# How to calculate an infrared SED from the specific intensities?

I have values of total infrared fluxes (SED) in literature expressed in Jy (Jansky) for galaxies. I want to assure that my infrared radial profiles of the same galaxies in MJy/sr (and other in Jy/pixel) give me the same integrated value as in the literature. How to get rid of the angular counterpart in steradian ? The data used to create radial profiles are HERSCHEL SPIRE 250um & 500um.

• Don't you just need to integrate over the solid angle/pixels? Sep 3, 2021 at 8:40
• Yes I think so, but the problem is to know how to do it when it is over the solid angle in steradian ? Sep 3, 2021 at 9:01

Say that you have an image with $$N \times N$$ pixels that covers a region of sky of $$\theta \times \theta$$ steradians. For each pixel $$i$$ you have a value of flux density $$J_i$$, expressed in Jy/sr. The image contains a galaxy and you want to calculate its the total flux.

If this were a continuum problem, you would need to do an integral

$$F = \int_{\Omega_{gal}} J(\theta,\phi) d\Omega$$

Since the problem is discrete, you have to do a sum instead

$$F = \sum_{i=0}^M J_i \Delta \Omega$$

Where the pixels $$i=0,..,M$$ are the ones that contain the galaxy. To carry out the sum you only need to notice that $$\Delta \Omega$$, which is the solid angle covered by one single pixel, can be expressed as $$\Delta \Omega = {\theta^2 \over N^2}$$. And you are done:

$$F={\theta^2 \over N^2} \sum_{i=0}^M J_i$$

• Thanks you very much for this explanation ! This is exactly what I was looking for ! Sep 3, 2021 at 9:30
• @PsycOx you also have the options of up-voting and clicking "accept" on the answer post if you so choose.
– uhoh
Oct 3, 2021 at 11:54