 47 31 27 11 04 01

1996 Nov. 5.1 Dec. 29.0

7 5

1997 Aug. 10.0 11.0 12.0 13.0

8

R(1, a) (mag)

(4341) Poseidon

(4957) Brucemurray

(5143) Heracles

(5587) 1990 SB

(7025) 1993 QA

(7341) 1991 VK

(7480) 1994 PC a a a

(7482) 1994 PC1

(7822) 1991 CS

19.13

TABLE I—Continued RA Minor planet

Decl. LPAB (deg)

BPAB (deg)

r (AU)

D (AU)

a (deg)

Errors (mag)

R(1, a) (mag)

17 53 41

22.4 22.7 22.9

3.2 3.1 3.0

1.338 1.349 1.355

0.376 0.381 0.383

22.7 20.7 19.6

0.05 0.06 0.07

18.58

9 8 8

09 38 09

27.0 26.7 26.5

22.0 22.1 22.2

1.153 1.152 1.152

0.160 0.158 0.157

12.5 10.7 9.1

0.035 0.035 0.035

36 25 22 33

20 20 20 22

01 33 40 50

172.7 172.0 171.8 160.9

21.7 22.9 23.2 211.2

1.846 1.854 1.856 1.887

0.857 0.861 0.863 0.969

4.0 2.2 2.4 16.8

0.035 0.03 0.05 0.07

12 12 12 15

14 26 39 44

57 57 57 41

48 42 29 46

120.0 120.9 122.1 147.2

32.9 33.4 34.1 43.5

1.082 1.077 1.070 0.978

0.220 0.215 0.210 0.162

58.0 59.1 60.4 87.0

0.04 0.04 0.04 0.07

19.04 19.07 19.09 20.07

1995 Apr. 3.0 4.0

12 12

22 39

20 26

31 43

184.5 185.7

11.2 15.1

1.058 1.055

0.065 0.065

24.8 30.4

0.06 0.06

20.87

1997 Feb. 1.2 2.0 3.0 3.9 7.0 8.0 10.0 10.7 11.8 17.0 17.9 25.0 26.8 28.9 Mar. 1.9 2.8 3.8 5.1 5.9 7.8

10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 8

07 07 06 05 01 00 57 56 54 44 42 26 22 16 14 12 09 06 04 59

31 32 33 34 36 37 39 40 41 45 46 52 53 54 55 55 56 57 57 58

42 23 14 01 45 39 26 04 03 38 24 02 19 44 23 56 32 17 44 43

138.8 138.8 138.8 138.8 138.8 138.8 138.7 138.7 138.7 138.6 138.6 138.8 138.9 139.0 139.1 139.2 139.4 139.5 139.6 140.0

12.2 12.6 13.0 13.4 14.8 15.2 16.1 16.5 16.9 19.2 19.6 22.6 23.3 24.1 24.5 24.9 25.3 25.7 26.0 26.7

1.386 1.383 1.378 1.375 1.361 1.356 1.347 1.344 1.339 1.315 1.311 1.278 1.270 1.260 1.255 1.251 1.246 1.240 1.236 1.227

0.421 0.417 0.413 0.409 0.397 0.394 0.388 0.386 0.383 0.374 0.373 0.369 0.370 0.371 0.371 0.372 0.373 0.374 0.374 0.376

14.9 14.9 15.1 15.3 16.5 17.0 18.4 19.0 19.8 24.7 25.6 33.2 35.2 37.4 38.4 39.3 40.3 41.6 42.4 44.3

0.05 0.035 0.025 0.03 0.02 0.035 0.03 0.03 0.04 0.035 0.04 0.06 0.03 0.04 0.03 0.05 0.025 0.03 0.03 0.025

1997 May 1.9 2.9 3.9 4.9

10 10 10 10

36 42 47 53

12 11 11 11

25 59 33 07

181.2 182.3 183.5 184.6

2.4 2.5 2.6 2.6

1.194 1.199 1.205 1.210

0.347 0.352 0.357 0.362

50.2 49.7 49.2 48.6

0.07 0.08 0.11 0.08

1997 Apr. 10.1 12.0 13.1

14 13 13

05 49 42

25 24 23

59 06 19

206.2 204.7 204.2

3.4 3.7 3.8

1.094 1.121 1.136

0.094 0.119 0.134

11.4 7.3 6.2

0.015 0.015 0.015

1997 Oct. 21.8 22.8 27.8 28.8 30.8 31.8 Nov. 1.8 3.8

21 21 22 22 22 22 22 22

43 47 07 10 18 22 25 33

26 25 24 24 23 23 22 22

17 59 27 08 32 13 55 19

347.7 348.7 353.3 354.2 356.1 356.9 357.8 359.6

5.2 5.1 5.0 5.0 4.9 4.9 4.8 4.8

1.286 1.289 1.308 1.312 1.320 1.325 1.329 1.338

0.477 0.482 0.508 0.514 0.526 0.532 0.538 0.552

43.5 43.3 42.4 42.2 41.9 41.7 41.5 41.2

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Date UT

h

m

8

9

1997 Sept. 26.0 28.0 29.0

1 1 1

59 56 55

17 16 16

1996 Oct. 12.0 13.0 13.9

2 2 2

08 04 00

1997 Mar. 8.0 12.0 13.0 Apr. 1.9

11 11 11 10

1995 Dec. 28.1 29.0 30.1 1996 Jan. 14.2

(8034) 1992 LR

1989 UQ

1992 CC1

19.74

1992 QN

1995 FX

1997 BR a a a a a a a a a a a a a a a a a a a a

1997 GH3

1997 GL3

1997 SE5

15.93 15.92 15.89 15.88 15.87 15.86 15.85 15.86

a The observations were calibrated but no mean reduced magnitude is given due to the fractional lightcurve coverage on each night, necessitating a combination of data from all nights for the construction of the composite lightcurve (see text).

128

129

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

TABLE II Geometric Circumstances and Mean Reduced Magnitudes for (3691) 1982 FT RA

Decl.

Cycle

Date UT

h

m

8

9

LPAB (deg)

BPAB (deg)

r (AU)

D (AU)

a (deg)

R(1, a) (mag)

1

1995 Dec. 28.823 29.852 30.005 30.069 30.173 1996 Jan. 14.721 14.867 15.063 15.838 15.931 16.046 16.715 16.851 21.723 21.949 22.110 1996 Jan. 24.914 25.005 29.919 30.011 30.064 30.198 30.771 31.057 31.210 31.956 Feb. 2.194 1996 Feb. 8.790 9.742 1996 Feb. 22.798 24.883 25.767 26.854 27.089 27.776 1996 Mar. 8.803 9.885 1996 Mar. 14.835 15.796 16.945 17.870 17.982 19.885 20.803 21.798

9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

35 34 34 34 34 12 11 11 09 09 09 08 07 56 55 55 57 47 35 34 34 34 32 32 31 29 26 09 07 43 40 39 38 38 37 31 31 32 32 32 33 33 34 34 35

49 49 49 49 49 51 51 51 52 52 52 52 52 52 52 52 52 52 52 52 51 51 51 51 51 51 51 50 50 46 45 45 44 44 44 40 39 37 37 36 36 36 35 35 34

38 48 50 50 51 56 56 57 01 02 02 05 06 18 19 19 18 17 00 00 59 59 55 53 52 47 38 25 11 08 21 01 36 30 14 07 39 33 08 39 16 13 25 01 36

119.4 119.5 119.5 119.5 119.5 120.5 120.5 120.5 120.6 120.6 120.6 120.6 120.6 120.7 120.7 120.7 120.8 120.8 120.9 120.9 120.9 120.9 120.9 120.9 120.9 120.9 121.0 121.2 121.3 122.5 122.8 122.9 123.1 123.1 123.3 125.4 125.7 127.0 127.3 127.7 128.0 128.0 128.6 128.9 129.3

25.5 25.5 25.5 25.5 25.5 25.0 25.0 25.0 25.0 24.9 24.9 24.9 24.9 24.4 24.4 24.4 24.1 24.1 23.4 23.4 23.4 23.4 23.3 23.3 23.2 23.1 22.9 21.7 21.5 18.5 18.0 17.8 17.5 17.4 17.2 14.4 14.1 12.7 12.4 12.1 11.8 11.8 11.2 11.0 10.7

1.843 1.839 1.839 1.839 1.838 1.783 1.782 1.781 1.779 1.778 1.778 1.775 1.775 1.757 1.756 1.755 1.745 1.745 1.726 1.726 1.726 1.725 1.723 1.722 1.721 1.718 1.714 1.689 1.685 1.636 1.628 1.624 1.620 1.619 1.616 1.578 1.574 1.556 1.552 1.548 1.544 1.544 1.537 1.533 1.529

1.009 1.000 0.999 0.998 0.997 0.886 0.885 0.884 0.880 0.879 0.878 0.875 0.874 0.850 0.849 0.848 0.837 0.836 0.820 0.820 0.820 0.820 0.818 0.817 0.817 0.815 0.812 0.803 0.802 0.808 0.812 0.814 0.816 0.816 0.818 0.846 0.849 0.867 0.871 0.875 0.879 0.879 0.887 0.891 0.895

