TIME ANALYSIS OF THE CO+ COMA OF COMET P/HALLEY BY IMAGE PROCESSING TECHNIQUES MARCOS RINCON VOELZKE Instituto Astronˆomico e Geof´ısico da Universidade de S˜ao Paulo, CP: 9638, 01065-970 S˜ao Paulo, Brazil. E-mail address: voelzke@astro1. iagusp.usp.br

WOLFGANG SCHLOSSER and THEODOR SCHMIDT-KALER Astronomisches Institut der Ruhr-Universit¨at Bochum, Universit¨atsstraße 150, D-44801 Bochum, Germany (Received and accepted 5 May, 1997) Abstract. Photographic and photoelectric observations of comet P/Halley’s ion gas coma from CO+ ˚ were part of the Bochum Halley Monitoring Program, conducted from 1986 February 17, at 4250 A to April 17 at the European Southern Observatory on La Silla (Chile). In this spectral range it is possible to watch the continuous formation, motion and expansion of plasma structures. To observe the morphology of these structures 32 CO+ photos (glass plates) from P/Halley’s comet have been analysed. They have a field of view of 28 :6 28 :6 and were obtained from 1986 March 29, to April 17 with exposure times between 20 and 120 minutes. All photos were digitized with a PDS 2020 GM (Photometric Data System) microdensitometer at the Astronomisches Institut der Westf¨alischen Wilhelms-Universit¨at in M¨unster (one pixel 25 m 25 m 4600 :88 4600 :88). After digitization the data were reduced to relative intensities, and the part with proper calibrations were also converted to absolute intensities, expressed in terms of column densities using the image data systems MIDAS (Munich Image Data Analysis System; ESO – Image Processing Group, 1988) and IHAP (Image Handling And Processing; Middleburg, 1983). With the help of the Stellingwerf-Theta-Minimum-Method (Stellingwerf, 1978) a period of 0:09) days results from analysis of structures in the plasma-coma by subtracting subse(2:22 quent images. This method is also compared with the Fourier method. There may be a second cycle with a period of about 3.6 days. The idea behind subtracting subsequent images is that rotation effects are only 10% phenomena on gas distribution. Difference images are than used to suppress the static component of the gas cloud.



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1. Introduction Comet P/Halley (1982i) was observed photographically from 1986 February 17, to April 17 at the European Southern Observatory (ESO), La Silla, by a group of the Astronomisches Institut der Ruhr-Universit¨at Bochum. Altogether 1216 images were taken in 57 of consecutive 60 nights with exposure times between 1 s and 170 min. Photoelectric photometry of the cometary coma was obtained from February 24 to April 17, 1986, using the 61 cm-Bochum telescope. The observations aimed at the study of structure, dynamics, and physical properties of the coma, dust and plasma tail in full spatial extent, and looked for correlations in different parts of the comet with the solar wind. Table I lists the combination of cameras, emulsions, filters and exposure times. Camera code ‘FFC’ means the Lichtenknecker Flat-Field-Camera f/4 with a focal Astrophysics and Space Science 250: 35–51, 1997. c 1997 Kluwer Academic Publishers. Printed in Belgium.

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Table I Combination of image data camera

emulsion

filter

FFC FFC FFC FFC FFC FFC FFC FFC FFC FFC FFC FFC FFC WFC1 WFC1 WFC1 WFC1 WFC2 WFC2 WFC2 WFC2 WFC2 WFC2 WFC3 WFC4 UVS BOC TEL

TP 2415 TP 2415 TP 2415 TP 2415 103 a-F 103 a-F 103 a-F 103 a-F 103 a-F 103 a-E 103 a-E 103 a-E 103 a-E III a-F II a-O III a-F II a-O III a-F III a-F II a-O II a-O III a-J III a-J III a-F III a-F II a-O 103 a-F 103 a-F

