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Subsections

8 Discussion

8.1 Reliability of our adopted magnitudes

To discuss the reliability of our adopted nuclear magnitudes, we performed a few tests by comparing different subsets of data. In Figs. 3a and 3b we compare the adopted nuclear magnitudes with respect to different quality classes. We group the comets of QC 1, 2 and 3 together, and compare them with those of QC 4. We find just minor differences between the two subsets. There are slightly more faint magnitudes in QC 4 than in the rest. This is consistent with the expectation in case the magnitudes are generally free of systematic errors. The only correlation in such a case should be due to the smallest nuclei being more difficult to observe and hence showing a preference for QC 4, just as we observe.

In Figs. 4a and 4b we use as a classification criterion the number of revolutions spanned by the observations. We distinguish two groups: comets that have been observed during several revolutions, and those observed at just one perihelion passage. While the marginal distribution in Fig. 4b indicates a trend for brighter nuclei of one-apparition comets, one easily sees from Fig. 4a that this is due to a preference of larger perihelion distances of one-apparition comets. This is, in turn, due to the fact that large-qcomets have a much shorter history of discoveries than their small-qanalogues.

Focussing on a range of $q \ ^{<}\!\!\!\!_{\sim}\> 2.5$ AU, where both classes of comets are well represented, one sees no significant difference between their $H_{\rm N}$distributions. Had such a difference appeared, this would have led to some worry over the quality of our magnitudes, especially if the one-apparition comets had shown brighter nuclei. It is true that these are often active near aphelion (see further Sect. 8.3), but apparently our $H_{\rm N}$ values are not seriously affected by this. Nonetheless, we generally give a low quality class to the adopted nuclear magnitude based on data taken on one passage; there is a larger fraction of comets with QC 4 compared to the ones with QC 1-3 in the set of one-passage comets (13:10) than in the set with more than one passage (28:54).


  \begin{figure}
{\resizebox{8.8cm}{!}{\includegraphics{ds1835f3.ps}} }
\end{figure} Figure 3: a) Adopted nuclear magnitudes vs. perihelion distance for comets in QC 1-3 (full circles) and comets in QC 4 (open circles), the numbers in parentheses correspond to the numbers of objects in the quality classes. b) The marginal distributions of magnitudes for the subsets shown in 3a


  \begin{figure}
{\resizebox{8.8cm}{!}{\includegraphics{ds1835f4.ps}} }
\end{figure} Figure 4: a) Adopted nuclear magnitudes vs. perihelion distance for comets with observations spanning more than one revolution (full circles) and observed just in the discovery passage (open circles), the numbers in parentheses correspond to the numbers of objects in the defined groups. b) The marginal distributions of magnitudes for the subsets shown in 4a


  \begin{figure}
{\resizebox{8.8cm}{!}{\includegraphics{ds1835f5.ps}} }
\end{figure} Figure 5: a) Adopted nuclear magnitudes vs. perihelion distance for comets with low activity at large heliocentric distances (classes L and I in Sect. 8.3) (full circles) and comets with high activity (classes H and V) (open circles), the numbers in parentheses correspond to the numbers of objects in the defined groups. b) The marginal distributions of magnitudes for the subsets shown in 5a

In the following test we use as a classification criteria the activity at large heliocentric distances (Figs. 5a and 5b). In Sect. 8.3 we explain the parameters used to classify the comets according to the activity. From the comparison of the two marginal distribution in Fig. 5b we note a high fraction of active comets at $H_{\rm N} \sim 16$. This value is mainly due to the cluster of comets at $q \sim 4$ AU seen in Fig. 5a. As in the previous test, focussing on a range of $q \ ^{<}\!\!\!\!_{\sim}\> 2.5$ AU one sees no significant difference between their $H_{\rm N}$ distributions.

  \begin{figure}
\par {\resizebox{6cm}{!}{\includegraphics{ds1835f6.ps}} }
\par {\...
...s}} }
\par {\resizebox{6cm}{!}{\includegraphics{ds1835f8.ps}} }
\par\end{figure} Figure 6: Comparison between a) Roemer, b) CCD and c) Scotti observations with our adopted magnitudes. The stars correspond to the mean value in bins of 1 AU in heliocentricdistance

   
8.2 Comparisons among observers

The differences between the reported nuclear magnitudes and our best estimates are plotted in Fig. 6 as a function of the heliocentric distances of the observations, for the data of Roemer's, CCD (general), and Scotti's nuclear magnitudes (magnitudes from Scotti reported as total are not considered). Each observation is represented as a dot. The stars correspond to the mean value in bins of 1 AU in heliocentric distance.

