Homework 2

Compute l for the core and photosphere of the sun

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r density of electrons ne to the mass density of ions). Compute l for the core and photosphere of the Sun, assuming mass fractions X = 0.75, Y = 0.24, and Z = 0.02; a proton/nucleon fraction Z/A ≈ ½. Estimate a rough random walk time for a core photon to reach the surface. (d) [20 pt] To better model the Sun, reconstruct your n=3 polytrope from homework 1, scaling to core parameters ρc = 146 g/cm3 and Pc = 2.3x1017 dyne/cm2 Compute the pathlength as a function of radius. How constant is the pathlength as a function of radius? At what radius does the pathlength become an appreciable fraction of the Solar radius? What part of this Sun would this point correspond to? (you will find the radius is a bit off because the n=3 polytrope model is not perfect for the Sun). (2) Adiabatic gradient for combined ideal and photon gases. Assume that the interior equation of state of a star is well-described by a combination of ideal (monotonic) and radiative pressures: P = Pgas + Prad = ρkT 1 + aT 4 µmH 3 where Pgas = β P and Prad = (1 − β )P (a) [10 pt] Show that: ∂β ∂T ∂β ∂P P 4 = − (1 − β ) T = T 1 (1 − β ) P (b) [10 pt] Show that the density thermal gradient δ is: δ≡− ∂ ln ρ ∂ ln T = P 4 − 3β β (c) [10 pt] Show that the heat capacity for constant pressure is: cP = k µmH 3 3(4 + β )(1 − β ) 4 − 3β + + 2 β2 β2 (d) [10 pt] Finally, using our parametric equation for the adiabatic gradient: ad = Pδ T ρ...
View Full Document

Ask a homework question - tutors are online