Uchuu Mock VLIM M★ — Run Summary

Uchuu N-body mock catalogues are matched to the BGS VLIM M★ samples by density, redshift range, and stellar-mass threshold. The summary statistics are computed with measure_MOCK_VLIM_Mstar.ipynb.

Cosmology: Planck18 (H₀ = 67.4, Ω_m = 0.315)

Survey footprint: 1/8 sky, RA ∈ [180°, 270°], Dec ∈ [−90°, 0°], area = 5 156.6 deg².

Redshift column: redshift_S (spectroscopic-like). Stellar mass column: log₁₀(obs_sm) (SHAM-assigned masses). Weights: uniform (no systematic correction).

Note

All samples use 100 jackknife regions (N_JK=100). Random catalogues are subsampled to 5 × N_gal before pair counting to keep corrfunc tree overhead manageable for small-volume samples.

Sample inventory

Sample key	N_gal	z_min	z_max	log₁₀M★_min	N_JK
MOCK_VLIM_ANY_Mstar9.29_z0.05-0.08	155 846	0.05	0.08	9.29	100
MOCK_VLIM_ANY_Mstar9.78_z0.05-0.12	408 958	0.05	0.12	9.78	100
MOCK_VLIM_ANY_Mstar10.24_z0.05-0.18	781 950	0.05	0.18	10.24	100
MOCK_VLIM_ANY_Mstar10.45_z0.05-0.22	936 461	0.05	0.22	10.45	100
MOCK_VLIM_ANY_Mstar10.65_z0.05-0.26	923 373	0.05	0.26	10.65	100
MOCK_VLIM_ANY_Mstar10.84_z0.05-0.31	793 669	0.05	0.31	10.84	100
MOCK_VLIM_ANY_Mstar11.03_z0.05-0.35	460 808	0.05	0.35	11.03	100
MOCK_VLIM_ANY_Mstar11.22_z0.05-0.35	157 946	0.05	0.35	11.22	100
MOCK_VLIM_ANY_Mstar11.39_z0.05-0.35	50 067	0.05	0.35	11.39	100

Output files

data/mocks/
├── twopcf/{key}-wtheta.h5          w(θ)   — Landy–Szalay, TreeCorr variance
├── twopcf/{key}-wp-pimax100.h5     wp(rp) — Landy–Szalay, TreeCorr variance
├── lf_smf/{key}-smf-vmax.h5        SMF    — 1/Vmax, jackknife covariance
└── joint/{key}-joint_smf_wp.h5     Joint SMF + wp, full jackknife covariance

Sample characterisation

Figures below are produced by make_mocks and show the match between the BGS observation (blue) and the Uchuu mock (orange). All 9 samples are now characterised.

M★ ≥ 9.29 (N = 155 846, z < 0.08)

Sky footprint of mock M*≥9.29 — Sky footprint (RA/Dec) of the M★≥9.29 mock.

Redshift and mass distributions M*≥9.29 — Redshift (left) and stellar-mass (right) distributions for the M★≥9.29 mock.

z-M* plane M*≥9.29 — Stellar-mass vs. redshift plane for the M★≥9.29 mock and the corresponding BGS sample.

M★ ≥ 9.78 (N = 408 958, z < 0.12)

Sky footprint of mock M*≥9.78 — Sky footprint (RA/Dec) of the M★≥9.78 mock.

Redshift and mass distributions M*≥9.78 — Redshift (left) and stellar-mass (right) distributions for the M★≥9.78 mock.

z-M* plane M*≥9.78 — Stellar-mass vs. redshift plane for the M★≥9.78 mock and the corresponding BGS sample.

M★ ≥ 10.24 (N = 781 950, z < 0.18)

Sky footprint of mock M*≥10.24 — Sky footprint (RA/Dec) of the M★≥10.24 mock. The mock covers the southern Galactic octant (RA ∈ [180°, 270°], Dec < 0°).

