How to obtain a luminosity from an SED

I have a spectral energy distribution (flux densities measured at several frequencies), and have fitted a 'greybody' model to these points.

I am confused about how I use this information to determine the luminosity of my source.

I think the integral of my fitted function gives me the total flux, but how is this related to the source's luminosity?

The luminosity is $$4\pi d^2$$ multiplied by the integral under your SED.

i.e. you cannot find the luminosity without knowing the distance $$d$$ to the source.

NB This assumes no extinction (unless that features in your SED model), that the radiation from the source is isotropic and that the source is not significantly redshifted or moving relativistically.

• Thank you for your answer. What counts as significantly redshifted? Some of my sources are z ~ 3 – jm22b Jan 7 at 9:48
• @jm22b It depends how accurately you want the luminosity but $z\sim 3$ is large. You will have to work out the "luminosity distance" to use as $d$, which depends on cosmological parameters. en.wikipedia.org/wiki/Distance_measures_(cosmology) – ProfRob Jan 7 at 10:15