Evaluating an 'odd' integral

[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.

 

[pmacias]

Hello,

Thank you for sharing your question about evaluating this 'odd' integral. I can understand your curiosity about this equation and its relevance to the topic of dark matter distribution and annihilation in the Milky Way.

To begin, let's break down the integral and understand its components. The integral is a line of sight (l.o.s) integral, which means it involves integrating along a line of sight. In this case, it is the line of sight through the Milky Way. The equation is called a prompt emission factor for annihilating dark matter particles, which suggests that it relates to the amount of energy emitted when dark matter particles annihilate.

To evaluate this integral, we need to understand the function inside the integral, which is the dark matter density profile. This profile describes the distribution of dark matter in the Milky Way. Depending on the model used, this profile can vary, and therefore, the integral will give different results. This is why it is important to use a well-supported model for the dark matter density profile when evaluating this integral.

As for graphing the integral, it would be helpful to plot the function inside the integral as a function of the line of sight, and then integrate over that function to get the total amount of prompt emission. This can be done using numerical methods or by breaking the integral into smaller, more manageable parts.

In terms of finding someone who is knowledgeable about this topic, I suggest reaching out to researchers or experts in the field of dark matter and astrophysics. They would be able to provide you with more detailed explanations and potentially answer your questions.

I hope this helps in your understanding of this 'odd' integral. Keep exploring and asking questions, as that is the essence of science. Good luck!