B Brightness of different layers of the Sun

[snorkack]

How much of the visible light of Sun originates from:

1. below the photosphere?
2. photosphere?
3. chromosphere?
4. corona?

The answers don´t seem easy to find, partly they are matters of definition, but definitions do exist.
4) should be relatively easy to approach. Just cover up the Sun with an obstacle like Moon and measure the brightness of the corona... except it will need adjusting. Moon also covers up the part of corona in foreground of Sun.
The corona-chromosphere border is one where a fairly clear definition is available. In a fairly thin transition layer, the temperature changes drastically.
But how are the other borders defined in the first place? Chromosphere-photosphere border, and photosphere bottom?

 

[DaveC426913]

Donning my Googles, I found a number of articles that go into detail about where in the sun photons are created, and where they spend much of their time.
Here's the first:
https://svs.gsfc.nasa.gov/11084/
Google to-taste.

 

[Orodruin]

Donning my Googles, I found a number of articles that go into detail about where in the sun photons are created, and where they spend much of their time.
Here's the first:
https://svs.gsfc.nasa.gov/11084/
Google to-taste.

That’s highly popularised and does not really answer the OP’s question.

 

[DrSteve]

Discounting exotic (higher order) processes, all photons associated with the sun originated in the core.

 

[snorkack]

Discounting exotic (higher order) processes, all photons associated with the sun originated in the core.

Nope, none of them do. In contrast to all the neutrinos.

 

[Orodruin]

Discounting exotic (higher order) processes, all photons associated with the sun originated in the core.

Essentially all the light that reaches the Earth is produced in the surface layers of the Sun, to a very good approximation radiating as a black body.

The energy released in the Sun that eventually dissipates to the surface is produced in the solar core, but the Sun itself is essentially opaque due to being mainly ionized plasma. The mean free path of a photon is exceedingly small under these conditions. The time scale of energy dissipation to the surface is long.

 

[DrSteve]

Let me clarify. Hydrogen fusion generates gamma rays which are then down-converted in energy through pair production, electron Compton scattering and the photoelectric effect. It is in this sense that all the energy that originates in the core is redistributed throughout the rest of the sun via these three processes.

 

[FactChecker]

A surprising (to me) amount is unknown about the Sun. For instance, we still don't know why the region of the corona is so much hotter than the surface of the Sun (1.8 million versus 10 thousand deg F). This is called the "Coronal heating problem".

 

[Orodruin]

Let me clarify. Hydrogen fusion generates gamma rays which are then down-converted in energy through pair production, electron Compton scattering and the photoelectric effect. It is in this sense that all the energy that originates in the core is redistributed throughout the rest of the sun via these three processes.

Sure, but again, that is not the OP's question.

 

[snorkack]

Essentially all the light that reaches the Earth is produced in the surface layers of the Sun, to a very good approximation radiating as a black body.

How much does Sun deviate from black body?
Obviously a black body would not have Fraunhofer lines.
Also, the corona in visible light may be dim compared to photosphere, but its far-UV is certainly far stronger than the Wien tail of black body would be...

 

[renormalize]

How much does Sun deviate from black body?

Have you done any research to answer this question yourself?
There are literally dozens of plots of the solar spectrum available on-line, such as this one:

 

[Hornbein]

Golly! I have learned something.

 

[Hornbein]

A surprising (to me) amount is unknown about the Sun. For instance, we still don't know why the region of the corona is so much hotter than the surface of the Sun (1.8 million versus 10 thousand deg F). This is called the "Coronal heating problem".

There are two good theories, neither of which excludes the other. I'm inclined to believe they are both correct and together explain at least most of the heating. It seems to me that magnetic reconnection must be important.

 

[snorkack]

Have you done any research to answer this question yourself?
There are literally dozens of plots of the solar spectrum available on-line, such as this one:
View attachment 356585

Which conspicuously shows that Sun deviates from black body spectrum (compare the line with the yellow). Using a different temperature blackbody would not eliminate the mismatch either.
This, incidentally, is the spectrum of the whole disc combined. Sun is not an uniform disc. The limb of Sun is both dimmer and redder than centre.

