Correlations In Observable Quantities

In order to disentangle the effects of particle size, composition, and structure, it is useful to look at the correlations among observable quantities. The spatially resolved observations of the dust coma of Hale-Bopp and comparisons of Hale-Bopp with other comets allow us to summarize with some confidence the trends and correlations in the scattering properties of comet particles. Table la compares the average observed properties in the inner coma of Hale-Bopp with similar measurements of comet P/Halley. Table lb makes a similar comparison for the jets and spirals in Hale-Bopp in February-April 1997 versus the background coma.

There is a clear correlation of higher polarization, redder polarimetric color, higher albedo, stronger silicate feature, higher infrared color temperature, and enhanced 3-5 jim thermal emission. (Although the color of the scattered light can also be diagnostic, (e.g., [34,21]), we do not have consistent color data for comparing Hale-Bopp and Halley.)

3.1. Polarization

As discussed in section 2.1, comets tend to form two groups with differing Pmax. The comets with higher Prr!ax generally exhibit a strong scattered light continuum and a conspicuous silicate feature. Hale-Bopp is consistent with this trend, displaying the highest polarization at a given phase angle and strongest silicate feature ever recorded. For grains of size comparable to the wavelength (X in the approximate range 2.5-6), polarization is higher for absorbing grains than for silicate grains and carbon grains lack the negative polarization produced by silicate grains. As X increases from 2.5 to 5, Pmax decreases for silicate grains, but increases for carbon grains with regular, but non-spherical, shapes [22]. Thus, increased polarization could mean more absorbing grains relative to silicate grains in the coma; however, this would contradict the correlation between higher polarization and stronger silicate emission. Only if there is a significant contribution to the scattering from particles with X < 2, then a decrease in particle size would produce an increase in polarization for both silicate and absorbing grains, consistent with the higher silicate feature and higher 3-5 jjm flux. However, for small grains, X < 1.5, polarization and albedo are anti-correlated, in contrast to the comet observations, and the negative polarization branch is lost.

Polarization by an aggregate particle depends on the porosity and the size of constituent grains (section 2.2).

Table 1.

Correlations among Observable Properties

Table 1.

Correlations among Observable Properties

a. Hale-Bopp versus Halley

Possible explanations

Polarization

higher

more small grains, X < 2 more absorbing grains, a ~ X

Polarimetrie Color

redder

more small grains, X < 2 more silicate grains, a ~ X

Albedo

higher

more small grains, a ~ 0.2 jxm more "clean" silicates

Continuum

stronger

more small grains more "clean" silicates higher dust/gas ratio

Silicate Feature

stronger

small silicate grains, a < 1 fim higher silicate/carbon abundance

Color

Temperature

higher

warmer silicates more small absorbing grains

3-5 um Flux

higher

more small absorbing grains, a < 0.5 |im

b. Jets versus Average Coma in Hale-Bopp

Polarization

higher

more small grains, X < 2 more absorbing grains, a ~ X

Polarimetric Color

redder

more small grains, X < 2 more silicate grains, a ~ X

Silicate Feature

stronger

smaller silicate grains, a < 1 urn higher silicate/carbon abundance warmer silicates

Color

Temperature

higher

more small absorbing grains

3-5 nm Flux

higher

more small absorbing grains, a < 0.5 nm

3.2 Polarimetric Color

Comets generally exhibit higher polarization at longer wavelength (red polarimetric color, P('k) > 0) and P('K) was redder in Hale-Bopp than in Halley. Two studies of non-spherical particles are described here. Yanamandra-Fisher and Hanner [22] carried out calculations for compact, non-spherical shapes, X = 1 - 5. Gustafson and Kolokolova [33] measured the polarization by aggregate particles with porosity approximately 50% and 90%. For small, compact grains, X < 2, a decrease in grain size causes a redder polarimetric color, for both absorbing and silicate materials. In the limit X « 1, P(k) = 0. An increase in polarization (P(k) > 0) was measured for porous aggregates of silicate spheres as X for the spheres decreased from 1.75 to 1.32. For X > 2, compact absorbing grains with constant refractive index have higher polarization at larger X, thus blue polarimetric color, while silicate grains have decreasing polarization with increasing X, thus red polarimetric color. A porous aggregate of spheroids, refractive index 1.7 - 0.2i and X ~ 4 displayed slightly red polarimetic color. Compact particles with X » 1 will tend toward neutral P('k) ~ 0. The aggregates of silicate spheres with X ~ 20 showed essentially neutral P(X).

