## 3. Modeling results and the possible dust propertiesFollowing Greenberg & Hage (1990), we model the comet dust of
P/Borrelly as fluffy aggregates of core-mantle interstellar particles.
The optical constants [the complex indices of refraction,
] for interstellar grains used in the modeling
of comet P/Borrelly are based on the determination of the composition
of interstellar core-mantle grains by fitting both the interstellar
extinction curve and interstellar polarization (Li & Greenberg
1997). For the 10 The porosity is treated as a free parameter
with a wide range of from 0 (compact) to 0.975
being considered. Our calculations show that, within the Halley size distribution, if
the particles (with organic residue mantles) are compact they are then
too cold to give excess emission at the silicate band. With the dust
size distribution adjusted to be greatly weighted toward smaller
grains, the silicate feature is enhanced as expected (Gehrz & Ney
1992) but is then far too narrow compared with the observation of
comet P/Borrelly. We have tried to fit the observation by both varying
the porosity and adjusting the dust size distribution. It turns out
that none of these attempts provides a satisfactory match. In Fig. 1a,
b, c we present the "best-fitting" (to the silicate emission) spectra
using amorphous olivine cores and organic residue mantles, calculated
from respectively. The corresponding grain size
distributions are plotted in Fig. 1d. It can be seen from these
figures that the theoretical spectra are a bit sharper than the
observation. In addition, the NIR spectrum (3 - 5
Suppose that the chemical composition of organics of SP comets
could have been modified by solar irradiation or possibly as proposed
by A'Hearn et al. (1996), that the original chemical composition for
the solar nebula out of which the SP comets were formed is different
from where LP comets were formed. This has led us to consider an
extreme case - amorphous carbon, which may be characteristic of the
most highly processed organics materials - highly depleted in H, O, N.
The indices of refraction of amorphous carbon are adopted from those
compiled by Rouleau & Martin (1991). As shown in Fig. 2a, a
satisfactory fit to the 10
Therefore we conclude that the amorphous olivine core - amorphous
carbon mantle model with a porosity (Fig. 2a)
provides the best fit to the observations. Integrating over the mass
range of interest in this work, the total dust mass required by the
model with is g . If we
assume an average outflow velocity for all the
grains rather than taking into account the outflow velocity
distribution as a function of grain size, following the formula given
by Hanner et al. (1985), we derive the dust production rate to be
. If we adopt the water production rate
measured at (A'Hearn et
al. 1995) scaled by a heliocentric evolution
(A'Hearn et al. 1995) as the gas production rate, the ratio of dust to
H Alternatively, we have also tried to model the IR emission spectrum in terms of a power law dust size distribution . We found that a model with and provides a good match. Actually, the modified Halley size distribution (for , see Fig. 2d) can be approximated by two power law distributions (for , ; for , ). It is possible that the carbonaceous mantle could have undergone partial evaporation in the coma. We have also taken this into account by considering a model with a thinner mantle, . Intuitively, we expect that, for a lower which leads to a lower dust temperature, a higher porosity and/or a steeper dust size distribution, which results in a higher temperature, are needed to account for the emission spectrum. In the case which implies that half of the mantle has evaporated, the original porosity then becomes . Using the same size distribution as derived for (see Fig. 2d), our calculations show that the fit by the model with and is reasonably good (plotted as dashed line in Fig. 2b), but the silicate feature is slightly too sharp and the NIR emission is a bit too low. Increasing the porosity or enhancing the small particles, the fit to the NIR emission gets better but the silicate feature becomes even sharper. Decreasing the porosity or enhancing the large particles, the silicate feature becomes broader but then the model fails to fit the NIR emission. For a mantle thickness , the match to the overall spectrum is even poorer. The modeling results as presented above clearly indicate some differences between the dust properties of P/Borrelly and those of P/Halley. First of all, the dust aggregates of P/Borrelly are somewhat more compact compared to P/Halley. The best fit to the P/Borrelly observation is provided by , while Greenberg & Hage (1990) have shown that, a higher porosity, in the range of , fits the silicate emission of P/Halley well. Moreover, the dust size distribution of P/Borrelly is steeper (weighted toward smaller size grains) than that of P/Halley. Furthermore, the organic mantle materials of P/Borrelly, best fit by amorphous carbon, appear to have been strongly processed and are depleted in H, O, N compared to P/Halley. These differences are not surprising. Actually, there is no reason
to expect the dust properties of P/Borrelly to be identical to those
of P/Halley. Since P/Borrelly has passed through the inner solar
system many more times than P/Halley and therefore been subjected much
more to the solar irradiation, the dust grains © European Southern Observatory (ESO) 1998 Online publication: September 8, 1998 |