# How do nuJ(nu) units work?

I'm working with (Nublado) Cloudy, which is essentially a spectral modelling tool for stellar matter. Using the software, I model my own stellar object and obtain its continuum.

According to Hazy, which is Cloudy's official document, the continuum is given in units of "Intensity per octave". Specifically, $$4 \pi \nu J_\nu$$ [erg $$cm^{-2} \ s^{-1}$$] units. However, I'm having difficulty making sense of this form of units. What is meant by "Intensity per octave", and why is there an additional factor of $$4\pi$$ and $$\nu$$? What exactly does $$J_\nu$$ refer to here, and how is it different to all the letters astrophysicists use when talking about spectra, like $$L_\nu$$, $$F_\nu$$ and $$I_\nu$$?

What would be the correct approach to integrate this spectra in order to get the luminosity of my object?

Finally, my main goal is to apply the Gaia passband filters to my spectra and integrate in order to get the flux and thus find $$(G, G_{bp} - G_{rp})$$ coordinates on the HR diagram. At its current form of supposedly $$4 \pi \nu J_\nu$$ as a function of the wavelength, can this be done directly or do I have to change my continuum in some way.

I have very little to no astrophysics background, so I appreciate your understanding. Thanks.

• I think you need to give some more details. Which continuum is given in these units? Is this an output from Cloudy - is this a photospheric continuum as received at the Earth? Is it in the interior of the star? Is it at the photosphere? Commented Jun 27, 2023 at 9:11
• Hi, this is an output from Cloudy. It is simply said to be the predicted spectrum of an optically thin object in a spherical geometry, I suppose just outside of it. Nothing Earth related or stellar for that matter. I just have an optically thin blob that is heated by an external source, and cloudy gives me a spectra. I hope this is enough clarification Commented Jun 27, 2023 at 9:23
• OK, so it isn't the spectrum of a star (which isn't an optically thin object). Commented Jun 27, 2023 at 11:13
• You're right, 'stellar matter' wasn't the right choice of words. Its just a ball of optically thin gas thats heated, and I'm trying to figure out how to correctly work with the continuum that cloudy gives me. From what I've read so far, I should be able to integrate my $4\pi \nu J_\nu$ array with respect to a $\nu$ array by manipulating my wavelength array in order to get the luminosity. Does this sound reasonable? The object comes out to have about a 100th of the luminosity of the sun if I do it this way, which for the object it is, seems reasonable. Commented Jun 27, 2023 at 20:50