Astron. Astrophys. 339, L9-L12 (1998)

3. Analysis

3.1. The LWS spectrum: water ice and dust emission

Besides gaseous H₂O lines, the LWS spectrum shows two emissions, a narrow one centred at 44 µm, and another broader one, around 65 µm. Although the former is near the edge of the LWS range, its reality is confirmed by the increase of flux at 41-44 µm in the ISO/SWS spectrum (see Crovisier et al. 1997a, 1997b). This structure is characteristic of crystalline water ice. Amorphous ice, with a broad band centred at 46 µm and no feature around 65µm, does not match the spectrum. Crystalline olivine, identified on comet Hale-Bopp from its bands at 16-34 µm (Crovisier et al. 1997a), and pyroxene, detected at smaller 's (Wooden et al. 1998), have structures beyond 40 µm (Koike et al. 1993; Koike & Shibai 1998; d'Hendecourt, priv. comm. ), but the exact wavelengths do not match the observed emissions (e.g., forsterite has weak features at 50 and 70 µm). The ice bands appear superimposed on a continuum which is attributed to emission from cometary dust. To model the H₂O ice emissions, we used optical constants determined by Trotta (1996) from laboratory measurements of crystalline ice at 145 K. Extinction and absorption efficiencies ( and ) were calculated from Mie theory (van de Hulst 1957) for various grain sizes (radius a).

The thermal emission of an ice grain was modelled as , where and is the temperature of sublimating ice grains. values of 140 and 170 K were tested. The absolute contribution of the ice emission to the flux was inferred from the contrast of the bands above the estimated continuum. In practice, the LWS spectrum was fitted by the sum of an emission due to ice and of a continuum dust emission which was modelled either by a blackbody at temperature or by a blackbody multiplied by an emissivity proportional to (Jewitt & Matthews 1997). We did not consider radiative transfer effects (reabsorption) between different ice grains and between dust and ice. We therefore modelled the LWS spectrum in terms of five parameters: a, , the emissivity power index , and the total emission cross sections for ice and dust ( and ).

The particle radius was determined from the general shape of the 44 and 65 µm bands, in particular the relative contrast of the two bands. For = 170 K, the best fit was determined for µm. Smaller particle sizes tend to produce too sharp a 44 µm band, while larger particles produce a general flattening of the spectrum which is not observed (Fig. 2). We consider that the particle size is determined within a factor of 2. One of the best overall fits to the data is shown in Fig. 1. At 44 µm, out of a total observed flux of  Jy, the ice emission contributes to about 60 Jy. This indicates a projected emitting area km², i.e., an effective diameter of 375 km. This implies that water ice is seen in the coma and not on the nucleus. For µm, this corresponds to about sublimating grains within the LWS beam (which corresponds to distances within km from the nucleus), for a total ice mass of kg. Similar numbers are found for = 140 K: µm, km², kg.

Fig. 2. The 40-90 µm region modelled with = 170 K and different ice particle sizes. Solid line: µm. Long-dashed line: µm. Short-dashed line: µm. The three bottom curves show the contribution of ice and the three top curves show attempts to fit the LWS data (histogram) with these three models

In the best fit models, the flux due to dust is about 170 Jy at 44 µm. Beyond 100 µm, the observed flux must be entirely of dust origin. The dust spectrum can be well fitted with a blackbody at 210 K, similar to the colour temperature fitting the 2.9 AU SWS spectrum at 7.5 and 13-15 µm (Crovisier et al. 1997a) and % above the equilibrium blackbody temperature ( K at 2.9 AU). The elevated colour temperature, yet lack of steep decrease in the flux at long wavelengths, indicates a broad size distribution for the dust: model calculations for a power law size distribution of carbon grains in the range 0.1 µm to 1 cm suggests .

The roughly constant spectral emissivity from 100-200 µm (slope ) contrasts with the millimetre/submillimetre region, where radiometric/interferometric data taken near perihelion indicate a spectrum much harder than a blackbody, with ranging from 0.6 at  mm (Jewitt, priv. comm. ) to 1.2 at 0.3-10 mm (Wink et al. 1998) and 1.39 at 1.4-2.1 mm (Senay et al. 1998). This strong decrease in emissivity precludes a large contribution from dust particles larger than several hundred µm near perihelion, while at 40-200 µm requires grains larger than m in radius. We adopt 100 µm as a typical grain size. This value is close to the maximum size of non-porous dust grains that can be lifted off a 70 km diameter (Weaver & Lamy 1998) nucleus given its activity at 2.9 AU ( CO molecules s^-1; Biver et al. 1997) (e.g., Delsemme & Miller 1971).

