Wavelength and radial velocity 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?
$$v_r = c\left( \frac{\lambda - \lambda_0}{\lambda_0}\right),$$
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.