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EVOLUTION OF SHELLS (SPIRAL JETS)

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EVOLUTION OF SHELLS (SPIRAL JETS) IN THE NEAR-NUCLEUS REGION OF COMET C/1995 O1 (HALE-BOPP) DURING MARCH-APRIL, 1997

Churyumov K.I., Evtushevsky A.M., Kravtsov F.I.

Astronomical Observatory and Department of Astronomy
and Space Physics of Kyiv Shevchenko University


 
Abstract

Some results of the study of shells (arcs) in the near-nucleus region of comet Hale-Bopp are presented. Nearly 270 images of the shells were obtained with the AZT-8 reflector (F=28 m, D=0.7 m) and the image intensifier "Filin-3" during March 24 - May 10, 1997 (23 nights) at Lisniky Station of the Astronomical Observatory of Kyiv Shevchenko University by A.M. Evtushevsky, F.I. Kravtsov and K.I. Churyumov. Images of the near-nucleus region of comet HB were obtained both in integral light (without filters) and using the narrow band interference IHW filters CO+ (426 nm), C3 (496 nm), C2 (514 nm), RC (red continuum, 684 nm). From our measurements we have received: 1) velocities of expansion of the shells (arcs) v are in the limits of 0.61-1.99 km/s, 2) accelerations of the shells g are in the limits from -18.3×10-3 m/s2 to 4.0×10-3 m/s2 and 3) the period of rotation of the comet nucleus T = 11.41h  (+/- 0.05h).

Observations and reductions

Shells (arcs) in the near-nucleus region of the comet Hale-Bopp (C/1995 O1) were observed during March 24 - May 10, 1997 at the Observational Station of the Astronomical Observatory of Kyiv Shevchenko University in Lisniky (near Kyiv) with the mirror telescope AZT-8 by A.M.Evtushevsky, F.I.Kravtsov and K.I.Churyumov (Churyumov et al., 1998). The images of the shells were photographed using the PHOTO-100 film from the converter tube "Filin-3" screen with the field of view ~100''. The images of the near nuclear region of comet HB were obtained both in integral light (without filters) and using the narrow band interference IHW filters CO+ (426 nm), C3 (496 nm), C2 (514 nm), RC (red continuum, 684 nm). Altogether about 270 images of the comet near-nucleus region were obtained. We have fixed from 1 to 4 shells (arcs) at the subsolar side of the comet formed due to twisting of a powerful jet of gas and dust ejected from the active area of the icy nucleus of comet HB (Figs. 1-2). Exposure time was of 1-5 s (without filters) and of 1-3 min (by using of filters or polaroid). General characteristics of observational data are given in Table 1.

In order to provide standardization during the same observational period the out-of-focus image of stars alpha Aur (0.08m, G8III), o Cas (4.54m, B2V), dzeta And (4.9m, KOIII-IV), 31 Per (5.03m, B5V) and 30 Per (5.46m, B8V0) were obtained (Evtushevsky and Milinevsky, 1993). With the aim to determine orientation of the images of the near-nucleus region of the comet as well as for determining exact value of the angle scales of the image the following double stars gamma And (9.8'', 2.3m, 5.0m, 63o), eta Per (28.3'', 3.9m, 7.9m, 301o) and 5 Lyn (96'', 5.6m, 8.1m, 272o) were photographed. In addition the orientation of the pictures was determined from the stars trails obtained by way of halting of the watch mechanism of the reflector. All these calibration procedures gave an opportunity to draw on each image a polar coordinate grid (rho, phi), where rho - the distance of the shell point from the nucleus (cometocentric distance in 104 km), phi- the polar angle measured with respect to the axis directed to the Sun. As the result of measurements we have obtained cometocentric coordinates of the shell mean line points with polar angle distances Delta phi = 10°.  For each observational night the series of 2-15 photographic images obtained during 1-2 hours were measured and the location of each shell as average was found (Fig. 2).

Fig. 1. Images of the Hale-Bopp comet shells registered in March-April 1997Fig. 1. Images of the Hale-Bopp comet shells registered in March-April 1997

Table 1. Number of images obtained at Lisniky Station with the telescope AZT-8 and
with image intensifier (16-mm input and 20-mm output windows)

Date LT With-out filters 426.0 CO+ 496.0 C3 514.0 C2 684.0 continuum 684.0
+ polaroid 
(x N series)
24.03
 20:43-20:49 3          
25.03
 03:50-04:03 4     >     
26.03
 21:36-21:47 6     1    >
30.03
 21:57-22:08 3   1 1    
31.03
 20:55-23:40 8 1   1 3 3 x 3
1.04
 21:16-22:26 6 1 1 1 1 3 x 2
2.04
 21:16-22:58 9 1 1 1 1 3 x 1
3.04
 20:44-22:06 10      
1
3 x 2
5.04
21:15-22:40
10
1
1
1
1
3 x 1
9.04
21:49-22:41
8
1
1
1
1
3 x 1
13.04
21:59-22:48
8
1
1
1
2
3 x 1
14.04
21:27-22:33
13
1
1
1
1
3 x 1
21.04
21:16-22:11
8
1
1
1
1
3 x 1
24.04
21:18-22:45
15
    
