Abstract

The familiar yellow or orange disks of the moon and sun, especially when they are low in the sky, and brilliant red sunsets are a result of the selective extinction (scattering plus absorption) of blue light by atmospheric gas molecules and small aerosols, a phenomenon explainable using the Rayleigh scattering approximation. On rare occasions, dust or smoke aerosols can cause the extinction of red light to exceed that for blue, resulting in the disks of the sun and moon to appear as blue. Unlike Earth, the atmosphere of Mars is dominated by micron-size dust aerosols, and the sky during sunset takes on a bluish glow. Here we investigate the role of dust aerosols in the blue Martian sunsets and the occasional blue moons and suns on Earth. We use the Mie theory and the Debye series to calculate the wavelength-dependent optical properties of dust aerosols most commonly found on Mars. Our findings show that while wavelength selective extinction can cause the sun’s disk to appear blue, the color of the glow surrounding the sun as observed from Mars is due to the dominance of near-forward scattering of blue light by dust particles and cannot be explained by a simple, Rayleigh-like selective extinction explanation.

© 2014 Optical Society of America

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    [CrossRef]

2011

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

2009

H. Moosmüller and P. Arnott, “Particle optics in the Rayleigh regime,” J. Air Waste Manage. Assoc. 59, 1028–1031 (2009).
[CrossRef]

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 844–878 (2009).
[CrossRef]

2006

J. Bell, D. Savransky, and M. Wolff, “Chromaticity of the Martian sky as observed by the Mars Exploration Rover Pancam instruments,” J. Geophys. Res. 111, E12S05 (2006).

2005

V. Hamilton, H. McSween, and B. Hapke, “Mineralogy of Martian atmospheric dust inferred from thermal infrared spectra of aerosols,” J. Geophys. Res. 110, E12006 (2005).
[CrossRef]

M. J. Berg, C. M. Sorensen, and A. Chakrabarti, “Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section,” Appl. Opt. 44, 7487–7493 (2005).
[CrossRef]

2004

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

2001

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

1999

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

1997

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

1995

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

1994

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

1992

1988

1979

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

1974

J. Hansen and L. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1969

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I. Direct reflection and direct transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

1951

G. Lothian, “Blue sun and moon,” Nature 168, 1086–1087 (1951).
[CrossRef]

1950

H. Hogg, “Blue Sun,” JR Astron. Soc. Can. 44, 241–245 (1950).

1937

J. Durward, “Blue colour of the sun and surrounding sky in a dust storm,” Q. J. R. Meteorol. Soc. 63, 54–64 (1937).
[CrossRef]

B. van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finite conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos Mag. 24, 141–176, 825–864 (1937).

1929

L. Rayleigh, “On the light from the sky, its polarization and color,” Philos. Mag. 41, 107–120, 274–279 (1929).

1908

G. Mie, “Beiträge Zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik, Vierte Folge 25, 377–445 (1908).

P. Debye, “Das Elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

1884

S. Bishop, “The remarkable sunsets,” Nature 29, 259–260 (1884).
[CrossRef]

Aitken, J.

J. Aitken, “On some phenomena connected with cloudy condensation,” in Collected Scientific Papers of John Aitken, LL.D. F.R.S. (Cambridge, 1923), pp. 279–280.

Arnott, P.

H. Moosmüller and P. Arnott, “Particle optics in the Rayleigh regime,” J. Air Waste Manage. Assoc. 59, 1028–1031 (2009).
[CrossRef]

Arnott, W.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 844–878 (2009).
[CrossRef]

Arnott, W. P.

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Bandfield, J.

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

Banfield, D.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Bell, J.

J. Bell, D. Savransky, and M. Wolff, “Chromaticity of the Martian sky as observed by the Mars Exploration Rover Pancam instruments,” J. Geophys. Res. 111, E12S05 (2006).

Bell, J. F.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Berg, M. J.

Bishop, S.

S. Bishop, “The remarkable sunsets,” Nature 29, 259–260 (1884).
[CrossRef]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Bouguer, P.

P. Bouguer, Essai d’Optique, sur la gradation de la lumiere (Chez Claude Jombert, 1729).

Bremmer, H.

B. van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finite conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos Mag. 24, 141–176, 825–864 (1937).

Brenner, R.

S. Hill and R. Brenner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. Barber and R. Chang, eds. (World Scientific, 1988), pp. 3–61.

Carlson, B. E.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Carlston, C.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Chakrabarti, A.

