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Use Wien's displacement law - as you suggest. Let's assume that the spectrum you have been given incorporates almost all the flux from the star. This might be ok, so long as the flux is heading towards small numbers at each end of the spectrum? If so, then you can use the temperature-independent shape of a blackbody function to argue that some fixed fraction ...

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The planet would reach an equilibrium where the amount of heat absorbed is the same as the amount of heat radiated. If there is no way to transfer heat on the planet (no conduction, no atmosphere), then that condition must apply locally. The flux radiated from a blackbody surface (in W/m$^2$) is given by $\sigma T^4$, where $\sigma$ is Stefan's constant and ...

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A question/answer over at physics.se discusses the issue of quasar spectral output. Part of one answer says, The percentage of radiation that is thermal versus non-thermal varies from quasar to quasar, and for a single quasar is going to be different at different wavelengths, so there isn't one simple answer (and also it depends on what angle you ...

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