The 100 µm flux (65 Jy) indicates a dust cross section of km², i.e., an effective diameter of 640 km. Assuming µm and a density of 2.5 g cm^-3, this gives dust grains in the beam, for a total mass kg. This calculation is equivalent to assuming an absorption cross section () of about 2.9 m² kg^-1 at µm. Jewitt & Matthews (1997) and Senay et al. (1998) used m² kg^-1 at 1 mm, with a dependence. Taking a typical of 1 between  mm and 100µm would give m² kg^-1. We note that so long as the emissivity is close to 1 at 40-200 µm, the inferred mass is proportional to particle radius and density, so it could be rescaled for any preferred values of these parameters. With our value the ice/dust mass ratio in the beam is % and the ratio of the cross sections is .

Dust ejected from the nucleus at an average velocity v (m s^-1) crosses the LWS half-beam ( km) in a time . Dust tail fits between 13 and 4 AU suggest velocities of 100 m s^-1 for 10 µm grains, with a size dependence (Fulle et al. 1998). Extrapolating to 100 µm would give about 60 m s^-1. This is a factor of about 2 larger than terminal dust velocities calculated from Crifo & Rodionov (1997). Here we take into account Hale-Bopp nucleus size and a CO-driven coma with mol s^-1 (Biver et al. 1997; Crovisier et al. 1997a). Conservatively we will use m s^-1, which gives a travel time of  s (21 days). Thus to compensate for the loss of dust, the dust production rate must be equal to kg s^-1. This mass production rate is comparable to values estimated for small grains from visible measurements. Indeed, the dust (as defined by A'Hearn et al. 1984) was 600-2000 m at 2.9 AU (Rauer et al. 1997; Weaver et al. 1997; Schleicher et al. 1997), which corresponds to in the range (0.7-2.5) kg s^-1 for grain radii of m and (2.5-8.2)10⁴ kg s^-1 for radii of m, assuming an albedo of 0.04 and grain velocities of 300 m s^-1 and 100 m s^-1, respectively. The ratio of to suggests a size distribution with exponent in the range 2.6-3.3 (2.8-3.6 if m s^-1 is assumed), in agreement with derived above from the colour temperature and with measurements in P/Halley (McDonnell et al. 1991; Waniak 1992) and other comets (e.g., Hanner 1984b). The CO production rate given above corresponds to = kg s^-1 from the nucleus, hence we obtain (the H₂O outgassing, probably due to the sublimation of the icy grains, is not included here).

3.2. The PHT spectrum: water ice signature at 3 µm

The PHT-S data (both on 26 September and 6 October) in the 2.4-4.9 µm range indicate the presence of an absorption between 2.8 and 3.6 µm, suggestive of water ice (Fig. 3). We here focus on the 6 October data for consistency with the LWS measurements. To model this absorption, we simply assumed that the reflectivity of the ice grains is , where is spectrally constant and = , where is the imaginary refractive index of ice and l an effective absorption path. This model thus assumes that the 3µm feature is due to absorption rather than scattering, which may not be true (see Hanner 1981). Although it is possible to calculate single scattering albedos from Mie theory for pure ice grains, such a model would not necessarily be relevant since the reflectivity of the grains is presumably considerably darkened by some mixing with dust. Indeed, for a total (dust + ice) cross section of km², the observed flux at 2.5 µm (0.6 Jy) indicates a geometric albedo . The 2.4-4.9 µm spectrum was modelled (outside the gaseous emission bands) as the sum of a solar component (S) and a thermal component (T). The solar component, which dominates at m, was fitted by the sum of a term due to the dust (constant reflectivity ) and a term due to the ice in the form above. S is proportional to , where K is a constant defining the relative contribution of ice and dust. Assuming that T is due to dust with a cross section of km² (sublimating ice at 140-170 K contributes negligibly), the continuum at m is fitted with a dust temperature of 210 K, consistent with the analysis of the LWS data. In addition, the 2.7 µm gaseous H₂O band, which exhibits emission wings up to m, was included in the model. An overall fit of the PHT spectrum is shown in Fig. 3 for two values of the effective absorption path µm and m. These two models have , in qualitative agreement with (see above). Neither of the two models gives a perfect fit to the data, which is not surprising given the extremely crude character of the models (which also neglect a possible additional thermal contribution at 3-5 µm from small hot dust grains (Williams et al. 1997)). Nevertheless, it is reassuring to find absorption paths of the order of a few µm, i.e., similar to the ice grain particle size derived from the analysis of the LWS spectrum.

Fig. 3. The PHT-S spectrum of October 6, 1996 at 2.4-4.9 µm (histograms) along with models including reflection by dust (with constant spectral reflectance ) and by ice (with reflectance , see text), thermal emission by dust at 210 K, and emission by gaseous H2O at 2.7 µm (calculated with s-1 and an expansion velocity m s-1 following Crovisier et al. (1997a)). Long dash - short dash: thermal component. Dashed lines: reflected component. Solid lines: sum of the two components. Thin lines are for an effective path of m and thick lines for m

© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998
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