{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sol6 - Astro 405/505 fall semester 2004 Homework 6th set...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Astro 405/505, fall semester 2004 Homework, 6th set, solutions. Problem 1: Eddington limit We cannot assume that the mean free path of photons is very small. Instead we explicitely calculate the force density on a population of electrons with density n e exerted by radially streaming photons with flux F = n ph c = L 4 π R 2 The momentum transfer per scattering depends on the scattering angle as δp = c (1 - cos θ ) and thus we calculate the force density as F = d Ω c (1 - cos θ ) F n e d Ω = n e L σ T 4 π R 2 c Gravitation pulls the gas (hydrogen for simplicity) inward with a force density F g = - G M n e m p R 2 Dominance of gravity then requires F g + F < 0 M > L σ T 4 π G m p c = (1 M ) L 1 . 3 · 10 38 erg / s For pair plasma we have to replace the proton mass in the gravitational force density by two times the electron mass. The required mass is therefore around a factor 1.000 higher than for ordinary gas, or for a given mass the maximum luminosity is correspondingly less.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}