OG 530 (Dust) CO+ No filter GG 410 No filter OG 530 (Dust) CO+ CN RG 645 OG 530 (Dust) CO+ CN GG 410 OG 530 (Dust) H2 O+ H2 O+ N+ 2 GG 375 + IF 4634 CO+ 2 CO+ 2 N+ 2 CO+ 2 N+ 2 CO+ CN CO+ 2 No filter RG 645

max. exposure time (in min.) 2 12 15 20 2 15 60 60 12 20 70 90 20 60 60 70 60 30 55 100 51 100 50 123 170 70 0.27 110

length of 760 mm used in combination with a Canon FTB camera housing for imaging the head of P/Halley on 35 mm film resulting in a field of view of 1: 8  2 :7 and a best angular resolution of 500 :: ‘WFCi’ indicate the use of one of the Hasselblad/Zeiss wide-field cameras 1; : : : ; 4 with a focal length of 110 mm, f/2. In order to detect the tail in its full extent these four wide-field cameras have the format 6  6 cm delivering a field of 28 :6  28 :6 and a resolution of approximately 3000 :: ‘UVS’ means UV-Sonnar and indicates a lens of 105 mm focal length, f/4.3 and high UV transmission. ‘BOC’ indicates the 61 cm-Bochum telescope. Some images were taken on 103a-F 35 mm film through the optical system of this telescope with a focal ratio of f/14 and a focal length of approximately 8.5 m. Its

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Table II List of digitized CO+ - and N2+ -filter WFC cometary images image no.

date

UT

exposure time (in minutes)

5468 5481 5492 5503 5518 5530 5546 5556 5573 5586 5602 5619 5638 5650 5675 5685 5693 5716 5732 5751 5771 5787 5804 5823 5853 5881 5913 5949 5994 6030 6139 6170 6142 6203

29.03.1986 29.03.1986 30.03.1986 30.03.1986 01.04.1986 01.04.1986 02.04.1986 02.04.1986 03.04.1986 03.04.1986 04.04.1986 04.04.1986 05.04.1986 05.04.1986 06.04.1986 06.04.1986 07.04.1986 07.04.1986 08.04.1986 08.04.1986 09.04.1986 09.04.1986 10.04.1986 10.04.1986 13.04.1986 13.04.1986 14.04.1986 14.04.1986 15.04.1986 15.04.1986 17.04.1986 17.04.1986 17.04.1986 17.04.1986

5:27 7:17 5:36 8:02 5:29 8:10 6:03 7:18 5:19 7:38 5:44 8:02 5:35 7:39 5:50 8:08 2:09 6:07 2:16 5:57 3:17 6:10 2:47 5:53 1:23 5:37 1:22 5:21 1:12 5:37 1:10 5:24 1:32 8:12

20 20 40 40 40 60 60 80 120 110 120 100 100 120 120 90 120 86 120 120 100 100 100 100 100 120 120 120 120 120 100 120 60 60

filter CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ CO+ N+ 2 N+ 2

angular resolution is seeing-limited. ‘TEL’ means telelens 300 mm, f/4, with a field of view of 4 :6  6 :9 and a resolution of 1200 :0. Here 103a-F 35 mm was used. A complete listing of the cometary images taken was published by Celnik et al. (1988).

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2. Data Reductions Thirty four CO+ - and N+ 2 -filter WFC cometary images and their spot calibrations were digitized (Table II) with a PDS 2020 GM (Photometric Data System) microdensitometer at the Astronomisches Institut der Westf¨alischen WilhelmsUniversit¨at in M¨unster (Tucholke, 1983). The step of the scan was x y 25 m so that one pixel is 25 m  25 m and corresponds approximately to 4600 :9  4600 :9. These data were saved in FITS-format (Flexible Image Transport System; Wells and Greisen, 1981) and processed with the image data systems MIDAS (Munich Image Data Analysis System; ESO – Image Processing Group, 1988) and IHAP (Image Handling And Processing; Middleburg, 1983). These 34 cometary images from 1986 March 29, to April 17 are the best series of images available because at this time the comet P/Halley was nearest to Earth so P/Halley’s coma is shown in maximal resolution (the resolution of the Wide-FieldCamera, WFC, is approximately 3000 :, about 10210 km at a distance from 0.52 A.U. (Celnik and Schmidt-Kaler, 1987)) and the comet P/Halley was visible all night at this time, thus per night two long plasma images could be taken (t  20 minutes). The other images either have too short of an exposure time (t < 20 minutes) or don’t make a pair per night, so they are inappropriate for the desired analysis.


