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What is the relation between the wavelength and the radial velocity? I have a data: wavelength and intensity and I would like to plot intensity with respect to radial velocity - similarly as in the picture (source)

EDIT

I have a file of alpha H with 2 columns - wavelength (in angstrom) and intensity (normalized for 1) and I would like to plot intensity with respect to radial velocity. I use in gnuplot:

c = 299792458
lambda_0 = 6562.817*10**(-10)
plot 'file.asc' using (c*($1*10**(-10)-lambda_0)/lambda_0):2

Why I get the wrong range on the x-axis?

enter image description here

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$$v_r = c\left( \frac{\lambda - \lambda_0}{\lambda_0}\right),$$ where $\lambda$ is the observed wavelength and $\lambda_0$ is the wavelength at rest. This gives an equivalent velocity with respect to the central wavelength of the line.

In your plot, what is shown is a line profile where the wavelength separation from $\lambda_0$ for that line (or from the measured centre of the line, I can't tell which) has been converted into a velocity.

Note that it makes little sense to plot more than a single line profile in this way.

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  • $\begingroup$ Thank you, I tried to plot my own line - it is in EDIT in my question. Do I have wrong units somewhere? $\endgroup$
    – Alex
    Commented Feb 24, 2020 at 11:55
  • $\begingroup$ @Alex Since I don't know what data you have and your plots are not labelled with units, it is difficult to say. If your raw x-axis values are in Angstroms and you intend your velocity data to be displayed in m/s, then this looks correct. $\endgroup$
    – ProfRob
    Commented Feb 24, 2020 at 12:33
  • $\begingroup$ @Alex Note that it make s little sense to plot more than a single line profile in this way. The numbers/velocities under other features in the spectrum are meaningless. $\endgroup$
    – ProfRob
    Commented Feb 24, 2020 at 12:34
  • $\begingroup$ OK, thank you very much $\endgroup$
    – Alex
    Commented Feb 24, 2020 at 13:33
  • $\begingroup$ Does (λ−λ0)/λ0 refer to the cosmological redshift or the Doppler redshift? $\endgroup$
    – user30617
    Commented May 11, 2020 at 17:18

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