Chakrabarty, R.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 844–878 (2009).
[CrossRef]

Chakrabarty, R. K.

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Chin, M.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Christensen, P.

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

M. Lane, R. Morris, and P. Christensen, “Spectral behavior of hematite at visible/near infrared and mid-infrared wavelengths,” in The Fifth International Conference on Mars, Pasadena, California, 1999.

Chýlek, P.

Clancy, R.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Colburn, D.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Debye, P.

P. Debye, “Das Elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

Doose, L.

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

Durward, J.

J. Durward, “Blue colour of the sun and surrounding sky in a dust storm,” Q. J. R. Meteorol. Soc. 63, 54–64 (1937).
[CrossRef]

Eck, T. F.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Engelbrecht, J. P.

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Flaser, F.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Frey, G.

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Ghosh, A.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Greeley, R.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Hamilton, V.

V. Hamilton, H. McSween, and B. Hapke, “Mineralogy of Martian atmospheric dust inferred from thermal infrared spectra of aerosols,” J. Geophys. Res. 110, E12006 (2005).
[CrossRef]

Hansen, J.

J. Hansen and L. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Hapke, B.

V. Hamilton, H. McSween, and B. Hapke, “Mineralogy of Martian atmospheric dust inferred from thermal infrared spectra of aerosols,” J. Geophys. Res. 110, E12006 (2005).
[CrossRef]

Hill, S.

S. Hill and R. Brenner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. Barber and R. Chang, eds. (World Scientific, 1988), pp. 3–61.

Hogg, H.

H. Hogg, “Blue Sun,” JR Astron. Soc. Can. 44, 241–245 (1950).

Holben, B. N.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Horvath, H.

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

Hovenac, E.

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Kahn, R.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

Kim, D.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Landis, G. A.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Lane, M.

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

M. Lane, R. Morris, and P. Christensen, “Spectral behavior of hematite at visible/near infrared and mid-infrared wavelengths,” in The Fifth International Conference on Mars, Pasadena, California, 1999.

Lemmon, M.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

Lock, J.

Lothian, G.

G. Lothian, “Blue sun and moon,” Nature 168, 1086–1087 (1951).
[CrossRef]

Malin, M.

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

McSween, H.

V. Hamilton, H. McSween, and B. Hapke, “Mineralogy of Martian atmospheric dust inferred from thermal infrared spectra of aerosols,” J. Geophys. Res. 110, E12006 (2005).
[CrossRef]

Metzig, G.

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

Mie, G.

G. Mie, “Beiträge Zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik, Vierte Folge 25, 377–445 (1908).

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Moosmüller, H.

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 844–878 (2009).
[CrossRef]

H. Moosmüller and P. Arnott, “Particle optics in the Rayleigh regime,” J. Air Waste Manage. Assoc. 59, 1028–1031 (2009).
[CrossRef]

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Morris, R.

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

M. Lane, R. Morris, and P. Christensen, “Spectral behavior of hematite at visible/near infrared and mid-infrared wavelengths,” in The Fifth International Conference on Mars, Pasadena, California, 1999.

Nussenzveig, H. M.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I. Direct reflection and direct transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

Pidek, D.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Pinnick, R.

Pollack, J.

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

Preining, O.

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

Pueschel, R.

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

Querry, M.

M. Querry, “Optical constants,” (U.S. Army Chemical Research and Development Center, 1985).

Rayleigh, L.

L. Rayleigh, “On the light from the sky, its polarization and color,” Philos. Mag. 41, 107–120, 274–279 (1929).

Savransky, D.

J. Bell, D. Savransky, and M. Wolff, “Chromaticity of the Martian sky as observed by the Mars Exploration Rover Pancam instruments,” J. Geophys. Res. 111, E12S05 (2006).

Sinyuk, A.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Skiba, M.

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

Smirnov, A.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Smith, M.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Smith, P.

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

Smith, P. H.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Sorensen, C. M.

Spanovich, N.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Squyres, S. W.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Srivastava, V.

Thompson, S.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Tomasko, M.

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
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M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
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H. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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B. van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finite conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos Mag. 24, 141–176, 825–864 (1937).

Wang, R.

Wegryn, E.

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

Whelley, P.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Whitney, B.

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Wolff, M.

J. Bell, D. Savransky, and M. Wolff, “Chromaticity of the Martian sky as observed by the Mars Exploration Rover Pancam instruments,” J. Geophys. Res. 111, E12S05 (2006).

