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
AU, where both classes of comets are
well represented, one sees no significant difference between their
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
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).
![]() |
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 |
![]() |
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 |
![]() |
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
.
This value
is mainly due to the cluster of comets at
AU seen in Fig. 5a.
As in the previous test, focussing on a range of
AU one sees no significant difference between their
distributions.
![]() |
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 |
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
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
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 ()
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
value is 0.6 magnitudes, and the largest
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.
![]() |
Figure 7:
Histograms of a) standard
deviation (![]() ![]() |
Scotti and CCD values give similar results for comets observed
at r > 4 AU, within the error bars. The set of points at
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.
Comet | phase | HST | Our | reference |
(![]() |
radius (km) | radius (km) | ||
19P/Borrelly | 38 | 1.8-4.4 | 3.0 | Lamy et al. 1998b |
45P/Honda-Mrkos-Pajdu
![]() |
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
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.
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 ()
of the data is greater than 2.0 mag, class H (high
activity) if the standard deviation
mag; class I
(intermediate activity) if
mag; class L (low or
vanishing activity) if
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
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 (
)
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
.
By contrast,
decreases in perihelion distance (
)
are usually associated
with moderate- to high-active comets. The fact that some JF comets with
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.
Comet | ![]() |
N. obs. | Class | 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 |
:
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.
:
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.
Copyright The European Southern Observatory (ESO)