Observations of P/Tempel 2 from 1899 to 1988 corresponding to 13 apparitions are analyzed in order to estimate the perihelion asymmetry of the gas production curve for different periods of its evolution. Using the correlation found by Festou et al. (1990) between the perihelion asymmetries and the delay in perihelion passage due to the action of nongravitational forces, we estimate the mass of the comet to be M approximately equals 1.6 plus or minus 0.5 x 10(exp 14) kg. Assuming a volume of 500 cu km, based on nuclear observations, a density of 0.3 plus or minus 0.1 g/cu cm is obtained

Festou, Michel C.

Kamel, L.

Rickman, Hans

Tancredi, Gonzalo

English

NASA Technical Reports Server

H. Rickman 1, M.C. Festou 2, G. Tancredi 1 and L. Kamdl 1
I Aslronomiska Observatoriet, Boz 515, S-75120 Uppsala, Sweden
20bservatoire Midi-Pyrendes, URA 285 du CNRS, 1_ Avenue E. Belin, F-31_00 Toulouse, France
Abstract
Observations of P/Tem_p! 2 from 1899 to 1988 corresponding to 13 apparitions are analysed in order
to estimate the perihelion a_mmetry of the gas production curve for different periods of its evolution.
Using the correlation found by Festou et al. (1990) between the perihelion asymmetries and the delay in
perihelion passage due to the action of nongravitational forces , we estimate the mass of the comet to be
M _ 1.6 4-0.5-1014 kg. Assuming a volume of 500 km 3, based on nuclear observations, a density of 0.3 4- 0.1
g/cm 3 is obtained.
Introduction
In a recent paper (Festou et al. 1990) we studied the correlation between the perihelion asymmetries
of the gas production curves of periodic comets and the nongravitational perturbations of their orbital
periods. The result was that, in general, the perihelion asymmetries give the dominant contribution to
these nongravitational effects and that for comets with strongly asymmetric production curves, a reasonable
approximation is to neglect any remaining contribution whatsoever. This means in particular that if the
asymmetry parameter E can be estimated in such a case, the reduced nongravitational effect AP _ for the
interval in question can be used to estimate the ratio Qo/M of the maximum gas production rate to the mass
of the nucleus. Since in general it is possible to estimate Qm with fair accuracy, cometary mass estimates
are thus sometimes feasible. For a discussion of uncertainties associated with this procedure, see Tancredi
et al. (1991).
A case of considerable interest is comet P/Tempel 2, being a candidate spacecraft target. Indeed, its
light curve data as compiled by Kam_l (1991) indicates a strongly asymmetric gas production curve. Only a
small amount of data is as yet available on the OH production rate, but the direct measurements are in good
agreement with the expectation based on visual magnitude (Roettger et al. 1990) so the light curves can
tentatively be used to indicate both the shape and the level of the gas production curve. Here we present
an analysis of light curves of P/Tempel 2 during the 20th century. The gas production curve of the comet
will thus be studied as a secularly evolving feature and correlated with the evolution of the non-gravitational
effect. The aim is to deduce an estimate of the mass and density of the nucleus.
Light Curves
Table 1 summarizes the magnitude data that we had available for 13 apparitions of P/Tempel 2 from
1899 to 1988. This is the data contained in the Comet Light Curve Catalogue/Atlas (Kam_l 1991). In order
to estimate reliably the value of E, it is important to have a good coverage of the light curve both before and
after perihelion. While in general terms the 1899, 1925, 1967, 1983 and 1988 apparitions were well observed,
the material is sometimes heavily weighted to either side of perihelion. Thus we have to restrict our analysis
to only a few composite light curves spanning several apparitions each. The 1957, 1972 and 1978 apparitions
were even too badly observed to be included at all (e.g., in 1978 all magnitudes are explicitly nuclear). Some
care has to be applied when joining the apparitions into composites since, as will be evident from Figs. 1-3,
the shape and level of the curve has not remained constant during this century.
Fig. 1 shows a composite of the 1899-1930 apparitions, denoted by different symbols as indicated. The
plot shows only magnitudes reported as total, but in some cases they are nonetheless so conspicuously faint
that they must be regarded as quasi-nuclear. The curve denoted "nuclear mag." is the magnitude of the
real nucleus, assumed to vary as mnu¢ = Mnuc + 51g r with Mnu¢ determined from the observations by Jewitt
and Luu (1989). We take the same approach as in earlier investigations (Rickman et al. 1987; Festou et
al. 1990), in general trusting the brightest magnitudes as the best approximations to the true heliocentric
