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Influence of the Spectral Dependence of Refractive Index on the Polarimetric Properties of Ice Particles

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Abstract

Water ice is widespread in the Solar System. Computer simulation of light scattering by ice particles designed to interpret the observational data should take into account the spectral dependence of the refractive index of water ice. However, in practice, a single fixed value of the refractive index is often used. In this paper, we show that poor choice of a fixed refractive index commonly leads to significant errors in estimating both the intensity and the degree of polarization of single-scattered light. We have found that a fixed value of the refractive index of ice particles m0 = 1.3078 in the spectral region from 0.4 to 0.9 μm leads to minimal differences between the calculated characteristics of the light scattered by ice particles and those that take into account the spectral behavior of the refractive index. The most suitable values of the fixed refractive index for the widely used R, V, and I filters have been found. We have also studied the effect of the fixed refractive index of ice on the spectral dependence of the main parameters of the phase dependence of the linear polarization degree of single-scattered light, such as the magnitude and position of the minimum of the negative branch, the magnitude and position of the maximum of the positive branch, the inversion angle, and the polarimetric slope. The results of the calculations can be used to interpret the polarization of various objects of the Solar System that contain ice particles.

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REFERENCES

  1. Anderson, J.D., Jacobson, R.A., McElrath, T.P., Moore, W.B., Schubert, G., and Thomas, P.C., Shape, mean radius, gravity field, and interior structure of Callisto, Icarus, 2001, vol. 153, p. 157.

    Article  ADS  Google Scholar 

  2. Belskaya, I.N., Bagnulo, S., Barucci, M.A., Muinonen, K., Tozzi, G.P., Fornasier, S., and Kolokolova, L., Polarimetry of Centaurs (2060) Chiron, (5145) Pholus, and (10199) Chariklo, Icarus, 2010, vol. 210, no. 1, pp. 472–479.

    Article  ADS  Google Scholar 

  3. Berger, E.L., Zega, T.J., Keller, L.P., and Lauretta, D.S., Evidence for aqueous activity on comet 81P/Wild 2 from sulfide mineral assemblages in Stardust samples and CI chondrites, Geochim. Cosmochim. Acta, 2011, vol. 75, no. 12, pp. 3501–3513.

    Article  ADS  Google Scholar 

  4. Capria, M.T., Coradini, A., and De Sanctis, M.C., C/1995 O1 Hale–Bopp: short and long distance activity from a theoretical model, Earth, Moon, Planets, 2002, vol. 90, pp. 217–225.

    Article  ADS  Google Scholar 

  5. Dollfus, A., Étude des planètes par la polarisation de leur lumière, Suppl. Ann. Astrophys., 1957, vol. 4, pp. 3–114.

    Google Scholar 

  6. Dougherty, L.M. and Geake, J.E., Polarization by frost formed at very low temperatures, as relevant to icy planetary surfaces, Mon. Not. R. Astron. Soc., 1994, vol. 271, no. 2, pp. 343–354. https://doi.org/10.1093/mnras/271.2.343

    Article  ADS  Google Scholar 

  7. Friedson, A.J. and Stevenson, D.J., Viscosity of ice-rock mixtures and applications to the evolution of icy satellites, Icarus, 1983, vol. 56, pp. 1–14.

    Article  ADS  Google Scholar 

  8. Gulkis, S., Allen, M., Backus, C., Beaudin, G., Biver, N., Bockelee-Morvan, D., Crovisier, J., Despois, D., Encrenaz, P., Frerking, M., Hofstadter, M., Hartogh, P., Ip, W., Janssen, M., Kamp, L., et al., Remote sensing of a comet at millimeter and submillimeter wavelengths from an orbiting spacecraft, Planet. Space Sci., 2007, vol. 55, no. 9, pp. 1050–1057.

    Article  ADS  Google Scholar 

  9. Hansen, J.E. and Travis, L.D., Light scattering in planetary atmospheres, Space Sci. Rev., 1974, vol. 16, pp. 527–610. https://doi.org/10.1007/BF00168069

    Article  ADS  Google Scholar 

  10. Hussmann, H., Sohl, F., and Spohn, T., Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-Neptunian objects, Icarus, 2006, vol. 185, no. 1, pp. 258–273.

