Nicole Drakos

Research Blog

Welcome to my Research Blog.

This is mostly meant to document what I am working on for myself, and to communicate with my colleagues. It is likely filled with errors!

This project is maintained by ndrakos

Annihilation Signal Scaling

For edits on my annihilation paper, I have a problem with how I’m rescaling my profiles, so I’m going to record my calculation here.

Rescale profiles

In particular, my annihilation signal is in units \(M_{\rm unit}^2 / r_{\rm unit}^3\), where \(r_{\rm unit}=r_s\) and \(M_{\rm unit}=M(<10 r_s)\) (assuming an NFW profile).

Therefore

\[\dfrac {M_{\rm unit}^2} {r_{\rm unit}^3} = \dfrac {M (10 r_s)^2 } {r_s^3} = \dfrac {M (10 r_s)^2 c^3 } {r_{\rm vir}^3}\]

And then, using \(200 \rho_c = M_{\rm vir} / (4/3 \pi r_{\rm vir}^3)\),

\[\dfrac {M_{\rm unit}^2} {r_{\rm unit}^3} = \dfrac {4\pi \times 200 \rho_c M (10 r_s)^2 c^3 } {3 M_{\rm vir}} = \dfrac{4}{3}\pi \times 200 \rho_c M_{\rm vir} c^3 \left( \dfrac {M(10 r_s)} {M_{\rm vir}} \right)^2\]

Concentration–mass relation

Now I need a way to choose a concentration for a halo of a given mass. I’m going to just assume it lies on the concentration–mass relation. I’ll use one of the Colossus functions. here. I chose the Ishiyama 2021 model, with the \(200\rho_c\) definition.


« Tidal Stripping of NGC 1052-DF2
What information can we get from the dwarf galaxy stellar particles? »