Kinematics and Physics of Celestial Bodies

, Volume 33, Issue 5, pp 217–230 | Cite as

Fourier analysis of spectra of solar-type stars

Physics of Stars and Interstellar Medium


Fourier transform techniques were used to determine the macroturbulent velocity under the condition that mictoturbulent and stellar rotation velocities are not known. In order to distinguish the effects of rotation from macroturbulence effects in slowly rotating stars, primarily the main lobe of residual Fourier transforms of the observed lines, which were taken from the solar spectrum and the spectra of two other stars, was used. This case of Fourier analysis of spectral lines is the most complicated one. The end results were in a satisfactory agreement with the data obtained using different methods. The average values of microturbulent, macroturbulent, and rotation velocities were 0.85, 2.22, and 1.75 km/s for the Sun as the star; 0.58, 1.73, and 0.78 km/s for HD 10700; and 1.16, 3.56, and 6.24 km/s for HD 1835. It was found that the macroturbulent velocity decreases with height in the atmosphere of the Sun and HD 1835. In the case of HD 10700, the macroturbulent velocity did not change with height, and the determined rotation velocity was two times lower than the one obtained using other methods. It was concluded that Fourier transform techniques are suitable for determining the velocities in atmospheres of solar-type stars with very slow rotation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. S. Gadun and V. A. Sheminova, Preprint No. ITF-88-87P (Institute for Theoretical Physics of the Ukrainian SSR Academy of Sciences, Kiev, 1988).Google Scholar
  2. 2.
    E. A. Gurtovenko and V. A. Sheminova, Preprint No. GAO-97-1P (Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, 1997). Scholar
  3. 3.
    V. A. Sheminova, “Turbulence in the photosphere of the Sun as a star. III. Micro-macroturbulence,” Soln. Dannye 8, 70–77 (1984).ADSGoogle Scholar
  4. 4.
    V. A. Sheminova, “Macroturbulence and microturbulence in the solar photosphere,” Kinematika Fiz. Nebesnykh Tel 1, 50–52 (1985).ADSGoogle Scholar
  5. 5.
    V. A. Sheminova and A. S. Gadun, “Fourier analysis of Fe I lines in spectra of the Sun, a Centauri A, Procyon, Arcturus and Canopus,” Kinematika Fiz. Nebesnykh Tel 14, 219–233 (1998). Scholar
  6. 6.
    M. Asplund, N. Grevesse, and A. J. Sauval, “The solar chemical composition,” in Proc. Symp. on Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis in honor of David L. Lambert, Austin, TX, June 17–19, 2004, Ed. by T. G. Barnes III and F. N. Bash (Astron. Soc. Pac., San Francisco, CA, 2005), in Ser.: ASP Conference Series, Vol. 336, pp. 25–38.ADSGoogle Scholar
  7. 7.
    P. S. Barklem and J. Aspelund-Johansson, “The broadening of Fe II lines by neutral hydrogen collisions,” Astron. Astrophys. 435, 373–377 (2005).ADSCrossRefGoogle Scholar
  8. 8.
    P. S. Barklem, N. Piskunov, and B. J. O’Mara, “A list of data for the broadening of metallic lines by neutral hydrogen collisions,” Astron. Astrophys. Suppl. Ser. 142, 467–473 (2000).ADSCrossRefGoogle Scholar
  9. 9.
    J. W. Brault and O. R. White, “The analysis and restoration of astronomical data via the fast Fourier transform,” Astron. Astrophys. 13, 169–189 (1971).ADSGoogle Scholar
  10. 10.
    D. H. Bruning, “The applicability of the Fourier convolution theorem to the analysis of late-type stellar spectra,” Astrophys. J. 281, 830–838 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    V. Caccin, A. Donati-Falchi, and R. Falciani, “Temperature variations in the solar photosphere. III: Kitt Peak measurements of the variations of photospheric line profiles with the heliographic latitude,” Sol. Phys. 46, 29–52 (1976).ADSCrossRefGoogle Scholar
  12. 12.
    J. R. Fuhr and W. L. Wiese, “A critical compilation of atomic transition probabilities for neutral and singly ionized iron,” J. Phys. and Chem. Ref. Data 35, 1669–1809 (2006).ADSCrossRefGoogle Scholar
  13. 13.
    A. S. Gadun and R. I. Kostyk, “Analysis of absorption line profiles in the spectra of the Sun and Procyon — Velocity field and size of inhomogeneities,” Sov. Astron. 34, 260–263 (1990).ADSGoogle Scholar
  14. 14.
    T. Gehren, K. Butler, L. Mashonkina, J. Reetz, and J. Shi, “Kinetic equilibrium of iron in the atmospheres of cool dwarf stars. I. The solar strong line spectrum,” Astron. Astrophys. 366, 981–1002 (2001).ADSCrossRefGoogle Scholar
  15. 15.
    D. F. Gray, “On the existence of classical microturbulence,” Astrophys. J. 184, 461–472 (1973).ADSCrossRefGoogle Scholar
  16. 16.
    D. F. Gray, “Atmospheric turbulence measured in stars above the main sequence,” Astrophys. J. 202, 148–164 (1975).ADSCrossRefGoogle Scholar
  17. 17.