Roemer's data is usually about two magnitudes brighter than our best estimates of the nuclear magnitudes (see Fig. 6a) at any heliocentric distance. This is a clear indication that Roemer's magnitudes are strongly affected by coma contamination. The observations closer to the Sun show a large scatter with a trend to increase the difference between Roemer's and our values, presumably due to the larger activity of comets closer to the Sun. We conclude that Roemer's data provide good values of the nuclear magnitudes only for low active comets, so all the conclusions about nuclear magnitudes of JF comets and masses derived from her data (e.g. Shoemaker & Wolfe 1982), should be revisited (see Fernández et al. 1999).

CCD data have strong signs of coma contamination in most of the observations done at r < 4 AU (see Fig. 6b). The scatter of the observations at r > 4 AU (except the data points at $r \sim
6$ AU, see below), and those that give fainter values than our estimated magnitudes can be explained as due to nucleus rotation and/or errors involved in the computation of the nuclear magnitude (error in the $\beta $ coefficient, color correction, etc.).

Scotti's nuclear magnitudes have to be treated with special care as most of these data are obtained by subtracting the coma contribution (see Sect. 3.2), and the validity of this method should be studied. Figure 6c shows a large scatter of the data at any heliocentric distance. The interpretation in this case is different from the case of Roemer or CCD data. The scatter in Scotti's data is not due to coma contamination as the method subtracts, in principle, the coma contribution. This scatter may be interpreted as an error induced by the subtraction method (cf. Sect. 3.2). To study the internal consistency of Scotti's method, we compute the mean value and the standard deviation ($\sigma $) of his determinations for all comets with more than three observations (see Fig. 7). Also the difference between Scotti's mean value and our adopted nuclear magnitude is computed. The mean $\sigma $ value is 0.6 magnitudes, and the largest $\sigma $ is 1.4 magnitudes. In most cases the observations of the same comet obtained at different heliocentric distances give coherent values with an error of some tenths of magnitude, but for some comets their magnitudes show a trend parallel to the one of the "coma unsubtracted'' magnitudes (e.g. comets 51P/Harrington, 110P/Hartley 3, 120P/Mueller 1, 24P/Schaumasse, and 9P/Tempel 1). Nevertheless, for most comets the method provides a reasonably good value with an error of some tenths of a magnitude, and it becomes very useful - and meaningful - when several determinations at different heliocentric distances can be collected and compared.


  \begin{figure}
{\resizebox{8.8cm}{!}{\includegraphics{ds1835f9.ps}} }
\end{figure} Figure 7: Histograms of a) standard deviation ($\sigma $) of Scotti's nuclear magnitude estimates for the same comet, and b) $\Delta H_V$ - the difference of the mean of his magnitudes and our adopted nuclear magnitude

Scotti and CCD values give similar results for comets observed at r > 4 AU, within the error bars. The set of points at $r \sim
6$ AU in both data sets mainly corresponds to observations of 29P/Schwassmann-Wachmann 1. This comet shows continuous activity with sporadic outbursts (Jewitt 1990). Note that those magnitudes were either reported as nuclear or a coma subtraction method was applied. The large scatter in the data indicates the difficulties of detecting a faint coma at large heliocentric distances.

 

 
Table 6: Comparison between the HST and our own comet radius estimates
Comet phase HST Our reference
  ($\deg$) radius (km) radius (km)  
19P/Borrelly 38 1.8-4.4 3.0 Lamy et al. 1998b
45P/Honda-Mrkos-Pajdu $\breve{\rm s}$áková 90 0.35 0.5 Lamy et al. 1997
22P/Kopff 3 1.65rr-1.92 1.8 Lamy et al. 1996
4P/Faye 6r-19 2.7 2.2 Lamy & Toth 1995
46P/Wirtanen 10 0.60 0.7 Lamy et al. 1998a
9P/Tempel 1 4 2.8r-r3.9 2.9 IAUC 7000


Considering that at small r CCD determinations are largely affected by coma contamination, Scotti's data at small r become decisive to estimate the nuclear magnitudes of those comets without observations at $r \ ^{>}\!\!\!\!_{\sim}\> 4$ AU, and permits to analyse if the comet is still active at large heliocentric distances by comparing the results with CCD observations.

