elucid 0.0.2

Exploring the local Universe with reconstructed initial density field

ELUCID - Exploring the Local Universe with reConstructed Initial Density field

This repository contains usage for the data products of the ELUCID project. For a complete description of the method and the simulation, see Huiyuan Wang et al. 2016 (ApJ 831, 164; Paper-III).

About the project

What we have done?

A method we developed for the reconstruction of the initial density field is applied to SDSS DR7 (North Cap, redshift $\approx 0 - 0.12$ ). A high-resolution N-body constrained simulation (CS; with $3072^3$ particles in a $500\ h^{-1}{\rm Mpc}$ box) is performed to evolve the reconstructed initial condition and recover the evolution history of the local Universe. Statistical properties of cosmic web and halo populations are found to be accurately reproduced by the CS.

Example usages of the constrained simulation

Robust quantification of the environments within which the observed galaxies reside

• Huiyuan Wang et al. 2018 (ApJ 852, 31; Paper-IV, galaxy quenching versus environment).

Input fields, halos and merger trees for galaxy formation models (hydrodynamical, semi-analytical or empirical)

• Xiaohu Yang et al. 2018 (ApJ 860, 30; Paper-V, neighborhood abundance matching);
• Renjie Li et al. 2022 (ApJ 936, 11; Paper-VII, hydro for Coma, SDSS Great Wall, and a void);
• Xiong Luo et al. 2024 (ApJ 966, 236; Paper-VIII, hydro for Coma with variants for feedback models).

Cosmic variance (CV)-free statistics of observed galaxies (even for a small sample)

• Yangyao Chen et al. 2019 (ApJ 872, 180; Paper-VI, CV-free galaxy luminosity and stellar mass functions);
• Ziwen Zhang et al. 2025 (Nature 642, 47--52; CV-free clustering measurements for SDSS dwarfs).

Tutorial

To use the data products, please refer to the specification given below for the details of the data formats.

Code samples are also provided to demonstrate how to read the data and process them to produce quantities often used in publications.

• load_trees.ipynb: load merger trees, find main branches, evaluate formation times.

Specification of the data products

List of data products

• The density field at $z \approx 0$ recovered from SDSS DR7 (North Cap, $z \approx 0-0.12$) with the Halo-Domain method (hereafter Halo-Domain Field).
• The reconstructed initial density field at $z = z_{\rm ini}=100$ with an HMCMC method (hereafter Reconstructed Initial Field).
• The snapshots (dark-matter particles) of the constrained simulation (CS) at various redshifts (here after CS snapshots).
• The catalogs of FoF halos and Subfind subhalos identified from the CS snapshots (hereafter CS halo/subhalo catalogs).
• The SubLink subhalo merger trees that links subhalos across different snapshots (hereafter CS subhalo merger trees).

Cosmology: the project is performed in a flat $\Lambda$-CDM cosmology with parameters consistent with the WMAP5 results (Dunkley et al. 2009): $\Omega_{\rm K,0}=0$, $\Omega_{\rm M,0}=0.258$, $\Omega_{\rm B,0}=0.044$, $\Omega_{\rm \Lambda, 0}=0.742$, $H_0 = 100\ h\ {\rm km\ s^{-1}\ Mpc^{-1}}$ with $h=0.72$, and a spectral index of $n=0.96$ with an amplitude specified by $\sigma_8=0.80$ for the Gaussian initial density field.

Configuration of the CS:

Property	value	explanation
$N_{\rm snapshot}$	101	Number of snapshots. Note that the last two snapshots are redundant -- just ignore the last one.
$N_{\rm chunks}$	2048	Number of files into which each snapshot are stored
$L_{\rm box}$	$500.0\ h^{-1}{\rm Mpc}$	Side length of the periodic cubic box
$N_{\rm cell, all}$	16777216	Number of space-filling (Peano-Hilbert) cells (i.e. $256^3$) used partition the simulation box
$N_{\rm p, all}$	28991029248	Total number of dark matter particles (i.e. $3072^3$) in a snapshot
$m_{\rm p}$	0.03087502	Mass (in $10^{10}\ h^{-1}\ M_\odot$) of each dark matter particle
$N_{\rm bit\ mask}$	36	Number of bits used to store the particle IDs
$\epsilon_{\rm DM}$	$3.5\ h^{-1}{\rm ckpc}$	Gravitational softening length (comoving)

