I have been reading some astrophysics papers on Fermi Bubbles and in a lot of them, diagrams depicting SEDs use a weird $ E^2 \, \frac{\text{d}N}{\text{d}E} $ quantity, in units of $ \left[ \frac{\text{eV}}{\text{cm}^2 \, \text{s} \, \text{sr}} \right] $. These units are similar to those of spectral radiance, with the exception of having a $ \frac{1}{\text{Hz}} $ or $ \frac{1}{\text{m}} $ term in the denominator, and they aren't spectral flux either, since there is a $ \frac{1}{\text{sr}} $ term there.
I'm pretty sure I've actually seen this $ N $ notation before, but I never really thought about asking what it's referring to until now.
So, I guess my questions is, what is this $ E^2 \, \frac{\text{d}N}{\text{d}E} $ quantity? And how can I convert spectral flux density data to this quantity?
Here is an example from Ackermann et al (2014). If needed I can cite a lot more examples, it really is used in practically every paper that discusses SEDs for Fermi Bubbles, but I didn't want to bog down my post with too many pictures.
Edit to add some more sources:
Su, Slatyer & Finkbeiner (2010): https://iopscience.iop.org/article/10.1088/0004-637X/724/2/1044/meta, page 11.
Mertsch & Sarkar (2011): https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.091101, the diagram can be seen in one of the available images, the full article is behind paywall.
Su & Finkbeiner (2012): https://iopscience.iop.org/article/10.1088/0004-637X/753/1/61/meta, page 3.
The example image from the post, Ackerman et al (2014): https://iopscience.iop.org/article/10.1088/0004-637X/793/1/64/meta, page 23.