22.0 21.8 21.8 21.7 21.7 18.5 18.5 18.4 18.4 18.3 18.3 18.2 18.2 18.0 18.0 18.0 18.1 18.1 18.7 18.7 18.7 18.7 18.9 18.9 18.9 19.1 19.4 21.4 21.8 27.3 28.2 28.6 29.1 29.2 29.5 33.7 34.1 36.0 36.4 36.7 37.1 37.1 37.7 38.0 38.4

15.452 6 0.03 15.431 6 0.01 15.303 6 0.02 15.375 6 0.01 15.451 6 0.02 15.572 6 0.015 15.662 6 0.04 15.707 6 0.03 15.567 6 0.04 15.499 6 0.045 15.454 6 0.01 15.287 6 0.01 15.229 6 0.01 15.090 6 0.02 15.075 6 0.015 15.132 6 0.01 15.660 6 0.02 15.552 6 0.025 15.481 6 0.015 15.489 6 0.02 15.505 6 0.02 15.434 6 0.02 15.265 6 0.015 15.299 6 0.02 15.299 6 0.03 15.180 6 0.01 15.628 6 0.03 15.529 6 0.04 15.404 6 0.02 15.667 6 0.04 15.529 6 0.01 15.820 6 0.02 15.914 6 0.035 15.682 6 0.03 15.721 6 0.045 15.758 6 0.025 16.015 6 0.02 15.637 6 0.02 16.062 6 0.03 15.987 6 0.04 15.885 6 0.03 15.854 6 0.025 15.763 6 0.05 16.228 6 0.03 16.039 6 0.035

2

3

4 5

6 7

to the mean level of the lightcurve, or more exactly, to the zeroth order (R) of the Fourier fit extrapolated to the zero phase angle using the H 2 G phase relation (Bowell et al. 1989). In best cases, several calibrated lightcurves were used and the mean absolute R magnitude (HR) and the slope parameter (GR) were derived, together with their formal errors. It must be noted, however, that in some

cases the systematic errors in these parameters can be large due to a possible change of aspect (caused by the motion of the PAB) during the apparition. If we judged that the systematic errors may be too large, or when a reasonable extrapolation could not be made (e.g., due to an insufficient phase angle coverage), we either abandoned the determination and gave no result for HR or assumed some value

´ PRAVEC, WOLF, AND SˇAROUNOVA

130

TABLE III Periods, Amplitudes, Absolute Magnitudes, and Phase Parameters Minor planet (1943) (2063) (2100) (3103)

Anteros Bacchus Ra-Shalom Egerb

(3122) Florence (3200) Phaethond (3691) (3752) (4341) (4957) (5143) (5587) (7025) (7341) (7480) (7482) (7822)

1982 FT Camillo Poseidon Brucemurray Heracles 1990 SB 1993 QA 1991 VK 1994 PC 1994 PC1 1991 CS g

(8034) 1992 1989 1992 1992 1995 1997 1997 1997 1997

LR UQ CC1 QN FX BR GH3 GL3 SE5

Synodic period (hr) 2.8695 14.904 19.797 5.7059

6 6 6 6

0.0002 0.003 0.003 0.0002

2.35812 6 0.00002 3.57 6 0.02 226.8 37.846 6.262 2.8924 5.05213 2.50574 4.20960 35.90 2.5999 2.3893 2.3897 3.6377 7.733 8.4958 5.9902 5.46 33.644 6.714 7.572 9.0583

6 6 6 6

0.7e 0.012 0.002 0.0001

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

0.00012 0.00004 0.00014 0.04 f 0.0002 0.0001 0.0002 0.0014h 0.007 0.0003 0.0002 0.02 i 0.009e 0.004 0.007 j 0.0007

2A2 (mag)

Ampl. (mag)

0.02a 0.10–0.18a 0.32 0.58–0.61 0.56 0.13 0.00a 0.14 0.38 0.85 0.06 0.07–0.20

0.09 0.22–0.42 0.41 0.77–0.90 0.72 0.18 0.11 0.26 0.5 1.1 0.08 0.10–0.26 ,0.1 0.80–1.25 0.32 0.28–0.70 .0.5 0.29 0.28–0.32 0.27 0.52 0.27 1.02 1.10 0.20 1.2 0.74 0.28 0.23

0.71–0.97 0.29–0.32 0.24–0.58 0.23 0.04–0.13a 0.22 0.19a 0.20 0.88 0.86 0.18 0.85 0.60 0.10a 0.14

HR 15.41 16.83 15.71 15.26

6 6 6 6

GR 0.13 0.14 0.07 0.09

(0.23 0.23 (0.12 (0.42

6 6 6 6

H 0.11) 0.10 0.04) 0.08)

15.96 17.25 16.07 15.74

6 6 6 6

0.14 0.2 0.08 0.10

(14.2)c (14.6) 14.36 6 0.2 14.91 6 0.11

(0.09 6 0.09) (0.23 6 0.11)

13.77 6 0.05

(0.42 6 0.08)

16.63 6 0.2 16.96 6 0.15

0.26 6 0.14 (0.23 6 0.11)

17.69 6 0.13 19.05 6 0.2

(0.23 6 0.11) (0.15120.2 0.15)

17.63 6 0.12

0.08 6 0.09

14.78 6 0.2 15.41 6 0.13 (15.6) (15.0)c 14.27 6 0.09 (13.6) (18.5)c 16.95 6 0.2 17.45 6 0.16 (16.8) (17.5)c 18.14 6 0.2 19.5 6 0.3 (15.5) (17.0)c (20.0)c 18.05 6 0.15 (17.0) (20.0) (15.0)c

a

The first harmonic dominates over the second harmonic. The first line is for July 1996, the second one for March 1997. See text for a discussion on the H and G values. c The calibrated observations, although insufficient for an independent estimate, are consistent with this value for H. d The first line is for November 1997, the second one for January 1995. e Significant discrepancies are present in the composite lightcurve of the slow rotator; a complex rotation is possible. f The poor lightcurve coverage makes this period determination somewhat uncertain, as the presence of only the second and fourth harmonics was assumed (see text). g The first line is for August 1996, the second one for March 1997. h A period twice as long is also possible (see text). i Two maxima/minima pairs per cycle were assumed. We cannot rule out a possibility of just one maximum/minimum pair per cycle; then the period would equal 2.73 h. j The lightcurve shape is complex and this period may not be related to a pure rotation. H in brackets were taken from the Minor Planet Circulars. b

for the slope parameter, together with its considered range (the reason for the particular assumption of GR is commented in the text), and derived just the mean absolute magnitude. For some cases in which the observations were taken at higher phase angles only (usually .208), the extrapolation to the zero phase angle was impossible and no value for HR is derived in spite of the fact that the lightcurves were calibrated. In Table III, the resulted HR and GR values are presented. (If GR was assumed rather than derived, it is given in parentheses, together with its considered range.) Since HR is a somewhat nonstandard

parameter and it also cannot be used for estimation of asteroid’s albedo and diameter, we had to correct it for V 2 R to obtain the mean absolute V magnitude (H 5 HV ). When no value for V 2 R was measured, we take V 2 R 5 0.45 6 0.1; this range covers most of known values for the color index in asteroids. The resulted H values are also given in Table III. We paid attention to make all the given errors realistic; they are relatively large and mostly reflect uncertainties in the extrapolations to the zero phase angle from the observations from only single apparitions. In cases when no reliable value for H could

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

TABLE IV Color Indices Minor planet (1943) (3103) (3752) (4957) (5143) (7341)

Anteros Eger Camillo Brucemurray Heracles 1991 VK 1997 SE5

V2R 0.55 0.48 0.50 0.52 0.50 0.32 0.50

6 6 6 6 6 6 6

0.05b 0.04 0.07 0.05 0.07 0.04 0.02

(1943) Anteros R2I

Classa

6 6 6 6 6 6 6

S E (S)

0.29 0.42 0.32 0.42 0.29 0.36 0.44

0.04b 0.03 0.04 0.03 0.03 0.04 0.02

V (C) (D)

a For (1943), (3103), and (5143), the published taxonomic classes are given; see text. For (3752), (7341), and 1997 SE5 , the classes are tentatively suggested according to the color indices. b From Pravec et al. (1997b).

be estimated, we give the value for H published in the Minor Planet Circulars, sometimes mentioning if they are consistent with our observations. The mean diameter (D in km) of the asteroid can be estimated from the mean absolute magnitude using (adapted from Tedesco et al. 1992)

D5

131

1329 2H/5 10 , ÏpV

(1)

where pV is the geometric albedo. When the equatorial profile was constrained from the observations, a limit on the equatorial axes ratio (a/b) is given in the text. For the description of this formalism, see, e.g., Magnusson et al. (1989). In Table IV, the measured color indices are given, together with the known or tentatively suggested taxonomic classes. 4. RESULTS FOR INDIVIDUAL ASTEROIDS

The main results are given in Tables III and IV, as described above. For each object, each apparition, one figure showing the asteroid’s composite lightcurve(s) is presented, with an exception of (5143) Heracles for which no period was derived. Most figures’ magnitude axes are in the same scale to facilitate comparison but this rule was not held in several cases due to a need to fit the data points into the figure or to enhance visibility of some features. The digital files of all the original data reported in this paper can be obtained either by request to P.P. (ppravec@ asu.cas.cz), or through data archives (e.g., Asteroid Photometric Catalog, [email protected], http://ftp. astro.uu.se/planet/apc – eng.html). Below, the results on individual asteroids are discussed.