Available snapshots of the CS: A total of 100 snapshots, from redshift $z=18.4$ to $0$, are output. Here we list the available snapshots ($s$) and the corresponding redshifts ($z$).

s	z	s	z	s	z	s	z	s	z
0	18.409561	20	9.661436	40	4.856104	60	2.216634	80	0.766834
1	17.837003	21	9.346719	41	4.683271	61	2.121703	81	0.714689
2	17.280867	22	9.041370	42	4.515537	62	2.029569	82	0.664085
3	16.741506	23	8.745069	43	4.352746	63	1.940156	83	0.614971
4	16.217927	24	8.457427	44	4.194778	64	1.853385	84	0.567310
5	15.709555	25	8.178270	45	4.041466	65	1.769170	85	0.521054
6	15.216655	26	7.907416	46	3.892679	66	1.687450	86	0.476161
7	14.737870	27	7.644537	47	3.748270	67	1.608133	87	0.432595
8	14.273472	28	7.389403	48	3.608146	68	1.531159	88	0.390316
9	13.822720	29	7.141798	49	3.472132	69	1.456453	89	0.349284
10	13.385178	30	6.901516	50	3.340146	70	1.383961	90	0.309461
11	12.960631	31	6.668300	51	3.212051	71	1.313599	91	0.270816
12	12.548667	32	6.442027	52	3.087756	72	1.245319	92	0.233310
13	12.148725	33	6.222355	53	2.967105	73	1.179053	93	0.196911
14	11.760799	34	6.009231	54	2.850019	74	1.114742	94	0.161586
15	11.384054	35	5.802351	55	2.736404	75	1.052330	95	0.127304
16	11.018653	36	5.601575	56	2.626131	76	0.991758	96	0.094034
17	10.663984	37	5.406766	57	2.519107	77	0.932976	97	0.061746
18	10.319644	38	5.217668	58	2.415254	78	0.875930	98	0.030411
19	9.985631	39	5.034165	59	2.314452	79	0.820565	99	0.000000

The coordinate system

The Halo-Domain Field is reconstructed from SDSS. For the CS to be run from the field, the SDSS survey volume is embedded into a cubic box. Thus, all of data products are given in the simulation frame, unless specifically clarified.

The Cartesian coordinates in the observation frame (J2000; hereafter denoted with a subscript J2000) and in the simulation frame (hereafter denoted with a subscript sim) are related through a translation along $\vec{x}_0$ and a rotation in the $x$-$y$ plane:

$$\vec{x}{\rm J2000} = \mathcal{R} (\vec{x}{\rm sim} - \vec{x}_{\rm 0})\ ,$$

where the translation vector $\vec{x}_{\rm 0} = (370, 370, 30)\ h^{-1} {\rm Mpc}$, the rotation matrix

$$ \mathcal{R} = \begin{pmatrix} {\rm cos}(\phi_0) & {\rm sin}(\phi_0) & 0 \ {\rm cos}(\phi_0 + \frac{\pi}{2}) & {\rm sin}(\phi_0 + \frac{\pi}{2}) & 0 \ 0 & 0 & 1 \end{pmatrix} , $$

and the rotation angle $\phi_0 = 39^{\circ}$.

The transformation is illustrated in the following figure:

Note that

• The Cartesian coordinates in the sim frame is defined so that one corner of the cubic box is at the origin, and three sides of the box are along the Cartesian axes. This means all coordinates in the sim frame are in the range of $[0, 500]\ h^{-1}{\rm Mpc}$.
• The Cartesian coordinates in the J2k frame is defined so that the $+x$ axis points to RA=0, Dec=0, the $+y$ axis points to RA=90 deg, Dec=0, and the $+z$ axis points to Dec=90 deg. This means $\vec{x}_{\rm J2000} = d_{\rm c} \left( \cos {\rm Dec} \cdot \cos {\rm RA}, \cos {\rm Dec} \cdot \sin {\rm RA}, \sin {\rm Dec} \right)$ for a galaxy at comoving distance $d_{\rm c}$, right ascension RA and declination Dec.
• Rotation matrix ${\bf R}$ is orthogonal (i.e. ${\bf R}^{-1} = {\bf R}^{\rm T}$ can be used to transform from J2000 back to sim coordinates).
• Vectors and tensors can also be transformed. For example, the velocity vector is transformed as $\vec{v}_{\rm J2000} = \mathcal{R} \vec{v}_{\rm sim}$.