Correlations between color and polarimetric color are discussed by Gustafson and Kolokolova [33] and Kolokolova et al. [34,21],

3.3. Albedo

The average albedo, A(Q), at a given phase angle can be determined from nearly-simultaneous measurements of thermal emission and scattered light. (Note that A(8) is neither the single-scattering albedo, which requires integration over all phase angles, nor the geometric albedo, defined for 0° phase [35]). Using the definition from Gehrz and Ney [36] we have f(v is) = A(e)

where/(vis) and/(IR) are the integrated apparent intensities, measured at phase angle 6, of the scattered and thermal energy distributions, respectively. Mason et al. [37] find 0.25 < A(e) < 0.40 for Hale-Bopp at 20° < e < 40°, significantly higher than the typical values of A(9) ~ 0.20 in comet Halley [36].

There are no reliable measurements of the albedo in the jets and spiral structures. Such measurements would require accurate co-registration of simultaneous infrared and optical images having similar spatial resolution and point spread function. Strong jet activity was observed to be associated with higher albedo and bluer color in comet Halley [38,39],

For compact, slightly or moderately absorbing grains (k < 0.25), the single-scattering albedo reaches a maximum at I m - 1 |X ~ 1.5, where m = n-ik is the refractive index and X is the size parameter; at X = 0.5 |im the maximum corresponds to grain radius ~ 0.2 ^m. Consequently, decreasing the mean size of the grains in the coma from micron-sized to a few tenths of a micron would tend to increase the albedo, whereas decreasing the mean grain size below ~ 0.2 |im would tend to lower the albedo. (Since we measure the albedo at a specific phase angle, any change in the angular scattering function would also affect the observed albedo.) Loss of absorbing mantles on small silicate grains is another means of increasing the albedo. For fully absorbing grains (k > 0.25), the albedo increases monotonically with increasing grain size, so a decrease in grain size will lower the albedo.

Trends with porosity of an aggregate particle will depend on the size and absorptivity of the constituent grains. Hage and Greenberg [40] have shown that, for aggregates having constituent grains with size parameter X ~ 0.2, the albedo will decrease as the porosity increases, particularly for porosity > 75%. In their aggregate model of cometary dust, Greenberg and Hage [41] and Li and Greenberg [42] assume that the aggregates are composed of core-mantle interstellar grains with core radius 0.1 |im and overall radius ~ 0.14 nm; for this model the albedo will decrease as porosity increases. Only if the constituent grains would have radii > 0.2 )jm and k < 0.25 would the albedo at X = 0.5 |jm increase with increasing aggregate porosity.

A very strong scattered light continuum, with respect to the gas emission, was observed in Hale-Bopp. The scattered light continuum was 100 times stronger than that of Halley at similar distances, while the gas production rate was ~ 20 times larger [4], The higher albedo of the dust in Hale-Bopp can account for only a small part of the implied factor of 5 increase in the dust/gas ratio; the total cross-section of dust must have been higher relative to the gas production as well

3.4. Silicate Feature

The 10 nm silicate emission feature (as defined by the ratio of the total flux to the interpolated continuum at 10 nm) was stronger in Hale-Bopp than in any previous comet; total flux/continuum ratio was ~ 3 near perihelion. To show a strong, narrow 10 nm emission feature requires silicate grains with radius, a < 1 nm (e.g., [43]). The strength of the feature in a comet depends on its visibility above the continuum produced by featureless grains of all sizes. Therefore, a stronger silicate feature could be due to a higher cross section of small silicates, relative to other dust components, or to a higher temperature of the silicates, making their feature more visible. The effect of refractory organic mantles on the silicate emission feature depends on the refractive index of the mantle material at both optical and infrared wavelengths; higher absorption at X < 1 |im will heat the mantled grains, increasing the visibility of the feature, whereas high opacity in the infrared will reduce the feature contrast (e.g. [41,42]).

Larger aggregate particles will generate a silicate feature only if the porosity is high enough for the radiation to interact primarily with the constituent submicron silicate grains. For their assumed size distributions, Greenberg and Hage [41] and Li and Greenberg [42] needed a porosity > 95% to produce a sufficiently strong silicate feature.

3.5. Thermal Emission

Comets typically have mid-infrared (5-13 |im) color temperatures, Tc 5-30% higher than that of an equilibrium blackbody; the ratio T/Tbb is often called the "superheat" (e.g., [36]). The high Tc can be explained by absorbing grains smaller than the infrared wavelengths. Such grains absorb sunlight at visual wavelengths more efficiently than they can radiate at X > 5 |jm; they must heat up until they achieve a balance between absorbed and emitted energy. Because the grains do not radiate as blackbodies, Tc is not necessarily the physical temperature of the grains and Tc can be wavelength-dependent. The 8-13 (am superheat observed for Hale-Bopp was about 1.38 near 1 AU [44], compared with ~ 1.15 in P/Halley [45], while the Tc at 3-5 ^m [44] and 5-8 jim [46] was ~ 1.8 times the blackbody temperature, far higher than that observed in any other comet [36], The 3-5 nm thermal flux is a particularly sensitive indicator of hot sub-micron sized grains (grain radius a < 0.5 nm).

Gehrz and Ney plotted a clear correlation between the superheat and the strength of the silicate feature in their sample of comets, and Hale-Bopp fits with their plot [37].

Thermal images (5-18 n-m) and spatially resolved 8-13 nm spectra were acquired by Hay ward et al. [44]. The thermal images show the same jets and spiral structures as optical images from the same time intervals. Either the same particles were responsible for the optical and thermal excess radiation in the jets, or the two grain populations have the same dynamical properties and thus similar spatial distributions. The 8-13 nm Tc and the 3-5 nm fluxes are higher in the jets than in the background coma. The silicate feature was consistently stronger by 10-20% in the jets and spirals. In summary, there was always a correlation between the Tc, the 3-5 nm flux, and the strength of the silicate feature, both over time and with position in the coma.

Calculations of the motions of grains ejected from discrete active areas on the nucleus, as a function of their ejection velocities and (3 =Frad/ Fgrav indicate that the observed spiral patterns in these images are consistent with small grains having p max < 1, but not small grains with P max > 2 [44]. That is, the morphology is consistent with the excess radiation in jets and spirals arising from small clean or slightly absorbing silicate grains, but not with sub-micron sized absorbing grains. For submicron silicate spheres, 3 max is < 1 when k < 0.1, where m = n- ik is the complex refractive index.

A value of k = 0.1 would cause a silicate grain with a > 0.5 nm to be as warm as a carbon grain. A grain of 0.1 nm radius would be significantly warmer than a blackbody, but -100 K cooler than a carbon grain at 1 AU; these grains probably could not produce the observed 3-5 nm flux in Hale Bopp. The temperature attained by a core/mantle particle depends on the refractive index and thickness of the mantle material (cf. [41] Figure 8).

3.6. Summary

No simple explanation is consistent with all of the parameters in Table 1. An increased abundance of small, slightly dirty (k < 0.05) silicate grains would cause a higher albedo, stronger silicate feature, and redder polarimetric color. However, their temperature would not be high enough to produce a high 3-5 n-m flux nor Tc > 7bb. Their polarization would be higher only if the size parameter X < 1.5. A simultaneous increase of hot submicron absorbing grains would increase the 3-5 nm flux, but would tend to decrease the albedo Whether core/mantle particles could be hot enough to give a high 3-5 jim flux, while still causing an increase in albedo is not yet clear.

A synthesis of all these trends into a single, consistent model for the cometary dust is well beyond the scope of this paper. Indeed, such modeling is just beginning. To date, authors have considered only subsets of these parameters. Issues to be resolved include the correlation of higher albedo with higher polarization, correlation of higher albedo and silicate feature with higher 3-5 nm flux, possible effects of evaporating grain mantles, and the role of porous aggregates.

Was this article helpful?

0 0

Post a comment