SS3 versus SS2

FTS atlas of the Third Solar Spectrum (SS3) and its relation to the Second Solar Spectrum (SS2)

When using these data, please refer to the material as follows:

“The data for this analysis have been provided in electronic form by IRSOL as a compilation by Stenflo (2014)”

  • Stenflo, J.O. 2014, in R. Ramelli (ed.),


The FTS atlas of the Third Solar Spectrum (SS3) represents the ratio between the intensity spectrum at µ = 0.145 and the intensity spectrum at disk center (µ = 1.0), both in units of the intensity of the local continuum level. This ratio spectrum covers the range 4084.29 – 9950.50 Å and can be viewed in three different pdf files, each of which showing a 10 Å wavelength section per plot page. Each file contains a comparison of the ratio atlas with two other atlases, so there are three panels per plot page. The files are also extensively described in the following paper:

Stenflo, J.O. 2015, FTS atlas of the Sun’s spectrally resolved center-to-limb variation. A&A 573, A74 (2015)

Due to the exceptional nature of the Kitt Peak/McMath FTS, a powerful instrument constructed by Jim Brault, both the limb and disk center spectra are fully resolved and free from stray light, in addition to being nearly noise-free and having a well-defined continuum level. The three pdf files are:

  • siratio.pdf (range 4084.29 – 9950.50 Å)
    • Top panel: FTS spectrum at disk center.
    • Middle panel: FTS spectrum at µ = 0.145.
    • Bottom panel: Ratio between the spectra in the middle and top panels (SS3).
  • SS312.pdf (4080 – 6990 Å)
    • Top panel: FTS spectrum at µ = 0.145.
    • Middle panel: Ratio spectrum (SS3).
    • Bottom panel: Second Solar Spectrum (SS2).
  • simodel.pdf
    • Top panel: FTS spectrum at disk center.
    • Middle panel: Ratio spectrum (SS3) with a model of it overplotted (dashed).
    • Bottom panel: Difference between SS3 and model of it (on the same relative scale as the middle panel).

The model that converts the disk-center spectrum sic into SS3 (simod) is defined as follows (where w is the wavelength):


The disk center FTS atlas representing the quiet Sun has been taken from the compilation of the Kitt Peak FTS-Spectral-Atlas in the digital form provided by H. Neckel, Hamburg. It is given here over the full range 3290-12508 Å in file DCatlas.pdf

The limb FTS atlas was recorded on October 2-3, 1978, and April 27-28, 1979, as part of the first survey of the Second Solar Spectrum that was published in Stenflo et al. (A&A Suppl. Ser., 54, 505-514, 1983). The spatial field of view with the Kitt Peak FTS polarimeter was a rectangular 17.5″ x 10″ aperture centered 10 arcsec inside the solar limb near one of the heliographic poles (to minimize the effect of magnetic fields). The 17.5 arcsec side was parallel to the limb, so the limb distance interval covered is 5-15 arcsec from the limb. At 10 arcsec limb distance, µ = 0.144. If we use as an example the limb darkening function valid for the continuum at 5000 Å (the limb darkening varies with wavelength and within the line profiles), then we find an intensity-weighted average µ of 0.145. This demonstrates that this average is insensitive to the choice of limb darkening function, and the effects are generally smaller than the errors in the positioning of the aperture on the Sun. Therefore we adopt µ = 0.145 as representing the disk position to which the limb spectrum refers.

Since the disk and limb spectra were recorded at different times they can be affected by small differential Doppler shifts due to different velocities between the telescope and the Sun (in particular due to the rotation and orbital elliptical motion of the Earth). Therefore we have used the disk center FTS spectrum as a reference and made the wavelength scale of the limb spectrum conform to the scale of this disk center spectrum by iterative least squares fitting of the two spectra, using shift and stretch as the two free parameters of the fit.

The SS2 atlas has been described in a previous section. In the representation of SS2 in the third panel of the SS312.pdf plots, a mild form of smoothing of SS2 based on wavelets has been used. No smoothing has been applied to the FTS limb, disk center, or ratio spectra.

Data Files

nwl: dimension, long(1843600)
wl: Wavelength (double), 3290-12508 Å
bdc: I/Ic (double)
nw: dimension, long(1173243).
w: Wavelength (double), dimension nw, 4084.29 – 9950.50 Å.
sidc: Disk center I/Ic (double), subset of bcd for the range needed for the plot, dimension nw.
silimb: Limb (µ = 0.145) I/Ic (float), dimension nw, interpolated to the same 5 mÅ wavelength grid as sidc.
siratio: limb / disk-center ratio, dimension nw.
n: dimension+1, long(335872).
lam: Wavelength (double), dimension n-1, original wavelengths for the limb spectrum before interpolation to the sidc wavelength grid, 4084.29 – 9950.50 Å.
sia: Original I/Ic limb spectrum (float), dimension n-1
sqa: Corresponding original Q/I (%) limb spectrum (float) from 1978, dimension n-1, only of historical interest.