Physical Properties of Comets
K. J. Meech
Institute for Astronomy, University of Hawai`i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
ABSTRACT
There have been several recent reviews of the physical properties of cometary nuclei, most concentrating on
the specics of the rotation periods, shapes, sizes and the surface properties. This review will present an
updated summary of these properties based on recent observations. There are nucleus parameters known for
26 nuclei. These comet nuclei are relatively small prolate ellipsoids of low albedo. The axis ratios range
between 1.1{2.6 which when combined with rotation periods constrains the density lower limits. Typically
the nuclei are found to have very small fractional active areas. Little direct observational evidence exists
for the internal physical properties, however, the results to date suggest a strengthless agglomeration of
gravitationally bound planetesimals with a bulk density between 0.5-1.0 gm cm,3 .
INTRODUCTION
With recent advances in theoretical models of the early solar system it is becoming increasingly important
to have a good understanding of the physical properties of cometary nuclei, so that they may be used to
constrain models of solar nebula evolution. Early models of the comet formation environment suggested
that most comets formed in the Uranus-Neptune zone at temperatures between 25{60K. Our current understanding of the early solar system suggests that the proto{planetary disks are much more massive than
previously believed. Lissauer (1987) shows that the accumulation of Jupiter's core required a solar nebula
surface density many times larger than the minimum mass solar nebula. Furthermore, observations show
that 25-50% of pre{main sequence stars have massive circumstellar disks which extend to beyond 100 AU
from the central star with masses up to 1 M (Beckwith and Sargent, 1993). In these more massive models,
the innermost region for comet formation occurs between the heliocentric distances r = 14{16 AU (i.e. near
60K as determined by the volatile composition of comets), and the most distant region between 80{110 AU
(Yamamoto, 1985). As summarized by Weissman (1995), the current comet formation paradigm is that the
comets which originated in the Uranus{Neptune zone were dynamically ejected out to the Oort cloud, while
comets forming further out in the region now known as the Kuiper Belt (KB), remained in{situ. As shown
by Levison and Duncan (1993) and Holman and Wisdom (1993), the KB comets are the most predominant
source of the observable short{period comets. While there is now a much better understanding of the general
comet formation environment, there is presently no self{consistent scenario leading from the coagulation of
the m{sized interstellar dust grains to the km{scale planetesimals. Lunine et al. (1991) have argued that
with the thicker disks it is probable that shock heating during infall to the disk mid{plane will cause some
sublimation of the primordial ices (the extent to which this occurs will be a function of radial distance from
the protostar). Furthermore, gas turbulence in the nebula will not allow planetesimal formation via simple
Van der Waals sticking and gravitational collapse (Weidenschilling, 1988). Weidenschilling and Cuzzi (1993)
have shown that turbulent models for m-sized to m{sized planetesimal growth may be developed that predict possible radial and vertical mixing in the nebula. These eects might be observable as compositional
dierences in meteorites or comets. However, the stage of planetesimal formation from m{sized to km{sized
is not understood at all, and is sensitive to the disk turbulence (hence disk mass and convection within the
disk). The still poorly understood km{scale planetesimal stage of evolution is accessible through observations of today's comets, and by assessing their physical properties as a function of formation location, we
can place some invaluable constraints on the solar nebula models. The rate of the protoplanetary growth
1
as a function of r depended on the size and mass distribution of the km-sized planetesimals (which have
survived as today's comets), their surface density in the nebula and their velocity distributions (Lissauer
and Stewart, 1993). Unfortunately, as observations and detectors are becoming more sophisticated, we are
nding that comets exhibit activity and dust comae out to much larger distances than previously believed
(Meech, 1994), so that probably most historical comet observations do not pertain to the nuclei. In fact,
until recently, we probably had very little direct knowledge of the nucleus properties.
Techniques for Measurement of Nucleus Properties
Not only are the global physical properties important for the understanding of the early solar system accretion models, but the nucleus size, albedo and rotational periods are critical parameters which aect the solar
energy distribution on the surface which will dictate the nature of a comet's activity. Even more dicult
to observe, but more important to the understanding of cometary activity and ultimately to the origins of
the comets, are the internal physical properties, including the volatile composition, dust{to{gas mass ratios,
and the thermo{physical properties of the nucleus: thermal conductivity, pore size, porosity and nucleus
bulk density. The evolution of activity in the nucleus is closely tied to the rate at which heat penetrates
into the interior, as dictated by the thermal parameters. The porosity, tensile strength and nucleus density
play critical roles in outbursts, splitting and tidal disruption, as well as in the observed non{gravitational
motions. However, as will be shown below, information about the internal properties of nuclei is much less
well{constrained than for the external properties. In this review, the discussion will be restricted to the
external physical properties and the thermo{physical properties.
Nucleus Size Distributions
Nucleus sizes were rst estimated from photographic measurements at large r when the nucleus was believed
to be inactive (Roemer, 1966). By making assumptions about the visual albedo, pv , the nucleus radius could
be estimated from the observed magnitude, m:
pv R2N = 2:24 1022 r2210,0:4(m,m)
[1]
where RN is in [m], r and in [AU] and m is the sun's magnitude. The disadvantage of this technique
was that the photographic plates are not very sensitive to the extremely low surface{brightness comae which
might be present. Often the nucleus radii so determined were upper limits (Sekanina, 1976). Additionally,
the unknown nucleus albedo created a range of size estimates. The rst application of the technique using
modern linear CCD detectors was with the recovery of comet P/Halley (Jewitt & Danielson, 1984). This
technique was subsequently used extensively by Jewitt and Meech (1985, 1987, 1988a). This is the most
reliable easily applied means of remote determination of RN when the nucleus is inactive. Nevertheless, it is
dependent upon the unknown nucleus albedo. The sensitivity of CCD detectors is required to measure the
scattered radiation of these relatively small low{albedo objects when they are far from the sun. Radiometry,
a direct method for determining the Bond albedo of an object was rst applied to asteroids in the 1970s
(Allen, 1970), and a second technique utilizing thermal ux measurements and optical photometry of active
comets was used to determine the albedo of the dust grains (O'Dell, 1971). The rst technique allows both
the albedo and diameter to be determined from a simultaneous IR and optical detection if a comet is large
enough and suciently close to the sun that it can be detected in the IR, but before the observations are
contaminated by dust. These techniques have been applied to only a few nuclei. A summary of albedos
of coma material (Meech, 1987), shows that the albedo of the dust is generally low (0.03 < pv < 0.14).
Finally, Lamy and Toth (1995) have recently developed an indirect technique to model and remove the
coma contribution from high{resolution (HST) images of active comets in order to infer the nucleus size.
In total, we have reasonable physical size estimates for 2 dozen comet nuclei (cf. Table 1). The nuclei
are quite small, and in fact, estimates of sizes have continued to decrease as better techniques emerge, and
it is likely that we are seeing cometary activity at larger distances than previously believed (Meech, 1994).
This forces the observations to be made at large r where they are more dicult. This evolution of nucleus
size estimates, which is leading to a decrease in the inferred sizes is shown in Fig. 1. The top panel plots
the directly measured radii from Table 1. Recently, large telescope time has been dedicated to obtaining
upper limits on the radii of periodic comets with well{known orbits (Hainaut et al., 1994). This technique
uses a non{detection or a measurement of nucleus plus coma as an upper limit to the nucleus ux. The
distribution for these directly measured upper limits is shown in Fig. 1b. While the distribution is wider than
2
1 | Comparison of nucleus size
distributions determined by several direct and indirect techniques: (a) direct
measurements of bare nuclei (cf. Table 1); (b) periodic comet and dynamically new nucleus upper limits (Hainaut
et al., 1994; Meech, 1994); (c) coma corrected measurements (Scotti, 1994); (d)
CLICC visual observation extrapolations
(data from Kamel, 1992); and (e) normalized comparison of the direct observation
technique [a-c] with the CLICC method,
showing that the \traditional" estimates
of nucleus size tend to be too large because of coma contamination.
Fig.
that of the directly observed nuclei, it is clear that the populations show similar sizes. Scotti (1994) has
been using the Spacewatch Telescope on Kitt Peak to make astrometric observations of a large number of
comets, and has extracted \nuclear magnitudes from the data by estimating and removing any coma contribution. The measurements of over 60 comets which were made by this technique are shown in Fig. 1c. A
fourth technique for nucleus size estimatation uses the data of Kamel (1992) who has produced an enormous
periodic comet light{curve catalogue/atlas (CLICC) covering the period from 1899{1989. By plotting the
light curves as a function of r and comparing them with the expected r,2 light curve dependence for a bare
nucleus, one can estimate at which point in the orbit the comet
is inactive and from this estimate the nucleus size for an assumed
albedo. This has traditionally been the basis for many estimates
of nucleus sizes. The results of this are shown in Fig. 1d. A comparison of the directly estimated bare nucleus measurements and
the inferred nucleus sizes from Kamel are shown in Fig. 1e. The
size distribution for the CLICC comets is clearly broader than the
other distributions, which probably reects the fact that this is not
a reliable way to infer the absence of a dust coma. In particular,
for many of these comets, observations don't extend much beyond
r = 3 AU, and clearly experience with comet P/Halley has shown
that H2 O{ice activity can begin as early as r = 6 AU (Meech et
al., 1986).
The exciting new discoveries of the Trans{Neptunian (TNO) or
Kuiper Belt (KB) Objects (Jewitt and Luu, 1995) are giving us
our rst look at the physical properties (e.g. sizes and colors) of
| Comparison of the IRAS asteroid the small bodies (comets) populating the outer solar system. The
size distribution (scaled to 1/20), with those of size distributions of the comets from Table 1 and the TNOs are
the TNOs, and directly measured short-period plotted in Fig. 2 in comparison with that of the asteroids (which
comet nuclei.
represent a collisionally evolved population, although the curve in
Fig.
2
3
Table 1.
MEASURED COMET NUCLEUS PROPERTIES
Comet
q[AU]1 RN 2 pv 3 Rot4 [hrs] A:B5
Arend-Rigaux
1.385
5.2 0.03
13.56
1.9
Borrelly
1.365
24.7
2.5
Chiron
8.454
90 0.13 5.9178
1.1
d'Arrest
1.346
2.7
5.17
Encke
0.331
3.1
15.08
1.8
Faye
1.655
2.7
1.3
Giacobini-Zinner
1.035
3.0
Grigg-Skjellerup
0.997
2.9
Halley
0.596
5.5 0.04
88.6
2.0
Honda-Mrkos-Padj. 0.532 0.35
Hyakutake
0.230
6.3
IRAS-Araki-Alcock 0.991
3.5
51.0
2.3
Kop
1.579 2.8,1.8
12.91
1.4
Levy P/1991 L3
0.983
8.2
8.34
1.3
Machholz 1
0.125
2.8
6.38
1.4
Neujmin 1
1.549 10.4 0.03
12.67
1.6
Phaethon
0.139
2.6 0.09
3.604
1.4
SW1
5.743 15.4 0.13
14
2.6
SW2
2.027
3.1
5.58
1.6
Swift-Tuttle
0.962 11.8
69.36
Tempel 2
1.482
5.9 0.02
8.876
1.7
Wild 2
1.582
2.0
Wild 3
2.301
3.1
Wilson
1.199 <6.0
Wilson-Harrington 1.000
2.0
6.1
1.2
Wirtanen
1.064
1.0
>6
Frac6
0.001
0.1
0.00015
0.002
Ref7
1,2
3
4-9
10,11
12,13
14
11
11
0.2
15,16
0.1
17
18
0.002-0.01 19,20
0.1
11,17
21
0.005
11,22
0.001
23-25
3.5x10,5
26
0.06
27,28
0.1
29
0.03
30,31
32,33
11
11
34
0.0002
11,35-36
0.25
37-39
: 1 Perihelion distance; 2 Nucleus radius in km; 3 Measured visible geometric albedo; 4 Nucleus rotation period in hours;
Nucleus axis ratio; 6 Fractional nucleus active area; 7 References: [1] Jewitt & Meech (1985); [2] Millis et al. (1988); [3] Lamy
(1995); [4] Bus, et al. (1989); [5] Bus et al. (1996); [6] Meech et al. (1996); [7] Marciales & Buratti (1993); [8] Meech & Belton
(1990); [9] Altenho & Stump (1995); [10] Fay & Wisniewski (1978); [11] Meech, unpublished; [12] Jewitt & Meech (1987);
