Английская Википедия:Doppler parameter
Шаблон:Short description Шаблон:Orphan
The Doppler parameter, or Doppler broadening parameter, usually denoted as <math>b</math>, is a parameter commonly used in astrophysics to characterize the width of observed spectral lines of astronomical objects. It is defined as
- <math> b = \sqrt{2} \sigma </math>,
where <math>\sigma</math> is the one-dimensional velocity dispersion Шаблон:Harv. Given this parameter, the velocity distribution of the line-emitting/absorbing atoms and ions proximated by a Gaussian can be rewritten as
- <math> p = \frac{1}{\sqrt{2\pi}}\frac{1}{\sigma}e^{-(v-v_0)^2/2\sigma^2} = \frac{1}{\sqrt{\pi}}\frac{1}{b}e^{-(v-v_0)^2/b^2}</math>,
where <math>p\mathrm{d}v</math> is the probability of the velocity along the line of sight being in the interval <math>[v, v + \mathrm{d}v]</math>.
The line width is also often specified in terms of the FWHM (full width at half maximum), which is
- <math> \mathrm{FWHM} = 2\sqrt{2\ln 2}\sigma = 2\sqrt{\ln 2} b \approx 1.665b </math>.
Distribution
The Doppler parameters of Lyman-alpha forest absorption lines are in the range 10–100 km s−1, with a median value around <math>b_m = 36\ \mathrm{km\ s}^{-1}</math> that decrease with redshift Шаблон:Harv. Analyses of the HST/COS dataset of low-redshift quasars gives a median <math>b</math> parameter of around <math>33\ \mathrm{km\ s}^{-1}</math> (Шаблон:Harvnb, Шаблон:Harvnb).
See also
References