    Article  ADS  Google Scholar 

  11. Kelly, R. and Hall, D.K., Remote sensing of terrestrial snow and ice for global change studies, in Earth Observation of Global Change, Dordrecht: Springer-Verlag, 2008, pp. 189–219. https://doi.org/10.1007/978-1-4020-6358-9_9

  12. Kiselev, N.N. and Petrov, D.V., On errors in constructing the polarization phase dependences for Solar System bodies, Sol. Syst. Res., 2018, vol. 52, no. 3, pp. 282–285. https://doi.org/10.1134/S0038094618030073

    Article  ADS  Google Scholar 

  13. Kolokolova, L. and Kimura, H., Comet dust as a mixture of aggregates and solid particles: Model consistent with ground-based and space-mission results, Earth, Planets Space, 2010, vol. 62, no. 1, pp. 17–21.

    Article  ADS  Google Scholar 

  14. Kossacki, K.J., Sublimation of cometary ices in the presence of organic volatiles II, Icarus, 2019, vol. 319, pp. 470–475.

    Article  ADS  Google Scholar 

  15. Leroux, C., Lenoble, J., Brogniez, G., Hovenier, J.W., and De Haan, J.F., A model for the bidirectional polarized reflectance of snow, J. Quant. Spectrosc. Radiat. Transfer, 1999, vol. 61, no. 3, pp. 273–285.

    Article  ADS  Google Scholar 

  16. Lv, Y. and Sun, Z., The reflectance and negative polarization of light scattered from snow surfaces with different grain size in backward direction, J. Quant. Spectrosc. Radiat. Transfer, 2014, vol. 133, pp. 472–481. https://doi.org/10.1016/j.jqsrt.2013.09.010

    Article  ADS  Google Scholar 

  17. Lyot, B., Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres, PhD Thesis, Orléans: H. Tessier, 1929.

  18. Mishchenko, M.I. and Travis, L.D., Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation, Appl. Opt., 1994, vol. 33, no. 30, pp. 7206–7225.

    Article  ADS  Google Scholar 

  19. Mishchenko, M.I., Travis, L.D., and Mackowski, D.W., T-matrix computations of light scattering by nonspherical particles: a review, J. Quant. Spectrosc. Radiat. Transfer, 1996, vol. 55, no. 5, pp. 535–575.

    Article  ADS  Google Scholar 

  20. Mishchenko, M.I., Travis, L.D., and Lacis, A.A., Scattering, Absorption, and Emission of Light by Small Particles, Cambridge: Cambridge Univ. Press, 2002.

    Google Scholar 

  21. Moore, W.B., Thermal equilibrium in Europa’s ice shell, Icarus, 2006, vol. 180, pp. 141–146.

    Article  ADS  Google Scholar 

  22. Muinonen, K., Light scattering by Gaussian random particles, Earth, Moon, Planets, 1996a, vol. 72, pp. 339–342.

    Article  ADS  Google Scholar 

  23. Muinonen, K., Light scattering by Gaussian random particles: Rayleigh and Rayleigh-Gans approximations, J. Quant. Spectrosc. Radiat. Transfer, 1996b, vol. 55, no. 5, pp. 603–613. https://doi.org/10.1016/0022-4073(96)00004-0

    Article  ADS  Google Scholar 

  24. Muinonen, K., Introducing the Gaussian shape hypothesis for asteroids and comets, Astron. Astrophys., 1998, vol. 332, pp. 1087–1098.

    ADS  Google Scholar 

  25. Peltoniemi, J., Hakala, T., Suomalainen, J., and Puttonen, E., Polarised bidirectional reflectance factor measurements from soil, stones, and snow, J. Quant. Spectrosc. Radiat. Transfer, 2009, vol. 110, no. 17, pp. 1940–1953. https://doi.org/10.1016/j.jqsrt.2009.04.008

    Article  ADS  Google Scholar 

  26. Petrov, D.V. and Kiselev, N.N., Positive branch of asteroid polarization: observational data and computer modeling, Sol. Syst. Res., 2017, vol. 51, no. 4, pp. 271–276. https://doi.org/10.1134/S0038094617040049

    Article  ADS  Google Scholar 

  27. Petrov, D. and Kiselev, N., Computer simulation of position and maximum of linear polarization of asteroids, J. Quant. Spectrosc. Radiat. Transfer, 2018, vol. 204, no. 18, pp. 88–93.

