a. (4 pts) An interstellar cloud might be heated by ultraviolet radiation from stars, and cooled by emitting infrared ra

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A 4 Pts An Interstellar Cloud Might Be Heated By Ultraviolet Radiation From Stars And Cooled By Emitting Infrared Ra 1 (190.49 KiB) Viewed 26 times

a. (4 pts) An interstellar cloud might be heated by ultraviolet radiation from stars, and cooled by emitting infrared radiation. It is well known that dust grains have much higher opacity the optical than in the IR. What is the opacity kuv of dust grains in the visible range if the cross section of each grain is Ovis na, the grain radius is a = 0.1 pm, the internal density of each grain is p= 3g cm-3 and the dust-to-gas mass ratio is 0.01. Repeat for the opacity Kir at a wavelength 1 = 10 um if the infrared cross section per grain is OIR πα? (2π/λ). b. (6 pts) Let's say a grain in space away from the cloud is exposed to a background radiation field with mean intensity J, W B,(Tx), where W = 4 x 10-7 and B,(Tm) is the Planck function at the stellar temperature Tt 6000 K. If the grain absorbs radiation at a rate = = S* 72,0, dv TJyou and emits at a rate 6* #B,(T)0, dv, a and these are in balance, integrate over frequency and derive a formula and numerical value for the grain temperature T. At what typical wavelengths does the grain absorb radiation? At what typical wavelengths does the grain emit radiation? Use the appropriate values for the cross section o, in each frequency range.