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3. Analysis of the Structures in the CO+ -Coma After digitization the cometary images were reduced to relative intensities. To watch the development from the plasma structures during several hours (between 1h 50m and 6h 40m ) the successive images in one night were subtracted; that means: the first image of each night was subtracted from the second. With this procedure it is possible to recognize a rotation period, because in this way the static component of the gas from these cometary images are suppressed. At the beginning the brightest point (the brightest pixel) of each image was found. Afterwards the coordinates of this point were calculated and the points were overlapped. After this procedure the subtraction between the pair of images was made. In general, image A was subtracted from image B resulting in image C. This was watched with the image data system IHAP and through the difference of its colours it is possible to see the development and motion in the plasma structures along the tail and around the coma during the time between image A and B. (Figures 1 to 6. In all these figures north is at the top and west is right.) The structures around the coma were investigated and for each C image the positions (the coordinates) of the structures were calculated. These positions were measured in degrees and they were counted from the radius-vector sun – comet (at the radius-vector’s line is the angle per definition zero degree and measured in clockwise direction).

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Figure 1. CO+ cometary image number 5732 from 1986 April 8 (2:16 U.T.). The sun is at a position angle of 119 :9 (measured from north to east), that means approximately in southeast.

Figure 2. CO+ cometary image number 5751 from 1986 April 8 (5:57 U.T.). The sun is at a position angle of 121 :0 (measured from north to east), that means approximately in southeast.

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Figure 3. Difference image between the CO+ cometary images number 5732 and 5751.

Figure 4. CO+ cometary image number 5913 from 1986 April 14 (1:22 U.T.). The sun is at a position angle of 173 :9 (measured from north to east), that means approximately in south.

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Figure 5. CO+ cometary image number 5949 from 1986 April 14 (5:21 U.T.). The sun is at a position angle of 175 :7 (measured from north to east), that means approximately in south.

Figure 6. Difference image between the CO+ cometary images number 5913 and 5949.

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From 1986 March 29, to April 17 16 C-images were observed (15 CO+ -filter and one N+ 2 -filter). During the digitization it was discovered that the image number 5650 is a double exposure. It shows two nuclei for P/Halley, so it is inappropriate. Thus it and its pair image number 5638 have been rejected. A position angle (see above) was determined for the structures near the coma each day (per C-image). The data pairs (time; angle) were analysed with the Stellingwerf-method (Stellingwerf, 1978) in order to find periods from the comet P/Halley’s coma.

4. Period Analysis The methods of period analysis that are now most commonly used are the methods based on Fourier analysis (Kurtz, 1985; Deeming, 1975) and the methods of phase dispersion minimization (PDM) (Lafler and Kinman, 1965). The methods based on Fourier analysis are very well suited for the determination of periods. The typical nonequidistant distribution of the observation moments, however, makes it impossible to apply the usual properties of the Fourier periodogram. When the periodogram is defined with the aid of the harmonic analyses formulae, statistical properties of the periodogram of unequidistant observations can be derived such as the significance of a period, i.e., the probability that it is not a noise manifestation (Scargle, 1982). It is noted that the estimates of detectability at small signal-to-noise ratios as given by Horne and Baliunas (1986) are too optimistic. The accuracy of the periods found in equidistant observations has been computed by several authors. All agree that the accuracy is inversely proportional to the total time range, the signal-to-noise ratio, and the square root of the number of observations. There is, however, no agreement on the appropriate proportionality factor. Although generally assumed to be true, there is no theoretical proof that the same accuracy estimates are valid when the observations are nonequidistant. Experiments by Horne and Baliunas (1986) indicate that the accuracy is underestimated when the formulae of the equidistant case are used for nonequidistant cases. When the periodogram is computed iteratively, the Fourier methods are among the period determination methods with the shortest calculation times. Optimum performance of the Fourier methods is, however, only reached for purely sinusoidal signals. The phase dispersion minimization methods can be used to determine periods with oscillation curves of various shapes. When bin indices are used to sort the data into bins, the calculation time becomes very short even when covers as defined by Stellingwerf (1978) are used. The relation between the Fourier periodogram and the period determination statistic defined by Jurkevich (1971) is generalized, as given by Swingler (1985), to the Stellingwerf statistic with the covers. This relation indicates how the trial statistics contain information of all harmonic components at each trial frequency in contrast to the Fourier periodogram that contains only

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Figure 7. CO+ -filter data pairs time-angle.

