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Astron. Astrophys. 363, 323-334 (2000)

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6. Activity of the comet

6.1. Observed light curves

Additional information and an independent test for the orbital solutions follow from observable light curves. Information on the total brightness of the comet is rather poor. A small number of observers and observations must be due to the comet's faintness (peak magnitude [FORMULA]). The analysis of the comet's brightness in the period 1924-1984 was based on The Comet Light Curve Catalogue/Atlas (Kamel 1991). The catalogue contains reduced magnitudes, corrected for the geocentric distance. For photographic observations a colour correction is used. In the case of the comet Wolf-Harrington, magnitudes are additionaly corrected for observational effects, e.g. the sky brightness and altitude. During the first discovery apparition in 1924 the comet was observed very shortly and remained very faint, never becoming brighter than [FORMULA] magnitude. There are only four total brightness estimates from the 1958, 1965 and 1978 apparitions. In that case the four apparitions mentioned above have been omitted in the analysis of the comet's light curves. The light curves extracted from the Catalogue for the 1951, 1971 and 1984 apparitions are represented by 25, 7 and 20 magnitude estimates, respectively, all made by 21 observers. The magnitude data used in the study of the comet's brightness in the 1991 and 1997 apparitions were reported in The International Comet Quarterly (Numbers 77-80; 101, 103-107) by 6 and 26 observers, respectively. The total number of magnitude estimates was 39 for 1991 and 85 for 1997. To construct the light curves, all of the available data were used and they were reduced to 1 AU geocentric distance. The small number of estimates provided by each observer did not allow to find the systematic personal errors. Furthermore, no corrections for telescope apperture were applied. All derived light curves are presented in Fig. 4 as the heliocentric magnitudes versus time from the perihelion passage. The magnitude data are marked with open circles. The solid and dashed lines are the theoretical light curves obtained on the basis of the orbital solutions.

[FIGURE] Fig. 4. Heliocentric magnitude of the comet 43P/Wolf-Harrington for the 1952, 1971, 1984, 1991 and 1997 apparitions. The observed brightnesses are marked with open circles. The water production rate, Q, converted into [FORMULA] are shown with full triangles. The theoretical light curves derived from Model A and B for the spotty nucleus are plotted with solid and dashed lines, respectively.

6.2. Theoretical light curves

To compare the observed brightness variations of the comet with the modeled profile of its activity the Model A and Model B have been applied. For each active region the rotational-averaged water sublimation rates per unit surface area (km2):


have been derived over each orbit under consideration. The averaged sublimation rates for the whole comet nucleus are as follow:


where [FORMULA]. The constants [FORMULA] derived from orbital calculations are given in Table 6. If the appropriate region was inactive at any time then [FORMULA]. The profiles of the outgassing curves for the Model A are shown in Fig. 5 as the logarithm of the modeled sublimation rates [FORMULA] versus time to perihelion in successive apparitions. Variations of shapes are evident due to initiation and deactivation of the regions and evolution of the orbit as well. One can see that until the 1971 apparition the maxima occured before perihelion passages, for 1984 and 1991 apparitions they fall clearly after perihelion but during the last return of the comet the shift was slightly negative again.

[FIGURE] Fig. 5. Rotational-averaged water sublimation rate in function of the perihelion time derived from Model A and B for all apparitions of comet 43P/Wolf-Harrington.

Next, [FORMULA] was transformed into the total water production rate, Q, expressed in molecules per second, using the relation: [FORMULA], where [FORMULA] is the total outgassing area. In the other words the vertical shift between the Q and [FORMULA] yields the active area on the comet surface. Finally the water production rate was related to the heliocentric magnitude. The empirical law in the form of linear dependences between the logarithm of the production rate and the visual magnitude were proposed by several authors (Jorda et al. 1992, Festou 1986, Sekanina 1989). For the comet P/Wolf-Harrington there is a possibility to verify this relationship because OH production rates derived from the narrow-band photometry are available (Schleicher et al. 1993). The four pre-perihelion [FORMULA] estimates from the 1991 and one post-perihelion data from the 1984 combine with the observed brightness of the comet were used to establish the first coefficient in the calibration formula:


The second coefficient comes from Jorda et al. (1992) and is close to the value usually used. The water production rate is related to the OH production rate by: [FORMULA]. Five water sublimation estimations given by Schleicher et al. were converted into [FORMULA] and marked with triangles in Fig. 4. Theoretical light curve can be express by:


The shape of the [FORMULA] curve is determined by an insolation pattern in each apparition but their amplitude depends on the outgassing area as well. To establish the total size of the active area, [FORMULA], the level of the observed and theoretical light curve should be compared. The theoretical light curve from 1991 was scaled by an active area to reach the observed level of the comet's brightness in this apparition. In a result for [FORMULA] was adopted value of 3.76 km2 (Model A) and 4.90 km2 (Model B). The total outgassing area is a sum of areas of every regions ([FORMULA]) and on the other hand: [FORMULA]. Thus it is possible to determine the area of each active spot on the nucleus and the variation of [FORMULA] in the successive apparitions, too. The appropriate total outgassing areas, [FORMULA] are given in Table 8. Taking into account these values, the variations of the comet brightnesses [FORMULA] could be calculated from Eq. (10). They are plotted in Fig. 4 by solid and dashed lines for Model A and Model B, respectively. To compare the observed and theoretical light curves the apparitions 1951, 1971, 1984, 1991 and 1997 with known brightness estimates have been chosen only. It should be noticed that theoretical curves are fitted quite well to observed ones.


Table 8. Maxima of the theoretical light curves measured in magnitudes and its time shift respect to successive perihelions between 1924 and 2010 with corresponding to them the total ougassing areas and the active fractions of the nucleus calculated for the radius nucleus amounted to 1.07 km (Model A) and 1.12 km (Model B).

The shifts of maxima of the brightness curves with respect to perihelion in the successive returns of the comet, [FORMULA], and their maximum values [FORMULA] measured in magnitudes are listed in Table 8. In Columns 5 (Model A) and 10 (Model B) the activity level understood as the fraction of the total surface participating in the outgassing were given. The active fractions were calculated from the expression [FORMULA]. For the nucleus radius, R, the values 1.07 km (Model A) and 1.12 km (Model B) were assumed (see Sect. 7).

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000