 

[D H]

Have you done any research to answer this question yourself?
There are literally dozens of plots of the solar spectrum available on-line, such as this one:
View attachment 356585

That is an awful diagram. It is unsourced and it is just wrong. While estimates of the Sun's effective temperature (ideal blackbody temperature) do vary, the variance is not that much, from 5772 to 5780 kelvins. That is well above 5250 °C, or 5523 kelvins.

 

[renormalize]

That is an awful diagram. It is unsourced and it is just wrong. While estimates of the Sun's effective temperature (ideal blackbody temperature) do vary, the variance is not that much, from 5772 to 5780 kelvins. That is well above 5250 °C, or 5523 kelvins.

Thanks, I did neglect to cite the source: https://en.m.wikipedia.org/wiki/Spectrum_(physical_sciences) of that graphic. And I agree that ~5800°K is the consensus blackbody temperature of the sun. But I still consider that plot to be a helpful tool to visually identify the significant differences between the solar spectrum and a blackbody. After all, as @snorkack points out:

Which conspicuously shows that Sun deviates from black body spectrum (compare the line with the yellow). Using a different temperature blackbody would not eliminate the mismatch either.

 

[Ken G]

But how are the other borders defined in the first place? Chromosphere-photosphere border, and photosphere bottom?

Different sources define them differently, but the one I like bases it on the different energy transport. The photosphere carries the luminosity radiatively (so not convectively like the region below), the chromosphere has net heating so it emits more light than it absorbs (while most of the light just passes through), and the corona is also heated but a lot of that energy leaves via being conducted back down. If you define the photosphere that way, no light escapes clean through it, the convective region is just too deep.

 

[snorkack]

Different sources define them differently, but the one I like bases it on the different energy transport. The photosphere carries the luminosity radiatively (so not convectively like the region below), the chromosphere has net heating so it emits more light than it absorbs (while most of the light just passes through), and the corona is also heated but a lot of that energy leaves via being conducted back down. If you define the photosphere that way, no light escapes clean through it, the convective region is just too deep.

The problem here is granulation of Sun.
Do you prefer to define the base of photosphere as a smooth sphere/ellipsoid, or something which is corrugated and in motion with the granules?
Actually, watching the formation of new granules might be a way to look through photosphere?

 

[Ken G]

The problem here is granulation of Sun.
Do you prefer to define the base of photosphere as a smooth sphere/ellipsoid, or something which is corrugated and in motion with the granules?
Actually, watching the formation of new granules might be a way to look through photosphere?

If one goes with the energy transport way of defining the photosphere, in which the photosphere is in "radiative equilibrium" (meaning it just passes along whatever radiation is welling up from below with no additional local heating going on), then granulation doesn't affect what you are calling the photosphere. Granulation is simply a change in the temperature of the photosphere based on how much radiation is coming up from below in that area. The granulation is created in the convection zone, but above that, the heat brought up by convection is simply passed along like a "bucket brigade" carrying water to a fire (as a somewhat mixed metaphor for the Sun). Also, in this approach to the meaning of the photosphere, it is a physical region of gas, not some hypothetical surface, so yes, it would move up and down and get hot and cold, it is just a physical layer of gas with a particular energy transport mechanism ruling its local temperature.

 

[snorkack]

If one goes with the energy transport way of defining the photosphere, in which the photosphere is in "radiative equilibrium" (meaning it just passes along whatever radiation is welling up from below with no additional local heating going on), then granulation doesn't affect what you are calling the photosphere. Granulation is simply a change in the temperature of the photosphere based on how much radiation is coming up from below in that area. The granulation is created in the convection zone, but above that, the heat brought up by convection is simply passes along like a "bucket brigade" carrying water to a fire (as a somewhat mixed metaphor for the Sun).

Does it mean that at whatever level the bottom of photosphere is defined, the vertical speeds of gas go to zero and stay at zero?