[13] Luu & Jewitt (1990); [14] Lamy & Toth (1995); [15] Belton (1990); [16] Keller et al. (1987); [17] Lamy et al. (1996); [18]
Osip et al. (1996); [19] Hanner et al. (1985); [20] Sekanina (1987); [21] Fitzsimmons & Williams (1994); [22] Sekanina (1990);
[23] Wisniewski et al. (1986); [24] Jewitt & Meech (1988a); [25] Campins et al. (1987); [26] Meech et al., in prep. (1996); [27]
Cruikshank (1983); [28] Meech et al. (1993); [29] Luu & Jewitt (1992); [30] O Ceallaigh et al. (1995); [31] Yoshida et al. (1993);
[32] A'Hearn et al. (1989); [33] Mueller & Ferrin (1996); [34] Meech et al. (1995); [35] Osip et al. (1995); [36] Chamberlain et
al. (1996); [37] Bauer et al. (1996); [38] Jorda et al. (1995); [39] Boehnhardt et al. (1996).
Notes
5
this gure has not been corrected for observational bias and completeness). The KB sizes are large compared to known short{period comet nuclei, however, the statistics are so small on this population that we
cannot draw meaningful conclusions yet as to the implications. Clearly the active portion of a comet's
lifetime will result in a decrease in nucleus size ( 1 m per perihelion passage, for maybe a few x 103 orbits).
However, it seems unlikely that the present apparent dierence in sizes is due solely to cometary activity
in the short{period comets, since the nucleus size limits for the dynamically new comets are comparable to
those of the short{period comets, yet these comets have not spent as much time in the inner Solar System.
Thus mass{loss cannot explain the size distributions. The size distributions of the icy planetesimals were
constrained by the material density in the nebula, however interpretation of the observed distributions must
take into account the nebula dynamics. Recent models (Duncan, et al., 1996; Malhotra, 1995) suggest that
the heliocentric distance distribution of the KB objects was aected by the orbital migration of the outer
planets. The fundamental outer solar system dynamics and accretion processes and our understanding of
the volatile distribtuion and chemistry in the solar nebula are not well understood, thus observations of the
small body size distributions are important to constrain early solar system models.
Nucleus Rotation
When nucleus observations are obtained with sucient time resolution, it is possible to determine the rotation period of the comet. The rst determination of nucleus rotation periods utilized indirect techniques
4
(e.g. the Halo method (Whipple, 1982), and Sekanina's non{gravitational force models (1981)) which were
dependent upon uncertain physical assumptions (see A'Hearn, 1988; Belton, 1991) for a review of these
techniques). However, because of the inherent assumptions, the periods determined by indirect means don't
necessarily represent the true rotational state of the nucleus. Faye and Wisniewski (1978) obtained the
rst direct photometric rotational light curve of a comet | comet P/d'Arrest, and in the 1980's the more
sensitive CCD detectors were used to determine the rotational periods from observations of bare nuclei.
The simultaneous in{phase visible and infra{red observations of comet P/Arend{Rigaux (Millis et al., 1988)
showed for the rst time that the rotational lightcurve was due unambiguously to the prolate shape of the
nucleus rather than to albedo features. The range of the bare{nucleus light curve is related to the projected
axis ratio of the comet. All of the directly determined nucleus rotation periods are summarized in Table 1,
the distribution of the periods is shown in Fig. 3, and all the bare nucleus lightcurves are shown in Fig. 4.
