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
For Bradley’s paper, we want one “realistic” example. So I’m going to set up a simulation for the ultra diffuse galaxy NGC 1052-DF2, guided by the model in Ogiya et al. 2022.
They found that this UDGF was better described by a cored dark matter profile. This was created by modifying an NFW profile (with \(M_{200} = 6 \times 10^{10} M_{\odot}\). \(c = 6.6\), \(z=1.5\)). This corresponds to \(r_s=12.24\) kpc, \(r_{vir} = 80.76\) kpc.
The stellar component was modelled using a Sérsic profile with a stellar mass of \(M_* = 2 \times 10^8 M_{\odot}\), a Sérsic index of \(n=1\), and effective radius of \(R_e = 1.25\) kpc.
For our case, we want to use a double alpha profile (for simplicity).
The stellar component was created with the same total mass and \(\alpha\) parameter. The scale radius was found from finding the peak in \(\log_{10} r^2 \rho\). This corresponds to \(\alpha = 0.44\), \(r_s = 1.10\), and \(\rho_0 = 3.07\times 10^7\).
Our dark matter halo was created with the same scale radius, alpha parameter and virial mass, \(r_s = 6.91\), \(M (6.6 r_s) = 6 \times 10^{10} M_{\odot}\), \(\alpha=0\). This corresponds to \(\rho_0 = 6.62 \times 10^7\), and \(M_{\rm tot} = 9.15 \times 10^{10}\).
Here is a comparison of the model in Ogiya et al. to our model:
The Ogiya et al. 2022 paper uses a time-varying NFW potential, and the merger happens from \(z=1.5\) to \(z=0\). I will take the host properties at \(z=0\): \(M_{200}=1.1 \times 10^{13} M_{\odot}\), \(c=6.8\).
Using the critical density in a Plank cosmology at redshift 0, this corresponds to \(r_{\rm vir} = 458.76\) kpc, and \(r_s = 67.46\) kpc
Ogiya et al. 2022 uses orbital parameters \(x_c = r_c(E)/r_{200} = 1\), and \(\eta = L/L_c(E) = 0.3\)
If will use an infall radius and velocity of \(458.73\) kpc and \(61.85\) km/s. This corresponds to \(x_c = 1.39\) and \(\eta=0.3\).
Going back to my unit system of \(M_{ sat}=1\), \(G=1\), \(r_{1}=1\), I can put this together as:
alpha1 =0.44
alpha2 = 0.0
r1 = 1.0
r2 = 11.12
M2divM1 = 457.5
NFW_Mvir = 120.22
NFW_C = 6.8
SAT_C = 84.5
r_orb = 417.03
v_orb = 0.10
This corresponds to an orbital period of \(1950 t_{ unit }\). This is about 10x slower than the other orbits I have looked at, so this might take a while to run.