Astro 160: The Physics of Stars

Knowing that l∼ h we can derive the following relationshipnσ = κρ ρ = nσ Tl = 1κ T nσ = h = k bT¯mgthus we find that the density is given by and assuming ¯m ≈ m pρ =¯mgk b κ T T ≈ 8.26 × 10−4 g/cm 3b) In reality, the surface of the sun is so low that hydrogen is primarily neutral. There are thus not thatmany free electrons to Thompson scatter off of. The opacity at the surface of the sun is instead due to theH − ion and is given by κ ≈ 2.5 × 10 −31 ρ 1/2 T 9 cm 2 g −1 . Using this (correct) opacity, repeat the estimatefrom a) of the density at the photosphere of the sun.Substituting the opacity given into the above expression yieldsρ 3/2 =¯mg2.5 × 10 −13 kT 10b()¯mg 2/3⇒ ρ =2.5 × 10 −31 k b T 10 ≈ 9.8 × 10 −8 g/cm 3c) Just beneath the photosphere, energy is transported by convection, not radiation, for the reasonsdiscussed in class (in fact, the photosphere is the place where photons travel so freely out of the star thatenergy transport by radiation finally dominates over convection). Estimate the convective velocity nearthe photosphere given your density from b).The convective heat flux is given byF c = 1 ( 2Fc2 ρv3 c v c =ρand knowing thatF c = L4πr 2we find that the convective velocity is given byv c =) 1/3( ) 2L 1/34πr 2 ≈ 1.09 × 10 6 cm/sρd) What is the characteristic timescale for convective ”blobs” to move around near the pho-tosphere?How does this compare to the observed timescale for granulation on the surface of the sun, which was afew min in the movie we watched in class?since we know that the characteristic time scale is given byt blob = l v c≈ h v cwe know that h which is the scale height of the sun is given byh = kTg ¯m = 1.7 × 107 cm10