2
2
3 x 1
25.04
21:18-21:32
11
          
26.04
21:16-22:05
9
          
27.04
21:15-22:53
11
          
28.04
21:15-21:58
5
    
1
1
3 x 1
29.04
21:20-22:51
8
    
1
1
3 x 1
4.05
21:37-21:54
4
    
2
1
  
5.05
21:37-21:50
6
          
8.05
21:33-21:42
2
          
10.05
21:35-21:46
5
          
Total number in each registration regime
172
8
8
16
17
3 x 16 series = 48
Total number from March 24 to May 10, 1997 (23 nights)
269

Motion of the shells and rotation period of the nucleus

For analysis of the data the following assumptions of the physical model were accepted:

1. On the icy nuclear of the comet HB there is an active area (volcano or geyser), from which a powerful jet of gas and dust is continuously ejected; ejection parameters are stable during a few rotations.

2. The comet nucleus is rotated around its own axis with the period T and as a result a gas and dust jet forms a spiral, which projection on the sky as the concentric shells (or arcs) is well seen from the subsolar side of the comet.

3. Upon dust particles of the shells the force of solar light pressure is acting, or, dust particles in the shells are moving with some acceleration under the force of the solar light pressure.

4. Time interval between formation of neighboring shells is equal to the period T of rotation of the comet HB nucleus.

 Then the distance between neighboring shells according to the work (Kravtsov, 1987) is equal to
rhon+1 - rhon = vT + gT2 ((phi -phi0)/360 + n +1/2)cos(phi) ,                         (1)
where n is the ordinal number of a shell starting from the comet nucleus, v is the velocity of shell motion, g is acceleration under the force of solar light pressure, phi0 - the polar angle in which the first shell during the given observational night is started. Parameter phi0 is introduced as an additional direction in procedure of measurements by (Kravtsov, 1987).
Fig. 2. Spiral formations (shells) of HB comet in polar coordinates rho (104 km) and phi.
Fig. 2. Spiral formations (shells) of HB comet in polar coordinates rho (104 km) and phi (measurements distance Delta phi = 10°)

In this work the parameters v, g and T are defined in two steps. Using formula (1) and the measurement results of rn we have calculated combinations of physical parameters vT and gT2 with their errors for distances between both shells 1-2 (rho2-rho1) and shells 2-3 (rho3-rho2).

Unfortunately, the model does not allow to determine separately values v, g and T. Therefore, it is necessary to determine one of these parameters using some other method, which gives an opportunity to determine two other parameters. The parameter, which can be determined independently, is mean velocities v of the shell motion. During some nights the shells were observed for several hours. For instance, during the night of March 24/25 the shells were observed during 7 hours. We can to determine approximately the mean velocity of the shell motion and the mean period of rotation of the nucleus T. Then we used displacement of the same shell from night to night. Ten pairs of the neighboring nights with common shells in the images were found. For example, if in the first night the shells had the positions with n=1 or n=2, then in the second night they were observed with n=3 or n=4, respectively. We have obtained the mean period of the nucleus rotation of T=12.3h (+/- 1h) as the first step of its estimation.

As the mean period of the nucleus rotation is close to 1/2 day, we can write:

T = Delta t / (N + Delta N) = Delta t / (N + Delta psi / 360) = 360 × Delta t / (360 N + Delta psi),                    (2)

where Delta t is an interval between observations, N is the nucleus rotation number during Delta t rounded off to the nearest integer, Delta N is correction to N (-0.5<Delta N<0.5) caused by absence of exact multiplicity Delta t/T, Delta psi is a visible angle displacement of the nucleus active area relative to the comet-Sun direction during the time interval Delat t.

If we take Delta t = 1 day, then the first estimation of T = 12.3h  (+/-1.0h) gives N = 2 and

T = 360 / (720 + Delta psi),                (3)

where for value of T we have received the day unit and Delta psi is in degrees/day. It is seen from (3) that determination of the nucleus rotation period is reduced to definition of Delta psi from observation. By items 1 and 2 of the accepted model it follows that the phi-coordinate of the points of the spiral is proportional to time, thus in the rectangular coordinate system (rho, phi) the spiral has a form of the straight line (Fig. 3). Further procession based on this fact was made using the least square method in approximation of straight line rho = rho0 + k × phi, that allowed to calculate the parameters rho0 and k.

Fig. 3. Spirals in the rectangular coordinate system rho, phi.
Fig. 3. Spirals in the rectangular coordinate syst