magnitude. The abscissa of the diagram is u = 4- lg(r/q), where the sign is that of the true anomaly and q
is the osculating perihelion _listance for the apparition in question. Thus the chain of straight-line segments
https://ntrs.nasa.gov/search.jsp?R=19930010042 2020-03-17T07:27:30+00:00Z
510 Asteroids, Comets, Meteors 1991
fitting the upper envelope of the set of points means that we are modelling the heliocentric magnitude mH(r)
by means of stepwise constant photometric indices. Using the formula lgQoH = 32.0 - 0.4mH (Festou
1986), we get a locally exponential gas production curve which can easily be integrated to yield the value
of E. The fit must be regarded as very uncertain concerning the leftmost segment owing to the lack of
observations with u _ -- 0.08, but ourch0ice of a steep increase_is supported by the fact that Jewitt and Luu
(1989) purportedly observed the bare nucleus at u _ -0.2. After perihelion we have two alternatives marked
by (a) and (b). The (a) curve gives credence to a Critical observation in Nov. i920 by Barnard (1931),
for which the aperture correction is important. The (b) curve assumes that this particular magnitude is
too bright. The rapid fall-off of curve (a) just after the critical point is based on assumed similarity to a
post-perihelion fit to later apparitions [curve (a) in Fig. 2]. The values of E obtained from fits (a) and
(b) in Fig. 1 are E = 0.19 AU and E = 0.16 AU, respectively, indicating a pronounced post-perihelion
excess. Nonetheless, the post:per|heii0n magnitudes appear undersampled, and-thus it is likely that these
fits underestimate the rea[value of E-. ':_:_=:_
.... in Fig. 2'the"i_46-_i967=apparitions are comblne_: Comparing with--Fig: i, we note a marked change of
the light curve. The bright magnitude at u = -0.01, observed by Van Biesbroeck (1946), is of low accuracy
and possibly half a magnitude too bright. Therefore we have disregarded it. It seems that a change in
the comet's physical behaviour must have occurred, such that it settled on a lower level of activity than
at previous apparitions with a broader maximum for several apparitions to come. This change might, for
instance, be the mantling of a previously active region on the nucleus. In view of the results by Rickman et
al. (1991) on rapid mantling and purging in response to changes in the perihelion distance, one is tempted
to look for a correlation with orbital changes. Although not conclusive, an encouraging feature is that the
1946 apparition is unique among those hitherto observed in that q had a sudden increase by 0.075 AU with
respect to the preceding ones. Thus a dust mantle might persist on a previously protected part of the nuclear
surface. :................. : :
In this case the coverage is reasonably uniform all over the curve although the spread in magnitude is
considerable. Our pre-perihelion fit disregards a few observations in 1967 that are deemed too bright, in
part due to the observed lack of activity at u _-. -0.2 in 1988. Analogously to Fig. 1, we have plotted two
alternative post-perihelion fits, and the critical observation was made in Nov. 1946 by Giclas (1947). The
(a) curve, giving credence to this observation, yields a steep fall-off reminiscent of curve (a) in Fig. 1. The
(b) curve, disregarding Giclas' observation, indicates a much slower fall-off reminiscent of curve (b) in Fig.
1. The E values differ considerably, being E = 0.42 AU for curve (a) and E = 0.28 AU for curve (b).
Fig. 3 shows a composite of the 1983 and 1988 apparitions. The shape of the light curve seems to have
changed again, but there is still serious uncertainty over its post-perihelion behaviour. In addition, there is
a problem with the pre-perihelion observations made in 1988 (u-values from -0.15 to -0.1). Negative results
obtained at the same time, in part by the same observers, indicate a lower brightness. Nevertheless, we
Table I. Statistics of available magnitude data for
P/Tempel 2. Ntot is the total number of magni-
tude estimates available, with Np_ and Npo, t as the
number of pre- and post-perihelion estimates, respec-
Table II. Results. Symbols are explained in the text
tively.
Apparition Ntot Np_e Npo, t
1899 IV 83 61 22
1920 II 22 1 21
1925 IV 94 83 11
1930 VII 11 5 6
1946 III 25 6 19 --_:_::i .... :
1951 VIii 19 14 5 :::- :_:::: _ : :
1957 II 3 0 3 :
1962 VI 24 9 15 -
1967 X ........ 112 80 32
1972 X 8 7 i
1978 V 4 1 3
1983 X _: : 206 18 188
1988 XlV 308 241 67
Linkage Q,_ (102s s-1)E (AU) M (101' kg)
1899-1930 9.3 0.18 1.1
i946-1967 3.8 0.35 1.7
1983-1988 9.7 0.27 1.6
Asteroids, Comets, Meteors 1991 511
, , , I ' ' i L' ' ' I i i ,
s 5o18_9rv' _ ' -
tD
: * 1920II _tio_l.c,,. :
,0 1o-, 19zsrv /i_ o "_'..'_ -
•,-, 14 _ b)%, -:
o.-°°"'° L7-4--_:2/
<> 18 i
i T I I I I I I I I I I I I I
-.4 -.2 0 .2 .4
U
Light curve data for comet P/Tempel 2, 1899-1930. Magnitudes obtained at different apparitions