In Table 6 we compare the HST radius estimates with our own values. Note that we have included comets 19P/Borrelly and 45P/Honda-Mrkos-Pajdusáková that were observed at large phase angles, although they were not included in our data set (i.e. our estimates do not take into account the HST observations for these objects). Taken into account that for our adopted magnitude we include data from many other observers, our estimates show good agreement with the HST observations, including the cases of the comets observed at very large phase angles.

   
8.3 Activity at large heliocentric distances

Activity at large heliocentric distances (r > 4 AU) is not a rare phenomenon. Licandro et al. (1999a) present observations of 18 comets, and find that six of them, observed at r > 4 AU, had coma and even tail. Another indication of this kind of activity and the problems to detect it can be observed in the comets that present a trend to increase the estimate of the nuclear brightness with the heliocentric distance, like comets: 2P/Encke, 26P/Grigg-Skjellerup, 103P/Hartley 2, and 10P/Tempel 2. This trend, opposite to the rest of the comets and to the common sense, can only be explained if some remaining activity can be masked in a stellar-like brightness profile.

The data compiled in the present paper can be used to analyse the activity level of the well observed comets. From the plots of reduced magnitudes vs. heliocentric distances (r) shown in Appendix B, we can classify the comets with respect to the degree of activity at large r that can be read off from the dispersion of the brightness observed at large r.

Considering all the observations done at r>3 AU (total and nuclear estimates) we classify the comets with more than 10 observations into four classes defined as follows: class V (very high activity) if the standard deviation ($\sigma $) of the data is greater than 2.0 mag, class H (high activity) if the standard deviation $1.0 \leq \sigma < 2.0$ mag; class I (intermediate activity) if $0.4 < \sigma \leq 1.0$ mag; class L (low or vanishing activity) if $\sigma \leq 0.4$ mag. The limit of 0.4 mag was chosen because for a nucleus of axial ratio a/b=2 observed with its spin axis perpendicular to the line of sight, the typical lightcurve half-amplitude just due to rotation is $\sim 0.4$ magnitudes. Table 7 contains the classes ascribed to a total of 61 comets. Nearly 60% of the comets are of class H or V. The explanation for this predominance of remote activity is likely to involve several mechanisms:

Licandro et al. (1999a) found a strong correlation between activity at large heliocentric distances and recent downward jumps in perihelion distances. They relate this correlation to the hypothesis of mantle formation. The large grains cannot be lifted by the outflowing gases and thus remain on the nucleus forming a crust of dust. If the comet remains at a given perihelion distance for a few revolutions, a thin crust is formed that chokes off the sublimation of the ices (Rickman et al. 1990). When a downward jump occurs, the temperature rises, the vapour pressure increases, and the marginally stable crust is blown off. Large areas of fresh ices are then exposed to the Sun; the gas flux, and consequently the dust flux, increases.

Information related to the recent downward jumps is also presented in Table 7, obtained from an updated version of the numerical integrations of the dynamical evolution of Jupiter family comets (Tancredi & Rickman 1992). These data are graphically presented in Fig. 8. The maximum relative change in the perihelion distance ( $\delta q/q$) experienced by the comet during the last 20 revolutions is plotted against the minimum perihelion distance reached by the comet in the observed period, for the three classes defined above. As expected, there is a strong concentration of low-active JF comets toward $\delta q \sim 0$. By contrast, decreases in perihelion distance ( $\delta q < 0$) are usually associated with moderate- to high-active comets. The fact that some JF comets with $\delta q \sim 0$ are rather active is an indication that other factors, besides reduction in q, are at work in producing an enhancement in the cometary activity as, for instance, splittings.


 