    Article  ADS  Google Scholar 

  28. Petrov, D.V., Shkuratov, Yu.G., Stankevich, D.G., Shevchenko, V.V., and Kozlova, E.A., The area of cold traps on the Lunar surface, Sol. Syst. Res., 2003, vol. 37, no. 4, pp. 260–265. https://doi.org/10.1023/A:1025022130047

    Article  ADS  Google Scholar 

  29. Petrov, D., Synelnyk, E., Shkuratov, Y., and Videen, G., The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size, J. Quant. Spectrosc. Radiat. Transfer, 2006a, vol. 102, no. 1, pp. 85–110.

    Article  ADS  Google Scholar 

  30. Petrov, D., Synelnyk, E., Shkuratov, Y.G., Videen, G., Scotto, C., Hart, M., and Eversole, J., Photopolarimetric properties of analytic models of some biological particles with irregular shape, J. Quant. Spectrosc. Radiat. Transfer, 2006b, vol. 102, no. 1, pp. 111–120.

    Article  ADS  Google Scholar 

  31. Petrov, D., Shkuratov, Yu.G., and Videen, G., Sh-matrices method as applied to scattering by particles with layered structure, J. Quant. Spectrosc. Radiat. Transfer, 2007, vol. 106, nos. 1–3, pp. 437–454.

    Article  ADS  Google Scholar 

  32. Petrov, D., Shkuratov, Yu.G, and Videen, G., Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: analytic solution using Sh-matrices, J. Quant. Spectrosc. Radiat. Transfer, 2008, vol. 109, no. 4, pp. 650–669.

    Article  ADS  Google Scholar 

  33. Petrov, D., Shkuratov, Yu.G., and Videen, G., Light scattering by a finite cylinder containing a spherical cavity using Sh-matrices, Opt. Commun., 2009, vol. 282, no. 2, pp. 156–166.

    Article  ADS  Google Scholar 

  34. Petrov, D., Shkuratov, Yu.G., and Videen, G., An analytical solution to the light scattering from cube-like particles using Sh-matrices, J. Quant. Spectrosc. Radiat. Transfer, 2010, vol. 111, no. 3, pp. 474–482.

    Article  ADS  Google Scholar 

  35. Petrov, D., Shkuratov, Yu., and Videen, G., Electromagnetic wave scattering from cuboid-like particles using Sh-matrices, J. Quant. Spectrosc. Radiat. Transfer, 2011, vol. 112, no. 2, pp. 155–162.

    Article  ADS  Google Scholar 

  36. Petrov, D., Shkuratov, Yu., and Videen, G., Light scattering by arbitrary shaped particles with rough surfaces: Sh-matrices approach, J. Quant. Spectrosc. Radiat. Transfer, 2012, vol. 113, no. 18, pp. 2406–2418.

    Article  ADS  Google Scholar 

  37. Petrov, D.V., Kiselev, N.N., and Zhuzhulina, E.A., Application of the Sh-matrices method to stimulate the scattering properties of atmosphereless celestial bodies, Izv. Krym. Astrofiz. Obs., 2018, vol. 114, no. 1, pp. 64–69.

    Google Scholar 

  38. Prialnik, D., Crystallization, sublimation, and gas release in the interior of a porous comet nucleus, Astrophys. J., 1992, vol. 388, pp. 196–202.

    Article  ADS  Google Scholar 

  39. Price, M.C., Kearsley, A.T., Burchell, M.J., Hörz, F., Borg, J., Bridges, J.C., Cole, M.J., Floss, C., Graham, G., Green, S.F., Hoppe, P., Leroux, H., Marhas, K.K., Park, N., Stroud, R., et al., Comet 81P/Wild 2: the size distribution of finer (sub-10μm) dust collected by the Stardust spacecraft, Meteorit. Planet. Sci., 2010, vol. 45, pp. 1409–1428.

    Article  ADS  Google Scholar 

  40. Pugacheva, S.G., Feoktistova, E.A., and Shevchenko, V.V., Deposits of water ice on the Lunar surface, Perspekt. Nauki, 2015, no. 10 (73), pp. 183–188.

  41. Schubert, G., Anderson, J.D., Spohn, T., and McKinnon, W.B., Interior composition, structure and dynamics of the Galilean satellites, in Jupiter: The Planet, Satellites and Magnetosphere, Bagenal, F., Dowling, T., and McKinnon, W.B., Eds., Cambridge: Cambridge Univ. Press, 2004, pp. 281–306.

