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Churyumov K.I., Evtushevsky A.M., Kravtsov F.I.
Astronomical Observatory and Department of Astronomy
and Space Physics of Kyiv Shevchenko University
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).
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).
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) |
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24.03
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20:43-20:49 | 3 | |||||
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25.03
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03:50-04:03 | 4 | > | ||||
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26.03
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21:36-21:47 | 6 | 1 | > | |||
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30.03
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21:57-22:08 | 3 | 1 | 1 | |||
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31.03
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20:55-23:40 | 8 | 1 | 1 | 3 | 3 x 3 | |
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1.04
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21:16-22:26 | 6 | 1 | 1 | 1 | 1 | 3 x 2 |
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2.04
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21:16-22:58 | 9 | 1 | 1 | 1 | 1 | 3 x 1 |
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3.04
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20:44-22:06 | 10 |
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5.04
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9.04
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13.04
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14.04
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21.04
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24.04
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25.04
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26.04
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27.04
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28.04
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29.04
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4.05
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5.05
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8.05
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10.05
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| Total number in each registration regime |
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| Total number from March 24 to May 10, 1997 (23 nights) |
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Motion of the shells and rotation period of the nucleus
For analysis of the data the following assumptions of the physical model were accepted:
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.
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.
At this step of procession, taking into account the visible displacement of the shells in the sequence of the images obtained from night to night, a new parameter psi0 was introduced, which is the total angle of nucleus rotation from the beginning of spiral formation to the moment of observation. In the case of comet HB due to the combination of parameters Delta psi, N and Delta t the apparent slow displacement of the shells was observed from night to night. By distance ro0, which corresponds to the polar angle phi = 0, we divided our observational data into 7 temporal sets of shells. In each set the shells with increasing values rho0 and psi0 were included. In reality in slow displacement of "like one shell" the set of different shells observed during 20-25 days took part.
As it is seen from Fig. 4, the parameters rho0 and psi0 are proportional to time:
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rho0
= rho00 + v × t,
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psi0
= psi00 + Delta psi × t,
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(4) |
where rho00 and psi00 are some constants. By the least square method the parameters rho00, v, psi00 and Delta psi were calculated and then the values t0 for rho0 = 0 and psi0 = 0 were defined (see Table 2). The intervals T(r0) and T(psi0), in which Delta psi is accumulated to one rotation (360°), can be found from the difference between values t0 for the near sets (Fig. 4) or by relations
| T(rho0) = 360/Delta psi(rho0), | |
| T(psi0) = 360 / Delta psi(psi0). | (5) |
and the average value of Delta psi0 from Table 2:
Fig. 4. Distance rho0 vs
time for the shell sets No.2-No.6
Using (2), we have defined also the final average value of the nucleus rotation period T = 11.41h (+/- 0.05h), that is in good agreement with the results of other authors: Licandro J. et al. (1998), T=11.35h; Farnham Tony L. et al. (1998), T=11.33h. As a completion of the second step of the data processing by this value of period T we calculated velocities v and accelerations g of the shells (Table 3).
Table 2. The values of t0 and Delta psi0 for 5 shell sets
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calculated by rho0 |
° /day |
calculated by psi0 |
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Table 3. Velocities v and accelerations g of the shells
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Conclusion
By the measurements of about 270
images of the shells (arcs) in the near-nucleus region of comet Hale-Bopp
observed 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 the period
of the comet nucleus rotation was determined: T = 11.41h (+/-
0.05h). Velocities of expansion of the shells (arcs)
v
are in the limits of 0.61-1.99 km/s and accelerations of the shells g are
in the limits from -18.3×10-3 m/s2 to 4.0×10-3
m/s2. Obtained us the values of velocities of the helix structures
expansion in the near nucleus region of comet Hale-Bopp are in good agreement
with the values of velocities of expansion from 0.41 to 2.00 km/s for 18
shell structures observed in the head of comet Donati (C/1858 V1) and measured
by Schmidt (1863a, 1863b).
References
Churyumov K.I., Evtushevsky O.M., Kravtsov F.I., Helix structures in the near-nucleus region of comet Hale-Bopp (C/1995 O1) and rotation of its nucleus, Prospects of astronomy and astrophysics for the new millenium, JENAM 98, Abstracts, p. 72, 1998.
Evtushevsky A.M., Milinevsky G.P., Brightness calibration of extended luminous ionospheric objects. Proceedings of Europto Series, SPIE, Airglow and Aurora, vol. 2050, p.161-164, 1993.
Farnham Tony L., David G. Schleicher, Elizabeth A. Blount, and Eric Ford, The First International Conference on Comet Hale-Bopp, Tenerife, Canary Island, Abstracts, p. 16, 1998.
Kravtsov F.I. Surface photometry and physical conditions in the atmosphere of comet Kohoutek (1973 XII), Deposition in UKRNIINTI, No. 2870, 60 p., in Ukrainian, 1987.
Licandro J., Nanci Sabalisk, P.Santos, M.Serra, M.Kidger, L.Bellot, R.Casas, A.Gomez, L.Jorda, G.-P. Tozzi, D.Osip, H.Boehnhardt. B. Goets, R.West, The rotation period of comet 1995 O1 (Hale-Bopp) at perihelion, The First International Conference on Comet Hale-Bopp, Tenerife, Canary Island, Abstracts,p. 16-17, 1998.
Schmidt J.F.J., Donati's Cometen, Astron Nachr., 59, p. 97-108, 1863a.
Schmidt J.F.J.,
Donati's Comet 1858, Publ. Athen. Obs., Ser. 1, 1863b.