Zooming In

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            = 100zstart               = 127levelmin             = 7levelmin_TF          = 10levelmax             = 14padding              = 7overlap              = 4region               = ellipsoidhipadding            = 1.05region_point_file    = /n/home01/bgriffen/data/caterpillar/ics/lagr/H1079897NRVIR4align_top            = nobaryons              = nouse_2LPT             = nouse_2LLA             = noperiodic_TF          = yes​[cosmology]Omega_m              = 0.3175Omega_L              = 0.6825Omega_b              = 0.049H0                   = 67.11sigma_8              = 0.8344nspec                = 0.9624transfer             = eisenstein​[random]seed[10]              = 34567seed[11]              = 1079897seed[12]              = 2159794seed[13]              = 3239691seed[14]              = 4319588​[output]format               = gadget2_doublefilename             = ./icsgadget_num_files     = 8gadget_spreadcoarse  = yes​[poisson]fft_fine             = yesaccuracy             = 1e-05pre_smooth           = 3post_smooth          = 3smoother             = gslaplace_order        = 6grad_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.

 Snap Scale Factor Redshift Time 0 0.0213 46.0000 0.0535 1 0.0290 33.5029 0.0851 2 0.0367 26.2557 0.1212 3 0.0444 21.5245 0.1613 4 0.0521 18.1929 0.2051 5 0.0598 15.7199 0.2522 6 0.0675 13.8114 0.3025 7 0.0752 12.2940 0.3557 8 0.0829 11.0586 0.4117 9 0.0906 10.0333 0.4704 10 0.0983 9.1687 0.5316 11 0.1060 8.4297 0.5952 12 0.1138 7.7909 0.6612 13 0.1215 7.2331 0.7294 14 0.1292 6.7419 0.7998 15 0.1369 6.3060 0.8723 16 0.1446 5.9166 0.9469 17 0.1523 5.5666 1.0234 18 0.1600 5.2503 1.1018 19 0.1677 4.9630 1.1821 20 0.1754 4.7011 1.2642 21 0.1831 4.4611 1.3481 22 0.1908 4.2406 1.4337 23 0.1985 4.0371 1.5210 24 0.2062 3.8489 1.6098 25 0.2139 3.6742 1.7003 26 0.2216 3.5117 1.7923 27 0.2294 3.3601 1.8858 28 0.2371 3.2184 1.9808 29 0.2448 3.0856 2.0772 30 0.2525 2.9608 2.1749 31 0.2602 2.8435 2.2741 32 0.2679 2.7330 2.3745 33 0.2756 2.6286 2.4762 34 0.2833 2.5299 2.5792 35 0.2910 2.4364 2.6834 36 0.2987 2.3477 2.7888 37 0.3064 2.2635 2.8953 38 0.3141 2.1835 3.0029 39 0.3218 2.1072 3.1116 40 0.3295 2.0346 3.2213 41 0.3372 1.9652 3.3321 42 0.3449 1.8990 3.4438 43 0.3527 1.8356 3.5565 44 0.3604 1.7750 3.6701 45 0.3681 1.7169 3.7846 46 0.3758 1.6612 3.9000 47 0.3835 1.6077 4.0161 48 0.3912 1.5563 4.1331 49 0.3989 1.5069 4.2508 50 0.4066 1.4594 4.3693 51 0.4143 1.4137 4.4884 52 0.4220 1.3696 4.6082 53 0.4297 1.3271 4.7287 54 0.4374 1.2861 4.8497 55 0.4451 1.2465 4.9714 56 0.4528 1.2083 5.0936 57 0.4605 1.1713 5.2163 58 0.4683 1.1356 5.3395 59 0.4760 1.1010 5.4632 60 0.4837 1.0675 5.5873 61 0.4914 1.0351 5.7118 62 0.4991 1.0037 5.8367 63 0.5068 0.9732 5.9620 64 0.5145 0.9437 6.0876 65 0.5222 0.9150 6.2135 66 0.5299 0.8871 6.3396 67 0.5376 0.8601 6.4660 68 0.5453 0.8338 6.5927 69 0.5530 0.8082 6.7195 70 0.5607 0.7834 6.8465 71 0.5684 0.7592 6.9737 72 0.5761 0.7357 7.1010 73 0.5838 0.7128 7.2284 74 0.5916 0.6905 7.3559 75 0.5993 0.6687 7.4835 76 0.6070 0.6475 7.6111 77 0.6147 0.6269 7.7387 78 0.6224 0.6067 7.8663 79 0.6301 0.5871 7.9939 80 0.6378 0.5679 8.1215 81 0.6455 0.5492 8.2490 82 0.6532 0.5309 8.3764 83 0.6609 0.5131 8.5038 84 0.6686 0.4956 8.6310 85 0.6763 0.4786 8.7581 86 0.6840 0.4619 8.8851 87 0.6917 0.4456 9.0119 88 0.6994 0.4297 9.1385 89 0.7072 0.4141 9.2649 90 0.7149 0.3989 9.3912 91 0.7226 0.3840 9.5172 92 0.7303 0.3694 9.6430 93 0.7380 0.3551 9.7685 94 0.7457 0.3410 9.8938 95 0.7534 0.3273 10.0188 96 0.7611 0.3139 10.1436 97 0.7688 0.3007 10.2680 98 0.7765 0.2878 10.3922 99 0.7842 0.2752 10.5160 100 0.7919 0.2627 10.6395 101 0.7996 0.2506 10.7627 102 0.8073 0.2386 10.8855 103 0.8150 0.2269 11.0081 104 0.8228 0.2154 11.1302 105 0.8305 0.2042 11.2520 106 0.8382 0.1931 11.3734 107 0.8459 0.1822 11.4944 108 0.8536 0.1715 11.6151 109 0.8613 0.1611 11.7354 110 0.8690 0.1508 11.8552 111 0.8767 0.1406 11.9747 112 0.8844 0.1307 12.0938 113 0.8921 0.1209 12.2124 114 0.8998 0.1113 12.3307 115 0.9075 0.1019 12.4485 116 0.9152 0.0926 12.5659 117 0.9229 0.0835 12.6828 118 0.9306 0.0745 12.7994 119 0.9383 0.0657 12.9155 120 0.9461 0.0570 13.0311 121 0.9538 0.0485 13.1464 122 0.9615 0.0401 13.2611 123 0.9692 0.0318 13.3755 124 0.9769 0.0237 13.4894 125 0.9846 0.0157 13.6028 126 0.9923 0.0078 13.7158 127 1.0000 0.0000 13.8283