The brightness modulation due to nucleus rotation can be observed through some coma, as long as the coma
brightness does not overwhelm the contribution from the nucleus. By decreasing the aperture size used for
observation (possible only under conditions of good seeing), the ratio of the nucleus ux to the total ux
can be increased, allowing the rotational modulation to be detected | as was the case for P/Schwassmann{
Wachmann 1 (Meech et al., 1993). By observing how the light curve amplitude changes as a function of
aperture size, and using the observed brightness distribution of the coma, it is possible to infer the axis ratio
of the comet and the product of the nucleus cross section times the albedo. The observed light curve range
for an active comet depends on:
m(p) = ,2:5 log
BN2
BN1
+BC (p)
+BC (p)
[2]
where BN2 and BN1 are the light scattered at minimum and maximum brightness, respectively, and BC (p)
is the contribution from the coma within aperture of radius p. This equation can be parameterized in terms
of only the ratio of the scattered light from minimum to maximum nucleus cross section, , the average nucleus scattered
light, BN , (related to size and albedo), and the measured
coma surface brightness gradient, G:
zBN
zBN
m(p) = ,2:5 log 1+
1+
+ pG+2
+ pG+2
[3]
where z = (G + 2)=b, and b = SB0p,0 G for a particular
point in the coma (p0,SB0). By measuring m(p) versus p,
it is possible to t for and BN (Meech et al., 1993).
Fig. 3
Extensive narrowband photometry of comet P/Halley (Millis and Schleicher, 1986) showed that by observing the variations in the column density of gaseous species, the signature
of the nucleus rotation could be detected even in an active comet where the nucleus scattered light was negligible.
Here, the coma brightness variations reect the uctuations
in cometary activity as areas of greater volatility on the sur| Directly measured comet nucleus and NEA face rotate into and out of sunlight.
rotation period distributions.
Although it is unlikely that neither the nucleus shapes nor the rotation rates are primordial owing to mass
loss, it is interesting to compare these properties with those of the Near{Earth{Asteroids (NEAs), many of
which may be inactive comets. Whipple (1982) originally found that the period distribution of the comets
was signicantly dierent than that of the NEAs, however, Fig. 3 shows that the distributions are similar
when using only the directly determined periods. With repeated perihelion passages and mass loss, it is
expected that comets will acquire a mantle of non{volatile material which will result in reducing the active
fraction of the nucleus surface. Sustained activity over several orbits from specic active areas should give
rise to torques which will result in rotational spin{up and will eect the non{gravitational orbital motion of
the comet and is a possible cause for nucleus splitting. However, the rotational evolution of a comet will
5
4 | Rotational lightcurves for well-observed bare comet nuclei.
The comets are arranged in order of increasing nucleus size (see Table
1). All the y{axes are scaled the same for direct comparison of the
lightcurves. The t for the phases have been selected to align all the
lightcurves; the periods used are shown under each gure. [a] Wilson{
Harrington (Osip et al., 1995), [b] Phaethon (Meech et al., in prep.), [c]
Kop (Meech et al., in prep), [d] Schwassmann-Wachmann 2 (Luu &
Jewitt, 1992), [e] Encke (Jewitt & Meech, 1987; Luu & Jewitt, 1990),
[f] Arend{Rigaux (Millis et al., 1988), [g] Tempel 2 (Mueller & Ferrin,
1996), [h] Levy (P/1991 L3; Fitzsimmons & Williams, 1994); [i] Neujmin 1 (Jewitt & Meech, 1988a), [j] Chiron (Bus et al., 1989; Marcialis
& Buratti, 1993).
Fig.
o
6
depend on the location and number of active areas on the nucleus. As seen in Table 1, all comets for which
we have observations have fractionally small active areas, which implies localized regions of activity. Belton
(1991) and Samarasinha & Belton (1995) give excellent reviews on the subject. There is now evidence for
complex rotation for 3 comets: P/Halley (Belton et al., 1991), P/Schwassmann{Wachmann 1 (Meech et al.,
1993) and P/Tempel 2 (Mueller & Ferrin, 1996), in which the authors have observed a change in period.
Likewise, a change in rotation period was reported for comet C/1990 K1 (Levy; Feldman et al., 1992).
Samarasinha et al. (1996) use numerical simulations to show that the nucleus of 46/P Wirtanen is a likely
candidate for signicant changes in spin period during one apparition. Finally, accurate knowledge of the
spin state can also provide information about the comet's internal properties.
