The Line-Spread Function and the Comparison of Synthetic and Observed Spectra

SPECTRUM computes the synthetic spectrum at very high resolution (for instance, a spacing of 0.01Å at 5000Å corresponds to a resolution of $R = 500,000$). Very few spectrographs yield this sort of resolution, and thus the very high resolution synthetic spectrum must be ``smoothed'' or convolved with a line-spread function (usually a Gaussian or near-Gaussian) to match the resolution of the spectrograph. The line-spread function is generally a function of the wavelength. This line-spread function can be determined from careful measurement of the emission lines from a comparison lamp, but often is adequately determined by trial and error. The SPECTRUM auxiliary program SMOOTH2 may be used to convolve a Gaussian of specified width with the output of SPECTRUM. Some spectrographs have a line-spread function with more extensive wings than a Gaussian. The program CUSTOMSM provides a line-spread function that is a hybrid of a Gaussian and a Lorentzian profile. These two programs are discussed more extensively in §  and § .

Spectral line profiles may also be affected by stellar rotation, macroturbulence and other effects. The programs VSINI and AVSINI may be used to apply rotational broadening to a synthetic spectrum. Like rotation, macroturbulence broadens a spectral line but, unlike microturbulence, does not strengthen it. Thus rotational broadening and macroturbulent broadening can be applied, at least to first order, after the synthetic spectrum has been computed by convolving the spectrum with the appropriate line-spread functions. The program MACTURB may be used to apply macroturbulent broadening. In practice, Gaussian smoothing, rotational broadening and macroturbulent broadening together will probably be needed to adequately match the line profiles in an observed spectrum. The exact parameters to use in these convolutions must generally be determined by trial and error. The macroturbulent velocity and the rotational velocity should be independent of the wavelength. As mentioned above, the resolution is generally dependent on the wavelength. Logically, macroturbulent and rotational broadening should be applied first, and Gaussian smoothing last.

Many stars, including the sun, show somewhat asymmetrical line profiles due to velocity fields in the photosphere. Such asymmetries can only be accounted for in a fundamental way by carrying out detailed 3D hydrodynamical calculations of the stellar atmosphere.