This Amor asteroid was observed by Wisniewski et al. (1997) in 1990 and Pravec et al. (1997b) in 1994. In both works no period was determined but the authors suggested that there was present a variation with amplitude 0.05–0.1 mag. Combining the 1990 and 1994 observations, Pravec et al. derived the mean absolute magnitude H 5 16.01 with formal error 0.09 but systematic error possibly exceeding 0.1 mag. They also measured V 2 R 5 0.55 6 0.05 and R 2 I 5 0.29 6 0.04, consistent with the S classification based on the eight-color asteroid survey (Tholen 1989). We observed the asteroid on four nights from 1997 July 28.9 to Aug. 28.0. The synodic period (2.8695 6 0.0002) h was detected. The lightcurve has an amplitude of 0.09 mag with most signal in the first harmonic and complex shape with the best fit Fourier series significant up to the 6th order. A possibility that the detected period corresponds to a half rather than a full rotation period is unlikely since in that case only even orders of the Fourier fit (for a period of 5.739 hr) are significant up to the 12th order; the lightcurve would be quite symmetric with respect to a 1808 rotation that is unlikely considering the moderate phase angles of the observations. We believe that the detected period corresponds to the true rotation period. The lightcurve shape did not change significantly during the 30-day observational interval; the composite lightcurve is shown in Fig. 1. Knowing the period, we can see that the 4.9-h lightcurve from 1990 January 26.2 (Wisniewski et al. 1997) showed, similarly to the 1997 lightcurve, just one maximum/minimum pair per period with amplitude P0.05 at the PAB differing by 1408 from that of the 1997 observations. The 1994 observations were taken in a direction of the PAB nearly perpendicular (1038) to the 1997 observations, but again the amplitude was not greater than P0.1. From the 1997 observations the absolute R magnitude HR 5 15.41 6 0.13 was derived, assuming GR 5 0.23 6 0.11, which is typical for S class asteroids (Bowell et al. 1989). Correcting it for V 2 R, we get H 5 15.96 6 0.14. If we use the same GR assumption for the 1994 data, we get H 5 15.97 6 0.06. Wisniewski et al. obtained H 5 15.82 6 0.14 from the 1990 data, using the same assumption of G 5 0.23 6 0.11. Having the evidence for the low amplitudes in the different positions of the PAB, we conclude that the asteroid’s mean equatorial profile is nearly circular; i.e., the shape is not far from spheroid (a/b , 1.1). The relative size of the polar axis and the orientation of the spin vector remain undetermined; the nearly same H values in the different apparitions indicate that either the aspects were similar (probably not far from equatorial) in all the apparitions or the polar flattening is small. A cause of the dominance of the first harmonic in the 1997 and the 1990 lightcurves is not identified; both a small shape irregularity and a hemispherical albedo variegation are possible.

132

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 1. Composite lightcurve of (1943) Anteros.

(2063) Bacchus This Apollo asteroid made an approach to 0.068 AU to Earth on 1996 March 31. It was observed by radar in the week before the closest approach. We observed it on eight nights during 1996 March 26.1–April 17.9. The synodic period (14.904 6 0.003) h was derived from the lightcurve observations. This value was obtained as a weighted mean of solutions from two methods, one based on a formal fit of the second order Fourier series to all the lightcurve data, giving (14.906 6 0.003) h, and the other using times of minima of the first and second harmonics of the best Fourier fits to the three composite lightcurves (see below), giving (14.899 6 0.006) h. In Fig. 2, the three composite lightcurves, each constructed from data taken on nearby nights, are presented. The very fast apparent motion of the asteroid—reaching a maximum of 5.48/day on March 31—caused a large change of the viewing geometry during the observational interval (see Table I). Consequently, the lightcurve amplitude and shape evolved quite fast. While the composite lightcurves of 1996 April 7.0–7.9 and 1996 April 15.9–17.9 can be considered as a good representation of the actual lightcurves of those days, the composite lightcurve constructed from the data taken on the nights 1996 March 26.1 and 28.0 and April 1.0 is only a rough approximation of the actual lightcurves of those days, as its different parts were taken under very different geometric conditions. The lightcurve amplitude decreased from 0.42 to 0.22 mag during the observational interval; the positive correlation with the solar phase angle is apparent, although an aspect-induced change is also possible. There is only one persistent feature—the highest maximum present around the rotational phase 0.9 in all the three composite lightcurves; the first harmonic corresponding to this maximum dominates the lightcurve. The shape of the maximum

as well as other parts of the lightcurve changed on a time scale of several days. An occurrence of several pairs of local maxima/minima is evident from the observations during 1996 April 7.0–17.9. All the features are uncommon in asteroidal lightcurves and their combination suggests that the Bacchus’ shape may be unusual. The best fit of the phase relation to the data taken at phase angles ,408 (see Table I for the magnitudes) gives the mean absolute R magnitude HR 5 16.83 and slope parameter GR 5 0.23 with errors of 0.14 and 0.10, respectively. Although there may be present a systematic error in these values due to a possible effect of changing aspect, the derived G value is consistent with the range for Q and S classes (Bowell et al. 1989), the former being suggested for Bacchus by Hicks et al. (1998) from analysis of its spectrum. Considering this classification, we estimate that the Bacchus’ effective diameter is 1.1 km, taking values of 0.20 and 0.42 for its geometric albedo and V 2 R, respectively, that are close to typical values for Q asteroids. The radar observations of Bacchus made before the closest approach in March 1996 (Benner et al. 1998) show a bifurcated appearance of the asteroid’s echoes. An inversion of the combined radar and the lightcurve data (from this paper) yielded single-lobe and two-lobe models that define lower and upper bounds on the degree of bifurcation (Benner et al. 1998). Both models have a prominent central concavity and modestly asymmetric shapes, explaining the main asymmetries apparent in the lightcurves. (2100) Ra-Shalom This Aten asteroid is classified as a C-type (Tholen 1989). Observations made in August–September 1981 (Ostro et al. 1984, Harris et al. 1992) revealed that its lightcurve has a period of 19.79 h and an amplitude of 0.35 mag. We observed Ra-Shalom on 7 nights during 1997 August

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

133

FIG. 2. Composite lightcurves of (2063) Bacchus constructed from three subsets of data from 1996 Mar. 26.1–Apr. 1.0, Apr. 7.0–7.9, and Apr. 15.9–17.9. Shifts mentioned in the legend were applied so that the points within each of the three subsets were reduced to the same phase angles, which are 398 and 258 for the Apr. 7.0–7.9 and 15.9–17.9 lightcurves, respectively. See text for a comment on the meaning of the Mar. 26.1–Apr. 1.0 composite lightcurve.

31.0–September 12.0. The synodic period (19.797 6 0.003) h was derived from the data, confirming the result by Harris et al. (1992). The composite lightcurve (Fig. 3) has an amplitude of 0.41 mag and its shape is very similar to that

of the 1981 lightcurve obtained at similar phase angles but at the PAB differing by about 438 (see Ostro et al. 1984, their Fig. 4). Also the brightness levels in both apparitions were the same: Harris et al. (1992) combined the 1981

FIG. 3. Composite lightcurve of (2100) Ra-Shalom. Shape of the lightcurve at rotational phases around 0.2 is uncertain.

134

´ PRAVEC, WOLF, AND SˇAROUNOVA

observations with an additional 1978 lightcurve and obtained the phase parameters H 5 16.06 6 0.07 and G 5 0.12 6 0.04. If we assume the same range for G and take V 2 R 5 0.36 (derived from the spectral slope measured by Luu and Jewitt 1990; it is also consistent with its C classification), we get from our observations HR 5 15.71 6 0.07; hence H 5 16.07 6 0.08, in perfect agreement with the Harris et al. result. This same brightness level of both the 1981 and the 1997 observations, together with the lightcurve shape similarity, indicates that the aspects on both apparitions were similar. (3103) Eger Wisniewski (1987) observed this Apollo asteroid on two nights in July 1986. He derived the synodic rotation period of 5.71 h and the lightcurve amplitude of 0.9 mag and suggested that it is an X-type asteroid (i.e., E, M, or P) according to his colorimetry. Veeder et al. (1989) identified it as a taxonomic type E based upon its high albedo (0.53– 0.63; the effective diameter 1.4–1.5 km) derived from infrared observations made also in July 1986 and combined with the absolute magnitude given by Wisniewski (1987). Wisniewski (1991) obtained a more accurate synodic period, 5.709 h, from additional lightcurves made in January and February 1987. Gaffey et al. (1992) suggested that Eger is probably either a major or the primary source body of the enstatite achondrite meteorites. They suggested that it was most probably derived from the Hungaria region at the innermost edge of the main belt of asteroids. They also showed from a combination of the infrared and visual observations that the Eger lightcurve with the amplitude as high as 0.9 mag is due to a rotation of the elongated body, not by a large-scale albedo variation. Radar observations of Eger in July 1991 and July 1996 (Benner et al. 1997) set the lower bounds of 1.5 and 2.3 km, respectively, on the minimum and maximum breadth of the asteroid’s pole-on silhouette, implying a geometric albedo less than the values derived by Veeder et al. but still consistent with the Etype classification. We observed Eger on five nights in July 1996 and one night in March 1997. The July observations were made in support of the radar observations (Benner et al. 1997). The lightcurves are presented in Figs. 4 and 5. On July 15.0, the following color indices were measured: V 2 R 5 0.48 6 0.04 and R 2 I 5 0.42 6 0.03, which are somewhat redder than typical for E-type asteroids. The synodic period (5.7059 6 0.0002) h was derived from the July 1996 observations. This value is slightly but significantly different from the synodic period derived from the 1987 observations (Wisniewski 1991; it is (5.7081 6 0.0003) h according to our reanalysis of his data), which is probably due to quite different motions of the asteroid’s PAB in January/ February 1987 and July 1996. An information on the Eger’s