    D. F. Gray, The Observation and Analysis of Stellar Photospheres (Wiley, New York, 1976).Google Scholar
  18. 18.
    D. F. Gray, “A test of the micro-macroturbulence model on the solar flux spectrum,” Astrophys. J. 218, 530–538 (1977).ADSCrossRefGoogle Scholar
  19. 19.
    D. F. Gray, “The temperature dependence of rotation and turbulence in giant stars,” Astrophys. J. 262, 682–699 (1982).ADSCrossRefGoogle Scholar
  20. 20.
    D. F. Gray, “Precise rotation rates for five slowly rotating A stars,” Astron. J. 147, 81 (2014).ADSCrossRefGoogle Scholar
  21. 21.
    D. F. Gray and K. I. T. Brown, “The rotation of Arcturus and active longitudes on giant stars,” Publ. Astron. Soc. Pac. 118, 1112–1118 (2006).ADSCrossRefGoogle Scholar
  22. 22.
    E. A. Gurtovenko and V. A. Sheminova, “‘Crossing’ method for studying the turbulence in solar and stellar atmospheres. I: Application to the Sun,” Sol. Phys. 106, 237–247 (1986).ADSCrossRefGoogle Scholar
  23. 23.
    B. Gustafsson, B. Edvardsson, K. Eriksson, et al., “A grid of MARCS model atmospheres for late-type stars. I. Methods and general properties,” Astron. Astrophys. 486, 951–970 (2008).ADSCrossRefGoogle Scholar
  24. 24.
    K. Hinkle and L. Wallace, “The spectrum of Arcturus from the infrared through the ultraviolet,” in Proc. Symp. on Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis in honor of David L. Lambert, Austin, TX, June 17–19, 2004, Ed. by T. G. Barnes III and F. N. Bash (Astron. Soc. Pac., San Francisco, CA, 2005), in Ser.: ASP Conference Series, Vol. 336, pp. 321–326.ADSGoogle Scholar
  25. 25.
    J. S. Jenkins, H. R. A. Jones, Y. Pavlenko, et al., “Metallicities and activities of southern stars,” Astron. Astrophys. 485, 571–584 (2008).ADSCrossRefGoogle Scholar
  26. 26.
    R. I. Kostik, “Damping constant and turbulence in the solar atmosphere,” Sol. Phys. 78, 39–57 (1982).ADSCrossRefGoogle Scholar
  27. 27.
    F. Kupka, N. Piskunov, T. A. Ryabchikova, et al., “VALD–2: Progress of the Vienna atomic line data base,” Astron. Astrophys. Suppl. Ser. 138, 119–133 (1999).ADSCrossRefGoogle Scholar
  28. 28.
    R. L. Kurucz, “Atlas: A computer program for calculating model stellar atmospheres,” SAO Special Report No. 309 (Smithson. Astrophys. Obs., Cambridge, MA, 1970).Google Scholar
  29. 29.
    L. Mashonkina, T. Gehren, J.-R. Shi, et al., “A non-LTE study of neutral and singly-ionized iron line spectra in 1D models of the Sun and selected late-type stars,” Astron. Astrophys. 528, A87 (2011).ADSCrossRefGoogle Scholar
  30. 30.
    Ya. V. Pavlenko, J. S. Jenkins, H. R. A. Jones, et al., “Effective temperatures, rotational velocities, microturbulent velocities and abundances in the atmospheres of the Sun, HD 1835 and HD 10700,” Mon. Not. R. Astron. Soc. 422, 542–552 (2012).ADSCrossRefGoogle Scholar
  31. 31.
    P. Scott, M. Asplund, N. Grevesse, et al., “The elemental composition of the Sun. II. The iron group elements Sc to Ni,” Astron. Astrophys. 537, A26 (2015).CrossRefGoogle Scholar
  32. 32.
    M. A. Smith, “Applications of Fourier analysis to broadening of stellar line profiles. IV. A technique for separating macroturbulence from rotation in solar-type stars,” Astrophys. J. 208, 487–499 (1976).ADSCrossRefGoogle Scholar
  33. 33.
    M. A. Smith, “Rotational studies of lower main-sequence stars,” Publ. Astron. Soc. Pac. 91, 737–745 (1979).ADSCrossRefGoogle Scholar
  34. 34.
    M. A. Smith and J. F. Dominy, “The dependence of macroturbulence on luminosity in early K-type stars,” Astrophys. J. 231, 477–490 (1979).ADSCrossRefGoogle Scholar
  35. 35.
    M. A. Smith, L. Testerman, and J. C. Evans, “Applications of Fourier analysis to broadening of stellar line profiles. III. Solar microturbulence and macroturbulence from iron lines,” Astrophys. J. 207, 308–324 (1976).ADSCrossRefGoogle Scholar
  36. 36.
    M. Steffen, E. Caffau, and H.-G. Ludwig, “Micro-and macroturbulence predictions from CO5BOLD 3D stellar atmospheres,” Mem. Soc. Astron. Ital. Suppl. 24, 37–52 (2013).ADSGoogle Scholar
  37. 37.
    Y. Takeda, “Analyses of line profiles in the solar flux spectrum for determining rotation and micro/macro turbulence,” Publ. Astron. Soc. Jpn. 47, 337–354 (1995).ADSGoogle Scholar
  38. 38.
    J. A. Valenti and D. A. Fischer, “Spectroscopic properties of cool stars (SPOCS). I. 1040 F, G, and K dwarfs from Keck, Lick, and AAT planet search programs,” Astrophys. J. Suppl. Ser. 159, 141–166 (2005).ADSCrossRefGoogle Scholar
  39. 39.
    J. A. Valenti and N. Piskunov, “Spectroscopy made easy: A new tool for fitting observations with synthetic spectra,” Astron. Astrophys. Suppl. Ser. 118, 595–603 (1996).ADSCrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Main Astronomical ObservatoryNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations