Interested in the average refractive index of interstellar medium (inside the Milky Way and at gamma frequencies would be the best).
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- 2$\begingroup$ At gamma frequencies the refractive index of the ISM will be indistinguishable from 1 $\endgroup$Riley Scott Jacob– Riley Scott Jacob2025-08-21 13:05:16 +00:00Commented Aug 21 at 13:05
- 1$\begingroup$ @RileyScottJacob I am aware it will be very close to 1. Would appreciate a more quantitative answer, thanks. $\endgroup$skytak picus– skytak picus2025-08-22 16:49:16 +00:00Commented Aug 22 at 16:49
- $\begingroup$ The RI everywhere for all wavelengths is a vast subject if extreme accuracy is required. $\endgroup$my2cts– my2cts2025-08-25 16:27:24 +00:00Commented Aug 25 at 16:27
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1 Answer
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1 We can model the interstellar medium as an electron plasma with dispersion relation $$\omega^2=\omega_p^2+c^2k^2,$$ where $$\omega_p^2=\frac{Ne^2}{\varepsilon_0m_e}$$ is the square of the plasma frequency with electron number density $N$ and electron mass $m_e$. Given the refractive index $n=ck/\omega$, we have $$n^2=1-\frac{\omega_p^2}{\omega^2},$$ and we can approximate $$n=1-\frac{1}{2}\frac{\omega_p^2}{\omega^2}.$$
The strongest effect will be in highly ionized regions, where we may have an electron density of order $N\approx10^{10}\,\mathrm{m}^{-3}$. In neutral regions it will be much lower, perhaps $N\approx10^{4}\,\mathrm{m}^{-3}$. For a typical gamma frequency of $10^{21}\,\mathrm{Hz}$, this gives us a range for the refractive index of $$1-10^{-37}\lesssim n\lesssim 1-10^{-31}.$$
- 1$\begingroup$ Do we have any idea how good this approximation is? The interstellar medium is certainly not just a thin electron gas. $\endgroup$AfterShave– AfterShave2025-08-25 16:20:31 +00:00Commented Aug 25 at 16:20