spin vector is derivable from the difference of the synodic periods and will be analyzed in a future paper, collecting all available lightcurve data. The July 1996 observations show an evolution of the lightcurve shape during the observational interval. The lightcurves are asymmetric with the second maximum (around rotational phase 0.45 in Fig. 4) having the decreasing branch much less steep (and therefore longer) than that of the first maximum (around phase 0.00). The primary minimum (around phase 0.21) has deepened by 0.13 mag during July 15.0–22.0. The long, slowly decreasing branch from the second maximum to the secondary minimum (around phase 0.81) contains a hump (or perhaps temporarily two humps) that evolved on time scale of a few days. The observed lightcurve asymmetry is relatively large and unusual for the high amplitude lightcurve of the asteroid seen, according to Benner et al. (1997), nearly equator-on. This indicates that the asteroid’s figure is asymmetric on a global scale. The hump (and its evolution) visible on the slowly decreasing branch is probably due to a topographic feature observed in changing geometric conditions. The March 1997 lightcurve (Fig. 5) taken at smaller phase angle and at the PAB direction differing by about 1608 from those in July 1996 (see Table I) is nearly symmetric but still shows different depths of its minima. Its average amplitude is consistent with the asteroid’s figure pole-on elongation about a/b 5 1.5 derived by Benner et al. (1997). The mean absolute R magnitude HR 5 15.26 6 0.09 was derived from the data by taking GR 5 0.42 6 0.08 given for E-type asteroids by Bowell et al. (1989). Correcting it for V 2 R 5 0.48 6 0.04, we get the mean absolute V magnitude H 5 15.74 6 0.10. A. W. Harris (of JPL; pers. commun.) redid an analysis of the Wisniewski data (1987, 1991) and used it in combination with our data for an improved determination of the phase dependence, taking advantage of the full range of phase angle coverage from 13.68 to 44.98. Neglecting changes in aspect during and between each of the observed apparitions, he got H 5 15.61 6 0.15, G 5 0.31 6 0.11 and Hmax 5 15.47 6 0.09, Gmax 5 0.44 6 0.08, respectively, for the lightcurve mean and maximum levels. Both the mean and the maximum G values are consistent with the value expected for E-type asteroids (see above), although that of the maximum is more suitable for physical interpretation since an effect of limb darkening has lesser influence when brightness is at its maximum than when it is at minimum (A. W. Harris, pers. commun.). In Table III, we give our values for the mean absolute magnitudes, for consistency with the values for other asteroids. The Hmax value derived by Harris is fainter by 0.31 mag than that originally given by Wisniewski (1987) from the 1986 observations because Wisniewski assumed a much lower value of G (and hence steeper phase relation). The fainter H value implies that the albedo derived by Veeder

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

135

FIG. 4. Composite lightcurves of (3103) Eger of July 1996. They were reduced to the same phase angle but some were shifted up or down to show more clearly the evolution of the lightcurve shape (see text).

et al. (1989) using the Wisniewski’s H value is too high. We recalculated their albedo (0.53–0.63) using the Harris maximum absolute magnitude and applying the approximate method by Harris and Harris (1997); we got the

corrected albedo 0.41–0.49. Corresponding effective diameters for the Eger’s orientations at the moments of the maximum and mean light levels are 1.7–1.5 and 1.6–1.4 km, respectively. This correction of the albedo and diameter is

FIG. 5. Lightcurve of (3103) Eger of 1997 March 8.0 taken at the solar phase angle 23.78.

136

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 6. Composite lightcurve of (3122) Florence.

in the direction consistent with that found by Benner et al. (1997) from the radar observations, although they suggest even larger diameter and therefore even lower albedo. A new derivation of the albedo and diameter using new simultaneous infrared and visual observations would be desirable to derive more reliable values. The next observing opportunity will occur in July 2001, or better in February 2002 (the latter provides lower phase angles allowing a more reliable determination of H). (3122) Florence Six lightcurves of this Amor asteroid cover the 122day interval from 1996 October 3.1 to 1997 February 2.0. Although the position of the PAB changed by 338 and the phase angle decreased from 46.98 to 9.28, this large change of geometric conditions surprisingly did not cause any significant change of either the asteroid’s lightcurve shape or the synodic period. All the lightcurves are fitted well with the same fourth-order Fourier series with most power in the second harmonic and the synodic period (2.35812 6 0.00002) h (see Fig. 6). This is the shortest period presented in this paper, and the fourth shortest presently known among NEAs. Considering the observations from 1986 March 19 from Wisniewski et al. (1997) at the PAB (204.58, 219.68) and the phase angle 15.18 when the lightcurve amplitude was about the same or smaller than that of 1996/ 1997 in quite different (roughly perpendicular) position of the PAB, we can judge that the asteroid’s mean equtorial profile cannot be too elongated and its shape is probably not too far from spheroid (a/b P 1.2). The relative size of the polar axis remains unconstrained. (3200) Phaethon This Apollo object was identified as being genetically related to the Geminid meteor stream and therefore possi-

bly being of cometary origin (see, e.g., Weismann et al. 1989). However, no signs of cometary activity have been found despite a number of attempts to detect them. Its photometric characteristics are unusual, as most spectral and color observations found it blue and it is classified as a rare F type (Tholen 1985, Luu and Jewitt 1990, Meech et al. 1996). Its rotation period was suggested to be slightly under 4 h with a lightcurve amplitude in excess of 0.4 mag in December 1984 (Tholen 1985). Wisniewski et al. (1997) derived a period of (4.08 6 0.08) h but it is based on only one night’s (1989 October 9.4) lightcurve with amplitude 0.12 mag. First reliable determination of the Phaethon’s period was made by Meech et al. (1996) based on lightcurves obtained on 1994 December 27, 1995 January 4 and 5: the synodic period was (3.604 6 0.001) h. We observed Phaethon on 1995 January 4.8 (just in between the last two nights of Meech et al., see above) and on 1997 November 1.1 and 2.1. From the two consecutive 1997 November nights we derived the synodic period (3.57 6 0.02) h that confirms the result by Meech et al. Although the data are noisy, the composite lightcurve presented in Fig. 7 shows only one maximum/minimum pair per cycle and has all signal in the first harmonic only. The lightcurve of 1995 January 4.8 (Fig. 8) covers about 80% of the rotation; it shows two maxima/minima per cycle and has a greater amplitude than the 1997 November one. The difference between the lightcurves is probably due to different aspects of the two apparitions: Phaethon was seen probably more pole-on on 1997 November 1 than on 1995 January 4. A combination with further observations is needed to derive the Phaethon’s pole and shape. The relatively fast rotation, however, indicates that its bulk density must be .1.1 g/cm3 to resist a centrifugal force by a selfgravitation only (see Harris (1996) for the relevant formula).

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

137

FIG. 7. Composite lightcurve of (3200) Phaethon of 1997 Nov. 1.1 and 2.1 taken at the solar phase angle of 498.

(3691) 1982 FT We observed this Amor asteroid on 27 nights during 1995 December 28–1996 March 21. According to Luu and Jewitt (1990), it has a nearly flat spectrum with (dS/d l)/ S600nm 5 15.5% (or 2%, when corrected to the zero phase angle). Thus, below we consider tentatively that (3691) belongs to C class, which is the most common asteroidal class with flat spectrum, and take V 2 R 5 0.42 derived from the spectral slope (cf. Eq. (2) in Luu and Jewitt). Since its period turned out to be very long and a combination of all the data taken on many nights was necessary for its determination, we tied all the observations carefully to Landolt standards; the magnitudes are consistent at a level of 0.01 mag. In Table II, the geometric circumstances and the measured R magnitudes reduced to unit geocentric and

heliocentric distances are listed. Each point represents an average of 1 to 12 (with median of three) image measurements taken in quick succession. The synodic period (9.45 6 0.03) days 5 (226.8 6 0.7) h was detected. For the period determination, the linear phase dependence was assumed; the best fit was achieved for the phase coefficient of 0.028 mag/deg with error ,0.001 mag/deg. The mean absolute R magnitude HR 5 14.52 and the slope parameter GR 5 0.20 with formal errors of 0.04 and 0.03, respectively, correspond to the best-fit phase dependence; their systematic errors due to a possible aspect change, however, may be several times greater. If we take a value of 0.09 6 0.09 for G (this range is given for C class asteroids by Bowell et al. 1989), we get HR 5 14.36 6 0.2 (H 5 14.78 6 0.2). Figure 9 shows the composite lightcurve constructed using the derived period and phase coefficient.

FIG. 8. Lightcurve of (3200) Phaethon of 1995 Jan. 4.8 taken at the phase angle of 648. Shape of the lightcurve at rotational phases in a range of 0.75–0.95 is uncertain.

