# What is the spectral energy distribution (SED)?

I see the SED being referred to as several different things and now I am confused about what it actually is and what are its units. In particular, I find the SED Wikipedia page not understandable.

The Flux $$F$$ of a star/galaxy is related to its luminosity $$L$$ by $$F=\dfrac{L}{4\pi d_L^2}\,,$$ where $$d_L$$ is the luminosity distance. If we differentiate the quantities and remembering that the emitted wavelength $$\lambda_{em}$$ is related to the observed one by $$\lambda_{obs}=(1+z)\lambda_{em}$$, where $$z$$ is the redshift, we can have two quantities:

• $$\dfrac{dF}{d\lambda_{obs}}\equiv f_{\lambda}$$
• $$\dfrac{dL}{d\lambda_{em}}\equiv l_{\lambda}$$

I think $$f_{\lambda}$$ is the specta (units of [Energy][Time]$$^{-1}$$[Lenght]$$^{-3}$$) and $$l_{\lambda}$$ is the SED (and therefore has units of [Energy][Time]$$^{-1}$$[Lenght]$$^{-1}$$). Is this correct? Can you give me some resources (eg. papers or books) where this is written down? Thank you.

• SED = Spectral Energy Distribution. It can be in flux units or in luminosity units, but is quoted as flux per unit wavelength (or sometimes flux per unit frequency). – ProfRob Mar 2 '20 at 14:24
• @RobJeffries, I am sorry but I didn't understand it. Since it is "distribution", I assumed it is always per unit of wavelength (or frequency). Additionally, it has a name and $l_{\lambda}$ and $f_{\lambda}$ are two intrinsically different things, so how can we call the same to both? – Catarina Alves Mar 2 '20 at 15:01
• Because one is just the other multiplied by $4\pi d^2$. We call a spectrum a spectrum, but that can mean a lot of different things. I guess you might distinguish between an observed SED (always flux) and an intrinsic SED. – ProfRob Mar 2 '20 at 15:04
• The most important thing is: both show exactly the same frequency (or wavelength) dependence - multiplied by a constant factor (the distance to the source does not change in this regard; its distance is only important when you need the overall luminosity) – planetmaker Mar 2 '20 at 17:14
• @CatarinaAlves the photon count matters when you are dealing with a quantum sensor, such as a CCD or the human retina. These things detect photons, not "wave energy" – Carl Witthoft Mar 3 '20 at 12:56