Tidal Stripping of NGC 1052-DF2

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.

Subhalo Model

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:

Host 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

Orbit

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 $\eta=0.3$.

Units

Going back to my unit system of $M_{ sat}=1$, $G=1$, $r_{1}=1$, I can put this together as:

IC parameters

alpha1 =0.44
alpha2 = 0.0
r1 = 1.0
r2 = 11.12
M2divM1 = 457.5

Host potential parameters

NFW_Mvir = 120.22
NFW_C = 6.8
SAT_C = 84.5

Orbit parameters

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.

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