138

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 9. Composite lightcurve of (3691) 1982 FT. The scatter of points around the best fit second order Fourier series is several times greater than observational errors of the points.

The mean residual of the points with respect to the best fit second order Fourier series is 0.088 mag. (The third and higher Fourier orders are not detected significantly.) This is 33 to 43 greater than the typical errors of the points. No observational error was found to cause the discrepancy. We consider two possible causes of the large scatter: 1. Evolution of the lightcurve shape with time. 2. Complex rotation. Ad 1. Changing viewing and illumination geometry might cause an evolution of the lightcurve shape. The distributions of points from individual rotational cycles around the best fit curve, however, do not indicate a presence of any systematic trend in the residuals that could be easily attributable to the systematic lightcurve shape evolution only. Remarkable in this sense is the point from cycle 6 at the rotational phase 0.49 (see Fig. 9, the star symbol) that indicates the brightness fainter by about 0.4 mag than it was at similar rotational phases in previous and following cycles and also points from cycles 2 and 3 (plusses and crosses) around the phase of 0.4 that indicate a large change of the lightcurve shape (by 0.18 mag, while the points were accurate to about 0.02 mag) between the two consecutive cycles in almost the same geometric observing conditions (see Table II). No such behavior is expected for a periodic asteroidal lightcurve. Ad 2. The diameter of (3691) is estimated roughly 7 km (taking albedo 0.045 typical for the C class). According to Harris (1994), the estimated damping time scale for an asteroid of this size and rotation period 227 h is longer than the age of the Solar System. It means that (3691) is expected to be in an excited rotation state. The complex rotation may be responsible for the discrepancies apparent in certain parts of the lightcurve (see the previous paragraph). No additional periodicity was detected in the resid-

uals of the lightcurve points with respect to the best fit second order Fourier series. We conclude that the observed scatter of the lightcurve points of (3691) may be caused by a combination of both the evolution of the lightcurve shape due to the changing aspect and the asteroid’s complex rotation. Further observations with higher temporal resolution and better coverage are needed to confirm this hypothesis. No shape constraint can be given until the rotation state is known. (3752) Camillo This Apollo asteroid was observed on 14 nights during 1995 August 3.0–29.9. The synodic period (37.846 6 0.012) h was derived. For the period determination, the linear phase dependence with the phase coefficient of 0.033 mag/ deg was assumed (see below for its derivation). V 2 R 5 0.50 6 0.07 and R 2 I 5 0.32 6 0.04 were also measured. The composite lightcurve shown in Fig. 10 constructed using the derived period and phase coefficient is only an approximation of the actual Camillo’s lightcurves of the observing dates, since its different parts were taken in different geometric conditions. An evolution of the lightcurve shape due to the changing observing conditions is a probable explanation of the discrepancies between the points from different nights that are apparent in some parts of the composite lightcurve; see, e.g., points around the rotational phases 0.2 and 1.0. The large amplitude (1.1 mag at the phase angle about 158) of the Camillo’s lightcurve indicates that its mean equatorial profile is elongated with the axes ratio a/b . 2. The relative size of the polar axis remains unconstrained. The linear phase coefficient of (0.033 6 0.003) mag/deg was derived as giving the best fit of 11 (from the 14) nightly lightcurves which were taken outside the minima, i.e., the points of 1995 August 4.0, 18.9, and 23.0 were excluded

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

139

FIG. 10. Composite lightcurve of (3752) Camillo. The discrepancies between some of the points taken on different nights are real and indicate an evolution of the lightcurve shape with changing geometric conditions.

from the phase coefficient determination. The mean absolute R magnitude HR 5 14.83 and the slope parameter GR 5 0.15 with formal errors of 0.08 and 0.07, respectively, correspond to the best-fit phase dependence. We cannot, however, exclude systematic errors due to a possible aspect change. That is why we adopt the value HR 5 14.91 6 0.11 derived for the assumed value for GR 5 0.23 6 0.11 that is typical for S class asteroids. (Note that the measured color indices and also the spectrum obtained by Luu and Jewitt (1990)—its slope corresponds to V 2 R 5 0.52—are consistent with that classification.) Considering the measured V 2 R, the mean absolute V magnitude is H 5 15.41 6 0.13. (4341) Poseidon The observations on 10 nights from 1997 May 2.0 to 18.0 were made in nearly the same position of the PAB but with decreasing phase angle (from 41.78 to 21.38). A low amplitude lightcurve was revealed (see Fig. 11). Although the data are noisy, the synodic period (6.262 6 0.002) h was detected and other periods seem to be ruled out. The second most probable period is 7.206 h but it gives a poorer

fit and we consider it to be an artifact of the noisy measurements made about local midnights of the short spring nights. (Note that it is almost exactly 3/10 day, giving 10 cycles in 3 days, while the period 6.262 h gives 11.5 cycles in 3 days.) No significant change of the lightcurve shape was detected during the observational interval. No shape constraint can be obtained from the observations. (4957) Brucemurray This Amor asteroid was observed by Pravec et al. (1996) in October 1994–January 1995. They derived the synodic rotation period (2.8921 6 0.0001) h and detected a change of the lightcurve amplitude during that interval. We observed Brucemurray on two nights of 1996 November 5.1 and December 29.0. On the former night V 2 R 5 0.52 6 0.05 and R 2 I 5 0.42 6 0.03 were also measured, indicating a red color of the asteroid’s surface in this spectral range. Searching around the value found in 1994/1995, we have detected the synodic period (2.8924 6 0.0001) h in the 1996 data. This is only slightly and maybe insignificantly different from the 1994/1995 value. The lightcurves are presented in Fig. 12. Due to the asteroid’s orbital period

140

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 11. Composite lightcurve of (4341) Poseidon taken at the phase angles 218–428.

of 1.96 years, the 1996 observations were made in similar but not quite the same geometric conditions as the 1994/ 1995 ones. Comparison between the lightcurves from these two apparitions shows that they are qualitatively similar, having most signal in the second harmonic but showing some asymmetries—there are relatively large signals also in other harmonics, though this feature is more pronounced in the 1994/1995 data than in the 1996 ones. The lightcurves continue the same trend of the amplitude decrease from October–November (2A2 5 0.20–0.24 for BPAB . 08, a 5 408–508) to December (2A2 5 0.07–0.11 for BPAB , 08, a P 208) in each of the 2 years. How the lightcurve characteristics are related to pole and shape of the asteroid remains to be seen from further research.

(5143) Heracles We observed this Apollo asteroid on four consecutive nights during 1997 August 10.0–13.0. On all the nights its brightness (reduced to the same phase angle) was constant to 60.035 mag, but there was marginally detected an increase of brightness by P0.07 mag in 4 h on each night. (In Table I the means of the nightly magnitudes are given.) Similar behavior (slow trends in the nightly data) was observed also on 1996 October 14.9 and November 3.9 and 4.7 at the PAB of 338, 1148 (different by 638 from that of the 1997 August observations). The observations suggest that the Heracles’ lightcurve was of low amplitude on both apparitions but cannot constrain its period. A possibility that the period is long, as suggested by the trends on the

FIG. 12. Lightcurves of (4957) Brucemurray. The magnitude scale is valid for the 1996 Nov. 5.1 lightcurve; the shift of the Dec. 29.0 lightcurve is arbitrary.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

141

FIG. 13. Composite lightcurves of (5587) 1990 SB constructed from two subsets of data from 1997 Mar. 5.9–10.8 and Apr. 7.9–8.9 taken at the phase angles about 128 and 23.58, respectively. No Fourier fit is presented due to the noise and not ideal coverage of the lightcurves that do not make such fits reliable in higher orders.

individual nights, must be confirmed by further observations of higher accuracy and better coverage on a next apparition. On 1997 August 12.0 we also measured color indices V 2 R 5 0.50 6 0.07 and R 2 I 5 0.29 6 0.03, which are consistent with the V classification given for Heracles by Xu et al. (1995). Assuming GR 5 0.42 6 0.08, which is the range for V-type asteroids (Bowell et al. 1989), we obtain HR 5 13.77 6 0.05; hence H 5 14.27 6 0.09. (5587) 1990 SB We observed this large Amor asteroid on five nights divided into two blocks: 1997 March 5.9–10.8 and April 7.9–8.9. The synodic period (5.05213 6 0.00012) h was derived from the observations. The lightcurves have a large amplitude that increases significantly with increasing phase angle; 2A2 5 0.71 and 0.97 at a about 128 and 23.58, respectively, indicating an elongated shape with a/b about 2 or greater. See Fig. 13 for the composite lightcurves.

