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Some comments on Hapke's comments
ICAaUS
~ 160-161 (1966)
Some Comments on Hapke's Comments THOMAS GEHRELS Lunar and Planetary Laboratory, University o] Arizona, Tucson, Arizona Communicated by Carl Sagan Received August 1, 1965 Most observations in photometry and polarimetry of the Moon and asteroids can be explained with a tenuous surface texture. The scattering elements or particles may be interconnected rather than freely suspended.
The Moon shows two relationships between reflectivity and percentage polarization: darker regions have stronger polarizations, and the lower reflectivity in the ultraviolet also is accompanied by stronger polarizations. Furthermore it is noted that polarization-phase dependencies, especially at phases a > 40 °, show agreement with the Fresnel laws. The Fresnel laws may be applicable to a part of the light [the part Rp/R explained in expression (14) of Paper III (Gehrels, Coffeen, and Owings, 1964), and quoted by Hapke (1965, preceding paper)]. The part RF/R may be reflected by the lunar surface and ( l - Rv/R) by the particles; it is noted that these parts have about the same proportions as the differential coloring and the general reddening, respectively (Paper III, Sec. XIV K). In Paper III, the ( 1 - Rp/R) part is interpreted with the Mie theory. At phases a 40 ° there is not much polarization in the Mie calculations for the particles in question; "peaks and valleys and reversals" (Hapke, 1965) occur, and on the average there is little polarization. At phases ~ < 40 °, the Fresnel polarization is so small that the Mie theory can be relatively important. Incidentally, our model would not cause limb-brightening of the full moon. At the limb, only the slopes of mountains, etc., would be observed and the particle density would in fact be relatively low.
Hapke's reference to the observations of Wattson and Danielson is trivial. First, these observations were not made near 0 ° phase and, therefore, they do not pertain to the normal reflectivity (Paper III, Sec. XV). Second, our numbers were not intended to be interpreted with a precision such that this criticism would be meaningful. The maximum reflectivity of the lunar surface may well occur near 2.7~ and, combined with a refractive index of 1.6, the particle size still is near 1 ~. In general, in our papers we have indicated that the interpretations are tentative ones (see Gehrels, 1964, p. 491). The interpretations were pm'posely made only on the observations of Paper III, free from previous notions, so as to stimulate new approaches. The principal error may well be in our usage of Hapke's own phase function. However, even this error does not cause a serious deviation from the General Model: "the outer layer of the Moon has a dark, reddish, and very porous microstructure with dimensions in the micron-millimeter range" (Gehrels, 1964). The material density then is not 0.5%, and the particles may not be much in suspension. Even Hapke needs "filamentary and complex" structures on his particles; what would be the size of these structures? The Mie theory and the Fresnel laws may be applicable. within limits, and perhaps they can be useful tools. 160
SOME COMMENTS ON HAPKE'S COMMENTS
I hope Hapke will continue with explanations of the negative polarization, the luminescence effects observed on the Moon, the opposition effect in greater detail, the isotropy and uniformity and reddishness of the Moon and asteroids, the increased reddening with phase for the Moon and asteroids, the uniformity of the polarization inversion angles on the Moon, and the difference in polarization inversion angles of Pallas, Ceres, Iris, and Vesta (see Paper III).
161
REFEREN CES GEHRELS, T. (1964). A model of the lunar surface. Icarus 3, 491--496. GEHRELS, T., COFFEEN, T., AND OWINGS, D. (1964). Wavelength dependence of polarization. III. The lunar surface. Aslron. J. 69, 826-852 (Paper III). HAPKE, B. (1965). Some comments on Gehrels' model of the lunar surface, Icarus 5, 154 (preceding paper).
~ 160-161 (1966)
Some Comments on Hapke's Comments THOMAS GEHRELS Lunar and Planetary Laboratory, University o] Arizona, Tucson, Arizona Communicated by Carl Sagan Received August 1, 1965 Most observations in photometry and polarimetry of the Moon and asteroids can be explained with a tenuous surface texture. The scattering elements or particles may be interconnected rather than freely suspended.
The Moon shows two relationships between reflectivity and percentage polarization: darker regions have stronger polarizations, and the lower reflectivity in the ultraviolet also is accompanied by stronger polarizations. Furthermore it is noted that polarization-phase dependencies, especially at phases a > 40 °, show agreement with the Fresnel laws. The Fresnel laws may be applicable to a part of the light [the part Rp/R explained in expression (14) of Paper III (Gehrels, Coffeen, and Owings, 1964), and quoted by Hapke (1965, preceding paper)]. The part RF/R may be reflected by the lunar surface and ( l - Rv/R) by the particles; it is noted that these parts have about the same proportions as the differential coloring and the general reddening, respectively (Paper III, Sec. XIV K). In Paper III, the ( 1 - Rp/R) part is interpreted with the Mie theory. At phases a 40 ° there is not much polarization in the Mie calculations for the particles in question; "peaks and valleys and reversals" (Hapke, 1965) occur, and on the average there is little polarization. At phases ~ < 40 °, the Fresnel polarization is so small that the Mie theory can be relatively important. Incidentally, our model would not cause limb-brightening of the full moon. At the limb, only the slopes of mountains, etc., would be observed and the particle density would in fact be relatively low.
Hapke's reference to the observations of Wattson and Danielson is trivial. First, these observations were not made near 0 ° phase and, therefore, they do not pertain to the normal reflectivity (Paper III, Sec. XV). Second, our numbers were not intended to be interpreted with a precision such that this criticism would be meaningful. The maximum reflectivity of the lunar surface may well occur near 2.7~ and, combined with a refractive index of 1.6, the particle size still is near 1 ~. In general, in our papers we have indicated that the interpretations are tentative ones (see Gehrels, 1964, p. 491). The interpretations were pm'posely made only on the observations of Paper III, free from previous notions, so as to stimulate new approaches. The principal error may well be in our usage of Hapke's own phase function. However, even this error does not cause a serious deviation from the General Model: "the outer layer of the Moon has a dark, reddish, and very porous microstructure with dimensions in the micron-millimeter range" (Gehrels, 1964). The material density then is not 0.5%, and the particles may not be much in suspension. Even Hapke needs "filamentary and complex" structures on his particles; what would be the size of these structures? The Mie theory and the Fresnel laws may be applicable. within limits, and perhaps they can be useful tools. 160
SOME COMMENTS ON HAPKE'S COMMENTS
I hope Hapke will continue with explanations of the negative polarization, the luminescence effects observed on the Moon, the opposition effect in greater detail, the isotropy and uniformity and reddishness of the Moon and asteroids, the increased reddening with phase for the Moon and asteroids, the uniformity of the polarization inversion angles on the Moon, and the difference in polarization inversion angles of Pallas, Ceres, Iris, and Vesta (see Paper III).
161
REFEREN CES GEHRELS, T. (1964). A model of the lunar surface. Icarus 3, 491--496. GEHRELS, T., COFFEEN, T., AND OWINGS, D. (1964). Wavelength dependence of polarization. III. The lunar surface. Aslron. J. 69, 826-852 (Paper III). HAPKE, B. (1965). Some comments on Gehrels' model of the lunar surface, Icarus 5, 154 (preceding paper).