Infrared absorption features for tetrahedral ammonia ice crystals

ICARUS 8 0 , 2 2 0 - 2 2 3

(1989)

Infrared Absorption Features for Tetrahedral Ammonia Ice Crystals ROBERT

A. WEST,*

GLENN

AND E A R L

S. O R T O N , *

BRUCE

T. D R A I N E , t

A. HUBBELL$

*MS 169-237, Earth and Space Sciences Division, Jet Propulsion Laboratory, California Institute o f Technology, Pasadena, California; ?Princeton University Observatory, Princeton University, Princeton, New Jersey; and $Califi)rnia Institute o f Technology, Pasadena, California Received September 16, 1988; revised January 3, 1989

We have computed extinction cross sections for 0.5- and 1-pm volume-equivalent radius tetrahedral NH3 ice crystals with and without nonabsorbing foreign cores to determine how particle shape and composition affect the strength and shape of resonant absorption features at 9.4 and 26 p m . The peak of the resonance is shifted relative to that for spherical particles, the maximum is smaller (except for 1-/zm particles at 9.4 # m ) , and the integrated strength of the absorption falls in approximate proportion to the volume fraction of the core. It appears that small (r < 5 pm) NH3 particles cannot be the principal component of the Jovian haze in the 300- to 500-mbar region. © 1989Academic Press, Inc.

Introduction. It is generally believed that the upper tropospheric clouds in the Jupiter and Saturn atmospheres are composed mainly of NH3 ice crystals (see West et al., 1986, for a review of clouds and chemistry in the Jovian atmosphere). It is puzzling that no spectral features for NH3 ice are seen in observations of Jupiter in the 9.4- and 26-~m regions where NH3 ice has a large resonant cross section. Marten et al. (1981) argued that particle mean radii must be about 30 p~m or greater, since the spectral features show strong peaks only for smaller particles. Orton et al. (1982) concluded that the particles must be larger than about 10 /Lm ff the particle scale height is greater than 0.5 times the gas scale height. Recently Shaffer and Samuelson (1989) derived particle radii near 1 or near 2.7 /zm. Particle sizes estimated from infrared analyses generally give larger sizes than those based on studies at shorter wavelengths. From a comparison of optical depths in hot spot regions from visible and 5-~m observations, West et al. (1985) concluded that the upper several optical depths (at visible wavelengths) of the aerosol are composed of particles near 1/~m radius or smaller since the optical depth at 5 tzm is a small fraction of its value at visible wavelengths. Several authors (Orton et al. 1982, West et al., 1986) have remarked that the rejection of I-txm-radius or smaller particles on the basis of the absence of observed features at 9.4 and 26 ~m may be flawed. The studies by Marten et al. (1981) and by Orton et al. (1982) relied on computations of the shape of these resonance features for spherical particles, since corn-

putations for nonspherical ice particles are difficult. Yet the fact that particle shape can have a strong influence on the shape of resonant absorption features is well documented (see, e.g., Huffman and Bohren 1980, Bohren and Huffman, 1983). Another factor which can influence the strength of the absorption feature is the inclusion of foreign material into the ice particle. Foreign particles may be present as condensation nuclei. Their formation may be due to photochemical processes which can produce N2H4, solid phosphorus, or hydrocarbons on Jupiter, and to upwelling of particles such as HaO ice, NH4SH ice, and solid sulfur from deeper levels. The purpose of the calculations presented here is to determine quantitatively the effects of nonspherical shape and inclusion of foreign material on the resonance features at 9.4 and 26/~m, for particles whose volume-equivalent radius is in the range 0.5-1 p.m. Method. We used a computational technique called the discrete dipole approximation (DDA) to calculate the optical properties (extinction, scattering, and absorption cross sections, and particle scattering phase matrix) of arbitrarily shaped and heterogeneous particles. The method was devised by Purcell and Pennypacker (1973) who used it to calculate optical properties of small interstellar grains. In the DDA method, an arbitrarily shaped, heterogeneous particle is dissected into many small elements, each of which is homogeneous in composition. These elements are small enough (small compared to the wavelength of incident radiation) that they may be represented by point elec220 0019-1035/89 $3.00 Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.