Nucleus Colors
There are very few published measurements of the colors of bare comet nuclei. Extensive work by Hartmann
et al. (1982) has shown that observations of outer solar system objects may be classied by their position
in a VJHK color diagram; this is correlated with albedo and surface material composition. Hartmann and
Cruikshank (1984) applied this technique to active comets and found that the colors were correlated with r,
with the redder colors found closer to the sun. This was interpreted as either a change in mean particle size
or composition as the icy material sublimated closer to the sun. Jewitt and Meech (1988b) repeated this
experiment on a similar set of active comets and did not nd a trend in color as a function of r. It is dicult
to interpret these results because for active comets a change in the grain size distribution will eect the
colors. More recently, Luu (1993) has obtained spectra of distant inactive comet nuclei and suspected comet
nucleus candidates and has found a wide range in colors ranging from slightly blue to very red compared to
solar colors. Figures 5a and 5b show the distribution of colors for comets observed in a long{term program
to monitor cometary activity as a function of r (Meech, unpublished). Not all of the measurements refer to
the bare nuclei, however, care was taken to only include measurements from comets far from the sun so that
gas contamination was not likely to be a problem for the color measurements; i.e. that they either pertain to
the nucleus or the nucleus plus dust. The colors are plotted as a function of r in Fig. 6. With the exception
of Chiron (r = 10{11 AU), a trend of reddening with increasing r appears to be evident in these observations.
The colors of the Sun and some representative Centaurs are shown for comparison in Fig 5 which show
that comet nuclei / comae are generally redder than the sun | exhibiting a wide range in colors. With
the discovery that Pholus and 1993 HA2 (Centaurs) were extremely red came the suggestion that the red
surfaces (indicative of organic solids) are the result of cosmic{ray irradiation (Owen et al., 1995; Cruikshank
et al., 1996). The authors suggest that exposure to UV radiation as the objects approach the sun causes
a loss of hydrogen which results in a attening of the spectra to the more neutral spectra typical of dark
objects. In this case, it might be expected that objects in the Kuiper Belt should exhibit very red surfaces.
The actual color distribution, while not known, appears to be similar to those of the comets in Fig. 5, and
the diversity in colors may reect a combinaation of irradiation processes and surface impacts (Luu, 1996).
| V{R colors for bare comet nuclei and coma
plus nucleus (Meech, unpublished). The V{R colors of
the sun and 2 Centaurs are also shown for comparison.
5b | R{I colors for bare comet nuclei and coma
plus nucleus (Meech, unpublished). The R{I colors of the
sun and 2 Centaurs are also shown for comparison.
Fig. 5a
Fig.
7
| V{R color trends with distance. Filled circles
are for bare nucleus measurements, open squares for measurements of coma plus nucleus. Data are from Meech
(unpublished).
| R{I color trends with distance. Filled circles
are for bare nucleus measurements, open squares for measurements of coma plus nucleus. Data are from Meech
(unpublished).
Fig. 6a
Fig. 6b
Internal Properties
The internal properties of comet nuclei are not well understood, and all estimates to date rely on indirect
observations combined with modelling. Table 2 summarizes the evolution of density measurements, beginning with the analysis of the non{gravitational motions of P/Halley, which didn't lead to particularly
constraining results. The close jovian passage and subsequent break{up of comet Shoemaker{Levy 9 has
probably given us the rmest estimate of a comet nucleus density. All of the tidal models shown in Table
2 give consistent results. In the most recent paper Asphaug and Benz (1996) model the tidal elongation of
the rubble pile and the subsequent gravitational clumping using an N{body code arriving at a bulk density
of = 0:6 g cm,2 and a radius of 0.75 km for the progenitor. They were able to reconcile their small
nucleus size with the modelling done by Sekanina (1995) who examined an epoch when the comet fragments
had begun to elongate after disruption. From these models, it was shown that the best representation of
the nucleus was as a strengthless aggregate of cometesimals which were held together gravitationally. The
original idea of cometary rubble piles was proposed by Weissman (1986) and Donn and Hughes (1986),
and is now considered to be the likely result of comet accretion models (Weidenschilling, 1994). In this
scenario, grains continue to accrete collisionally until they are 10's of m in size. They don't clump into
gravitationally bound condensations until this size because of nebula turbulence. This creates a body with
strength in the sub{units but little strength against splitting, and because of packing ineciencies should
give rise to low bulk densities.