 

[Ken G]

Does it mean that at whatever level the bottom of photosphere is defined, the vertical speeds of gas go to zero and stay at zero?

No, not if you use these words to describe physically real regions of the Sun. The photosphere is connected to the convective regions below, so is put into motion by them, and carries waves and magnetic stresses, it is a real gas that has real dynamics, but its energy balance is simply to pass along the radiation introduced to it from below with no other important energy terms.

Of course, one can also use an idealized version of the "photosphere", in which it is some kind of "effective" sphere that doesn't really exist, but acts "as though" the Sun was some kind of hypothetical spherical blackbody. Some do use it to mean that, it's a matter of choice of how "real" you want the "photosphere" to be. There's not a right and wrong, but one needs to say what one means. And note if we use this latter meaning, your OP question becomes essentially purely by definition that everything that doesn't come from the chromosphere and corona is photospheric. That's also the answer with the meaning I like, but not purely by definition any more. In my case, it's the answer because the photosphere is "very optically thick," in the second case, it's the answer because that's how the hypothetical surface called the photosphere is defined.

 

[snorkack]

No, not if you use these words to describe physically real regions of the Sun. The photosphere is connected to the convective regions below, so is put into motion by them, and carries waves and magnetic stresses, it is a real gas that has real dynamics, but its energy balance is simply to pass along the radiation introduced to it from below with no other important energy terms.

Consider then a convective updraught propagating upwards towards the photosphere, to become a newly appearing granule.
Its energy balance contains the terms for

1. gas travelling upwards and carrying its latent heat with the vertical movement,
2. electromagnetic heat propagating ahead of the mass of charged and neutral particles which travel upwards, but are absorbed in cooler and still opaque mass of gas above.
3. electromagnetic heat which is emitted ahead, but unlike 2), is not absorbed above, but escapes into space.

Is it the case that there is a layer where only 2) is relevant and 1) and 3) are both negligible?

Of course, one can also use an idealized version of the "photosphere", in which it is some kind of "effective" sphere that doesn't really exist, but acts "as though" the Sun was some kind of hypothetical spherical blackbody. Some do use it to mean that, it's a matter of choice of how "real" you want the "photosphere" to be. There's not a right and wrong, but one needs to say what one means. And note if we use this latter meaning, your OP question becomes essentially purely by definition that everything that doesn't come from the chromosphere and corona is photospheric. That's also the answer with the meaning I like, but not purely by definition any more. In my case, it's the answer because the photosphere is "very optically thick," in the second case, it's the answer because that's how the hypothetical surface called the photosphere is defined.

Would you specify a specific optical depth for the bottom of photosphere? Or some other criteria, which make the optical depth of the bottom of photosphere an observable?

 

[Ken G]

Consider then a convective updraught propagating upwards towards the photosphere, to become a newly appearing granule.
Its energy balance contains the terms for

1. gas travelling upwards and carrying its latent heat with the vertical movement,
2. electromagnetic heat propagating ahead of the mass of charged and neutral particles which travel upwards, but are absorbed in cooler and still opaque mass of gas above.
3. electromagnetic heat which is emitted ahead, but unlike 2), is not absorbed above, but escapes into space.

Is it the case that there is a layer where only 2) is relevant and 1) and 3) are both negligible?

Yes, that's the convectively stable but very optically thick region that might be considered the "deep photosphere," if one uses the photosphere word to apply to the region of radiative equilibrium. If instead one uses the word to just mean some kind of surface of last interaction with the light, then one struggles to find any useful descriptor for the region you describe.

Would you specify a specific optical depth for the bottom of photosphere? Or some other criteria, which make the optical depth of the bottom of photosphere an observable?

Probably not formally an observable, if using the radiative equilibrium definition, because it's quite optically thick and so is not actually visible. But probably you mean, some attribute of the region that we could pick out in a model and say that's the deep photosphere. You would look for the region where the energy transport is via a radiative flux rather than a net advective flux of hot and cold gas. The convective flows themselves are not carrying much of a radiative flux, so the deep photosphere would be a region in a model, in which the physics of energy transport by advecting hot and cool gas is replaced by a radiative flux. One knows such a layer must be down there from theoretical considerations, though it is too opaque to actually be seen.

