How to plot Doppler profile corresponding to the spectral line? The spectral line was plotted from data: flux with respect to wavelenght and I know the temperature.

These two function are Doppler profile? What should I substitue for $\Delta \nu_{th}$, $\nu_0$ and $\Delta \nu$. These values are from wavelenght according to $\lambda = \frac{c}{\nu}$?

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Or could you recommend me another formula for plotting Doppler profile?

  • $\begingroup$ Thanks for the edit! $\endgroup$ – uhoh Oct 14 '19 at 12:53

$\nu_0$ is the frequency you would expect for the absorption/emission line in the absence of any broadening. i.e. It is the centre of the line profile.

$\delta \nu$ is just $\nu - \nu_0$. (i.e. it is the separation in frequency from the centre of the line profile and is equivalent to $f -f_0$ in the second expression).

$\Delta \nu_{th}$ is a measure of the broadening due to (I guess) thermal motions in whatever gas/plasma is emitting/absorbing the radiation. It is similar to the Gaussian "sigma" term in the expression $$ f(x) = \exp(-x^2/2\sigma^2)$$

If you have a gas that follows Maxwell-Boltzmann statistics, then $\Delta \nu_{th}$ will be related to the speeds of atoms/ions/molecules in the gas and hence to the temperature of the gas. $$ \Delta \nu_{th} \simeq \sqrt{\frac{2k_BT}{m}}\times \frac{\nu_0}{c} \,$$ where $m$ is the mass of the particle emitting the light.

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