# Confusion around units for SEDs, and how to tell what I'm looking at

I know that a spectral energy distribution (SED) is a plot of energy versus wavelength or wavelength of light, while a spectrum is a plot of flux density against wavelength, but I'm a bit confused about the units.

Firstly, Figure 4 in this paper purports to be an SED, but it has units of erg cm$$^{-2}$$ s$$^{-1}$$ Hz$$^{-1}$$, which seems to me to be a flux density, so according to my understanding should be described as a spectrum:

Secondly, SEDs can be shown in units of $$\nu F_{\nu}$$ (or equivalently $$\lambda F_{\lambda}$$), or just $$F_{\nu}$$, or in Jy. What are the relationships between these units?

Due to my confusion, I find it difficult to tell what kind of plot I'm looking at, unless the plot is actually named "SED of ..." or "Spectrum of ...".

In practice, the term "SED" is often used when combining a set of relatively broadband flux measurements, which may be very irregularly spaced and come from many different sources, like the red diamonds in the plot. Since individual points may come from observations through broadband filters spanning a wide range of wavelengths, it's common to use flux rather than flux density. But you can convert things to flux density if you want to.

"Spectrum", on the other hand, tends to be used for a regularly spaced set of narrow-band (often very narrowband) flux or flux density measurements, as would be produced by a spectrograph. Since each point has a rather well-defined wavelength, it's common to use flux density.

In that figure, the red diamonds form an SED; they're too widely and irregularly spaced to meet the standard/casual definition of a spectrum. But note that the caption refers to the continuous blue line as a template "spectrum", which makes sense in that it's regularly and finely spaced (so finely spaced that it's plotted as a continuous curve). So this is a plot with both a (template) spectrum and a (data-based) SED.

I realize this doesn't accord with the definitions you linked to at the start of your question, but that page is operating from a very precise (arguably fussy and overly nice) perspective, and I'm not sure most astronomers would agree with the idea that "a spectrum must be a plot flux density versus wavelength". I've certainly seen plenty of X-ray "spectra" where the units are photon flux density plotted versus photon energy....

SEDs can be shown in units of $$\nu F_{\nu}$$ ... or just $$F_{\nu}$$ or in Jy. What are the relationships between these units?

$$F_{\nu}$$ means flux density -- e.g., flux per unit frequency (examples: ergs cm$$^{-2}$$ s$$^{-1}$$ Hz$$^{-1}$$; W m$$^{-2}$$ MHz; etc.). If you multiply it by the frequency $$\nu$$ to get $$\nu F_{\nu}$$, then you remove the "per unit frequency" part and it becomes flux. "Jy" are Janskys, a specific unit of flux density ($$10^{−26}$$ W m$$^{−2}$$ Hz$$^{−1}$$).

• So, just by looking at a plot, does it even make sense to say 'this is an SED' or 'this is a spectrum' just from the units alone? Or is it more 'this is a narrowband energy per wavelength plot, therefore a spectrum'? Nov 12, 2021 at 9:28
• @Jim421616 I think the point is that it's not worth fussing over an exact name for the plot. The graph is tool; use it in good spirits without worrying about names. Nov 12, 2021 at 13:26
• @Jim421616 I think it’s maybe better to think in terms of datasets rather than plots. One can imagine a single plot containing with three different datasets: a spectrum (many evenly sampled, narrowband measurements) for one object, an SED (relatively few, perhaps unevenly spaced, broadband measurements) for another object, and a single photometric (e.g. R-band) measurement for a third, all using the same units. Though it displays both a spectrum and an SED, it doesn’t make sense to say the whole plot is one or the other. Nov 12, 2021 at 13:40