# How does a thin gas uphold its emission spectrum?

This question has been bothering me for many years and maybe I've been too embarassed to ask up until now. The reason why a thin atomic gas has an absorption spectrum has been explained to me by noting that the atoms absorb certain frequencies only and reemit the absorbed radiation in all directions. This explaines the effect for the usual experimental setup.

However, I think the sun's spectral lines cannot be explained in this way. Assuming the direction of reemission is random would mean that most of the solid angle from an atom in the sun's atmosphere would be facing outwards. This would lead one to expect the intensity at the absorption lines to be only slightly weaker, while the lines are in reality quite pronounced. What mechanism explains this behaviour?

Also what would be the emission spectrum of a thin atomic gas in thermal equilibrium? Would it have spectral lines?

• "Assuming the direction of reemission is random would mean that most of the solid angle from an atom in the sun's atmosphere would be facing outwards. This would lead one to expect the intensity at the absorption lines to be only slightly weaker..." I don't understand what you mean there. Can you clarify? – DanielSank Oct 28 '16 at 1:38
• I too am lost and, no offence intended , I think you have a misleading picture of what Daniel is referring to. Could I strongly suggest you draw a small picture of your idea, I have a feeling I know what it will look like. – user108787 Oct 28 '16 at 1:49
• My question is about what happens to the absorbed light. If it is reemitted at the same frequency in a random direction the only thing that matters (for the sun) is whether that light is emitted outwards or back towards the sun. Is just this effect ("random direction reemission") enough to explain the intensity of the absorption lines? – Adomas Baliuka Oct 30 '16 at 16:15

A simple way to think about the Sun's absorption spectrum is to think of the solar atmosphere as a cool layer on top of something that is much hotter that is emitting blackbody radiation. (In reality it is more like a smoothly varying continuum of layers, but this doesn't affect the argument).

A fraction of the blackbody photons are headed towards our spectrograph, but they have to get through the layer of cooler gas. Some of them are absorbed at particular wavelengths corresponding to atomic transitions and then re-emitted in all directions. Roughly half of the re-emission is directed outwards, but only a vanishingly small fraction of those re-emitted photons are in the original direction and thus we see an absorption line. However, other photons could be scattered into our line of sight from light that was not travelling in our direction originally. I think your confusion is over whether this compensates?

The answer is no, because the specific intensity of light emitted from the cooler overlying layer is much lower than that of light originating further in (it goes as $T^4$). So another way of looking at a spectral line is to imagine each wavelength originating at a particular depth (a gross simplification). The bottom of a spectral absorption line originates high up in the cooler part of the atmosphere, whilst the continuum originates in hotter interior layers.

An optically thin atomic gas would have an observed spectrum consisting of narrow emission lines. Exactly which lines and at what wavelengths depends what the gas is made of and its temperature and density.

• I don't understand the argument. You say: "only a vanishingly small fraction of the re-emitted photons are in the original direction". Why does it matter though? My first question would be how much of the absorbed light is reemitted at the same frequency (I would assume most). Then the next question is whether the direction of reemission is random. Finally for the sun the only thing that matters is how much of the reemitted light is directed outwards rather than in the original direction, which I would think is still quite a bit of light. Is this really enough to explain the spectral lines? – Adomas Baliuka Oct 30 '16 at 16:07
• Your problem is the statement "the only thing that matters...", which is totally incorrect. Your spectrograph can only detect light that is emitted exactly towards it. @AdomasBaliuka – Rob Jeffries Oct 30 '16 at 22:04
• The light we see from the sun is roughly the same in all directions. I would think that reemitted light that leaves the sun must contribute to it's spectrum. How can this be wrong? – Adomas Baliuka Oct 30 '16 at 22:40
• @AdomasBaliuka I have no idea what your first sentence means. Only light that is emitted towards your spectrograph can be detected by your spectrograph. – Rob Jeffries Oct 30 '16 at 23:10
• Ok, now I'm really confused. First thank you very much for your patience. Then: All light that leaves the sun contributes to its spectrum right? My basic question is why we don't see reemission of the frequencies corresponding to transitions of the atoms in the sun's atmosphere. The light which is absorbed by these atoms is mostly reemitted at the same frequency (is that true?) and in a random direction. From this it seems to me that at least half of the reemitted light should leave the sun. – Adomas Baliuka Oct 31 '16 at 17:50