    Google Scholar 

  42. Scully, J.E.C., Buczkowski, D.L., Neesemann, A., Williams, D.A., Mest, S.C., Raymond, C.A., Nass, A., Hughson, K.H.G., Kneissl, T., Pasckert, J.H., Ruesch, O., Frigeri, A., Marchi, S., Combe, J-P., Schmedemann, N., et al., Ceres’ Ezinu quadrangle: a heavily cratered region with evidence for localized subsurface water ice and the context of Occator crater, Icarus, 2018, vol. 316, pp. 46–62.

    Article  ADS  Google Scholar 

  43. Shkuratov, Yu.G. and Ovcharenko, A.A., Polarization of light scattered by surfaces with complex microstructure at phase angles 0.1°–3.5°, Sol. Syst. Res., 2002, vol. 36, no. 1, pp. 62–67.

    Article  ADS  Google Scholar 

  44. Shkuratov, Yu., Bondarenko, S., Kaydash, V., Videen, G., Muñoz, O., and Volten, H., Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles, J. Quant. Spectrosc. Radiat. Transfer, 2007, vol. 106, nos. 1–3, pp. 487–508. https://doi.org/10.1016/j.jqsrt.2007.01.031

    Article  ADS  Google Scholar 

  45. Stubbs, T.J. and Wang, Y., Illumination conditions at the Asteroid 4 Vesta: implications for the presence of water ice, Icarus, 2012, vol. 217, no. 1, pp. 272–276.

    Article  ADS  Google Scholar 

  46. Sun, Z. and Zhao, Y., The effects of grain size on bidirectional polarized reflectance factor measurements of snow, J. Quant. Spectrosc. Radiat. Transfer, 2011, vol. 112, no. 14, pp. 2372–2383. https://doi.org/10.1016/j.jqsrt.2011.05.011

    Article  ADS  Google Scholar 

  47. Sunshine, J.M., Groussin, O., Schultz, P.H., A’Hearn, M.F., Feaga, L.M., Farnham, T.L., and Klaasen, K.P., The distribution of water ice in the interior of Comet Tempel 1, Icarus, 2007, vol. 190, no. 2, pp. 284–294.

    Article  ADS  Google Scholar 

  48. Tanikawa, T., Hori, M., Aoki, T., Hachikubo, A., Kuchiki, K., Niwano, M., Matoba, S., Yamaguchi, S., and Stamnes, K., In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan, and northwest Greenland ice sheet, J. Geophys. Res.: Atmos., 2014, vol. 119, pp. 13946–13964.

    ADS  Google Scholar 

  49. Volten, H., Muñoz, O., Rol, E., de Haan, J.F., Vassen, W., Hovenier, J.W., Muinonen, K., and Nousiainen, T., Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm, J. Geophys. Res.: Atmos., 2001, vol. 106, no. 15, pp. 17375–17401. https://doi.org/10.1029/2001JD900068

    Article  ADS  Google Scholar 

  50. Warren, S.G., Optical constants of ice from the ultraviolet to the microwave, Appl. Opt., 1984, vol. 23, no. 8, pp. 1206–1225.

    Article  ADS  Google Scholar 

  51. Warren, S.G. and Brandt, R.E., Optical constants of ice from the ultraviolet to the microwave: A revised compilation, J. Geophys. Res.: Atmos., 2008, vol. 113, art. ID D14220. https://doi.org/10.1029/2007JD009744

    Article  ADS  Google Scholar 

  52. Waterman, P.C., Numerical solution of electromagnetic scattering problems, in Computer Techniques for Electromagnetics, Oxford: Pergamon, 1973, pp. 97–157.

    Google Scholar 

  53. Zhuzhulina, E.A., Kiselev, N.N., and Shakhovskoi, D.N., Aperture polarimetry of selected comets at the Crimean Astrophysical Observatory, Izv. Krym. Astrofiz. Obs., 2018, vol. 114, no. 2, pp. 37–39.

    Google Scholar 

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Funding

The research was funded by the Russian Foundation for Basic Research and the government of the Сrimean Republic of the Russian Federation, grant no. 18-42-910019\18.

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  1. Crimean Astrophysical Observatory, Russian Academy of Sciences (CrAO RAS), Crimea, Russia

    D. V. Petrov, E. A. Zhuzhulina & N. N. Kiselev

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Petrov, D.V., Zhuzhulina, E.A. & Kiselev, N.N. Influence of the Spectral Dependence of Refractive Index on the Polarimetric Properties of Ice Particles. Sol Syst Res 54, 70–83 (2020). https://doi.org/10.1134/S0038094620010086

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