Redshift and mass distributions M*≥10.24 — Redshift (left) and stellar-mass (right) distributions for the M★≥10.24 mock. Density is matched to within 0.001% of the observed value.

z-M* plane M*≥10.24 — Stellar-mass vs. redshift plane for the M★≥10.24 mock and the corresponding BGS sample.

M★ ≥ 10.45 (N = 936 461, z < 0.22)

Sky footprint of mock M*≥10.45 — Sky footprint (RA/Dec) of the M★≥10.45 mock.

Redshift and mass distributions M*≥10.45 — Redshift (left) and stellar-mass (right) distributions for the M★≥10.45 mock.

z-M* plane M*≥10.45 — Stellar-mass vs. redshift plane for the M★≥10.45 mock and the corresponding BGS sample.

M★ ≥ 10.65 (N = 923 373, z < 0.26)

Sky footprint of mock M*≥10.65 — Sky footprint (RA/Dec) of the M★≥10.65 mock.

Redshift and mass distributions M*≥10.65 — Redshift (left) and stellar-mass (right) distributions for the M★≥10.65 mock.

z-M* plane M*≥10.65 — Stellar-mass vs. redshift plane for the M★≥10.65 mock and the corresponding BGS sample.

M★ ≥ 10.84 (N = 793 669, z < 0.31)

Sky footprint of mock M*≥10.84 — Sky footprint (RA/Dec) of the M★≥10.84 mock.

Redshift and mass distributions M*≥10.84 — Redshift (left) and stellar-mass (right) distributions for the M★≥10.84 mock.

z-M* plane M*≥10.84 — Stellar-mass vs. redshift plane for the M★≥10.84 mock and the corresponding BGS sample.

M★ ≥ 11.03 (N = 460 808, z < 0.35)

Sky footprint of mock M*≥11.03 — Sky footprint (RA/Dec) of the M★≥11.03 mock.

Redshift and mass distributions M*≥11.03 — Redshift (left) and stellar-mass (right) distributions for the M★≥11.03 mock.

z-M* plane M*≥11.03 — Stellar-mass vs. redshift plane for the M★≥11.03 mock and the corresponding BGS sample.

M★ ≥ 11.22 (N = 157 946, z < 0.35)

Sky footprint of mock M*≥11.22 — Sky footprint (RA/Dec) of the M★≥11.22 mock.

Redshift and mass distributions M*≥11.22 — Redshift (left) and stellar-mass (right) distributions for the M★≥11.22 mock.

z-M* plane M*≥11.22 — Stellar-mass vs. redshift plane for the M★≥11.22 mock and the corresponding BGS sample.

M★ ≥ 11.39 (N = 50 067, z < 0.35)

Sky footprint of mock M*≥11.39 — Sky footprint (RA/Dec) of the M★≥11.39 mock.

Redshift and mass distributions M*≥11.39 — Redshift (left) and stellar-mass (right) distributions for the M★≥11.39 mock.

z-M* plane M*≥11.39 — Stellar-mass vs. redshift plane for the M★≥11.39 mock and the corresponding BGS sample.

Stellar mass function

Mock SMF overlay — Stellar mass function φ(M★) for all 9 Uchuu mock VLIM samples, estimated with the 1/Vmax method (coloured markers with jackknife errors). The cosmological area (5 156.6 deg²) is used for normalisation. Literature references overlaid as dashed/dotted lines: Baldry+2012 GAMA I, Driver+2022 GAMA DR4, Moustakas+2013 PRIMUS z<0.2, Xu+2025 DESI PAC (shaded band). See Literature Benchmarks for provenance.

