A Novel Technique for Measuring the Solar Radius from Eclipse Light Curves – Results for 2010, 2012, 2013, and 2015

Abstract

We report on a novel technique for measuring the solar radius during total solar eclipses that exploits light curves recorded just before and after second and third contacts. The measurements are performed by pre-programmed photometers that are deployed over the eclipse paths and are operated without supervision. The recorded light curves are compared to synthetic light curves calculated from high-accuracy ephemerides and lunar-limb profiles constructed from the topographic model of the Moon provided by the Kaguya lunar space mission. A minimization process between the two sets of curves yields the solar radius. Altogether, seventeen determinations have been obtained during the past four total eclipses with the following averages (at a wavelength of 540 nm and scaled to 1 AU): \(959.94\pm0.02~\mbox{arcsec}\) on 11 July 2010, \(960.02\pm0.04~\mbox{arcsec}\) on 13 November 2012, \(959.99\pm0.09~\mbox{arcsec}\) on 3 November 2013, and \(960.01\pm0.09~\mbox{arcsec}\) on 20 March 2015. Part of the differences between these four values may be attributed to weather conditions. Averaging the whole set of measurements yields a radius of \(959.99\pm0.06~\mbox{arcsec}\) (\(696{,}246\pm45~\mbox{km}\)), which agrees excellently well with the most recent data and supports an upward revision of the standard IAU value, as previously suggested.

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References

  1. Ajabshirzadeh, A., Koutchmy, S.: 2005, In: Danesy, D., Poedts, S., De Groof, A., Andries, J. (eds.) Proceedings of the 11th European Solar Physics Meeting “The Dynamic Sun: Challenges for Theory and Observations” 600, ESA, Noordwijk. ADS .

    Google Scholar 

  2. Auwers, A.: 1891, Der Sonnendurchmesser und der Venusdurchmesser nach den Beobachtungen an den Heliometern der deutschen Venus-Expeditionen. Astron. Nachr. 128, 361. DOI . ADS .

    Article  ADS  Google Scholar 

  3. Bazin, C., Koutchmy, S.: 2013, Helium shells and faint emission lines from slitless flash spectra. J. Advert. Res. 4, 307. DOI . ADS .

    Article  Google Scholar 

  4. Capitaine, N., Wallace, P.T., Chapront, J.: 2003, Expressions for IAU 2000 precession quantities. Astron. Astrophys. 412, 567. DOI . ADS

    Article  ADS  Google Scholar 

  5. Capitaine, N., Wallace, P.T., McCarthy, D.D.: 2003, Expressions to implement the IAU 2000 definition of UT1. Astron. Astrophys. 406, 1135. DOI . ADS .

    Article  ADS  Google Scholar 

  6. Djafer, D., Thuillier, G., Sofia, S.: 2008, A comparison among solar diameter measurements carried out from the ground and outside Earth’s atmosphere. Astrophys. J. 676, 651. DOI . ADS .

    Article  ADS  Google Scholar 

  7. Dunham, D.W., Thompson, J.R., Herald, D.R., Buechner, R., Fiala, A.D., Warren, W.H. Jr., et al.: 2005, SORCE Science Meeting September 14 and 16, Durango, Colorado ( lasp.colorado.edu/sorce/news/2005ScienceMeeting/ ).

  8. Emilio, M., Leister, N.V.: 2005, Solar diameter measurements at São Paulo Observatory. Mon. Not. Roy. Astron. Soc. 361, 1005. DOI . ADS .

    Article  ADS  Google Scholar 

  9. Emilio, M., Kuhn, J.R., Bush, R.I., Scholl, I.F.: 2012, Measuring the solar radius from space during the 2003 and 2006 Mercury transits. Astrophys. J. 750, 135. DOI . ADS .

    Article  ADS  Google Scholar 

  10. Fienga, A., Manche, H., Laskar, J., Gastineau, M.: 2008, INPOP06: a new numerical planetary ephemeris. Astron. Astrophys. 477, 315. DOI . ADS .

    Article  ADS  Google Scholar 

  11. Fok, H.S., Shum, C.K., Yi, Y., Araki, H., Ping, J., Williams, J.G., et al.: 2011, Accuracy assessment of lunar topography models. Earth Planets Space 63, 15. DOI . ADS .

    Article  ADS  Google Scholar 

  12. Hauchecorne, A., Meftah, M., Irbah, A., Couvidat, S., Bush, R., Hochedez, J.-F.: 2014, Solar radius determination from Sodism/Picard and HMI/SDO observations of the decrease of the spectral solar radiance during the 2012 June Venus Transit. Astrophys. J. 783, 127. DOI . ADS .

    Article  ADS  Google Scholar 

  13. Herald, D.: 2015, Occultation prediction Software, Occult v4.1.1, IOTA. www.lunar-occultations.com/iota/iotandx.htm .

  14. Hestroffer, D., Magnan, C.: 1998, Wavelength dependency of the Solar limb darkening. Astron. Astrophys. 333, 338. ADS .

    ADS  Google Scholar 

  15. Kilcik, A., Sigismondi, C., Rozelot, J.P., Guhl, K.: 2009, Solar radius determination from total solar eclipse observations on 29 March 2006. Solar Phys. 257, 237. DOI . ADS .

    Article  ADS  Google Scholar 

  16. Kuhn, J.R., Bush, R.I., Emilio, M., Scherrer, P.H.: 2004, On the constancy of the solar diameter. II. Astrophys. J. 613, 1241. ADS .

