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Cylindrical cosmological simulations with StePS

Overview

The global topology of the Universe can affect the long‑range gravitational forces through the boundary conditions. To study non-trivial topologies in detail, simulations that natively adopt such geometries are required. In this project, we introduce a compactified simulation framework that is only periodic along a single axis, while having infinite topology with isotropic boundary conditions towards the perpendicular directions. This non-trivial $S^1\times\mathbb{R}^2$ topological manifold has cylindrical symmetry, and the Lagrangian of a self-gravitating particle system in this space is invariant under translation along the cylinder’s axis. As a consequence of Noether’s theorem, the linear momentum along the cylinder’s axis and the angular momentum along the same axis are both conserved. Such a topology is particularly well-suited for studying naturally anisotropic environments such as filamentary structures.

Main simulation

To demonstrate the new simulation method, we run a new cosmological $N$-body simulation with our StePS simulation code in $S^1\times\mathbb{R}^2$ topology. We used best-fit Planck 2018 $\Lambda$CDM cosmological parameters, and a 2LPT method to generate the initial conditions of a periodic cylinder with height $L_{z} = 1.0\,\mathrm{Gpc}$, resolved radius $R_{\mathrm{sim}}= 500\,\mathrm{Mpc}$, and $N_{p} = 2.4 \cdot 10^7$ dark matter particles. The generated particle snapshots, halo catalogues, power spectra, and example notebooks can be downloaded from here.

Snapshots

These files are the primary output of the Simulation. They are in GAGDET-compatible HDF5 format, and containing particle positions, velocities, masses, and IDs. Overall 138 snapshots were saved during the simulation. These can be visualized with gadgetviewer or topsy.

Uncompressed size: 1.5 GB / snapshot

Mirrors

  • ELTE Kooplex: TBA
  • helsinkifi-my.sharepoint.com (only 4 snapshots): Download

Power spectra

The isotropic $P(k)$ power spectrum of the dark matter density field is a standard statistic used to quantify the clustering. We estimated the power spectra from particle snapshots using the Feldman–Kaiser–Peacock (FKP) method.

Mirrors

  • ELTE Kooplex: TBA
  • helsinkifi-my.sharepoint.com: Download

Halo Catalogues

These files contain all available information about the identified haloes. The haloes were identified with our own StePS_HF Spherical Overdensity (SO) halo finder code. Two formats are available to download:

  1. ASCII — one halo per row (click to expand)

    Identity and basics

    Halo identification and fundamental properties.

    Column indexFieldDescription
    1 ID Unique halo identifier
    2 Npart Number of particles
    3 VolResolved Volume-resolved flag
    4 Mvir Virial mass

    Virial sphere

    Properties measured within the virial radius. Also contains \(V_{\rm Max}\) and the Klypin scale radius, which are unique to this group.

    Column indexFieldDescription
    5 X Position X
    6 Y Position Y
    7 Z Position Z
    8 Rvir Virial radius
    9 Vvir_X Velocity X
    10 Vvir_Y Velocity Y
    11 Vvir_Z Velocity Z
    12 VRMSvir RMS velocity dispersion
    13 Vcircvir Circular velocity
    14 VMax Maximum circular velocity
    15 Rs_klypin Scale radius (Klypin definition)
    16 Jvir_X Angular momentum X
    17 Jvir_Y Angular momentum Y
    18 Jvir_Z Angular momentum Z
    19 Spin_Bullock Spin parameter (Bullock et al.)

    200b

    Properties within R200b — radius enclosing mean density 200 times the background density.

    Column indexFieldDescription
    20 M200b Mass
    21 R200b Radius
    22 V200b_X Velocity X
    23 V200b_Y Velocity Y
    24 V200b_Z Velocity Z
    25 VRMS200b RMS velocity dispersion
    26 Vcirc200b Circular velocity
    27 J200b_X Angular momentum X
    28 J200b_Y Angular momentum Y
    29 J200b_Z Angular momentum Z

    200c

    Properties within R200c — radius enclosing mean density 200 times the critical density.