 
Table 7: Classification of comets with regard to the degree of activity
Comet $\sigma $ N. obs. Class q (AU) $\delta q$ (AU) N. rev.
49P/Arend-Rigaux 0.36 13 L 1.37 0 -
47P/Ashbrook-Jackson 1.87 51 H 2.28 -1.5 7
19P/Borrelly 0.47 12 I 1.32 0 -
87P/Bus 0.64 16 I 2.18 -2.3 7
101P/Chernykh 1.18 26 H 2.36 -0.2 1
67P/Churyumov-Gerasimenko 0.58 13 I 1.29 -1.4 6
32P/Comas-Sola 1.13 46 H 1.77 -0.4 10
2P/Encke 0.74 61 I 0.33 0 -
4P/Faye 0.70 33 I 1.59 0 -
90P/Gehrels 1 1.92 12 H 2.94 0 -
78P/Gehrels 2 0.43 10 L 2.00 -0.3 4
82P/Gehrels 3 1.67 42 H 3.42 -2.3 3
P/1997C1 (Gehrels) 1.20 81 H 3.57 -1.0 1
21P/Giacobini-Zinner 0.67 37 I 0.93 -0.3 15
65P/Gunn 1.31 142 H 2.44 -1.1 7
110P/Hartley 3 1.63 16 H 2.45 -0.2 2
P/1993K2 (Helin-Lawrence) 0.91 45 I 3.09 -0.6 1
117P/Helin-Roman-Alu 1 1.11 81 H 3.71 -0.8 11
111P/Helin-Roman-Crockett 2.72 60 V 3.47 -1.8 3
88P/Howell 2.14 11 V 1.41 -0.3 3
P/1995A1 (Jedicke) 1.04 42 H 4.08 0 -
P/1996A1 (Jedicke) 0.95 140 I 4.06 0 -
48P/Johnson 0.26 26 L 2.20 0 -
59P/Kearns-Kwee 1.39 10 H 2.21 -2.1 4
68P/Klemola 0.34 15 L 1.76 0 -
70P/Kojima 0.80 10 I 1.63 +0.4 4
22P/Kopff 1.67 34 H 1.50 -0.9 18
99P/Kowal 1 1.31 21 H 4.66 +0.3 3
134P/Kowal-Vávrová 1.02 30 H 2.61 0 -
P/1993X1 (Kushida-Muramatsu) 1.03 17 H 2.75 -1.6 5
P/1997T3 (Lagerkvist-Carsenty) 0.54 46 I 4.24 -5.1 3
P/1997V1 (Larsen) 0.77 113 I 3.29 0 -
77P/Longmore 1.21 13 H 2.40 -0.7 5
P/1997G1 (Montani) 1.02 55 H 4.22 0 0
120P/Mueller 1 1.00 17 I 2.74 -0.9 5
136P/Mueller 3 1.10 21 H 3.00 -0.5 3
P/1993W1 (Mueller 5) 1.75 44 H 4.25 0 -
28P/Neujmin 1 0.25 12 L 1.53 0 -

39P/Oterma

1.11 115 H 3.39 -2.4 3
119P/Parker-Hartley 1.06 109 H 3.03 -1.4 2
7P/ Pons-Winnecke 0.67 13 I 0.77 0 -
30P/Reinmuth 1 0.87 15 I 1.86 0 -
44P/Reinmuth 2 1.53 17 H 1.87 0 -
94P/Russell 4 0.43 21 L 2.13 -0.3 4
29P/Schwassmann-Wachmann 1 1.33 245 H 5.45 0 0
31P/Schwassmann-Wachmann 2 1.34 48 H 2.07 -1.4 11
P/1994J3 (Shoemaker 4) 0.80 50 I 2.94 0 -
128P/Shoemaker-Holt 1 2.59 42 V 3.05 -1.1 2
121P/Shoemaker-Holt 2 2.37 22 V 2.65 -0.6 2
137P/Shoemaker-Levy 2 0.43 10 L 1.84 0 -
129P/Shoemaker-Levy 3 0.84 14 I 2.81 -6.3 13
118P/Shoemaker-Levy 4 1.56 33 H 2.02 0 -
135P/Shoemaker-Levy 8 1.40 18 H 2.71 -2.5 1
74P/Smirnova-Chernykh 1.18 109 H 3.55 -1.7 4
9P/Tempel 1 0.52 40 I 1.49 -0.4 10
10P/Tempel 2 0.58 63 I 1.31 0 -
53P/van Biesbroeck 1.28 52 H 2.40 0 -
36P/Whipple 1.04 56 H 2.45 -2.4 10
81P/Wild 2 1.60 27 H 1.49 -3.5 4
116P/Wild 4 2.06 19 V 1.99 -1.4 2
43P/Wolf-Harrington 0.61 15 I 1.58 -1.0 10

$\sigma $: Standard deviation of the all the observations at r > 3 AU.
N. obs.: Number of data points.
Class: L - Low-active; I - Intermediate-active; H - High-active; and V - Vey-High-active. $\delta q$: Change in perihelion distance. Negatives values correspond to downward jumps.
N. rev.: Number of revolutions from the last change in q to the last perihelion passage.



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