are marked by different symbols, as indicated. The observed magnitudes have been corrected for geocentric
distance and observational effects. The u coordinate used as abscissa is explained in the text. Two possible
fits to the post-perihelion data (u > 0) are shown as (a) -solid lines - and (b) - dashed line.
I_ I i i I I I i / i i I I I I I _I
8 I--o 1946III' # ' --I
o_ 16 \\
_.- -_._.
-,4 -.2 0 .2 .4
U
Light curve data for comet P/Tempel 2, 1946-1967. Explanations are given in the caption to Fig. 1.
I_ I I I I l I i ill.l, at.i i I I i i ._.I
8 po 19s3x' _ ' -_
I-x 1988XIV ,,,,/-tilt I _it.,'_, Jio (a
-.4 -.2 0 .2 .4
U
_ Light curve data for comet P/Tempel 2, 1983-1988. Explanations are given in the caption to Fig. 1.
512 Asteroids, Comets, Meteors 1991
have some faith in the plotted magnitudes on the basis of their shear number and internal consistency, as
shown by the fitted curve. After perihelion the two apparitions give quite different curves, and further work
is needed in order to elucidate the internal relationship between these two curves as well as their possible
similarity to earlier apparitions, in particular those in Fig. 1. For the moment we have only drawn the
two fits in order to use a mean value of E as a rough estimate. Curve (a), based on the 1988 data, yields
E = 0.35 AU, whereas curve (b), based on the 1983 data, yields E = 0.18 AU.
Analysis and Discussion
Under the assumptions mentioned above, using the theory of Festou el al. (1990), We get the mass of
the nucleus from:
(3'5AU)5/2 • 67rm(ug) • QmE
U ,,_ (GMo)3/2 Apr (1)
where G is the gravitational constant, M o is the solar mass, and iug) is the net outflow speed of the gas
from the nucleus averaged over the active part of the orbit. For the latter we estimate a value of 0.3 km/s
(Rickman et al. 1987), and thus we obtain the results listed in Table 2. For each time interval we have
taken an average of our two estimates of E and in average of the A2 values listed by Marsden (1989) for
computing AP r. Considering the uncertainties involved in estlmating E (and, to some extent, Qm), the
three mass values are quite consistent, indicating a true mass near 1.6 • 1014 kg. The nucleus of P/Tempel
2 would thus be a near twin of that of P/Halley, not only regarding size and shape (Jewitt and Luu 1989)
with a volume of around 500 km 3, but also regarding mass and density. The latter can beestimated at
0.3 g/cm _, in good agreement with the result for P/Halley by Rickman (1989). The probable error of this
estimate should amount to the order of +30% in the mass, adding to an uncertainty of at least this order
for the volume.
We note that the maximum water production rate inferred for the 1988 apparition from our composite
light curve (Fig. 3) is mor_ than twice as high as the ratesrep0rted from iUE observations and found to he
consistent with visual magnitudes by Roettger et al. (1990). Further work is needed in order to resolve this
discrepancy which has its origin in different correction procedures for the magnitudes. It should be evident
that our results for the gas production curve as well as the mass and density of the nucleus are only rough
estimates that further analysis may be able to refine to some extent. In any case a correlation seems to exist
between the lower values of the nongravitational effect on P/Tempel 2 that occurred a few decades ago and
the temporary drop in the level of gas production that we find from the light curves.
References
Barnard, E.E. (1931) Observations of comets (IV), Astron. J. 41, 180-184.
Festou, M.C. (1986) The derivation of OH gas production rates from visual magnitudes of comets. In
Asteroids, Comets , Meteors H (C.-I. Lagerkvist et al., eds.), Uppsala Univ., pp. 299-303.
Festou, M.C.; Rickman, H. and Kam_l, L. (1990) Using comet light-curve asymmetries to predict comet
returns, Nature 345,235-238.
Giclas, H.L. (1947) Observations of comets, Astron. J. 52, 206-208.
Jewitt, D. and Luu, J. (i§8-9-)-A CCD portrait of comet P/Tempei 2, Astron. J. 97, 1766-1790
Kam_l, L. (1991) The Comet Light Curve Atlas, Astron. Astrophys., in press.
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Rickman, H.; Kame!l, L.; Festou, M.C. and Froeschl_, C1. (1987) Estimates of masses, volumes and densities
of short-period comet nuclei. In Diversity and Similarity of Comets (E.J. Rolfe and B. Battrick, eds.), ESA
SP-278, pp. 471-481.
Rickman, H.; Froeschl_, C.; Kam_l, L. and Festou, M.C. (1991) Nongravitational effects and the aging of
periodic comets, Astron. J., in press.
Roettger, E.E.; Feldman, P.D.; A'Hearn, M.F. and Festou, M.C. (1990) Comparison of water production
rates from UV spectroscopy and visual magnitudes for some recent comets, Icarus 86, 100-ii4.
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Twentieth century light curves and the nucleus of comet P/Tempel 2

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