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

 Aquarius Level MUSIC levelmax Effective Resolution ​$10^4 h^{-3} M_\odot$ ​$10^4 h^{-3} M_\odot$ Force Softening $\epsilon$ (pc/h) 1 15 32768^ 3 0.25 0.37 36 2 14 1638 4^3 2 3 76 3 13 8096^3 16 24 152 4 12 4096^3 128 190 228 5 11 2048^3 1025 1527 452

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.

The LX15 run has currently only been run for one of the halos and has been temporarily paused at z = 1. This will be finished with a few others once the main suite has been completed.

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):

 In Gadget LX11 LX12 LX13 LX14 SofteningHalo 0.000610352 0.000305176 0.000152588 0.0000762939 SofteningDisk 0.002441406 0.001220703 0.000610352 0.000305176 SofteningBulge 0.004882813 0.002441406 0.001220703 0.000610352 SofteningStars 0.01953125 0.009765625 0.004882813 0.002441406 SofteningBndry 0.0390625 0.01953125 0.009765625 0.004882813

Temporal Resolution

Timesteps are spaced logarithmically in expansion factor to z = 6, then linearly spaced in expansion factor down to z = 0. Always be aware of this as it could be strength and a weakness of your study.

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

 Geometry Details BA Original MUSIC bounding box (e.g . the exac t boun ding box of lagr volu me). BB 1.2 bounding box extent BC 1.4 bounding box extent BD 1.6 bounding box extent CA Convex Hull Volume EA Original MUSIC Ellipsoid (e.g . the exact bounding box of Lagrangian volume). EB 1.1 padding EC 1.2 padding EX 1.05 padding

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.