Astronomy:Doppler parameter

Short description: Physical parameter commonly used in astrophysics

The Doppler parameter, or Doppler broadening parameter, usually denoted as $b$, is a parameter commonly used in astrophysics to characterize the width of observed spectral lines of astronomical objects. It is defined as

$b=\sqrt{2}\sigma$,

where $\sigma$ 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

$p=\frac{1}{\sqrt{2\pi }}\frac{1}{\sigma }{e}^{-(v-v_0{)}^2/2{\sigma }^2}=\frac{1}{\sqrt{\pi }}\frac{1}{b}{e}^{-(v-v_0{)}^2/b^2}$,

where $p\mathrm{d}v$ is the probability of the velocity along the line of sight being in the interval $[v,v+\mathrm{d}v]$.

The line width is also often specified in terms of the FWHM (full width at half maximum), which is

$\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}=2\sqrt{2\ln 2}\sigma =2\sqrt{\ln 2}b\approx 1.665b$.

Distribution

The Doppler parameters of Lyman-alpha forest absorption lines are in the range 10–100 km s⁻¹, with a median value around $b_m=36{\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$ that decrease with redshift (Kim Hu). Analyses of the HST/COS dataset of low-redshift quasars gives a median $b$ parameter of around $33{\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$ (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.