[Lewis Thomson (OP)]

Donald has submitted this question to be posted onto the forum,

"When photons are on their 1,000,000 year journey out of our sun, are they traveling at 'c', or are photons slowed by the electromagnetic soup called plasma. Also, since it takes energy to escape from the sun's gravity well, do photons lose some of their energy and shift frequency upon leaving the surface of the sun? How much energy and how much Doppler shift is there?"

Discuss in the comments below...

[alancalverd]

Doppler shift depends on the relative velocity of source and receiver. You can calculate the gravitational red shift knowing the sun's surface gravity is about 28g and assuming a massless receiver or one at 1g on the earth's surface. The spectrum will certainly be spread a bit by scattering from the solar wind.

[Halc]

When photons are on their 1,000,000 year journey out of our sun

First of all, it is dangerous/misleading to mix quantum and classic physics. Light might take a million year journey as you describe, but a photon is a quantum object which has no real evidence of existing until it is measured (absorbed) by something. It doesn't take a path. So let's stick with light, or a light pulse, both classic concepts.

are they traveling at 'c'

Light in a vacuum travels locally at c. Open space isn't a perfect vacuum, so it might travel less than c, but not measurably so most of the time. By locally, I mean the speed of a given light pulse is dependent on where it is measured, so relative to say an Earth clock, light leaving the sun travels slower than c and gains speed, surpassing c as it nears the orbital distance of Earth. This is due to changes in gravitational potential along the way. But were you to measure that pulse with any local experiment, it would be c in a vacuum.

are photons slowed by the electromagnetic soup called plasma.

Light generated within the sun (by say some fusion event) is very much slowed the progress of light. A given photon will be absorbed pretty much immediately and be re-emitted in a random direction. This random walk might cause any light generated in the core to take about half a million years to reach the surface and actually be emitted into space.

Also, since it takes energy to escape from the sun's gravity well, do photons lose some of their energy and shift frequency upon leaving the surface of the sun?

Frequency (and direction of travel even) of light is a frame dependent thing. Take a dark star emitting no light, but having the mass of our sun. We put a 580 nm (yellow) laser there and point it outward. If you measure it locally, you will measure 580 nm, but if you measure it at a distance of 1 AU, it will be red shifted to a longer wavelength. You might say that is the light losing energy along the way, or you might say that in the frame of the distant observer, the light was that lower frequency all along since it cannot emit move waves per second at the surface than are received at the distant observation point. There's nowhere for the extra waves to build up since the distance stays constant. So from that point of view, the light doesn't change frequency or wavelength along the way. It's constant, and just measured at a different potential.

How much energy and how much Doppler shift is there?

Doppler is due to the changing distance between emission and detection, so as long as the observer stays at a fixed distance from the sun, there is zero Doppler effect in light emitted from it.

You can calculate the gravitational red shift knowing the sun's surface gravity is about 28g and assuming a massless receiver or one at 1g on the earth's surface.

This is incorrect. Gravitational redshift is a function of difference in gravitational potential, not difference in gravitational force/acceleration.  So for instance, I weigh a lot more on Earth than I do on Mercury, but light from Earth would appear blue shifted (not red shifted as you suggest above) from an observer on Mercury. The gravity is under 0.4 g there, but the gravitational potential well is much deeper than here on Earth.

[Eternal Student]

Hi.

   It's not the same photon that exits from the sun as the one that might have started in the core.   That's the main thing that explains why the journey has taken so long.   Also there are widely varying estimates of the average journey time -  from a few thousand years to a million years.

In the core of the sun the protons and helium nuclei are so thick that an emitted gamma ray can't get very far before it is absorbed. If you imagine that a gamma ray is emitted right at the center of the sun then it will start out heading right for the surface. When it crashes into a proton the result of the collision is a proton with extra energy. The proton gives up that extra energy by emitting another gamma ray photon. But this one could head in any direction -- even right back where it started from. And so it goes, with the gamma ray heading from one collision to another, changing its direction each time it is absorbed and re-emitted.

https://sciencing.com/long-photons-emerge-suns-core-outside-10063.html

     Although they make the whole thing sound poetical by referring "the gamma ray",  it's clearly been absorbed  (it has gone, there is no gamma photon to be found for a while)  and  some other photon was re-emitted - this has happened several times over.

    In between collisions the gamma rays travel at a speed that is either c (the speed of light in a vaccum),  or else the speed of light through the medium (generally slower).   Exactly what speed it has travelled at depends on how complicated you want to get and whether you wish to consider a group velocity or a phase velocity for light waves.  Explaining group and phase velocity is beyond the scope of one thread.   
     The propagation of light in plasma is complicated and apparently still under research.  The older thinking is that plasma should slow light down and indeed it's almost completely opaque to EM radiation in the visible spectrum.   However, just to turn this upside down, there are some new articles suggesting that you can actually get the group velocity (but not the phase velocity) to go higher than c in some situations.   (https://www.sciencealert.com/pulses-of-light-can-break-the-universal-speed-limit-and-it-s-been-seen-inside-plasma ).

   Finally, the gravitational potential and the over-all redshift issue is also complicated.   As @Halc  mentioned the change in potential is what will be important    BUT....   the potential energy at the centre of a sphere (the sun) is a topic which might spill over to another thread.   So we probably do need to know exactly how deep within the sun the photon was when it was created.

Best Wishes.

[evan_au]

how much Doppler shift is there?

Each year, around 3-4th January (perihelion, closest to the Sun) and 3-4th July (aphelion, farthest from the Sun), the Earth is neither moving towards or away from the Sun, and there is no Doppler shift. Around October there is a maximum Doppler blue shift (Earth moving towards the Sun) and around May there is a maximum Doppler red shift (Earth moving away from the Sun).

As others have pointed out, all year long there is a gravitational red shift (or "Einstein shift"), as photons "climb out" of the Sun's gravitational well. Depending on your frame of reference, you could say some of the following things:
- Photons don't lose speed as they always travel at c
- Photons don't lose kinetic energy, since the photon is massless
- Photons do lose momentum
- The photon frequency does decrease

One way of looking at this frequency decrease is to consider Einstein's time dilation.
- Deep in a gravitational well (eg the surface of the Sun), time moves more slowly, compared to an observer on the surface of the Earth
- So a Hydrogen atom emitting a spectral line on the surface of the Sun will do so more slowly than a Hydrogen atom emitting the same spectral line on the surface of the Earth
- So when you compare the frequency of the light from the Sun with the frequency of light generated here on Earth, you will find the light from the Sun has a lower frequency.

Einstein shift will be a maximum at aphelion, and minimum at perihelion.

photons are on their 1,000,000 year journey out of our sun

Under the extreme conditions of a supernova, energy from the core of a star can reach the surface much more quickly - just hours.

But neutrinos don't interact much with matter; traveling at (pretty much) the speed of light, they can reach the surface of the star in just seconds.
- To date, such a "race" has only been observed once, when a supernova occurred in the nearby Large Magellanic Cloud (a dwarf galaxy orbiting our Milky Way galaxy).

https://en.wikipedia.org/wiki/SN_1987A#Neutrino_emissions