Each simulation folder has a configuration file for MUSIC (e.g. H1079897_EX_Z127_P7_LN7_LX14_O4_NV4.conf) which was used to construct the initial conditions.

There are a few things to note about the zoom-in parameter files when compared to the parent volume parameter file. First is we now specify a region_point_file which defines the x,y,z (normalized to the box width) of the particles to be re-sampled. We have added the parameter hipadding which our own modification to allow for expanded regions. 1.05, for example, represents an expanded ellipsoid (by 5%). See Section 2.3 of Griffen et al. (2015) for a more detailed description of these geometries and their impact on contamination.

We also draw the reader’s attention to the seed values. Note that we do not set the seed values for any level lower than the parent volume (10) which makes MUSIC smooth out any levels lower than 10. The seed values at 11 are simply the halo numbers and then each level higher scales by a factor of 2 of this original number. This was required because the ICs were generated through our automatic pipeline and each simulation needs unique values to seed the random noise field. The levelmin_TF is also set to be the same as the parent volume (10). The padding and overlap parameters are the same for all simulations.

MUSIC Parameter File

# H1079897_EX_Z127_P7_LN7_LX14_O4_NV4.conf
[setup]
boxlength            = 100
zstart               = 127
levelmin             = 7
levelmin_TF          = 10
levelmax             = 14
padding              = 7
overlap              = 4
region               = ellipsoid
hipadding            = 1.05
region_point_file    = /n/home01/bgriffen/data/caterpillar/ics/lagr/H1079897NRVIR4
align_top            = no
baryons              = no
use_2LPT             = no
use_2LLA             = no
periodic_TF          = yes
​
[cosmology]
Omega_m              = 0.3175
Omega_L              = 0.6825
Omega_b              = 0.049
H0                   = 67.11
sigma_8              = 0.8344
nspec                = 0.9624
transfer             = eisenstein
​
[random]
seed[10]              = 34567
seed[11]              = 1079897
seed[12]              = 2159794
seed[13]              = 3239691
seed[14]              = 4319588
​
[output]
format               = gadget2_double
filename             = ./ics
gadget_num_files     = 8
gadget_spreadcoarse  = yes
​
[poisson]
fft_fine             = yes
accuracy             = 1e-05
pre_smooth           = 3
post_smooth          = 3
smoother             = gs
laplace_order        = 6
grad_order           = 6

Halo Selection

We selected halos with the following environmental requirements:

• halos mass between $0.7 \leq M_{vir} \leq 3 \times 10^{12} M_\odot$ (6564 candidates)

• no halos larger than $7 \times 10^{13} M_\odot$ within 7 Mpc

• no halos larger than $7 \times 10^{12} M_\odot$ within 2.8 Mpc (2122 candidates)

This is roughly in line with Tollerud et al. (2012), Boylan-Kolchin et al. (2013), Fardal et al. (2013), Pfiffel et al. (2013), Li & White (2008), van der Marel et al. (2012), Karachentsev et al. (2004) and Tikhonov & Klypin (2009). This avoids Milky Way-sized systems near clusters but does not make them overly isolated necessarily. Halos were also selected to not be preferentially near the very edge of the simulation volume as a matter of convenience. The first 24 Caterpillar halos are highlighted within the parent volume below.

Temporal Resolution

The time steps were set to be log of the expansion factor, following a similar convention to that used by the Millenium and Millenium-II simulations. The following table shows the various measures for time/size at each snapshot.

Be sure to use the halo utility module (haloutils) in Python for quickly getting the temporal quantity for a given snapshot. See data access for more information.

The majority of the information about the zoom-in runs can be found in Griffen et al. (2016). Here we simply outline some details which were left out of the publication for the sake of brevity.

Resolution Levels

Each panel represents one single realization of the Cat-1 halo at different resolutions. The far left is an LX11 run and the far right is an LX14 run.

We have complete (modified) ROCKSTAR halo catalogues (together with consistent-trees merger trees) and z = 0 SUBFIND catalogues.

Force Softening

Softening was 1/80th the inter-particle separation. We adopt the formula: boxwidth/lx^2/80 but stagger the force softening for each higher level as 4 x base, 8 x base, 32 x base, 64 x base where base is the base force softening. For each of the zooms, this equates to (units of Mpc/h):

Temporal Resolution

This image shows the difference between the time step resolutions used in Caterpillar and those used in the Aquarius simulation. We wanted higher resolution at all redshifts for many purposes. At z > 6 we wanted to model Lyman-Werner radiation which requires timesteps of order the lifespan of Population III star formation. At low redshift we wanted timesteps of roughly 50-60 Myrs which is the disruption time scale of many small dwarf galaxies of the Milky Way. This also allows detailed modelling of the pericentric passages of infalling satellite systems, which is a crucial parameter for determining post-infall mass loss, for example.

Contamination Study

A number of contamination studies have been carried out. This involves changing the Lagrangian geometry in some way to keep the contamination (distance to the nearest particle type 2 as far as possible) low whilst conserving CPU hours. Our selected test geometries were as follows

We did this for both 4 and 5 times the virial radius at z = 0 (marked by the letter 4 or 5 at the end of the abbreviated geometry). Making a total of ~18 test halos per Caterpillar halo. Our requirement was that there was no contamination (particle type 2) within 1 Mpc of the host at the LX11 level.

We also looked at how the geometry of the Lagrangian volume affected the contamination radius. As outlined in Griffen et al. (2015), we did not find any correlation with geometry and overall level contamination. Every simulation requires its own tailored geometry to achieve our contamination requirements.

The size of the Lagrangian volumes were also another challenge to overcome. If a halo had LX11 ICs which were larger than 300mb, we found that we could not run these at LX14 on national facilities. The size and distance became our two biggest obstacles when running the Caterpillar suite.

Our ROCKSTAR catalogues only use the high-resolution particles. This means that there will be halos in the outskirts of the simulation which are contaminated. These are shown clearly below. Be sure not to just take all halos within the ROCKSTAR catalogues as some of them will be contaminated (underestimated masses, wrong profiles etc.). As a safety, one should only take halos which are within the contamination distance. This changes as a function of redshift so make sure you update your cut for each snapshot. The plots below are for z = 0.