information on the trial frequency itself. The relation also clarifies why the use of covers smooths the trial statistics. A smooth statistic facilitates the determination of the extrema. A new analysis of the characteristics of the trial statistics in the vicinity of the minimum resulted in an estimate of the expected value of the period determination statistic for signals with relatively large signal-to-noise ratios. Although the distribution of the Jurkevich statistic is known, the distribution of the statistic computed with the covers is still unknown. An accurate description of the distributions of the extrema is known for none of the statistics. The significance and the accuracy of the periods found with these methods can, therefore, only be given approximately. The permutation test proposed by Nemec and Nemec (1985) is distribution free and thus recommended for a significance test in the case of an unknown distribution. However, a detailed study of this test is necessary since the simulations are not completely consistent with the theory. Further study on the accuracy of the periods is also required, but an estimate of a confidence interval is given by Cuypers (1987). This estimate is based on the properties of the trial statistics and its usefulness has been confirmed by numerical simulations. The Fourier methods and the phase dispersion minimization methods are both suitable for determining periods. The phase dispersion minimization methods are most applicable since they can handle non-sinusoidal signals and signals with variable periods without loss of accuracy. The statistical properties of the Fourier methods have been more thoroughly studied, however, and so the significance and accuracy of a sinusoidal signal found with these methods are more reliable. It is thus recommended that more than one method be used to determine periods.

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Table III CO+ -filter data pair time-angle date

day

1986 March 29 1986 March 30 1986 April 01 1986 April 02 1986 April 03 1986 April 04 1986 April 06 1986 April 07 1986 April 08 1986 April 09 1986 April 10 1986 April 13 1986 April 14 1986 April 15 1986 April 17

29.26 30.28 1.28 2.28 3.27 4.29 6.29 7.17 8.17 9.20 10.18 13.15 14.14 15.14 17.14

time in days

angle in degrees

0.26 1.28 3.28 4.28 5.27 6.29 8.29 9.17 10.17 11.20 12.18 15.15 16.14 17.14 19.14

0 300 90 0 280 120 0 90 180 0 300 0 250 300 270

5. Results From the 16 data pairs (time; angle) (15 CO+ -filter images and one N+ 2 -filter image) only the 15 CO+ -filter images were analysed with the phase dispersion minimization method (Table III and Figure 7). 5.1. PHASE DISPERSION MINIMIZATION METHOD The phase dispersion minimization (PDM) method defined by Stellingwerf (1978) was first chosen to analyse the 15 data pairs (time; angle) because the observations are not equidistant. There are no observations on 1986 March 31, April 05, 11, 12, and 16 so the data pairs (time; angle) have a nonequidistant distribution. The properties of this method are analysed by Voelzke (1993). The 15 data pairs (time; angle) illustrated in Table III were first analysed with a bin structure Nb ; Nc 3; 2 . Resolution of the mean curve increases with M Nb  Nc , but accuracy is lost if Nb  N=5, where N means the number of observations (Stellingwerf, 1978). With this procedure a period T1 of 2:14  0:14 days has been found. The periodogram has a time interval between 1.0 and 20.0 days and has 100 basepoints, each 0.19 days separated from the other. Its bin structure (3,2) (Figure 8) shows the frequency f1 as well as some of its harmonics and subharmonics, whose values are in Table IV. After f1 had been discovered the time interval was reduced in order to obtain more accurate results. The time interval was reduced between 1.0 and 3.0 days so

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Figure 8. CO+ -filter data pairs (time; angle) periodogram for the bin structure (3,2). Table IV Significant theta-minima in P/Halley’s periodogram for a bin structure (3,2)

f in (day) 0.467 0.533 0.701 0.156 0.234 0.288 0.192

1

T in days 2:14 1:88 1:43 6:42 4:28 3:47 5:20

 0:14  0:06  0:16  0:20  0:08  0:18  0:08

 0.75 0.81 0.86 0.91 0.99 0.84 0.89

remark

interpretation

f1

a, ground or main frequency b, subharmonic of second type c, harmonic of first type d, harmonic of first type e, harmonic of first type , second main frequency , harmonic of first type

1 f1 3=2 f1 f1 =3 f1 =2

( ) f2

(2=3)f2

Figure 9. Reduced CO+ -filter data pairs (time; angle) periodogram for the bin structure (3,100).