(7025) 1993 QA Observations of this Apollo asteroid were made on four nights of 1996 February 25.0, 26.1, and 27.0 and March 16.0. The synodic rotation period (2.50574 6 0.00004) h was derived. The lightcurve (Fig. 14) has a regular shape with most signal in the second harmonic, which indicates that a symmetric figure (like ellipsoid) is a good approximation of the asteroid’s shape. Independent Fourier fits to the February and March points revealed that the lightcurve amplitude changed by a small but significant amount during the 20-day observational interval; 2A2 decreased from 0.32 to 0.29. Since the phase angle increased during the same interval, which would normally cause an increase of the amplitude, a change of aspect is probably responsible for the amplitude decrease—the aspect was probably more polar on March 16 than on February 26. This finding is in agreement with the fact that the amplitude of the lightcurve of (7025) observed by other observers (A. Erikson, pers. commun.) on earlier dates in February 1996 was much greater (roughly 0.5 mag), suggesting more equatorial view

142

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 14. Composite lightcurves of (7025) 1993 QA. The best fit sixth-order Fourier series to the February points is represented by the curve.

than that we observed. The equatorial axes ratio (a/b) of the ellipsoid best representing the asteroid’s shape is greater than 1.3. The relative size of the polar axis remains unconstrained. (7341) 1991 VK We observed this Apollo asteroid on six nights from 1996 October 14.9 to December 4.8. Four of the six lightcurves cover a full rotation cycle and we used them for derivation of the synodic period (4.20960 6 0.00014) h. The four lightcurves are presented in Fig. 15. The increase of the lightcurve amplitude during the observational interval is apparent. It correlates with the increase of the phase angle from 15.88 to 77.08. The position of the PAB changed by 118 during the interval; although we cannot remove a possible effect of an aspect change, the amplitude increase is probably due to the phase effect mainly. The lightcurves have the most signal in the second harmonic, but there is also some signal in other harmonics, indicating asymmetries in the lightcurves. On 1996 October 14.9 we measured V 2 R 5 0.32 6 0.04 and R 2 I 5 0.36 6 0.04; the color of the asteroid’s surface is nearly neutral with respect to solar. This is typical for C-type asteroids, thus we tentatively consider that this NEA belongs to the C class. The best fit phase dependence to the mean levels (zero orders) of the R lightcurves taken at phase angles 15.88– 60.48 (see Table I for the R(1, a) values) gives HR 5 16.63 6 0.10 and GR 5 0.26 6 0.07, corresponding to H 5 16.95 6 0.11. An influence of possible aspect change (up to 678) makes this derivation somewhat uncertain— the systematic errors may be in order of or even greater than the formal errors, if the PAB moved in an asteroid’s pole direction. In Table III, we thus subjectively give errors twice as large as the formal errors.

(7480) 1994 PC This Amor asteroid was observed on four nights during 1996 December 28.9–1997 January 16.9. A long-period brightness variation was revealed. Because of a poor coverage of the lightcurve, we assumed that the lightcurve is symmetric with all signal in the second and fourth harmonics only. Then the synodic period of (35.90 6 0.04) h was derived, together with the formal linear phase coefficient of (0.024 6 0.004) mag/deg. Although the systematic error of the derived period may be somewhat greater than the obtained formal error due to possible deviations from the assumed lightcurve symmetry, there remains no ambiguity in the derived synodic period as long as the lightcurve has two maxima/minima pairs per rotation cycle—a plausible assumption for the high amplitude lightcurve observed at not large phase angles. The formal solution for the phase coefficient is not reliable for a derivation of the absolute magnitude due to the not-large-enough range of phase angles covered. Thus, we assume GR 5 0.23 6 0.11, which is the range for S-type asteroids (Rabinowitz (1998) suggests this classification for the asteroid), and obtain HR 5 16.96 6 0.15. Using V 2 R 5 0.49 6 0.05 obtained by Rabinowitz (1998) we get H 5 17.45 6 0.16. Figure 16 shows the composite lightcurve constructed using the derived period and phase coefficient. Less than 50% of a full rotational cycle is covered. Due to the synodic period near 3:2 commensurability with the Earth rotation, two of the observing nights cover the same maximum and the other two fall on the same decreasing branch. Although this distribution of observational data allowed us to derive the unambiguous value for the synodic rotation period, the shape of the lightcurve’s unobserved parts is quite uncertain.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

143

FIG. 15. Composite lightcurves of (7341) 1991 VK.

(7482) 1994 PC1 Four lightcurves of this Apollo asteroid were taken during 1997 January 26.8–February 2.8, within 2 weeks after its approach to 0.065 AU to Earth on 1997 January 21. The observing geometry was extreme; the asteroid’s heliocentric distance was ,1 AU, the phase angle was about 1018 and its apparent motion was very fast (5.08/day on the first night). Incidentally, the phase angle was nearly constant during the observational interval; it increased by 28 only. Although the PAB direction changed by 238, no significant change of the lightcurve shape was detected and all the four lightcurves are fitted well with the same fifthorder Fourier series with most power in the second harmonic and the synodic period (2.5999 6 0.0002) h. The composite lightcurve (Fig. 17) is relatively regular, which is somewhat surprising considering the extreme phase angle. No shape constraint can be given from the observations. (7822) 1991 CS From the observations of this Apollo asteroid made on seven nights in August 1996 and on three nights in March 1997 we derived the synodic periods (2.3893 6 0.0001) h and (2.3897 6 0.0002) h, respectively. The difference between them may be insignificant, considering their errors. The lightcurves are shown in Figs. 18 and 19. While

the March 1997 lightcurves taken at phase angles around 328 indicate no change of the lightcurve shape during the 5-day interval, the August 1996 ones taken at phases about 668 show a fast evolution of their shape. Remarkable is also the fact that while the March lightcurve looks normal (with most signal in the second harmonic), all the August lightcurves have most of the signal in the first harmonic. The second harmonic’s amplitude was only 0.15 times that of the first harmonic during 1996 August 7–19—the lightcurve had only one clearly recognizable maximum/ minimum pair (see first two composite lightcurves in Fig. 18). The second harmonic’s amplitude grew during last three nights of 1996 August 22, 23, and 24, with the secondto-first harmonic amplitude ratios 0.35, 0.48, and 0.66, respectively; the secondary maximum/minimum pair became progressively more apparent there. Considering the large phase angle of the observations, a relatively small irregularity of the asteroid’s figure in combination with the fast motion of the PAB (see Table I) are probably responsible for the lightcurve shape and evolution. (8034) 1992 LR We observed this Amor asteroid on three nights during 1997 September 26.0–29.0. The observations revealed a lightcurve that can be described either as first harmonic-

144

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 16. Composite lightcurve of (7480) 1994 PC. Although the lightcurve shape is largely uncertain, there remains no ambiguity in the derived synodic period.

dominated with a period of 3.638 h or as second harmonicdominated with period twice as long and the odd harmonics weak or insignificant. We do not have sufficient ground to resolve this ambiguity. The lightcurve shape—the sharp deep minimum and very broad nearly flat maximum (see Fig. 20)—seems to be more compatible with the shorter period. On the other hand, an other than doubly periodic lightcurve of such large amplitude is virtually unknown among well-studied objects (A. W. Harris, JPL, pers. commun.). Generating a single deep minimum (in the case of the shorter period solution) requires a very contrasty albedo hemispherical variation, not observed for asteroids yet. Cellino et al. (1989) give examples of artificial lightcurves for some modelled asymmetric shapes; a few of the lightcurves somewhat resemble the observed one with the broad maximum and

sharp deep minimum, yet they are double-periodic. Thus even the peculiar lightcurve shape may be consistent with the longer period solution. In Table III, we give the shorter period solution with the synodic period (3.6377 6 0.0014) h. The possible longer period solution is (7.277 6 0.003) h. From our observations we also derived HR 5 17.69 6 0.13 (H 5 18.14 6 0.2), assuming GR 5 0.23 6 0.11 based on the S-classification given for this object by Wisniewski et al. (1997). Wisniewski et al. (1997) obtained lightcurves for this asteroid on three nights around 1992 August 28 and derived a period of (7.283 6 0.004) h, i.e., our longer period solution. Examining their lightcurves we found that they could be satisfied also with the 3.638-h period if the beginning and the end parts of the 1992 August 28.3 lightcurve contains a small systematic error in order of a few hundredths of

FIG. 17. Composite lightcurve of (7482) 1994 PC1 taken at the solar phase angles about 1018.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

145

FIG. 18. Composite lightcurves of (7822) 1991 CS from August 1996.

magnitude—perhaps a plausible hypothesis. Their lightcurve (taken at a phase angle of about 158) has an amplitude of 0.44 mag and shape similar to our lightcurve; there is a deep minimum and a broad flat maximum, each covering about half of the 3.64-h period. They also derived H 5

18.15 6 0.11 for the same G-value assumption as we used. Both the lightcurve shape similarity and the same absolute magnitudes of the 1992 and 1997 observations suggest similar aspects on both apparitions. No shape constraint can be given until the period ambiguity is resolved.

FIG. 19. Composite lightcurve of (7822) 1991 CS from March 1997 taken at the phase angles around 328.

146

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 20. Composite lightcurve of (8034) 1992 LR for the shorter period solution. The period twice as long is also possible; in that case the actual lightcurve can be constructed by doubling the presented one (see text).

This small (estimated 0.5 km) Aten asteroid was observed on three successive nights 1997 Oct. 12.0–13.9. The synodic period (7.733 6 0.007) h was derived from the observations. There are relatively large irregularities in the composite lightcurve (Fig. 21); while most of the signal is in the second harmonic, other harmonics are also relatively powerful. Considering the relatively small phase angle of the observations, it suggests a presence of some irregularities in the asteroid’s shape.

(8.4958 6 0.0003) h was derived from the observations. The composite lightcurve (Fig. 22) has an amplitude of $1.02 mag. The small phase angles 2.28 and 2.48 on March 12.0 and 13.0, respectively, when the amplitude was measured indicate that the asteroid’s equatorial profile is very elongated with the axes ratio a/b $ 2.5, one of the most elongated figures found among minor planets. Only small increase of the amplitude (by less than 10%) was found on April 1.9, when the phase angle was 16.88 and the PAB direction was different by 148.

