Charles,

Can you trace individual photon in lab? If it is testable in lab ,then why there are so many different results?

Debajyoti,

In my younger days the diffusion timescales arose from simple calculation of the scattering presumed in a gas of given density. One knows the mass of the Sun, one knows its volume. One then presumes, if one wants to, something about the structure of the Sun in terms of its density profile. With a scattering model one then turns the handle as the rest is arithmetic.

This link (note well the sentence that starts "While the estimates of the diffusion..." may be useful. The ADS is a wonderful service, if your library doesn't carry many titles.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1992ApJ...401..759M&db_key=AST&page_ind=0&data_type=GIF&type=SCREEN_VIEW&classic=YES

The vagaries of stellar physics suggests to me that current predictions may well be accurate to within a factor of a few.

As for experimental verification?

No, I cannot imagine how one would trace a photon from a star's core.

What is your research topic that prompted this question?

James

Thanks for the link. The work is interesting. Actually this question comes to my mind when I was reading a book on solar physics.

I understand, as Charles points out, that a specific photon never propagates from the interior of the Sun to its exterior - emitted photons are almost immediately absorbed and subsequently re-emitted. This might seem to be a minor point, but it is a point of confusion for many.

For an example, http://sunearthday.nasa.gov/2007/locations/ttt_sunlight.php states:

"Once a photon of light is born, it travels at a speed of 300,000 km/sec until it collides with a charged particle and is diverted in another direction."

Yet the caption of an inset image states:

"Light escapes the sun's core through a series of random steps as it is absorbed and emitted by atoms along the way."

Moreover, the scatter vs. absorption question would seem to be critical to the problem solution, since a photon could presumedly be scattered or deflected with little delay, while an absorption/re-emission process could include significant delay.

http://en.wikipedia.org/wiki/Sun#Core explains:

"The gamma rays (high-energy photons) released in fusion reactions are absorbed in only a few millimeters of solar plasma and then re-emitted again in a random direction and at slightly lower energy. Therefore it takes a long time for radiation to reach the Sun's surface. Estimates of the photon travel time range between 10,000 and 170,000 years.[58] In contrast, it takes only 2.3 seconds for the neutrinos, which account for about 2% of the total energy production of the Sun, to reach the surface. Since energy transport in the Sun is a process which involves photons in thermodynamic equilibrium with matter, the time scale of energy transport in the Sun is longer, on the order of 30,000,000 years. This is the time it would take the Sun to return to a stable state if the rate of energy generation in its core were suddenly to be changed.[59]

"During the final part of the photon's trip out of the Sun, in the convective outer layer, collisions are fewer and far between, and they have less energy. The photosphere is the transparent surface of the Sun where the photons escape as visible light. Each gamma ray in the Sun's core is converted into several million photons of visible light before escaping into space..."

Also see http://en.wikipedia.org/wiki/Raman_scattering#Stokes_and_anti-Stokes_scattering.

This question might also to apply to the surface of last scattering and the emission of the CMB...

The main source of uncertainty in photon diffusion time is related to the opacity in different layers of the sun as inferred from various solar models. Also this opacity will change as the sun evolves so the photon diffusion time is not constant. Convection in the interior of the sun also complicates this this issue.

A simple random walk calculation combined with a simple density gradient model for the sun is a relatively clean calculation.

http://adsabs.harvard.edu/full/1992ApJ...401..759M (a 2 page paper)

is a good source for this and is the source for the 170,000 yr timescale.

The average Mean free path of a photon inside the sun is estimated as 0.5 mm. We derived this conclusion from standard modelling of Our sun with well organised data.

With considering mentioned mean free path we gave up the conclusion of 30000 years. But we don't have proper experimental study of what was proposed. For that we should have proper understanding of helio seismology. I thing may be using Neutrino imaging we can find some results as Neutrino photographs of sun will image the center of sun.

Please see http://sunearthday.nasa.gov/2007/locations/ttt_sunlight.php - it states:

"... Because the density of the sun changes from the core to the surface, it is common to represent the interior of the sun as a collection of nested shells of matter, each with a typical average density. You then calculate how many steps it takes for a photon to travel through each shell. During each step, the photon travels at the speed of light so you can calculate the time required for each step. By multiplying this by the number of steps taken, you can calculate how long it takes the photon to traverse each shell, and then add up all the times for the other shells."

It goes on:

"When this random walk process is applied to the interior of the sun, and an accurate model of the solar interior is used, most answers for the age of sunlight come out to be between 10,000 and 170,000 years. Rarely do you get answers greater than a million years unless you have made a serious error! Why do you still see these erroneous estimates of '10 million years' still being used? Because textbook authors and editors do not bother to actually make the correct calculation themselves, and rely on older published answers from similar textbooks."

As I understand, a random-walk solution based on an "average Mean free path of a photon inside the sun" yields only a very gross approximation.

again

the original and most correct source for this kind of calculation is

http://adsabs.harvard.edu/full/1992ApJ...401..759M (a 2 page paper)