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            = 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≤Mvir≤3×1012M⊙0.7 \leq M_{vir} \leq 3 \times 10^{12} M_\odot (6564 candidates)

  • no halos larger than 7×1013M⊙7 \times 10^{13} M_\odot within 7 Mpc

  • no halos larger than 7×1012M⊙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

104h−3M⊙10^4 h^{-3} M_\odot

104h−3M⊙10^4 h^{-3} M_\odot

Force Softening ϵ\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.

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