how many years does it take for heat generated in the Sun' core to reach its outer layer, the photosphere?

Answer 1

Good question! And the answer is not as long as you might think --- or at least, not as long as some books imply and as even some professional astrophysicists ( who should know better) think.

One of the major times associated with the Sun is its so-called Kelvin-Helmholtz time, or t_KH. This is the time for the Sun to radiate away all the gravitional energy released so far (from its material "falling from infinity to its present size"), at something like its present luminosity.

Before we learned about nuclear energy release, this was how Kelvin (and Helmholtz, independently) had calculated the probable maximum possible age of the Sun. (The trouble was, this gave only ~ 3 x 10^7 or thirty million years; yet there were alreday indications from rocks on Earth that IT was more than a billion [U.S.] years old, clearly a significant contradiction.) We now know that nuclear energy release could sustain the Sun for a time of order 10 billion years.

Many people have confused the solar value of t_KH with the time t_diff for energy to get from its centre to its surface, the photosphere. (This time is the so-called "diffusion timescale.") But the two timescales are NOT the same or even remotely the same, EXCEPT for massive stars --- which the Sun is definitely NOT.

For years I set my students a problem of calculating this diffusion timescale, after they had learned about diffusive radiative energy transfer inside stars and some general properties of stellar interiors.

Most graduate students, and the better 3rd and 4th year undergraduate students, could obtain the following result:

For massive stars, where their radiative energy content is comparable to their gaseous heat content, the diffusion time is indeed comparable with the K-H timescales for those stars.
However, for medium to low-mass stars like the Sun, the diffusion time is their K-H timescale times a (small) fraction, the ratio of the radiative energy content to the total gaseous energy content.

The students got these results by making insightful approximations in the relevant equations governing the internal structure of stars. This is no place to go into those! However, they were able to interpret their algebraic results in this way:

The K-H timescale is "the time to lose ALL the star's internal energy content." However, from the expressions obtained, one can view the diffusion process as one that only carries the RADIATIVE ENERGY to the surface, so that when that is only a small fraction of all the energy, it takes that much less time to deplete it. (I realise that this is hard to follow without knowing more about it, and you might even think I'm pulling the wool over your eyes somehow -- but the students were in fact justified in drawing that conclusion.)

The Sun's internal radiative energy content is such a small fraction of its overall internal energy (> 99.9% gaseous) that the time for some given parcel of heat to reach the surface by the diffusion processes going on throughout the majority of its mass is of the order of only ten to thirty thousand years or so. (I don't claim much more accuracy in this number than perhaps a factor of three, and I strongly doubt it's as much as even a hundred thousand years, or less than a tenth of the "million years" some others have asserted. Nevertheles, the point is that it's really quite a short time compared with both its nuclear timescale [~ 10^10 years] and its K-H "contraction timescale [~3 x 10^7 years]. Indeed, relative to both of those, it's virtually instantaneous! )

I hope this has helped.

Live long and prosper.

Answer 2

Light created in the core of the Sun takes about a million years to reach the surface, and heat would take a bit longer. This is because when the light is emitted, it is absorbed and then reradiated by the atoms it encounters on the way out. Light moves rapidly as radiation, but heat can be conducted both as radiation or as a mechanical force. This takes longer so heat would move more slowly.

Heat moves in three ways - radiation, conduction, and convection.

Answer 3

i think of you will discover that warmth in itself isn't something which could be measured. in basic terms that's consequence on something else. because of the fact the solar is often kind of the comparable temperature there is not any way you're able to ever be waiting to tell how long it took for the waste made from heat, brought about by employing the reaction in the middle, to attain the exterior layer. that's in simple terms an impossible calculation.

Answer 4

I looked this up once - I think it actually was about a million years for a single photon to escape due to all the collisions and scattering events along the way - the Sun is very dense near the core.

Answer 5

That is an awesome question, of which I have no idea.
Good luck