Planck law vs stars / microphysics of BlackBody emission

[r***@pla.net.invalid]

Hi there !

From time to time a student ask a question and you realize that you no
longer understand anything about your physics.
Here, regarding light emission mechanisms of stars ( nowadays, and 1st
generation ):
( disclaimer: not native english speaker )

How is it that stars emit (roughly) a Planck spectrum (let forget the
case of O & B here), while they are mostly composed of atomic/ionized H
and He ? (i.e. no mechanical degree of freedom other than velocity).

- Are the "metals" and dust (if there is any left) doing the job ?
but then the first generation of stars would not have radiated as a
Planck spectrum ? ( while they do, right ? )

- May the recombination and jump lines enough to explain the spectrum ?
- Possibly with the help of Doppler blurring of the lines ?

- When the species are largely ionized, might it be that the EM
waves are directly emitted by the electron plasma (in ~continuous modes,
therefore) ? but it seems doubtful to cover the visible frequencies with
this.

- Something else ?

thanks !

[Michael Dworetsky]

[[Mod. note -- I apologise to the author and to s.a.r readers for the
long delay in posting this article, which arrived in the s.a.r moderation
system on 2022-Mar-29. (Google's software misclassified this article
as spam and I failed to notice it promptly in my spam folder. I only
just now discovered it there.)
-- jt]]

Post by r***@pla.net.invalid
Hi there !
From time to time a student ask a question and you realize that you no
longer understand anything about your physics.
Here, regarding light emission mechanisms of stars ( nowadays, and 1st
( disclaimer: not native english speaker )

These are all questions covered in courses on stellar atmospheres, and
access to a good textbook might help a lot.

Post by r***@pla.net.invalid
How is it that stars emit (roughly) a Planck spectrum (let forget the
case of O & B here), while they are mostly composed of atomic/ionized H
and He ? (i.e. no mechanical degree of freedom other than velocity).

This "problem" only applies in the case of stars with significant
amounts of neutral H in excited states, for example stars of classes
B7-A3. Here, the peak of the Planck distribution (used as the source
function in stellar atmospheres' calculations done in LTE) is around the
same wavelength as the Balmer Jump (the ionization energy needed to get
from level n=2 in H to ionization). This gives rise to a big
discontinuity in opacity around 3650A, so the actual energy distribution
of the star is not a black body. Similarly, in hotter stars the Lyman
discontinuity has the same effect, at 912A, for temperatures of around
30000K.

Post by r***@pla.net.invalid
- Are the "metals" and dust (if there is any left) doing the job ?
but then the first generation of stars would not have radiated as a
Planck spectrum ? ( while they do, right ? )

Stars are still mostly made of hydrogen. Metals dominate opacity in the
spectra of cool stars, classes K and M. No dust, but there are many
molecules in the atmospheres of cool stars.

Post by r***@pla.net.invalid
- May the recombination and jump lines enough to explain the spectrum ?

Yes, as above, around A0 class.

Post by r***@pla.net.invalid
- Possibly with the help of Doppler blurring of the lines ?

This doesn't affect the overall distribution much.

Post by r***@pla.net.invalid
- When the species are largely ionized, might it be that the EM
waves are directly emitted by the electron plasma (in ~continuous modes,
therefore) ? but it seems doubtful to cover the visible frequencies with
this.

In much hotter stars (e.g., class O) the main source of atmospheric
opacity is electron scattering, which is essentially continuous, so yes,
broadly speaking.

Post by r***@pla.net.invalid
- Something else ?
thanks !

You are welcome.

--
Mike Dworetsky