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Figure 10. CO+ -filter data pairs (time; angle) periodogram for the bin structure (5,2). Table V Significant theta-minima in P/Halley’s periodogram for a bin structure (5,2)

f in (day)

1

T

in days

3:66 1:38 2:20 1:69 6:89

0.273 0.727 0.454 0.590 0.145

 0:16  0:10  0:14  0:06  0:16

 0.56 0.60 0.77 0.85 0.77

remark

interpretation

f1

a1, ground or main frequency b1, subharmonic of second type c1, subharmonic of second type d1, subharmonic of second type 1, second main frequency

1 1 1

f1 2f1 (3=2)f1 f2

that the 100 basepoints of the periodogram are separated by 0.02 days. For a better resolution the bin structure (3,2) was changed to a (3,100) bin structure. With this bin structure a period T1 of 2:22  0:09 days was found (Figure 9). The bin structure (5,2) was also utilized for the 15 data pairs (time; angle). The time interval of this periodogram lies between 1.0 and 20.0 days and the distance between each of the 100 basepoints is 0.19 days. With this procedure a period T1 of 3:66  0:16 days has been found which has great similarity with the frequency f2 from the bin structure (3,2). It is possible that besides the main cycle, the data showed a second period, namely 3:56  0:18 days. The periodogram shows the frequency f1 for a bin structure (5,2) (Figure 10) as well as some of its subharmonics, given in Table V. Because the analysis was based only upon 15 points the results from the bin structure Nb ; Nc 5; 2 are doubtful. This occurs because the parameter Nb would be less or equal to N=5, where N means the number of observations (Stellingwerf, 1978). Thus the more probable value for comet P/Halley’s period is 2:22  0:09 days.

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Figure 11. CO+ -filter data pairs (time; angle) spectral window.

Table VI Power spectral window for comet P/Halley

f in (day) 0.260 0.130 0.740 0.390 0.220 0.450 0.325

1

T in days 3:85 7:69 1:35 2:56 4:54 2:22 3:08

 0:13  0:63  0:02  0:11  0:23  0:08  0:13

amplitude

remark

interpretation

0.322 0.091 0.078 0.076 0.066 0.193 0.168

f1 f1 =2 1 f1 (3=2)f1 1 3f1 f2 1 (3=2)f2

a, ground or main frequency b, harmonic of first type c, subharmonic of second type d, harmonic of first type e, subharmonic of second type , second main frequency , subharmonic of second type

5.2. FOURIER METHOD

The Fourier method defined by Deeming (1975) was applied to make a comparison with the phase dispersion minimization defined by Stellingwerf (1978). The 15 data pairs (time; angle) illustrated in Table III were also analysed with the Fourier method with a frequency interval from 0.01, high frequency index equal to 100 and low frequency index equal to 0 (Deeming, 1975). With this procedure a period T1 of 3:85  0:13 days has been found, comparable to the second period of the PDM method. The spectral window has a time interval between 1.0 and 10.0 days and has 91 basepoints. It shows the frequency f1 as well as some of its harmonics and subharmonics (Figure 11), whose values are in Table VI.

