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set2-f5 - we now want to know the temporal evolution of the...

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Astro 405/505, fall semester 2005 Homework, 2nd set, return before Friday, September 30, 4pm. Don’t forget to give your name. Problem 3: Radiation spectra under LTE A supernova remnant has an angular diameter θ = 4 . 3 arcmin and a flux a 100 MHz of F 100 = 1 . 6 · 10 - 19 erg / cm 2 / s / Hz Assume the emission is thermal and emitted under LTE conditions. a) What would be the temperature of the radiation material, if the emission were optically thick? (This is called the brightness temperature) b) At what frequency would the remnant have its radiation maximum, if the emission were optically thick? c) Given the above, what can you say about the temperature of the radiating material? Problem 4: Time-dependent line profiles Let us as in class consider the optically thin line profile resulting from material that is expelled in a supernova explosion. In contrast to the time-independent treatment that we used in class,
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Unformatted text preview: we now want to know the temporal evolution of the line pro±le. Assume all particles have the same velocity P ( v ) = δ ( v-v ) , have been expelled isotropically at the same location and time ( t = 0 ). a) Suppose a particle emits at time t . At what time would be observe the emission? Assume the distance between observer and supernova, d , very much larger that any distance the radiating particle may reasonably propagate. Can you use an approximation to simplify the time relation, so it is linear in t ? b) Assuming the particles decay exponentially after instantaneous injection as would be±t a radioactive particle ( P ( t ) = exp(-t/t ) Θ( t ) ), calculate the time-dependent line pro±le. Explain the evolution of the derived pro±le qualitatively....
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