1. Testing Our Understanding

2. The Challenge Astronomers claim to know the reactions going on in the core of the sun, and their rates. Did my explanations convince you? If not, can we test our claims directly?

3. Two Problems 1. We can’t see directly into the center of the sun. 2. The brightness of the sun right now only tells us how vigorous the reactions were some time ago.

4. Analogy When the oven’s heating elements are turned off, how quickly does it cool down? (It stays hot for a while!) Similarly, how do we know the sun is undergoing any reactions right now? Maybe it’s “turned off!”

5. Size of the Sun 2.3 light-seconds 2.3 light-seconds

6. Information Delayed If the sun were transparent, the photons leaving the core would escape in about 2 seconds (and reach Earth 8 minutes later) In fact it takes about half a million years for them to percolate out from the center!

7. Diffusion: The ‘Random Walk’

8. …a.k.a. the Drunkard’s Walk

9. Test This Yourself! Flip a coin umpteen times. (Say, N=100.) If it’s a head, take one step to the right. If it’s a tail, take one step to the left.

10. Statistical Analysis Proves: On average, after N steps, you will be about √N steps from your starting point – sometimes to the left, sometimes right. In our example, after N = 100 coin flips, you will find yourself (typically) about 10 steps from where you started. (√100 = 10)

11. Ten Thousand Steps!

12. Smell the Lilacs How does the fragrance reach you? Molecules of the scent drift into your nose, having made their way across the intervening space. Not by diffusion! Much too slow! We smell the flower because of air currents that carry the scent.

13. Let’s Consider Some Numbers [don’t memorize!] Inside the sun, light goes about 1 mm before running into an electron and ‘bouncing’ in some new direction. Call each of these one ‘step.’ The sun’s radius is ~700,000 km. That is about 700,000,000,000 ( = 7 x 10 11 ) mm – 700 billion steps. To cover that distance like a drunkard, the light must take N 2 steps ( ~50 x 10 22 ) in total – up, down, left, right,… Travelling at the speed of light, this takes several hundred thousand years.

14. Old Light! The light energy reaching us today was generated by nuclear reactions the best part of a million years ago!

15. So Forget About the Visible Light! It tells us essentially nothing about the current central state of the Sun’s ‘engine’. How can we learn about deep interior in some other way?

16. To Probe the Sun’s Deep Interior 1. Find something that comes straight out from the deep interior (not a photon, therefore); or or 2. Use a technique analogous to the seismic studies on Earth. That is, measure the ways in which the sun is vibrating, to learn about its internal structure.