Astronomy:Doppler parameter

Short description: Physical parameter commonly used in astrophysics

The Doppler parameter, or Doppler broadening parameter, usually denoted as [math]\displaystyle{ 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]\displaystyle{ b = \sqrt{2} \sigma }[/math],

where [math]\displaystyle{ \sigma }[/math] is the one-dimensional velocity dispersion (Draine 2011). Given this parameter, the velocity distribution of the line-emitting/absorbing atoms and ions proximated by a Gaussian can be rewritten as

[math]\displaystyle{ 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]\displaystyle{ p\mathrm{d}v }[/math] is the probability of the velocity along the line of sight being in the interval [math]\displaystyle{ [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]\displaystyle{ \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]\displaystyle{ b_m = 36\ \mathrm{km\ s}^{-1} }[/math] that decrease with redshift (Kim Hu). Analyses of the HST/COS dataset of low-redshift quasars gives a median [math]\displaystyle{ b }[/math] parameter of around [math]\displaystyle{ 33\ \mathrm{km\ s}^{-1} }[/math] (Danforth et al. 2016, Gaikwad et al. 2017).

See also

• Doppler broadening
• Doppler spectroscopy

References

• Danforth, Charles W.; Keeney, Brian A.; Tilton, Evan M.; Shull, Michael (2016). "An HST/COS Survey of the Low-redshift Intergalactic Medium. I. Survey, Methodology, and Overall Results". Astrophysical Journal 817 (2): 111. doi:10.3847/0004-637X/817/2/111. Bibcode: 2016ApJ...817..111D. 

• Draine, Bruce (2011). Physics of the Interstellar and Intergalactic Medium. Princeton University Press. ISBN 9780691122144. Bibcode: 2011piim.book.....D. 

• Gaikwad, Prakash; Srianand, Raghunathan; Choudhury, Tirthankar Roy; Khaire, Vikram (2017). "VoIgt profile Parameter Estimation Routine (viper): H I photoionization rate at z \< 0.5". MNRAS 467 (3): 3172–3187. doi:10.1093/mnras/stx248. Bibcode: 2017MNRAS.467.3172G. 

• Kim, Tae-Sun; Hu, Esther M.; Cowie, Lennox L.; Songaila, Antoinette (1997). "The Redshift Evolution of the Ly alpha Forest". Astronomical Journal 114: 1–13. doi:10.1086/118446. Bibcode: 1997AJ....114....1K.