    Article  ADS  Google Scholar 

  17. Makarova, E.A., Kharitonov, A.V.: 1977, Averaged data for the limb darkening of the quiet sun – The integrated spectrum. Soviet Astron. 21, 65. ADS .

    ADS  Google Scholar 

  18. Meftah, M., Hauchecorne, A., Crepel, M., Irbah, A., Corbard, T., Djafer, D., Hochedez, J.-F.: 2014, The plate scale of the SODISM instrument and the determination of the solar radius at 607.1 nm. Solar Phys. 289, 1. DOI . ADS .

    Article  ADS  Google Scholar 

  19. Neckel, H., Labs, D.: 1994, Solar limb darkening 1986 – 1990 (lambda 303 to 1099 nm). Solar Phys. 153, 91. DOI . ADS .

    Article  ADS  Google Scholar 

  20. Pierce, A.K., Slaughter, C.D.: 1977, Solar limb darkening. I – At wavelengths of 3033 – 7297. Solar Phys. 51, 25. DOI . ADS .

    Article  ADS  Google Scholar 

  21. Raponi, A., Sigismondi, C., Guhl, K., Nugent, R., Tegtmeier, A.: 2012, The measurement of solar diameter and limb darkening function with the eclipse observations. Solar Phys. 278, 269. DOI . ADS .

    Article  ADS  Google Scholar 

  22. Ribes, J.C., Nesme-Ribes, E.: 1993, The solar sunspot cycle in the Maunder minimum AD1645 to AD1715. Astron. Astrophys. 76, 549. ADS .

    ADS  Google Scholar 

  23. Rozelot, J.P., Damiani, C., Lefebvre, S.: 2009a, Variability of the solar shape (before space dedicated missions). J. Atmos. Solar-Terr. Phys. 71, 1683. DOI . ADS .

    Article  ADS  Google Scholar 

  24. Rozelot, J.P., Damiani, C., Pireaux, S.: 2009b, Probing the solar surface: The oblateness and astrophysical consequences. Astron. Astrophys. 703, 1791. DOI . ADS .

    ADS  Google Scholar 

  25. Scholz, M.: 2001, On the interpretation of stellar disc observations in terms of diameters. Mon. Not. Roy. Astron. Soc. 321, 347. DOI . ADS .

    Article  ADS  Google Scholar 

  26. Sigismondi, C.: 2009, Guidelines for measuring solar radius with Baily beads analysis. Sci. China Ser. G 52, 1773. DOI . ADS .

    Article  Google Scholar 

  27. Sigismondi, C., Raponi, A., Bazin, C., Nugent, R.: 2012, Towards a unified definition of solar limb during central eclipses and daily transits. Int. J. Mod. Phys. 12, 405. DOI . ADS .

    Google Scholar 

  28. Steiner, O.: 2005, Radiative properties of magnetic elements II. Center to limb variation of the appearance of photospheric faculae. Astron. Astrophys. 430, 691. DOI . ADS .

    Article  ADS  Google Scholar 

  29. Thuillier, G., Sofia, S., Haberreiter, M.: 2005, Past, present and future measurements of the solar diameter. Adv. Space Res. 35, 329. DOI . ADS .

    Article  ADS  Google Scholar 

  30. Thuillier, G., Claudel, J., Djafer, D., Haberreiter, M., Mein, N., Melo, S.M.L., et al.: 2011, The shape of the solar limb: Models and observations. Solar Phys. 268, 125. DOI . ADS .

    Article  ADS  Google Scholar 

  31. Wittmann, A.: 1977, The diameter of the Sun. Astron. Astrophys. 61, 225. ADS .

    ADS  Google Scholar 

  32. Wittmann, A.: 1980, The solar limb darkening function at 5012 A and its possible variations. Astron. Astrophys. 83, 312. ADS .

    ADS  Google Scholar 

  33. Wittmann, A.: 2003, Visual and photoelectric measurements of the solar diameter (1972 – 2002): Methods and results. Astron. Nachr. 324, 378. ADS .

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to Gonzague Bosch and Frédéric Bouchar of the TENUM company for their dedicated efforts to build the photometers in a very short time. We express our gratitude to Meleana Adams, Frédérique Arthaud, Charles Azymze, Jean-Pierre Barriot, Cyril Bazin, Brice Boclet, Ludovic Bousquet, Jack Brunet, Paul Castelnau, Isabelle Dhenin, Etienne Dumont, Jean-Christophe Guin, Eric Hervier, Xavier Jubier, Patrick Martinez, Jean-Claude Merlin, Jean Mouette, Alain Perret, Jason Poinot, Julie Prado, Jean-Louis Raynaud, Lydie Sichoix, and Stéphane Thomas for their participation in the deployments of the photometers, to the tour operators \(66^{\circ}\) Nord, Grand Nord Grand Large, Chasseurs d’Eclipses, and to the numerous unknown people who kindly hosted the photometers on their property. We thank Maurizio Emilio very much for providing his software to generate Figure 1. This work was supported by grants from the Centre National d’Etudes Spatiales.

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Correspondence to Philippe Lamy.

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Lamy, P., Prado, J., Floyd, O. et al. A Novel Technique for Measuring the Solar Radius from Eclipse Light Curves – Results for 2010, 2012, 2013, and 2015. Sol Phys 290, 2617–2648 (2015). https://doi.org/10.1007/s11207-015-0787-8

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Keywords

  • Sun
  • Sun: diameter
  • Sun: eclipses