A dierent technique can be used to place constraints on the nucleus density from the rotation by assuming
that comets will not be rotating faster than the centripital limit for break{up. By setting the centripital
acceleration [ac = (2=P )2a], where P is the rotational period, and a is the long axis of the comet, equal to
the gravitational acceleration, ag at the apex of a prolate spheroid, one can place lower limits on the nucleus
density. The gravity for the apex of the nucleus is given by (Luu & Jewitt, 1992):
ag = ,2G a F (f )
[4]
where G is the gravitational constant, the nucleus density, f is the axis ratio (b=a) and F (f ) is given by:
F (f ) = 2f
2
p ,f 2
1
+
p ,f 2 ,f 2
f 2 ln(f 2 ) + f 2 ln(2+2
(1,f 2 )1 5
:
1
[5]
)
8
The axis ratios versus rotation periods for the comets in Table 1
are plotted in Fig. 7, in addition to those of the NEAs for comparison. Lines of critical rotation are shown for several densities
ranging from 0.1 to 3.0 gm cm,3 . Many of the NEAs require densities greater than 1.0 gm cm,3 , in contrast to the comets. The
gure shows that density lower limits for comets allow densities
less than that of solid water{ice, = 1.0 gm cm,3 , which is consistent with the expected bulk density from the rubble pile model
described above.
| Rotation periods versus axis ratio,
a:b (from Table 1 and McFadden et al., 1989,
and Lagerkvist et al., 1989), for NEAs (circles)
and the comets in Table 1 (squares). The solid
lines show curves of critical rotation for densities of 0.1, 0.3, 1.0 and 3.0 gm cm,3 (from to
to bottom).
Fig. 7
Table 2.
Finally, Table 3 shows the evolution of the attempts to determine
the tensile strength for various comet analogue materials. Most of
the measurements which rely on tidal stress models have tensile
strengths in a range between 102{104 (Nt m,2 103), which is
similar to the estimated strengths for the interplanetary dust paricles (IDPs), many of which have cometary origins. Likewise, measurements from articial nuclei created in the lab have strengths
which are in the same range. Although there is not yet a clear
consensus on the tensile strength of cometary material, the results
in Table 3 suggest that the value is low | probably lower than
that of terrestrial snows.
EVOLUTION OF COMETARY NUCLEUS DENSITY ESTIMATES
Densityy
0.28 { 0.65
0.03 { 4.9
0.6 +0.9/-0.4
<0.7 { 1.5
0.5
0.55
0.6
<0.4
>0.3
>0.2
0.5
<1.0
Techniquez
H2O outgassing and non-grav analysis on P/Halley
H2O outgassing and non-grav analysis on P/Halley
H2O outgassing and non-grav analysis on P/Halley
P/SL9 theoretical models of tidal disruption
P/SL9 models of tidal break-up of primordial rubble pile
P/SL9 breakup models
P/SL9 breakup gravitational clumping models
Numerical simulation of comet rotational state evolution
Rotational analysis
Rotational analysis
Model of 14.3 AU outburst of P/Halley
HST obs of Coma of Chiron and bound atmosphere model
Referencex
1
2
3
4
5
6
7
8
9
10
11
12
Notes: yNucleus density in gm cm,3 103; zTechnique used to determine the nucleus density estimate; xReferences:
[1] Rickman, 1989, [2] Peale, 1989, [3] Sagdeev, et al., 1988, [4] Boss, 1994, [5] Asphaug & Benz, 1994, [6] Solem, 1995,
[7] Asphaug & Benz, 1996, [8] Samarasinha & Belton, 1995, [9] Jewitt & Luu, 1989, [10] Fitzsimmons & Williams,
1994, [11] Prialnik & Bar-Nun, 1992, [12] Meech, et al., 1996.
