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In the Gaia catalogue I have the magnitude of several stars in the G band. I also have the distances to these stars (parallax is known). Additionally, I oftentimes have the effective temperature in Kelvins.

Is there any way to convert this magnitude to an approximate spectral luminosity (units of W/Hz) at some frequency band? You may assume that we are in the Rayleigh Jean's regime (Intensity proportional to frequency2).

Glorfindel
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  • There are dozens of astrophysics web pages which discuss this in detail. – Carl Witthoft Jul 12 '19 at 14:40
  • @CarlWitthoft can you point me to one? I am not looking to convert to bolometric luminosity (W), rather, spectral luminosity (W/Hz) –  Jul 12 '19 at 14:40
  • I think you simply need to get the temperature of the Star and use Planck's Law to estimate the spectral distribution – Carl Witthoft Jul 12 '19 at 14:43
  • @CarlWitthoft Ah I see. So from there I can get spectral radiance at frequency v. How can I then obtain the spectral luminosity? Is it just this number time 4pidist^2? –  Jul 12 '19 at 15:00
  • Hi @Jake and Welcome to Stack Exchange! This site works a little different than other forums or Q&A sites. It uses more formal Question posts and Answer posts. Questions should usually contain a bit of research and effort if possible, not just "how do I..." It would be better if you do some reading first, and make an attempt to do the calculation first, even if it's wrong. This way it is easier for other people to see what data you are starting with and how you plan to manipulate it. That makes writing answers much easier. Thanks! – uhoh Jul 12 '19 at 15:03

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