Sancho Suite

The Sancho Suite of galaxy mock catalogs consist of \(240,000\) galaxy catalogs in redshift-space scanning across 11 cosmologies, 3 massive neutrino cosmologies, 6 non-Gaussian initial conditions and 11 Halo Occupation Distribution (HOD) model parameters. The average number density of each box is \(n_g \sim 3 \times 10^{-4} \,(h/\textrm{Gpc})\) at \(z=0.5\) and they are generated from the halo catalogs of Quijote simulations, each run with \(512^3\) particles on a \(1\, (\textrm{Gpc}/h)^3\) box. The fiducial HOD model is tailored such that the catalogs mock the CMASS galaxies observed by BOSS.

Organization

The Sancho catalogs are organized in the following way:

\(15,000\) mocks at the fiducial cosmological and HOD parameter values.

\(172,500\) mocks at \(23\) different cosmological/HOD parameter values and \(45,000\) mocks at different amplitudes of different types of non-Gaussian initial conditions. For each cosmology and HOD set of values, there are \(500\) N-body realizations and, for each of these, \(5\) realizations of the HOD are run, making a total of \(2500\) mocks.

Redshift space displacements are computed in the distant observer approximation along each of the axes. There are three different files for each realization/redshift.

Cosmologies and HOD implementation

We vary 5 cosmological parameters, \(\Omega_m\), \(\Omega_b\), \(h\), \(n_s\) and \(\sigma_8\) plus the sum of massive neutrinos \(\sum m_\nu\) and 3 different types of primordial non-Gaussianities, \(f_{\textrm{NL}}^{\textrm{local}}\), \(f_{\textrm{NL}}^{\textrm{equil}}\) and \(f_{\textrm{NL}}^{\textrm{equil}}\), following the same naming and step convention as the rest of the Quijote suite.

The HOD model adopted is as described in Zheng et al and it consists of 5 parameters:

\(M_{\textrm{min}}\) is the lowest mass of a halo that can host any galaxy

\(\sigma_{\log M}\) regulates the central galaxy occupation, which is modeled as a Bernoulli distribution

The satellite galaxy distribution is a Poisson distribution with a mean that depends on three parameters: \(M_0\), \(M_1\), and \(\alpha\).

> The code implementing this HOD algorithm has been developed by Juan Calles and is freely available here .

We summarize all cosmologies and HOD models in the following table:

	Cosmological Parameters									HOD parameters
name	\(\Omega_m\)	\(\Omega_b\)	\(h\)	\(n_s\)	\(\sigma_8\)	\(\sum m_\nu\)	\(f_{\textrm{NL}}^{\textrm{local}}\)	\(f_{\textrm{NL}}^{\textrm{equil}}\)	\(f_{\textrm{NL}}^{\textrm{ortho}}\)	\(\log M_{\textrm{min}}\)	\(\sigma_{\log M}\)	\(\log M_0\)	\(\alpha\)	\(\log M_1\)	realizations
fiducial	0.3175	0.049	0.6711	0.9624	0.834	0	0	0	0	13.0	0.2	13.1	0.75	14.25	15,000
step	0.01	0.002	0.02	0.02	0.015	*	100	100	100	0.025	0.025	0.2	0.2	0.2	500

* As for the mass of neutrinos, \(M_\nu\), there are three steps corresponding to the total mass of neutrinos of 0.1, 0.2, and 0.4 eV.

Access to data

Sancho can be accessed through the dedicated folder in Globus. Folders are organized in the same way as the rest of the Quijote suite: /Cosmology/#realization/files

Inside each of these directories you can find the following products:

Catalogs in Python binary including position, velocity and type (central or galaxy),
Power spectrum measurements including monopole, quadrupole and hexadecapole (see details in the next section),
Bispectrum measurements, for now monopole only, quadrupole coming soon!

The file naming for catalogs have the following structure:

A_HOD_B_NFW_C_1Gpc_z0.50_D_E.npz

where

A: cosmology with the same naming convention as Quijote products (fiducial,Om_p,Om_m,…)
B: HOD set of parameters. ‘fid’ is the fiducial set, and the rest of parameters are named as in previous section, using ‘_m’ and ‘_p’ to indicate steps.
C: ID of HOD realization (from 0 to 4)
D: RSD direction (1:x, 2:y, 3:z)
E: ID of run

Example: Mnu_p_HOD_fid_NFW_sample0_1Gpc_z0.50_RSD3_run0.npz

For power spectrum and bispectrum measurements, files have an additional string ps_sancho and bisp_sancho, respectively, at the beginning of the file name, and the file format is .dat.