1992 CC1

1992 QN

Observations of this Apollo asteroid were made on four nights from 1997 March 8.0 to April 1.9. The synodic period

This Apollo asteroid was observed on three nights of 1995 December 28.1–30.1 and on 1996 January 14.2. The

1989 UQ

FIG. 21. Composite lightcurve of 1989 UQ.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

147

FIG. 22. Composite lightcurve of 1992 CC1 .

synodic period (5.9902 6 0.0002) h was derived from the lightcurve data. The composite lightcurve presented in Fig. 23 shows, surprisingly, that the lightcurve shape did not change during the observational interval (at least at the rotational phases 0.5–1.0 covered also on the last night of January 14.2), although the phase angle increased from 588 to 878 and the PAB direction changed by 248. Although the large amplitude of the lightcurve is at least partly due to the large phase angle, it indicates that the asteroid’s equatorial profile is somewhat elongated. 1995 FX This small (estimated 0.4 km) Amor asteroid was observed on two consecutive nights 1995 April 3.0 and 4.0. Its fast apparent motion (7.38/day) made observing difficult and the resulting lightcurves are noisy. The synodic period (5.46 6 0.02) h was detected as giving the best fit of the second-order Fourier series to the lightcurve. The composite lightcurve (Fig. 24) is quite symmetric with the only significant signal in the second harmonic; thus we have no ground to resolve whether the 5.46-h period or its half is the real period of the asteroid and we must rely on the assumption that the lightcurve has two pairs of maxima/

minima per period. There exists another, less probable solution for the period 4.90 h; formally it gives a significantly worse fit to the lightcurve, but we cannot rule it out with full certainty. 1997 BR We observed this Apollo asteroid on 20 nights during 1997 February 1.2–March 7.8. All the observations were tied carefully to Landolt standards; the points are consistent at a level of 0.01–0.02 mag. The synodic period (33.644 6 0.009) h was detected. For the period determination, the linear phase dependence was assumed; the best fit was achieved for the phase coefficient 0.0322 mag/deg with a formal error of only 0.001 mag/deg. The mean absolute magnitude HR 5 17.63 and the slope parameter GR 5 0.08 with formal errors of 0.04 and 0.03, respectively, correspond to the best-fit phase dependence; their possible aspect change-induced systematic errors, however, may be several times greater. The obtained G value is consistent with its C or D classification inferred from colorimetry of this NEA by Rabinowitz (1998), although he cannot rule out an S classification with certainty. This led us to consider as possible the range for GR 5 0.08 6 0.09 (nearly identical

148

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 23. Composite lightcurve of 1992 QN.

with the range for C-type asteroids), which gives HR 5 17.63 6 0.12. Using V 2 R 5 0.42 6 0.09 obtained by Rabinowitz (1998), we get H 5 18.05 6 0.15. Figure 25 shows the composite lightcurve constructed

using the derived period and phase coefficient. The mean residual of the points with respect to the best fit seventhorder Fourier series is 0.076 mag. (All Fourier orders up to the seventh order are significant.) This is 23 to 33

FIG. 24. Composite lightcurve of 1995 FX.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

149

FIG. 25. Composite lightcurve of 1997 BR.

greater than the typical errors of the points. No observational error was found to cause the discrepancy. The largest discrepancies are apparent around phases of the lightcurve maxima, making them of quite different shapes on different dates. (Compare also the 1997 BR lightcurve with that of Camillo, Fig. 10, which is a similar case but shows, unlike the 1997 BR one, only the smooth lightcurve change that is attributable to a change of the viewing conditions.) As in the case of (3691), we consider two possible causes of the large scatter: (i) evolution of the lightcurve shape and (ii) complex rotation. While the former can contribute somewhat to the observed scatter, the character of the scatter indicates that there is also present another source of the scatter, changing the shape of the lightcurve on time scales in order of tens of hours. The complex rotation appears to be a plausible explanation for it; the damping time scale of the complex rotation of 1997 BR (diameter estimate 1.5 km) is estimated 3 3 109 years (Harris 1994). Although this value is uncertain by more than a factor of 10, it is probably longer than the asteroid’s collisional lifetime. We searched for another frequency in the residuals of the points from the best fit curve and found that there are two, each of them, when accounted for, leads to a reduction of the scatter of points around the fitted curve. These two

frequencies correspond to periods of 18.92 and 19.54 h, but we cannot resolve between them. For both of them, there is a single pair of maximum/minimum in the residuals per period. How these two periods, together with the most prominent 33.64-h period are related to the complex rotation possibly present in the asteroid remains to be seen from further investigations. 1997 GH3 We observed this Amor asteroid on four consecutive nights, 1997 May 1.9 to 4.9. The synodic period (6.714 6 0.004) h was detected. The composite lightcurve (Fig. 26) has a relatively large amplitude, but it may be partly due to the relatively high phase angle (about 508), so the asteroid figure’s equatorial profile may be only moderately elongated. 1997 GL3 This small (estimated 0.4 km) Apollo asteroid was observed on three nights during 1997 April 10.1–13.1. Due to its faintness, we used no filter and therefore no calibration was possible. The synodic period (7.572 6 0.007) h fits the three nights’ observations well. The composite

150

´ PRAVEC, WOLF, AND SˇAROUNOVA

FIG. 26. Composite lightcurve of 1997 GH3 taken at the solar phase angles about 508.

lightcurve is complex, containing several local maxima and minima (see Fig. 27). It does not resemble any other lightcurve presented in this paper, except perhaps the (2063) Bacchus lightcurves which, however, were taken at larger phase angles. No shorter period can fit the observa-

tions. Some longer periods are formally not ruled out but they give even more complex composite lightcurves and often show insufficient lightcurve coverage; thus we consider them even less likely than the 7.572-h period. The lightcurve contains several bumps and wiggles; this

FIG. 27. Composite lightcurve of 1997 GL3 .

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS

151

FIG. 28. Composite lightcurve of 1997 SE5 .

behavior may be due to an irregular surface and shape not showing a symmetry with respect to a 1808 rotation usual in asteroidal lightcurves taken at similarly small solar phase angles. However, we consider also a possibility that this object is in an excited rotation state. Since the damping timescale of excited rotation of an object of this size and rotation period is in order of 5 3 108 years (Harris 1994), longer than its probable age, we consider the excited rotation state of this asteroid as an alternative explanation of the observed lightcurve; the detected period can be related some way to characteristic periods of the complex rotation. 1997 SE5 This Amor asteroid has a cometary type orbit with the aphelion distance 6.21 AU; thus it is a particularly interesting research target. We observed it on eight nights 1997 October 21.8–November 3.8. The synodic period (9.0583 6 0.0007) h was detected. The composite lightcurve presented in Fig. 28 is unusual, showing three maxima/ minima pairs per period. The third harmonic’s amplitude is 0.82 times that of the second harmonic—this is the strongest third harmonic among all the lightcurves presented in this paper. It indicates that the object’s shape may be unusual, although the moderately large phase angle (428) could also contribute to this. No constraint on the shape can be given from the available observations. We also measured color indices V 2 R 5 0.50 6 0.02 and R 2 I 5 0.44 6 0.02, significantly redder in comparison to solar colors. The taxonomic class best corresponding to the colors is D; thus we tentatively classify 1997 SE5 as belonging to this class. Assuming an albedo of 0.05 typical for D-type asteroids and using H 5 15.0 (MPC 31590), we estimate its diameter to be 6 km. According to Marzari et al. (1995), the orbit of the kind of 1997 SE5 is typical not

only for short-period comets, but also for Trojan fragments escaped from stable orbits around the libration point after collisional events. Since both the colors and the orbit is consistent with the Trojan nature of 1997 SE5, we consider it together with (3552) Don Quixote, which is a similar case, as possible fragments of larger Trojans.

5. DISCUSSION AND CONCLUSIONS

Most of the derived synodic periods have been detected significantly and unambiguously from the lightcurves; the exceptions are (8034) 1992 LR, 1995 FX, and 1997 GL3 —in the former two cases we saw little or no signals in the odd harmonics and there remains an uncertainty whether the detected period is not half or twice that of the real period. An interpretation of most of the periods as being the rotation periods of the asteroids is based on the assumption that they are in basic rotational states; i.e., they rotate around their principal axes. In most cases this assumption seems to hold, where we have not detected any lightcurve changes nonattributable to evolutions of the asteroids’ illumination and viewing conditions. In two cases, (3691) 1982 FT and 1997 BR, the large deviations from the mean curves found cannot be easily understood unless we introduce the hypothesis of excited rotation. These two asteroids are both slow rotators and their damping time scales of excited rotations are estimated as being of the same order as, or longer than, the age of the Solar System (Harris 1994). Thus if an excited rotation state was set in these bodies in the past, it is expected to maintain until present. The finding by Giblin and Farinella (1997) that a significant fraction of the fragments from collisional break-up events are typically found in such a tumbling state supports the hypothesis that these two objects are in the excited rotational states.

