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Unformatted text preview: Homework # 1 Solutions 1. Show that an extinction of A Î» = 1 magnitude leads to a flux F Î» decrease to 40% of its original value. 1 magnitude is equivalent to a reduction of intensity of 10 âˆ’ 2 / 5 = 0 . 398. 2. Assuming dust grains are 0 . 1 Î¼ m in radius, that the gas density in the ISM is n H = 1 cm âˆ’ 3 , and the number density of dust grains is n d = 10 âˆ’ 12 cm âˆ’ 3 and uniformly distributed, find the column density N H of hydrogen to be expected along a line of sight in which a source is observed to have an extinction A V = 1 magnitude. What is the mean free path of light along this line of sight? What is the distance to the source? The mean free path â„“ = ( nÏƒ ) âˆ’ 1 where n is the number density of scatter- ers/absorbers and Ïƒ is the effective cross section. For dust interacting with light which has a wavelength smaller than the dust size, the effective cross section is Ï€r 2 d . Then â„“ = 1 n d Ï€r 2 d â‰ƒ 1 . 001 kpc ....
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This note was uploaded on 01/25/2012 for the course AST 346 taught by Professor Lattimer during the Spring '11 term at SUNY Stony Brook.
- Spring '11