How do you find the temperature of an HII region?

Thread starter Danielk010
Start date Mar 6, 2025
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Absorption Emission Spectral lines

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SUMMARY

This discussion focuses on determining the temperature of HII regions, specifically addressing the challenges of calculating it based on known background temperatures and the properties of the ionized cloud. The user explores the concept of optical thickness and references a specific cross-section value of 6.3 x 10^-18 cm² for the ionized cloud. They express uncertainty regarding the distance a particle travels (L) and the particle density (n), which are crucial for further calculations. The discussion emphasizes the need for a conceptual understanding rather than purely numerical solutions.

PREREQUISITES

Understanding of HII regions and their characteristics
Familiarity with optical thickness concepts in astrophysics
Knowledge of cross-section measurements in ionized gases
Basic principles of particle density and distance in astrophysical contexts

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Research methods for calculating temperatures in astrophysical HII regions
Study the implications of optical thickness on spectral line observations
Explore the relationship between particle density (n) and temperature in ionized clouds
Investigate the role of background temperature in astrophysical measurements

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Astronomers, astrophysics students, and researchers interested in the thermal properties of ionized gases and HII regions.

Mar 6, 2025

Danielk010

Homework Statement: Determine whether a spectral line is seen in emission, absorption, or not at all, and explain why. The vantage point is the surface of the Earth.

e. An HII region in front of a background quasar. The quasar has a brightness temperature of 75 k.

Relevant Equations: ##T < T_{B_{v_o}}## = absorption line (eq 1)
##T > T_{B_{v_o}}## = emission line (eq 2)

##\tau = L * n * \sigma##
##\sigma = 6.3*10^{-18} cm^2##
##E = 13.6 eV##
## T_{B_{v_o}} = T (\tau \gg 1)##

I first approached this problem with the idea that I could try to find the temperature of the HII region given that we already know the background temperature. Still, I am stuck on finding the region's temperature.

A second approach was to try to find if the cloud is optically thick, which would mean the spectral line is neither. I know from a table in my textbook that the cross-section for the ionized cloud is ##6.3*10^{-18} cm^2##, but I don't know L, the distance a particle travels, or n, the number of particles in the cloud. Maybe I can assume L is very far given the vantage point is on the surface of Earth, but then I don't know what n would be.

I am a bit stuck on where to start. I am assuming the answer is going to be more conceptual and less numeric but I don't get why they would give the background temperature then.

Thank you for any help.