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6. Brief Discussion of Periods Derived by Other Authors A series of authors give the 2.2-day periodicity, that are found in this work. The evidence for a periodicity of 52 to 53 hours or about 2.2 days was based on observations made in both 1910 (Sekanina and Larson, 1984) and 1985–86, and included the recurrence of dust jets and outbursts detected on the comet’s Earthbased images and the repeating appearance of the hydrogen halo detected by the Lyman- imager on the Suisei mission (Kaneda et al., 1986), when on the way to P/Halley. Belton et al. (1986) discovered periods of 53:96  0:03 and of 54:12  0:03 hours from pre-perihelic observations at heliocentric distances larger than 5.09 A.U.. Sagdeev et al. (1986a) found out a 53.5 hours period from images of Vega 1, Vega 2 and Giotto. The photographic analysis from CN shellstructures (Schlosser et al., 1986) and from the plasma tail (Celnik, 1986) revealed a period of 2.2 days. The analysis from CN-photographs showed that the origin of CN shells (Schulz and Schlosser, 1989), and CN jets and the oscillations from the column density profile as a function of time give a 2.2-day period. This period was subsequently confirmed by close-up imaging of the comet’s nucleus from the Vega and Giotto missions (Kaneda et al., 1986; Sagdeev et al., 1986b; Keller et al., 1986). Visual observations gave a 1.99-day period (Kosai, 1986). Vaisberg et al. (1986) and Celnik and Schmidt-Kaler (1987) discovered a period of 2.12 days. Millis and Schleicher (1986) have presented the results of their spectrophotometric observations of P/Halley on 37 nights in March and April 1986, finding strongly pronounced double-peak brightness variations with a period of 7.4 days. Williams et al. (1987), Sterken et al. (1987), Neckel and M¨unch (1987) and Vivekananda et al. (1990) confirm this periodicity in their photometric observations. Festou et al. (1987) obtained a period of 7.4 days from brightness measurements at large sun distance. Hoban et al. (1988) discovered a 7.4-day period from the CN jets analysis. The same period was also obtained by G´erard et al. (1987) by Schloerb et al. (1987) and by Colom and G´erard (1988) in the OH and CN radio range. Hanner et al. (1987) discovered a 7.4-day period in infrared, McFadden et al. (1987), Feldman et al. (1987) and Stewart (1987) in ultraviolet. The analysis from the column density profile and from the shell-structures of CN neutral gas revealed also a 7.4-day period (Schulz, 1990). Controversy concerning the two rotation periods arose, but the general feeling is that both the rotation and wobbling of the comet’s nucleus need to be considered. A dynamically significant property of P/Halley’s nucleus is its basic outlines, with one long and two short body axes in an approximately orthogonal configuration, with ratios of 1.9 : 1 : 1 (Sagdeev et al., 1986b). Unlike an oblate spheroid, the most probable position of the rotation axis is not immediately obvious. The situation is further complicated by the lack of any information on the structure and mass distribution in the comet’s interior, so that the moments of inertia about the three axes can only crudely be estimated. In addition, the highly nonspherical shape of the nucleus and the strongly collimated jets as seen on the Giotto images (Keller

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et al., 1986) suggest that the torque exerted on the nucleus by outgassing may not be negligible. The simple assumption of a homogeneous torque-free rigid rotator for Halley’s nucleus leads to a self-consistent model in which the 2.2-day period is assigned to the precession of the long axis of the nucleus and the 7.4-day period to the rotation about this axis (Sekanina, 1987). Julian (1987) modelled the comet P/Halley nucleus dynamically as a rigid homogeneous ellipsoid with three unequal principal axes in torque-free rotation about its centre of mass. Two qualitatively-distinct, free-precessional modes are found, each exhibiting both 2.2-day and 7.4-day periodicities. As viewed from the nucleus, the two modes are distinguished by the closed path (called a polhode) that the end of the angular velocity vector traces with a period of 7.4-days. The longaxis mode has a polhode that encloses only the long principal axis of the nucleus. It reduces to a motion proposed by Sekanina (1986a and 1987) when the minor axes are equal. However, because the polhode encloses the long axis in a long-axis mode, the resulting motion with a 7.4-day period around that axis conflicts with the Vega and Giotto images of the nucleus. The short-axis mode occurs when the minor axes are unequal and the polhode encloses only the short principal axis of the nucleus. The resulting motion is around the short axis and does not conflict with the spacecraft images.

7. Conclusions 1. The analysis with the Fourier method confirms the conclusion that the data show the main cycle and also a second period, because the second main frequency in the Fourier method is the same as the main frequency in the phase dispersion minimization method for a bin structure (3,100). 2. Optimum performance of the Fourier methods is only reached for purely sinusoidal signals while the phase dispersion minimization methods can handle non-sinusoidal signals and signals with variable periods without loss of accuracy. Thus the more probable value for comet P/Halley’s period calculated with the help of photographic plasma-images (CO+ -filter) made during the Bochum Halley campaign should be 2:22  0:09 days, which has been found out with the help of an analysis with the phase dispersion minimization method for a bin structure (3,100). 3. Observations provide evidence for approximately 2.2 day and 7.4 day periods in phenomena associated with the nucleus of comet P/Halley. Images of the comet P/Halley nucleus by the Vega and Giotto spacecraft (Sagdeev et al., 1986b; Sekanina and Larson, 1986; Vaisberg et al., 1986) and a compilation of recurring events (Sekanina, 1986b) show a ‘rotation’ period of roughly 2.2 days. In contrast, molecular emission intensities (C2 and CN) in the inner coma exhibit 7.4-day periodic variations (Millis and Schleicher, 1986). Based

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