NOTES tric dipoles. The method has been extended to include radiative reaction corrections (Dralne 1988). At the heart of the DDA technique is the solution to a set of equations for 3N complex variables, where N is the number of dipoles, and the factor of 3 accounts for the x, y, and z components of the dipole moments. The equations to be solved express the interaction terms of each dipole with the incident field and with the radiated fields of all the other dipoles in the particle. A number of methods have been devised to solve the interaction equations. The most straightforward method is to invert the 3N x 3N interaction matrix. While feasible when N is small, direct inversion is too slow for large N. Yung (1978) devised a steepest-descent conjugate gradients iterative method which solves the equations with much greater efficiency, but falls to converge to the correct solution when the particle refractive index becomes large. Draine (1988) employed a more robust conjugate gradients algorithm 5

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described by Petravic and Kuo-Petravic (1979). That algorithm was used to calculate the optical properties presented here. The accuracy of the method depends on the wavelength, the size of the particle, the distance between dipoles, and refractive index (or, alternatively, the dielectric tensor). The calculations performed here were designed to achieve an accuracy of about 10% in the worst case (where the magnitude of the complex refractive index is largest). That criterion required N to be about l03 or greater. The value of N for spherical particles is 1064, and the number for tetrahedral particles is 1047. The interdipole distance for tetrahedral particles was adjusted to achieve equal volume. A thorough discussion of the DDA method and its accuracy is given by Draine (1988). We checked the accuracy of our calculations by comparing the cross sections for spherical particles computed by the DDA method to those computed with a Mie code. We chose ,

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FIG. 1. The bottom panels show the real (n) and imaginary (k) components of the refractive index for ammonia ice in two resonant absorption regions (from Martonchik et al. 1984). The top panels show extinction efficiency factors, Q, for l-/~m-radius spheres and equal-volume tetrahedral particles. The efficiency factor is the ratio of the extinction cross section to the geometric cross section. Calculations for spheres made with the discrete dipole approximation method are shown as solid lines. Calculations using a Mie code are shown as dashed lines. The absorption cross sections are nearly as large as the extinction cross sections in the 20- to 33-/zm region, and the single scattering albedo is a few percent. In the 9-/~m region the single scattering albedo monotonically increases with wavelength from 0.03 at 9.17/.~m to 0.58 at 9.71 t~m for both spheres and tetrahedra.

222

WEST ET AL.

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(~m) FIG. 2. Calculations for 0.5-~xm-radius spheres and tetrahedral particles with and without nonabsorbing foreign cores. The parameter f i s the fractional volume of the core. The solid curve was computed with the DDA technique. A Mie code produced the dashed curve for the sphere. to model NH3 ice crystals as tetrahedral particles on the basis of the findings of Holmes et al. (1980). Other particle shapes are found in laboratory experiments (M. G. Tomasko, private communication, 1988) and probably exist in the Jovian atmosphere, but tetrahedral shape suffices to demonstrate what might be expected from nonspherical ice crystals. Ammonia ice refractive indices are from Martonchik et al. (1984). To synthesize particles with foreign cores, we examined NH3 tetrahedra with cubic cores of nonabsorbing material having refractive index n = 1.6. We approximated random orientation by averaging the results for three incident rays, one each in the x, y, and z directions (one face of the tetrahedron is in the x - y plane), and we averaged both linear polarizations, Results a n d conclusions. The results of this study are shown in Figs. 1 and 2. The following conclusions can be drawn: (1) Extinction cross sections of small NH3 ice particles in the 9.4- and 26-/~m resonant absorption regions depend on particle shape. The peak cross section for the 1-/zm tetrahedral particle at 26 ktm wavelength is only about half that for equal-volume spheres. The same is true for 0.5-t~m-radius particles at 9.4/zm, The peak for l-/xm particles at 9.4/~m is as high as that for spheres, but shifted to longer wavelength. The peak at 26/xm is also shifted to longer wavelength. (2) Ammonia ice crystals with nonabsorbing foreign cores have reduced extinction cross sections in resonance regions. The dilution effect is approximately proportional to the volume fraction of the core. Studies which rely on the details of the absorption profile should use appropriate caution if conclusions depend on calculations for spheres. The works by Marten et al. (1981) and Orton et al. (1982) used cross sections from Mie theory for spheres and may need to be revised. However, the fact that absorption features