SMF key values at the lowest complete stellar mass bin:

Sample	log₁₀M★_min	z_max	log₁₀M★_ref [dex]	φ [Mpc⁻³ dex⁻¹]
MOCK_VLIM_ANY_Mstar9.29	9.29	0.08	9.38	7.00 × 10⁻³ ± 1.6 × 10⁻⁴
MOCK_VLIM_ANY_Mstar9.78	9.78	0.12	9.88	5.53 × 10⁻³ ± 9.2 × 10⁻⁵
MOCK_VLIM_ANY_Mstar10.24	10.24	0.18	10.12	1.92 × 10⁻⁴ ± 2.9 × 10⁻⁶
MOCK_VLIM_ANY_Mstar10.45	10.45	0.22	10.38	8.67 × 10⁻⁴ ± 1.1 × 10⁻⁵
MOCK_VLIM_ANY_Mstar10.65	10.65	0.26	10.62	1.56 × 10⁻³ ± 1.6 × 10⁻⁵
MOCK_VLIM_ANY_Mstar10.84	10.84	0.31	10.88	1.51 × 10⁻³ ± 1.3 × 10⁻⁵
MOCK_VLIM_ANY_Mstar11.03	11.03	0.35	11.12	8.84 × 10⁻⁴ ± 9.2 × 10⁻⁶
MOCK_VLIM_ANY_Mstar11.22	11.22	0.35	11.12	7.88 × 10⁻⁵ ± 8.9 × 10⁻⁷
MOCK_VLIM_ANY_Mstar11.39	11.39	0.35	11.38	7.38 × 10⁻⁵ ± 9.2 × 10⁻⁷

Angular correlation function w(θ)

Mock w(theta) overlay — Angular two-point correlation function w(θ) for all 9 mock samples, measured with the Landy–Szalay estimator. Error bars are TreeCorr variance estimates. Bins: 30 log-spaced bins in [0.01, 60] arcmin.

Projected correlation function w_p(r_p)

Mock wp overlay — Projected correlation function w_p(r_p) for all 9 mock samples (π_max = 100 Mpc), measured with Corrfunc Landy–Szalay. Error bars are jackknife uncertainties from the joint covariance. Bins: 30 log-spaced bins in [0.01, 60] Mpc.

Representative w_p(r_p) values at r_p = 1 Mpc and 10 Mpc (from the joint covariance files, uniform weights):

Sample	log₁₀M★_min	w_p(1 Mpc) [Mpc]	w_p(10 Mpc) [Mpc]
MOCK_VLIM_ANY_Mstar9.29	9.29	164.8 ± 20.5	19.0 ± 14.1
MOCK_VLIM_ANY_Mstar9.78	9.78	201.4 ± 15.7	26.4 ± 11.8
MOCK_VLIM_ANY_Mstar10.24	10.24	222.6 ± 10.5	29.6 ± 7.8
MOCK_VLIM_ANY_Mstar10.45	10.45	238.6 ± 8.4	32.9 ± 7.3
MOCK_VLIM_ANY_Mstar10.65	10.65	255.1 ± 7.2	34.5 ± 5.2
MOCK_VLIM_ANY_Mstar10.84	10.84	274.8 ± 8.3	36.5 ± 6.7
MOCK_VLIM_ANY_Mstar11.03	11.03	317.4 ± 6.8	40.7 ± 3.9
MOCK_VLIM_ANY_Mstar11.22	11.22	395.7 ± 11.8	49.5 ± 4.4
MOCK_VLIM_ANY_Mstar11.39	11.39	571.4 ± 40.7	65.1 ± 6.6

Joint SMF + w_p covariance

The joint covariance matrix is estimated with 100-region spatial jackknife resampling. The data vector is \(\mathbf{d} = [\phi_1,\ldots,\phi_{N_\mathrm{SMF}},\, w_p^1,\ldots,w_p^{N_{w_p}}]\).

Mock joint correlation matrices — Pearson correlation matrices of the joint SMF + w_p data vector for all 9 mock samples. The dashed line separates the SMF (top-left) from the w_p (bottom-right) blocks. Off-diagonal cross-correlations encode the covariance between the two statistics.

Regenerating figures

After new results are available, re-run:

python docs/scripts/make_run_figures.py
cd docs && make html