Some astrophysical parameters can be extracted from a spectrum by the measurement of the spectral line profile. For example the measurement of the profile gives access to the temperature of surface of a star, at its disk speed, at the speed of expansion of gases, at the pressure, etc. Many quantities are often given: the equivalent width of the line and the line half-width and the peak intensity, the V/R ratio and the peak intensity.

Equivalent Width (W) is defined as the section of a surface counted between the level of the continuum, normalized to unity, and reference zero, having a surface identical to the profile of  line (see figure below). The equivalent width is thus measured in wavelength unit (in angströms for example). Sometimes the normalized equivalent width Wl is used, which is the equivalent width W divided by the wavelength of the line, which is useful to compare the shape of lines located at different wavelengths.

Mathematicaly we have:

with SUM( ) the sum operator over the significant profile line, Fc=1 the continuum level unit normalized, Fl the line profile level, and dl the sampling in wavelength unit. Note that W>1 for an absorption line and W<1 for an emission line.

A problem is when for example an emission line is superimposed on a large photospheric absorption line (it is often the case with Be stars). If W is the measured total equivalent width (emission + absorption) and if Wph is the equivalent width of the photospheric line, the true equivalent width We of the emission line is:

True the difficulty is here to know Wph which is often deduced starting from a theoritical profile of photospheric line or from interpolation of observational data..

Half-width (H) is equivalent to the full width of the spectral line at half maximum value or Full Width at Half Maximum (FWHM). FWHM is the width measured at half level between the continuum and the peak of the line. The FWHM is expressed either in wavelength unit or in speed unit when the objective is to measure expansion or disk speeds (if dl is the FWHM in wavelength, the width in km/s is given by c.dl / l, with c is the speed of the light = 3.10⁵ km/s). Exemple, suppose that the FWHM is of 2A at 6563A, the equivalent resolved velocity is about 90 km/s.

Note that the half-widths H measured had to be corrected for instrumental width, Hi, according to the equation:

Hi is the FWHM that one measured on a very fine line. It is also the theoritical spectral resolution of the spectrograph.

The V/R is usefull for the study of Be-stars. Often for these stars a central intensity minima devide emission into a Violet (V, at shorter wavelength) and a Red (R, at the long wavelength side) component. Relative intensities of these two components, V/R, measured from the continuum, check the assymetries of the observed profile. Assymetries are sometime also observed in single emission lines. In this case if V>R the violet flank is steeper than the red one and if R>V the reverse is found. Note that R>V is produced by expanding motion and V>R by contracting motion.

The peak intensity (P) is the ratio between the intensity at  the center of the line I and the intensity of the continnuum Ic:

It should be noticed that these definitions remain valid if the line is in emission or absorption compared to the continuum. It will be still noted also that the precision of the estimation of these parameters requires a good accuracy on the level of continuum, that implies the photometric procedures of calibration that we saw previously.