are not seen in the Jovian spectra cannot be explained by nonspherical particle effects on the extinction cross sections, possibly unless the particles are long needles or some highly nonspherical shape that broadens the spectral feature much more than for tetrahedral particles. Laboratory experience indicates the NH3 ice particles do not have large aspect ratios (M. G. Tomasko, private communication, 1988). The l-/xm particles shown in Fig. 1 display a spectral feature which is as strong as that for spheres. Some other property of the cloud composition or structure must play an important role in suppressing these features. Orton et al. (1982) and Shaffer and Samuelson (1989) pointed out that if the particles are confined to the region below the 500-mbar level, NH3 gas opacity in the overlying atmosphere obscures the deeper levels, and there is no information on particles in the 700- to 500-mbar region where NH3 ice is expected to be most abundant. Yet there is strong evidence from several other investigations that the top of the tropospheric cloud is in the 200- to 300-mbar region and that the highest-altitude particles have radii near 1 /zm or smaller (cf. West et al. 1986). Cloud particles in the 300- to 500-mbar region should produce an easily observed signature in the 9.4- and 26-1xm regions if they are ammonia particles. Figure 2 shows that a large fraction of the particle must be something other than NH3 ice if the absorption features are to be suppressed by foreign inclusions. ACKNOWLEDGMENTS We thank W. Shaffer and an anonymous referee for careful reviews. Marie Damas helped correct errors in the first version of this paper. We thank Y. Yung for assistance with his version of the DDA code and for helpful discussion of the method. We are grateful to the Alliant Corporation for providing, gratis, approximately 1000 hr of CPU time on an Alliant FX-4 computer. One of us (E. Hubbell) was supported under the Caltech Summer Undergraduate Research Fellowship program in 1987. This work was supported in part by Grant AST-8612013 from the National Science Foundation. A portion of the research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the Planetary Atmospheres program of the National Aeronautics and Space Administration. REFERENCES BOHREN, C. F., AND D. R. HUFFMAN 1983. Absorption and Scattering o f Light by Small Particles, pp. 325-356. Wiley-lnterscience, New York. DRMNE, B. T. 1988. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848-872. HOLMES, A., R. PAXMAN, H. P. STAHL, AND M. G. TOMASKO 1980. Light scattering by crystals of NH3 and H20. Bull. A m e r . Astron. Soc. 12, 705-706.

NOTES HUFFMAN, D. R., ANt) C. F. BOHREN 1980. Infrared absorption spectra of nonsphericai particles treated in the Rayleigh-ellipsoid approximation. In Light Scattering by Irregularly Shaped Particles (D. Schuerman, Ed.), pp. 103-111. Plenum, New York. MARTEN, A., D. ROUAN, J.-P. BALUTEAU, D. GAUTIER, B. J. CONRATH, R. HANEL, V. KUNDE, R. SAMUELSON, A. CHEt)IN, ANt) N. SCOTT 1981. Study of the ammonia ice cloud layer in the equatorial region of Jupiter from the infrared interferometric experiment on Voyager. Icarus 46, 233-248. MARTONCmK, J. V., G. S. ORTON, AND J. F. APPLEBY 1984. Optical properties of NH3 ice from the far infrared to the near ultraviolet. Appl. Opt. 23, 541547. ORTON, G. S., J. F. APPLEBY, AND J. V. MARTONCHIK 1982. The effect of ammonia ice on the outgoing thermal radiance from the atmosphere of Jupiter. Icarus 52, 94-116.

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PETRAVIC, M., AND G. Kuo-PETRAVIC 1979. An ILUCG algorithm which minimises in the Euclidean Norm. J. Comp. Phys. 32, 263-269. PURCELL, E. M., AND C. R. PENNYPACKER 1973. Scattering and absorption of light by nonspherical dielectric grains. Astrophys. J. 186, 705-714. SHAFFER, W. A., AND R. E. SAMUELSON 1989. Study of the ammonia cloud layer in the North Tropical Zone of Jupiter. Icarus, in press. WEST, R. A., P. N. KUPEERMAN, AND H. HART 1985. Voyager 1 imaging and IRIS observations of Jovian methane absorption and thermal emission: Implications for cloud structure. Icarus 61, 311-342. WEST, R. A., D. F. STROBEL, AND M. G. TOMASKO 1986. Clouds, aerosols, and photochemistry in the Jovian atmosphere. Icarus 65, 161-217. YUNG, Y. L. 1978. Variational principle for scattering of light by dielectric particles Appl. Opt. 17, 37073709.