Lecture 4 - Astro Pas Rochester

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Opacity and luminosity in stars (continued) ! However, the average value of the square of the position is not zero. Consider step N+1, assuming the chances of going left or right are equal: hx 2 N+1i = 1 2 h(x N l) 2 i + 1 2 h(x N + l) 2 i hx 2 N+1i = 1 2 hx2 N 2x N l + l 2 i + 1 2 hx2 N 2x N l + l 2 i hx 2 N+1i = hx 2 N i + l 2 ! But if this is true for all N, then we can find by starting at zero and adding , N times (i.e. using induction): <strong>Astro</strong>nomy 142 20
Opacity and luminosity in stars (continued) ! Thus to random-walk a distance , the photon needs to take on the average ! So far, we have discussed only one dimension of a threedimensional random walk. Three times as many steps need to be taken in this case, so to travel a distance R, the photon on the average needs to take <strong>Astro</strong>nomy 142 21
Page 1 and 2: Today in Astronomy 142: stellar str
Page 3 and 4: Principles of stellar structure (co
Page 5 and 6: These equations can be derived from
Page 7 and 8: Hydrostatic equilibrium Consider a
Page 9 and 10: Another way to derive this, using E
Page 11 and 12: The Sun’s interior, on the averag
Page 13 and 14: Central pressure in a star (continu
Page 15 and 16: For the Sun: Central pressure in a
Page 17 and 18: Central density and temperature of
Page 19: Diffusion of energy to the surface
Page 23 and 24: Diffusive approximations @f(x, t) @
Page 25: Summary ! Using hydrostatic equilib

Lecture 4 - Astro Pas Rochester

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