 

[snorkack]

Yes, that's the convectively stable but very optically thick region that might be considered the "deep photosphere," if one uses the photosphere word to apply to the region of radiative equilibrium. If instead one uses the word to just mean some kind of surface of last interaction with the light, then one struggles to find any useful descriptor for the region you describe.

What do you mean with "equilibrium" here? The convection may be driven from deeper layers, but the Doppler shift of granules shows that they move.
When a new granule approaches forming/bursting on surface, how does its upward propagation velocity, as shown by the speed of evolution of vertical heat distribution and spectrum, compare to the translatory (Doppler) velocity of the gas in it?

Probably not formally an observable, if using the radiative equilibrium definition, because it's quite optically thick and so is not actually visible. But probably you mean, some attribute of the region that we could pick out in a model and say that's the deep photosphere. You would look for the region where the energy transport is via a radiative flux rather than a net advective flux of hot and cold gas. The convective flows themselves are not carrying much of a radiative flux, so the deep photosphere would be a region in a model, in which the physics of energy transport by advecting hot and cool gas is replaced by a radiative flux. One knows such a layer must be down there from theoretical considerations, though it is too opaque to actually be seen.

For example, where is the photosphere in spots and pores? They are visibly holes in the Sun, depressed beneath the surface around them, but they are not dark, because umbra is said to have about 20% the brightness of surrounding disc.

 

[Ken G]

What do you mean with "equilibrium" here? The convection may be driven from deeper layers, but the Doppler shift of granules shows that they move.

Radiative equilibrium means that if you look at a parcel of gas, the same radiant energy enters it as leaves it. It doesn't put any requirements on movement of the gas, or lack thereof.

When a new granule approaches forming/bursting on surface, how does its upward propagation velocity, as shown by the speed of evolution of vertical heat distribution and spectrum, compare to the translatory (Doppler) velocity of the gas in it?

I don't understand the question, it seems to me the "upward propagation velocity" of a gas parcel is the same as the "translatory velocity" of the gas within it.

For example, where is the photosphere in spots and pores? They are visibly holes in the Sun, depressed beneath the surface around them, but they are not dark, because umbra is said to have about 20% the brightness of surrounding disc.

If one uses the meaning I take, that if one compares the heat being transported upward by advection versus radiative diffusion, the latter dominates in the photosphere and the former in the convection region beneath it, then it doesn't matter if there are depressions or how bright the gas is, you just pick some stationary hypothetical surface and ask by what means heat is crossing that surface. That tells you if the gas in that hypothetical surface lies in the photosphere or the convection zone, regardless of its motion through the surface, position relative to the outside of the star, or its temperature. It's a means of dividing up the regions of the outer stellar envelope such that you know the essential physics of heat transport you are dealing with. But as I say, some don't use that meaning, they just mean some kind of surface of last interaction of the photons, and they have no particular word for most of what lies above the convection zone but isn't the chromosphere or corona, which is why I'm not a fan of the latter meaning but of course the only essential requirement is being clear on one's definitions.

 

[snorkack]

Radiative equilibrium means that if you look at a parcel of gas, the same radiant energy enters it as leaves it. It doesn't put any requirements on movement of the gas, or lack thereof.

It does. Because if it moves to a layer of different temperature, how does it change temperature?

I don't understand the question, it seems to me the "upward propagation velocity" of a gas parcel is the same as the "translatory velocity" of the gas within it.

Not if the gas radiationally heats the gas ahead of it.

