Hollow spherical shell of gas around a star

[KaiserBrandon]

Homework Statement

f the Sun's atmosphere increased in temperature with radius at and above
the photosphere, how would our observation of the solar spectrum be different?
b) Consider a spherical hollow shell of gas around a star. If you observe this shell to produce
a bright ring around the star, what can you say about the optical thickness of the shell?
c) For the ring in part b, what can you say about its spectrum?

Homework Equations

none

The Attempt at a Solution

So for a, I figured that if the temperature is higher, it would produce broader and more intense spectral lines. For b, I'm not sure about whether it's optically thick or thin. If you can still see the star and a ring around it, wouldn't it be optically thin since the photons can pass through the gas...but why does it create a ring around the star? if you can only see a bright ring, would it not be optically thick and the ring is due to the gas absorbing photons and electrons gaining orbitals and coming down and releasing photons...but then why wouldn't you just see one big bright cloud? For part c, there would be absorption lines in the stars spectrum due to the absorption of certain wavelengths of light that is being emitted from the star as it passes through the gas...or am I wrong?

 

[Jhero]

a) Yes, if the temperature of the Sun's atmosphere increased with radius, the spectral lines would be broader and more intense. This is because the higher temperature would cause more atoms and molecules to be in higher energy states, leading to more emission and absorption of photons at different wavelengths.

b) If you observe a bright ring around the star, it is likely that the shell is optically thin. This means that photons can easily pass through the gas without being absorbed or scattered. The ring is created because the gas in the shell is emitting photons at specific wavelengths, creating a ring of light around the star.

c) For the ring in part b, the spectrum would show emission lines at specific wavelengths corresponding to the atoms and molecules in the gas shell. This is because the gas is emitting photons at those specific wavelengths, creating the bright ring around the star. However, there may also be some absorption lines in the spectrum due to the gas absorbing some of the star's emitted photons.