´ PRAVEC, WOLF, AND SˇAROUNOVA

152

Further observations are required to confirm this hypothesis. The periods span the range 2.3–230 h, i.e., two orders of magnitude. An analysis of a larger dataset of the NEA periods (prepared for another paper), including also the data from this paper, reveals that NEAs’ rotation rates accumulate in certain ranges; they can be divided into three groups: fast, normal, and slow rotators with periods ,3.3 h, 3.3–12 h, and .12 h, respectively. (Similar grouping was found for small, D , 50 km, main belt asteroids by Fulchignoni et al. 1995).) The NEA sample analyzed in this paper contains 6, 13, and 6 objects, respectively, in these three groups. This distribution is consistent with that found in the more abundant dataset, with about half of them being normal rotators, and each the fast and the slow rotating groups containing about a quarter of the NEA population. We have to note, however, that the population of the slow rotators may be underrepresented, since small amplitude slow rotators are difficult to detect by the photometric groundbased technique. The three groups differ in some characteristics. We discuss here only those which are apparent from the statistically small number of objects presented in this paper. At the fast rotation end of the distribution, we see the ‘‘barrier’’ to spins faster than 11 day21 (P , 2.2 h) implied by a theory of their ‘‘rubble pile’’ structure, as noted by Harris (1996). The fast rotating group does not contain large amplitude objects; the mean amplitude is 0.23, while it is 0.53 and 0.71, respectively, for the normal and slow rotators. This is also consistent with the rubble pile structure, since an elongated (high amplitude) fast rotator would split due to a large centrifugal force at its ends. The difference in the mean amplitudes between the normal and slow rotators may, however, be due only to the bias against low amplitude slow rotators in the photometric program. In the slow rotation group, damping time scales for several-kilometer sized objects are estimated to range from about 100 million years to longer than the age of the Solar System, i.e., comparable to or longer than their probable ages. Although there is observational evidence that some of them really are in the excited rotation states (see Harris (1994) for a discussion of others, in addition to the two suspected objects from this paper), the fraction of objects in excited rotation state is difficult to derive from the photometric observations. A more thorough research using a variety of techniques is needed on objects of this group to describe their nature. ACKNOWLEDGMENTS This work has been supported by the Grant Agency of the Academy of Sciences of the Czech Republic, Grant A3003708, and by the Grant Agency of the Czech Republic, Grant 205-95-1498. We are grateful to A. W. Harris (JPL) and P. Farinella for their thorough reviews and valuable comments that led to significant improvements of the paper.

REFERENCES Benner, L. A. M., R. S. Hudson, S. J. Ostro, K. D. Rosema, J. D. Giorgini, D. K. Yeomans, R. F. Jurgens, D. L. Mitchell, R. Winkler, R. Rose, M. A. Slade, M. L. Thomas, and P. Pravec 1998. Radar observations of asteroid 2063 Bacchus. Icarus, submitted. Benner, L. A. M., S. J. Ostro, J. D. Giorgini, R. F. Jurgens, D. L. Mitchell, R. Rose, K. D. Rosema, M. A. Slade, R. Winkler, D. K. Yeomans, D. B. Campbell, J. F. Chandler, and I. I. Shapiro 1997. Radar detection of near-Earth asteroids 2062 Aten, 2101 Adonis, 3103 Eger, 4544 Xanthus, and 1992 QN. Icarus 130, 296–312. Bowell, E., B. Hapke, D. Domingue, K. Muinonen, 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. Cellino, A., V. Zappala`, and P. Farinella 1989. Asteroid shapes and lightcurve morphology. Icarus 78, 298–310. Fulchignoni, M., M. A. Barucci, M. Di Martino, and E. Dotto 1995. On the evolution of the asteroid spin. Astron. Astrophys. 299, 929–932. Gaffey, M. J., K. L. Reed, and M. S. Kelley 1992. Relationship of E-type Apollo asteroid 3103 (1982 BB) to the enstatite achondrite meteorites and the Hungaria asteroids. Icarus 100, 95–109. Giblin, I., and P. Farinella 1997. Tumbling fragments from experiments simulating asteroidal catastrophic disruption. Icarus 127, 424–430. Harris, A. W. 1994. Tumbling asteroids. Icarus 107, 209–211. Harris, A. W. 1996. The rotation rates of very small asteroids: Evidence for ‘‘rubble pile’’ structure. Lunar Planet. Sci. XXVII, 493–494. Harris, A. W., and A. W. Harris 1997. On the revision of radiometric albedos and diameters of asteroids. Icarus 126, 450–454. Harris, A. W., J. W. Young, E. Bowell, L. J. Martin, R. L. Millis, M. Poutanen, F. Scaltriti, V. Zappala`, H. J. Schober, H. Debehogne, and K. W. Zeigler 1989. Photoelectric observations of asteroids 3, 24, 60, 261, and 863. Icarus 77, 171–186. Harris, A. W., J. W. Young, T. Dockweiler, J. Gibson, M. Poutanen, and E. Bowell 1992. Asteroid lightcurve observations from 1981. Icarus 95, 114–147. Hicks, M. D., U. Fink, and W. M. Grundy 1998. The unusual spectra of 15 near-Earth asteroids and extinct comet candidates. Icarus 133, 69–78. Landolt, A. U. 1992. UBVRI photometric standard stars in the magnitude range 11.5 , V , 16.0 around the celestial equator. Astron. J. 104, 340–371. Luu, J. X., and D. C. Jewitt 1990. Charge-coupled device spectra of asteroids. I. Near-Earth and 3:1 resonance asteroids. Astron. J. 99, 1985–2011. Magnusson, P., M. A. Barucci, J. D. Drummond, K. Lumme, S. J. Ostro, J. Surdej, R. C. Taylor, and V. Zappala` 1989. Determination of pole orientations and shapes of asteroids. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 66–97. Univ. of Arizona Press, Tucson. Marzari, F., P. Farinella, and V. Vanzani 1995. Are Trojan collisional families a source for short-period comets? Astron. Astrophys. 299, 267–276. Meech, K. J., O. R. Hainaut, M. W. Buie, M. A’Hearn, and C. Lisse 1996. CCD Photometry of Asteroid-Comet Transition Object 3200 Phaethon. Presented at the Asteroids, Comets, Meteors conference, Versailles, July 1996. Mottola, S., G. Hahn, P. Pravec, and L. Sˇarounova´ 1997. S/1997 (3671) 1. IAU Circ. 6680. Ostro, S. J., A. W. Harris, D. B. Campbell, I. I. Shapiro, and J. W. Young 1984. Radar and photoelectric observations of asteroid 2100 Ra-Shalom. Icarus 60, 391–403.

LIGHTCURVES OF 26 NEAR-EARTH ASTEROIDS Pravec, P., and G. Hahn 1997. Two-period lightcurve of 1994 AW1: Indication of a binary asteroid? Icarus 127, 431–440. Pravec, P., L. Sˇarounova´, and M. Wolf 1996. Lightcurves of 7 near-Earth asteroids. Icarus 124, 471–482. Pravec, P., M. Wolf, M. Varady, and P. Ba´rta 1995. CCD photometry of 6 near-Earth asteroids. Earth Moon Planets 71, 177–187. Pravec, P., M. Wolf, and L. Sˇarounova´ 1998. Occultation/eclipse events in binary asteroid 1991 VH. Icarus 133, 79–88. Pravec, P., M. Wolf, L. Sˇarounova´, A. W. Harris, and J. K. Davies 1997a. Spin vector, shape, and size of the Amor asteroid (6053) 1993 BW3. Icarus 127, 441–451. Pravec, P., M. Wolf, L. Sˇarounova´, S. Mottola, A. Erikson, G. Hahn, A. W. Harris, A. W. Harris, and J. W. Young 1997b. The near-Earth objects follow-up program. II. Results for 8 Asteroids from 1982 to 1995. Icarus 130, 275–286. Rabinowitz, D. L. 1998. Size and orbit dependent trends in the reflectance colors of Earth-approaching asteroids. Icarus 134, 342–346. Tedesco, E. F., G. J. Veeder, J. W. Fowler, and J. R. Chillemi 1992. The IRAS Minor Planet Survey, Tech. Rep. PL-TR-92-2049. Phillips Laboratory, Hanscom AF Base, MA.

153

Tholen, D. J. 1985. (3200) 1983 TB. IAU Circ. 4034. Tholen, D. J. 1989. Asteroid taxonomic classification. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 1139–1150. Univ. Arizona Press, Tucson. Veeder, G. J., M. S. Hanner, D. L. Matson, and E. F. Tedesco 1989. Radiometry of near-Earth asteroids. Astron. J. 97, 1211–1219. Weissman, P. R., M. F. A’Hearn, L. A. McFadden, and H. Rickman 1989. Evolution of comets into asteroids. In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 880–920. Univ. of Arizona Press, Tucson. Wisniewski, W. Z. 1987. Photometry of six radar target asteroids. Icarus 70, 566–572. Wisniewski, W. Z. 1991. Physical studies of small asteroids. I. Lightcurves and taxonomy of 10 asteroids. Icarus 90, 117–122. Wisniewski, W. Z., T. Michalowski, A. W. Harris, and R. S. McMillan 1997. Photometric observations of 125 asteroids. Icarus 126, 395– 449. Xu, S., R. P. Binzel, T. H. Burbine, and S. J. Bus 1995. Small main-belt asteroid spectroscopic survey: Initial results. Icarus 115, 1–35.