If one uses the meaning I take, that if one compares the heat being transported upward by advection versus radiative diffusion, the latter dominates in the photosphere and the former in the convection region beneath it, then it doesn't matter if there are depressions or how bright the gas is, you just pick some stationary hypothetical surface and ask by what means heat is crossing that surface. That tells you if the gas in that hypothetical surface lies in the photosphere or the convection zone, regardless of its motion through the surface, position relative to the outside of the star, or its temperature. It's a means of dividing up the regions of the outer stellar envelope such that you know the essential physics of heat transport you are dealing with. But as I say, some don't use that meaning, they just mean some kind of surface of last interaction of the photons, and they have no particular word for most of what lies above the convection zone but isn't the chromosphere or corona, which is why I'm not a fan of the latter meaning but of course the only essential requirement is being clear on one's definitions.

I found a definition:
http://astronomy.nmsu.edu/mcateer/thesis/online/node2.html
But it does not address the angle to which the optical depth applies!

 

[Ken G]

It does. Because if it moves to a layer of different temperature, how does it change temperature?

In radiative equilibrium, the temperature is set by the flux entering and leaving. As in any equilibrium, you drop all time dependent terms. It does not mean the temperature cannot change though, things change in equilibrium all the time. It's not a statement that the time derivative is zero, it is a statement that the time derivative is not an important term in setting the temperature.

Not if the gas radiationally heats the gas ahead of it.

I'm not following. You were talking about velocity, I don't see what heating has to do with it. The translational velocity of a parcel of gas is always the same thing as the average velocity of the gas in the parcel, so I still don't understand what question you are asking or what distinction you are making.

I found a definition:
http://astronomy.nmsu.edu/mcateer/thesis/online/node2.html
But it does not address the angle to which the optical depth applies!

Yeah that's an arbitrary choice of tau between 0.1 and 3. Again, they are free to define it any way they wish, but they have left themselves with no term for the gas below tau=3. Sure the light comes from a region, but the region deeper than that is doing essentially exactly all the same things, so there's just not much point in treating tau=3 as some kind of important boundary. It's also not like the temperature is fixed in the region they specify, the T is probably 30-40% higher at tau=3 as it is at tau=0.1. But it's whatever, you use a term, you define it any way you like.

 

[snorkack]

I'm not following. You were talking about velocity, I don't see what heating has to do with it. The translational velocity of a parcel of gas is always the same thing as the average velocity of the gas in the parcel, so I still don't understand what question you are asking or what distinction you are making.

My question was about the vertical velocity of the pattern of above normal temperature. If a rising parcel of hot gas radiationally heats the gas ahead of it, the pattern of hotter than average temperatures is moving faster than the gas in the pattern.

Yeah that's an arbitrary choice of tau between 0.1 and 3. Again, they are free to define it any way they wish, but they have left themselves with no term for the gas below tau=3. Sure the light comes from a region, but the region deeper than that is doing essentially exactly all the same things, so there's just not much point in treating tau=3 as some kind of important boundary. It's also not like the temperature is fixed in the region they specify, the T is probably 30-40% higher at tau=3 as it is at tau=0.1.

Indeed, and that is a very important thing. The light of the Sun does not come from a thin surface of uniform temperature. It comes from various parts of a thick, partially transparent layer - some of the light from deeper, hotter layers passes through the shallower and cooler layers. Which means that Sun is not a black body of a definite temperature.

 

[Hornbein]

For example, where is the photosphere in spots and pores? They are visibly holes in the Sun, depressed beneath the surface around them, but they are not dark, because umbra is said to have about 20% the brightness of surrounding disc.

Sunspots occur when a portion of a gargantuan flux tube floats above the "surface" of the sun. That's why sunspots always come on pairs. They are dark because they are colder and less bright than the surrounding areas. They float because they are less dense.

The sun is plasma so it doesn't have a discontinuous surface. The apparent surface is where the mean free path of a photon becomes sufficiently large.

 

[snorkack]

Sunspots occur when a portion of a gargantuan flux tube floats above the "surface" of the sun.

No. See Wilson effect. When the sunspots are seen near the limb, the near side penumbra, and even closer to the limb, umbra are occulted. Showing that sunspots are beneath, not above the surface of Sun.