CONCLUSIONS
Whereas there have been tremendous technological innovations which have facilitated a recent rapid growth
in our understanding of the physical properties of cometary nuclei, we still have knowledge of only a small
sample of nuclei | not enough for statistically meaningful comparisons with small asteroids, or with the
Trans{Neptunian Object population. The observed nuclei are generally small, with sizes ranging from 1 { 83 km, with the average size estimates decreasing with detectors better able to detect activity. The
measured albedos are uniformly low, between 0.02{0.04. The Jupiter family comet sizes are similar to the
NEA small asteroid population, however, we see evidence that the comet size distribution changes in the
outer solar system where much larger bodies are observed. However, it should be noted that these trends
are still plagued by selection eects. Comet nuclei can be described as prolate ellipsoids with axis ratios
varying between 1.1{2.6, and rotation periods ranging from 5 hours to several days. The rotation rates of
the comets have been found to be similar to the NEA rotation rates, however, there is evidence for complex
9
Table 3.
COMETARY MATERIAL STRENGTH ESTIMATES
Tensile Strengthy
103
4.3 103
103
2
10 { 103
2.7 103
102 { 104
104
103 { 105
108
108
2 102 { 103
105
3.5 105
(1{5) 103
(1{5) 103
6 106 { 4 108
4 108
Techniquez
Referencex
tidal stress; sungrazer Ikeya-Seki (=1.0)
1
tidal stresses on Brooks 2 at perijove (=1.0)
1
mantle
icy dirtball nucleus models
2
electrostatic fragmentation of P/Halley dust (Giotto)
3
P/SL9
tidal breakup models
4
analysis of cometary spin & size characteristics
5
ram pressure from outgassing from nucleus
6
laboratory measurements of articial nuclei
1
shock strength during Tunguska breakup
1,7
survival of sungrazers { for non{porous ice
8
dry snow icy dirtball nucleus models
2
snow
50% porous snow
8
porous ice icy dirtball nucleus models
2
meteoroids fragmentation ram pressure, Draconids
9
IDPs
analysis of interplanetary dust particles
10
chondrites measurements of chondrites
11
iron
measurements of iron meteorites
11
Material
Notes: yTensile Strength in Nt m,2 103; z Technique used to determine the tensile strength estimate; xReferences:
[1] Mendis et al. (1985); [2] Mohlmann, (1995); [3] Boehnhardt & Fechtig (1987); [4] Greenberg et al. (1995); [5]
Hughes (1991); [6] Sekanina (1982); [7] Sekanina (1983); [8] Green (1989); [9] Sekanina (1985); [10] Bradley & Brownlee
(1986); [11] Wasson (1974).
rotational states for 3 comets: P/Halley, P/SW1 and P/Tempel 2. The colors of the nuclei suggest a very
diverse population with a wide range in colors which are generally redder than solar. The colors of the short
{period comet nuclei are similar to the C and D class asteroids, and show the same spread in colors that
are seen in the Trans{Neptunian Objects.
In contrast to the external physical properties, there are no direct measurements of the internal properties. The indirect techniques used to infer the bulk internal properties suggest a wide range in values.
Bulk nucleus densities fall between 0.3{1.0 gm cm,3 , implying a relatively large porosity, and the tensile
strengths are estimated to be low | similar to the strengths found for interplanetary dust particles, but
less than that of snow. If we are to ever better constrain the solar models, and close the gap between theory
and observation, in particular in the realm of the evolution from m{sized to km{sized planetesimals, we
need better observational constraints. For the rst time we have the ability to begin to determine the size
distribution of bare comet nuclei; however, as our estimates are getting revised to smaller sizes, and given
our knowledge of the low albedos, we require larger and larger telescope aperture to make these observations.
ACKNOWLEDGEMENTS
This work was supported in part by grants from the NASA Planetary Astronomy Program (NAGW-1897
and NAGW-5015), the National Science Foundation (AST-92-21318), and the Space Telescope Science Institute (GO-03769.01-91A and GO-05834.01-94A). I would especially like to thank O. Hainaut for help with
formatting the latex for this paper and our librarian, K. Robertson, for all her help with database searching
for references for this paper.
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