set4-06-sol

set4-06-sol - Astro 346, Spring Semester 2006 Homework, 4th...

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Astro 346, Spring Semester 2006 Homework, 4th set, solutions Problem 10.6 In 100 years one has accreted N H = (10 - 8 M ¯ yr - 1 ) (100yrs) 1 m p 10 51 atoms We know that by fusion we can get 0 . 03 m p c 2 in energy per actual Helium nucleus produced, hence the total nuclear energy released is E = 0 . 03 m p c 2 4 N H 10 46 erg If all that was released in a month ( 3 · 10 6 seconds), the average luminosity would be L 3 · 10 39 erg s - 1 The accretion luminosity was calculate in problem 10.5 (not 10.1!) and is, neglecting the initial potential energy, L acc = ˙ M 2 G M r i 5 · 10 34 erg s - 1 The total gravitational energy gain is much higher than the accretion luminosity. So the nuclear energy dominates, partly because we accumulate material for some time and partly because the gravitational well of a white dwarf is not so deep. Problem 11.1 Take a small path length element dx along the photon’s direction of motion. The number of dust particles per unit area is then
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