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 $$\lambda = \frac{c}{\nu}$$?

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

• Thanks for the edit! – 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.