    Column indexFieldDescription
    30 M200c Mass
    31 R200c Radius
    32 V200c_X Velocity X
    33 V200c_Y Velocity Y
    34 V200c_Z Velocity Z
    35 VRMS200c RMS velocity dispersion
    36 Vcirc200c Circular velocity
    37 J200c_X Angular momentum X
    38 J200c_Y Angular momentum Y
    39 J200c_Z Angular momentum Z

    500c

    Properties within R500c — radius enclosing mean density 500 times the critical density.

    Column indexFieldDescription
    40 M500c Mass
    41 R500c Radius
    42 V500c_X Velocity X
    43 V500c_Y Velocity Y
    44 V500c_Z Velocity Z
    45 VRMS500c RMS velocity dispersion
    46 Vcirc500c Circular velocity
    47 J500c_X Angular momentum X
    48 J500c_Y Angular momentum Y
    49 J500c_Z Angular momentum Z

    1000c

    Properties within R1000c — radius enclosing mean density 1000 times the critical density.

    Column indexFieldDescription
    50 M1000c Mass
    51 R1000c Radius
    52 V1000c_X Velocity X
    53 V1000c_Y Velocity Y
    54 V1000c_Z Velocity Z
    55 VRMS1000c RMS velocity dispersion
    56 Vcirc1000c Circular velocity
    57 J1000c_X Angular momentum X
    58 J1000c_Y Angular momentum Y
    59 J1000c_Z Angular momentum Z

    2500c

    Properties within R2500c — radius enclosing mean density 2500 times the critical density.

    Column indexFieldDescription
    60 M2500c Mass
    61 R2500c Radius
    62 V2500c_X Velocity X
    63 V2500c_Y Velocity Y
    64 V2500c_Z Velocity Z
    65 VRMS2500c RMS velocity dispersion
    66 Vcirc2500c Circular velocity
    67 J2500c_X Angular momentum X
    68 J2500c_Y Angular momentum Y
    69 J2500c_Z Angular momentum Z
  2. Binary HDF5 — containing the same information as the ASCII catalogues, plus particle data (IDs, coordinates, velocities, masses) within \(r < 1.5\cdot R_{\mathrm{vir}}\).

Mirrors

  • ELTE Kooplex (ASCII): TBA
  • ELTE Kooplex (HDF5 + particles): TBA
  • helsinkifi-my.sharepoint.com (ASCII): Download
  • helsinkifi-my.sharepoint.com (HDF5 + particles): Download

Notebooks:

These jupyter notebooks contain examples of how to load, visualise, and analyse the provided simulation data.

Mirrors

  • helsinkifi-my.sharepoint.com: Download

Companion simulations

These $S^1\times\mathbb{R}^2$ simulations were run with the same code and cosmological parameters as the simulation above, but with lower resolution and in smaller volumes. The purpose of these is to test analysis pipelines on much smaller datasets in $S^1\times\mathbb{R}^2$ topological manifold. The compressed files contain the initial conditions, the particle snapshots, the estimated power spectra, and the SO halo catalogues.

Run \(R_{\mathrm{sim}}\) \(L_{z}\) \(N_{p}\) Uncompressed Size Download
Small #1 \(750\,\mathrm{Mpc}\) \(50.0\,\mathrm{Mpc}\) \(5.0\cdot10^5\) 441 MB Download
Small #2 \(750\,\mathrm{Mpc}\) \(100.0\,\mathrm{Mpc}\) \(1.0\cdot10^6\) 840 MB Download
Small #3 \(750\,\mathrm{Mpc}\) \(200.0\,\mathrm{Mpc}\) \(2.0\cdot10^6\) 1730 MB Download

Particle mass range (all companion runs):
$M_{p} = 1.89 \cdot 10^{11}\,\mathrm{M_\odot} - 1.85 \cdot 10^{14}\,\mathrm{M_\odot}$.