Doppler parameter

The Doppler parameter, or Doppler broadening parameter, usually denoted as formula_1, is a parameter commonly used in astrophysics to characterize the width of observed spectral lines of astronomical objects. It is defined as
where formula_3 is the one-dimensional velocity dispersion . Given this parameter, the velocity distribution of the line-emitting/absorbing atoms and ions proximated by a Gaussian can be rewritten as
where formula_5 is the probability of the velocity along the line of sight being in the interval formula_6.
The line width is also often specified in terms of the FWHM (full width at half maximum), which is 
Distribution.
The Doppler parameters of Lyman-alpha forest absorption lines are in the range 10–100 km s−1, with a median value around formula_8 that decrease with redshift . Analyses of the HST/COS dataset of low-redshift quasars gives a median formula_1 parameter of around formula_10 (, ).