The anomalous redshift on the sun’s limb and that measured by Pioneer-6 are interesting for the process of absorption of light and the spatial density of matter around the sun. Here we derive a 3D solution for the diffusion equation in the case of the steady state, which is then adopted as the density of the ionized matter around the sun. In order to deal with the observed light’s intensity, two integrals along the line of sight are evaluated. Alternatives to the Doppler shift have been considered as mechanisms: a thermal model, a plasma effect, the interaction of a low density electromagnetic wave with an electron and the interaction of light with a low density Fermi gas in standard QED. These four models are compared in the case of the Pioneer-6 signal.
References
[1]
Adams, W.S. (1910) An Investigation of the Displacements of the Spectrum Lines at the Sun’s Limb. Astrophysical Journal, 31, 30-61. https://doi.org/10.1086/141722
[2]
Adam, M.G. (1959) A New Determination of the Centre to Limb Change in Solar Wave-Lengths. MNRAS, 119, 460-474. https://doi.org/10.1093/mnras/119.5.460
[3]
Higgs, L.A. (1960) The Solar Red-Shift. MNRAS, 121, 421-435. https://doi.org/10.1093/mnras/121.5.421
[4]
Appenzeller, I. and Schröter, E.H. (1967) Center-to-Limb Variations of the Intensity and the Wavelength of Several Fraunhofer Lines along the SUN’s Polar and Equatorial Diameter. Astrophysical Journal, 147, 1100. https://doi.org/10.1086/149098
[5]
Salman-Zade, R.K. (1969) Limb Effect of the Fraunhofer Lines in the Solar Spectrum. Soviet Astronomy, 13, 466.
[6]
Allen, C.W. (1949) Centre-Limb Variations of Fraunhofer Line-Breadths and Intensities. MNRAS, 109, 343. https://doi.org/10.1093/mnras/109.3.343
[7]
Hart, M.H. (1974) An Explanation of the Solar Limb Shift. Astrophysical Journal, 187, 393-401. https://doi.org/10.1086/152645
[8]
Marmet, P. (1989) Red Shift of Spectral Lines in the Sun’s Chromosphere. IEEE Transactions on Plasma Science, 17, 238-243. https://doi.org/10.1109/27.24630
[9]
Trinchera, A. (2020) Redshift Anomaly on the Solar Disk as Multiple Interactions between Photons and Electrons. Journal of High Energy Physics, Gravitation and Cosmology, 7, 1-51. https://doi.org/10.4236/jhepgc.2021.71001
[10]
Goldstein, R.M. (1969) Superior Conjunction of Pioneer 6. Science, 166, 598-601. https://doi.org/10.1126/science.166.3905.598
[11]
Ferencz, C. and Tarcsai, G. (1970) A New Experimental Possibility of Investigating the Solar Corona: Frequency Measurements on Radio Sources When Occultated by the Sun. Planetary and Space Science, 18, 1213-1223. https://doi.org/10.1016/0032-0633(70)90213-8
[12]
Ferencz, C. and Tarcsai, G. (1971) Theoretical Explanation of the Solar Limb Effect Planetary and Space Science, 19, 659-667. https://doi.org/10.1016/0032-0633(71)90058-4
[13]
Ferencz, C. (1971) Interaction of Gravitational and Electromagnetic Fields or Another Effect? Nature, 233, 404-406. https://doi.org/10.1038/233404a0
[14]
Ferencz, C. (1974) Redshift during Pioneer-6 Solar Occultation—Unexplained or Predicted. Nature, 252, 615. https://doi.org/10.1038/252615a0
[15]
Merat, P., Pecker, J.C. and Vigier, J.P. (1974) Possible Interpretation of an Anomalous Redsbift Observed on the 2292 MHz Line Emitted by Pioneer-6 in the Close Vicinity of the Solar Limb. Astronomy & Astrophysics, 30, 167-174.
[16]
Accardi, L., Laio, A., Lu, Y. and Rizzi, G. (1995) A Third Hypothesis on the Origin of the Redshift: Application to the Pioneer 6 Data. Physics Letters A, 209, 277-284. https://doi.org/10.1016/0375-9601(95)00868-3
[17]
Weidner, H. (2014) Pioneer 6 Anomalous Redshift near the Sun.
[18]
Trinchera, A. (2021) Redshift Anomaly of the 2292 MHz Radio Signal Emitted by the Pioneer-6 Space Probe as Multiple Interactions with Photo-Ionized Electrons in the Solar Corona. Journal of High Energy Physics, Gravitation and Cosmology, 7, 1107-1156. https://doi.org/10.4236/jhepgc.2021.73066
[19]
Freund, J. (2008) Special Relativity for Beginners: A Textbook for Undergraduates. World Scientific Press, Singapore. https://doi.org/10.1142/6601
[20]
Lang, K.R. (1999) Astrophysical Formulae. Third Edition, Springer, New York. https://doi.org/10.1007/978-3-662-21639-2
[21]
Valente, M.B. (2018) Einstein’s Redshift Derivations: Its History from 1907 to 1921. Circumscribere, 22, 1-16. https://doi.org/10.23925/1980-7651.2018v22;1-16
[22]
Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.
[23]
Brynjolfsson, A. (2004) Redshift of Photons Penetrating a Hot Plasma.
[24]
Brynjolfsson, A. (2009) Plasma-Redshift Cosmology: A Review. In: Potter, F., Ed., 2nd Crisis in Cosmology Conference, Vol. 413 of Astronomical Society of the Pacific Conference Series, Astronomical Society of the Pacific, San Francisco, 169-189.
[25]
Weidner, H. (2014) Limb Redshift of the Fraunhofer Lines in the Solar Spectrum.