Metadata

To access relevant metadata of each catalog, a simple code metadata.py is available at the parent folder of the Sancho suite. Usage:

python metadata.py --cat_file "catalog_file.npz"

The code will output a JSON file with metadata listing cosmology, simulation , HOD and measurements specifications.

How to read catalogs

After download, the catalogs can be used in Python with the following script:

import numpy as np
filename = 'filename.npz'
cat = np.load(filename)
pos = cat['pos']        # shape: (N_galaxies, 3) --> X,Y,Z position of each galaxy in Mpc/h
vel = cat['vel']        # shape: (N_galaxies, 3) --> Vx, Vy, Vz velocity of the galaxy in km/s
gtype = cat['gtype']    # shape: scalar --> Type of galaxy, central: 1, satellite: 0

Power spectrum and Bispectrum

We measure the galaxy redshift power spectrum using the public code PBI4. We use a fourth-order density interpolation and interlacing scheme described in Sefusatti et al. Bins have width of \(\Delta k = 2 k_f\), where \(k_f=0.006 h/Mpc\) is the fundamental frequency of the box, and are computed up to \(k_{\rm max} = 0.3 h/Mpc\).

The structure of the Power spectrum files is:

\(k\,\,\) | \(\,\,k_{\textrm{avg}}\,\,\) | \(\,\,P_0(k)\,\,\) | \(\,\,P_2(k)\,\,\) | \(\,\,P_4(k)\,\,\) | \(\,\,N_{\textrm{modes}}\,\,\)

where \(k_{\textrm{avg}}\) is the value of \(k\) inside a bin averaged over the bin, in units of \(h/Mpc\). \(P_0\), \(P_2\) and \(P_4\) are the monopole, quadrupole and hexadecapole, respectively. The units of the power spectra are \((\textrm{Mpc}/h)^3\). On the third line of each file, you can find two numbers, corresponding to the number of galaxies for this catalog, and the related Poisson shot-noise.

In python, the files can be read as

import numpy as np
filename = 'ps_sancho_fiducial_HOD_fid_NFW_sample0_1Gpc_z0.50_RSD1_run1.dat'
k, avgk, pk,avgP2, avgP4, Nmodes= np.loadtxt(filename, unpack=True)

To get shot-noise:

def getSN(filename):
    f = open(filename)
    fline = f.readline()
    fline = f.readline()
    fline = f.readline()
    psn = float(fline.split(' ')[-1])
    f.close()
    return psn

Using the same binning, we also measure the bispectrum for each galaxy catalog, resulting in 1654 triangles up to \(k_{\textrm{max}} = 0.3 h/\textrm{Mpc}\).

The structure of the Bispectrum files are:

\(\,\,k_1/k_f\,\,\) | \(\,\,k_2/k_f\,\,\) | \(\,\,k_3/k_f\,\,\) | \(\,\,P(k_1)\,\,\) | \(\,\,P(k_2)\,\,\) | \(\,\,P(k_3)\,\,\) | \(\,\,B(k_1,k_2,k_3)\,\,\) | \(\,\,B(k_1,k_2,k_3)+{\textrm{SN}}\,\,\) | \(\,\,N_{\textrm{tr}}\,\,\)

where \({\textrm{SN}} = 1/n^2 + (P(k_1) + P(k_2) + P(k_3)) / n\) is the bispectrum Poisson shot-noise and \(N_{\textrm{tr}}\) is the number of triangles in a give triangle bin.

In python, the files can be read as

import numpy as np

k1, k2, k3, Pk1, Pk2, Pk3, B0, B0+BSN, N_tri= np.loadtxt(filename, unpack=True)

Team

The Sancho Suite of galaxy mock catalogs was developed in 2023 by:

Matteo Biagetti (Area Science Park, Italy)
Juan Calles (PUCV, Chile)
Jacky Yip (UW–Madison, USA)
Emilio Bellini (IFPU, Italy)

If you use data from Sancho, please cite the Yip, Biagetti, Cole, Bellini, Calles, Shiu (2023).