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Yu, H.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

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G. Mie, “Beiträge Zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik, Vierte Folge 25, 377–445 (1908).

Appl. Opt.

Atmos. Chem. Phys.

D. Kim, M. Chin, H. Yu, T. F. Eck, A. Sinyuk, A. Smirnov, and B. N. Holben, “Dust optical properties over North Africa and Arabian Peninsula derived from the AERONET Dataset,” Atmos. Chem. Phys. 11, 10733–10741 (2011).
[CrossRef]

Atmos. Environ.

H. Horvath, G. Metzig, O. Preining, and R. Pueschel, “Observation of a blue sun over New Mexico, U.S.A.,” Atmos. Environ. 28, 621–630 (1994).
[CrossRef]

Geophys. Res. Lett.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-tropospheric aerosols: implications for aerosol remote-sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

J. Air Waste Manage. Assoc.

H. Moosmüller and P. Arnott, “Particle optics in the Rayleigh regime,” J. Air Waste Manage. Assoc. 59, 1028–1031 (2009).
[CrossRef]

J. Geophys. Res.

V. Hamilton, H. McSween, and B. Hapke, “Mineralogy of Martian atmospheric dust inferred from thermal infrared spectra of aerosols,” J. Geophys. Res. 110, E12006 (2005).
[CrossRef]

J. Pollack, D. Colburn, F. Flaser, R. Kahn, C. Carlston, and D. Pidek, “Properties and effects of dust particles suspended in the Martian atmosphere,” J. Geophys. Res., 842929–2945 (1979).
[CrossRef]

J. Bell, D. Savransky, and M. Wolff, “Chromaticity of the Martian sky as observed by the Mars Exploration Rover Pancam instruments,” J. Geophys. Res. 111, E12S05 (2006).

P. Christensen, R. Morris, M. Lane, J. Bandfield, and M. Malin, “Global mapping of Martian hematite mineral deposits: remnants of water-driven processes on early Mars,” J. Geophys. Res. 106, 873–885 (2001).

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
[CrossRef]

M. Tomasko, L. Doose, M. Lemmon, P. Smith, and E. Wegryn, “Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder,” J. Geophys. Res. 104, 8987–9007 (1999).
[CrossRef]

J. Math. Phys.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I. Direct reflection and direct transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

H. Moosmüller, R. Chakrabarty, and W. Arnott, “Aerosol light absorption and its measurement: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 844–878 (2009).
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Philos Mag.

B. van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finite conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos Mag. 24, 141–176, 825–864 (1937).

Philos. Mag.

L. Rayleigh, “On the light from the sky, its polarization and color,” Philos. Mag. 41, 107–120, 274–279 (1929).

Phys. Z.

P. Debye, “Das Elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

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J. Durward, “Blue colour of the sun and surrounding sky in a dust storm,” Q. J. R. Meteorol. Soc. 63, 54–64 (1937).
[CrossRef]

Science

M. Lemmon, M. Wolff, M. Smith, R. Clancy, D. Banfield, G. A. Landis, A. Ghosh, P. H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J. F. Bell, and S. W. Squyres, “Atmospheric imaging results from the Mars exploration rovers: spirit and opportunity,” Science 306, 1753–1756 (2004).
[CrossRef]

Space Sci. Rev.

J. Hansen and L. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Other

H. Moosmüller, J. P. Engelbrecht, M. Skiba, G. Frey, R. K. Chakrabarty, and W. P. Arnott, “Single scattering Albedo of fine mineral dust aerosols controlled by iron concentration,” J. Geophys. Res.117, doi:10.1029/2011JD016909 (2012).
[CrossRef]

M. Querry, “Optical constants,” (U.S. Army Chemical Research and Development Center, 1985).

M. Lane, R. Morris, and P. Christensen, “Spectral behavior of hematite at visible/near infrared and mid-infrared wavelengths,” in The Fifth International Conference on Mars, Pasadena, California, 1999.

S. Hill and R. Brenner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. Barber and R. Chang, eds. (World Scientific, 1988), pp. 3–61.

H. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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http://www.jpl.nasa.gov/video/index.php?id=954 .

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Figures (11)

Fig. 1.
Fig. 1.

Martian sunset over the Gusev crater overlaid with scattering angles. The image of the sunset was taken by NASA’s Mars Exploration Rover Spirit on May 19, 2005. Image credit: NASA/JPL/Texas A&M/Cornell.

Fig. 2.
Fig. 2.

Extinction curve. (a) The extinction curve for a spherical particle with refractive index n=1.4 computed using Mie’s solution (upper curve) and the anomalous diffraction approximation (lower curve). The interval corresponding to the visible spectrum for a particle of radius 0.65 μm is indicated. (b) Anomalous diffraction approximation of the extinction efficiency versus the size parameter: Qext versus phase shift parameter.

Fig. 3.
Fig. 3.

Extinction curve for an absorbing particle. (a) The extinction curves for a spherical particle with refractive index n=1.4+ik where k=0 (solid), 0.05 (dashed), and 0.15 (dotted). (b) The extinction curve Qext estimated using formula 7 versus size parameter x for a spherical particle with refractive index n=1.4+ik where k=0 (solid), 0.05 (dashed), and 0.15 (dotted).

Fig. 4.
Fig. 4.

Effect of wavelength-dependent absorption on the shape of the extinction curve for a particle with radius r=0.475μm. The index of refraction is n=1.35+ik where k=0 for the upper curve, and k decreases linearly from 0.5 to 0 as the wavelength increases from 0.4 to 0.7 μm in the lower curve.

Fig. 5.
Fig. 5.

Effect of wavelength dependence on bluing using the anomalous diffraction approximation. Left: Plot Qext versus wavelength (λ in μm) and radius (r in μm) computed using Eq. (7) with refractive index n=1.4. Right: Plot Qext versus wavelength and radius computed using Eq. (7), where n=1.4+ki with k decreasing linearly from 0.1 at λ=0.4μm to 0 at 0.7 μm.

Fig. 6.
Fig. 6.

Imaginary part (solid) and real part (dashed) of the refractive index of hematite from [30].

Fig. 7.
Fig. 7.

Dust model parameters. (a) The real (dashed) and imaginary (solid) parts of the index of refraction of the simulated Martian dust. (b) Size distribution of the simulated Martian dust.

Fig. 8.
Fig. 8.

Extinction efficiencies for the simulated Martian dust. (a) Contour plot of Qext versus radius and wavelength. (b) Plot of Qabs (dashed), Qsca (dotted), and Qext (solid) computed using Mie theory for a 3% hematite mixture (black), a 5% hematite mixture (blue), and a 20% mixture (red).

Fig. 9.
Fig. 9.

Relative intensity (S12+S22) of scattered light versus scattering angle for a 3% hematite dust mixture (solid curves) and the pure substrate with no hematite (dashed curves). The blue curves correspond to blue light (425 nm), and the red curves correspond to red light (694 nm). Note that in the near-forward directions, the curves are insensitive to hematite, while in the region approaching a scattering angle of 180°, hematite concentration plays a significant role. Without hematite, red and blue light would be backscattered in equal amounts, and Mars would not be known as the red planet.

Fig. 10.
Fig. 10.

Observation of scattered light at sunset. Light seen by the observer scattered from a dust particle at position 1 appears blue since θ<28°, so the intensity of near-forward blue light is much greater than that for red. The dominance by blue is lost at position 2 where ϕ>28°.

Fig. 11.
Fig. 11.

Relative intensity (S12+S22) of scattered light versus scattering angle for a 3% hematite dust mixture computed using Mie’s solution (solid curves), the p0 term of the Debye series (dashed curves) and only diffraction (dotted curves). The left curves correspond to blue light (425 nm), and the right curves correspond to red light (694 nm).

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

βabs=i=1nσabsiVandβsca=i=1nσscaiV,
σext=σsca+σabsandβext=βsca+βabs.
PPo=eβextz.
S1=n2n+1n(n+1)(anπn+bnτn)S2=n2n+1n(n+1)(anτn+bnπn).
12[1Rn22p=1Tn21(Rn11)p1Tn12].
Q˜ext=24ρsinρ+4ρ2(1cosρ),
r=0.26μm/(m1),
Q˜ext=f(ρ)=24eρtanβcosβρsin(ρβ)4eρtanβ(cosβρ)2cos(ρ2β)+4(cosβρ)2cos2β
tanβ=km1,
Q˜ext=q(r,λ)=f(4πr(m1)/λ).
n2=n02nA2+2n02+2vA(nA2n02)nA2+2n02vA(nA2n02),
N(r)=Kr(13b)/bexp[r/(ab)].
a=0r3N(r)dr0r2N(r)dr.
b=0(ra)2r2N(r)dra20r2N(r)dr.
I(θ)=Io[x21+cos2θ2J1(xsinθ)xsinθ]2,

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