How Do You Evaluate a Line of Sight Integral for Dark Matter Annihilation?

[majormuss]

Hi all,
I attached a picture of an integral that I need to evaluate and graph. It is a line of sight (l.o.s) integral which I have never come never come across before. The equation is called a prompt emission factor for annihilating dark matter particles for the milky way. Could someone please show me how its done? Also if there's anyone who knows this topic really well (dark matter distribution and annihilation in the milky way) please let me know. I have a few questions that I can't find answers to online. Thanks!

 

[mfb]

If you have the dark matter density, the integral should be easy to evaluate - square the density, calculate the integral.

Is your question where that formula comes from? Or how to calculate back to the dark matter density if we know the flux observed in all directions?

 

[majormuss]

Thanks mfb. I was confused about how to evaluate an l.o.s integral. I mean do I evaluate it as a normal integral? or does it need a special consideration since it is l.o.s? I also heard the l.o.s integral have some angle dependencies. Is this right?

 

[mfb]

It is just a regular, one-dimensional integral. "Line of sight" just determines which part of the density you look at.