radial_profiles.RadialProfile.add_core#

RadialProfile.add_core(r_core, alpha)[source]#

Add a core to the pre-existing profile.

Parameters:

r_core (float) – The core radius in kpc.
alpha (float) – The power-low index inside the exponential.

Notes

add_core is implemented by taking the existing profile \(f(r)\) and altering it such that

\[f'(r) = \left(1-\exp\left(\frac{-r}{r_{core}}\right)^\alpha\right) f(r).\]

This will cause any cuspy profile (i.e. one for which \(\left.\frac{d}{dr} f(r)\right|_{r=0} > 0\) and which grows faster than the exponential term added to instead contain a core and go to 0 in its limit.