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4 years ago in Astrophysics , Spectroscopy By Cole

What is optical depth, and how does it relate to FWHM and temperature?

I'm analyzing emission lines from a stellar atmosphere simulation. My output gives me an optical depth τ and a Gaussian FWHM for each line. I understand τ indicates opacity and FWHM relates to velocity dispersion, but how does the gas temperature formally link these two quantities? Does a higher temperature always increase both the line width and the effective optical depth?

Optical Depth FWHM

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By Vishal Answered 3 years ago

The key link is thermal motion. In a gas at temperature T, particles move with a distribution of velocities. This causes Doppler shifts, broadening the spectral line into a Gaussian profile whose FWHM is proportional to the square root of T. So, higher T means a broader line. Optical depth (τ) is a separate measure of opacity at the line's central wavelength. However, they interact: if the line is very broad (high T), the same amount of absorbing material is spread over more wavelengths, which can actually reduce the peak τ at the line center for a fixed total column density. In my modeling work, I have to solve the radiative transfer equation self-consistently to account for this coupling between the line profile and the absorption.

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What is optical depth, and how does it relate to FWHM and temperature?

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