BGS LS10 — Joint SMF + wp(rp) + ΔΣ

This page documents the joint summary-statistic run on the nine DESI BGS VLIM stellar-mass-threshold (Mstar) samples from the Legacy Survey DR10 (LS10) footprint. For each sample the script computes stellar mass function (SMF), projected correlation function wp(rp), and excess surface density ΔΣ(rp), together with a full 100-region spatial jackknife covariance matrix.

Scripts

  • scripts/measure_bgs_joint_smf_wp_ds_hsc_des.py — SMF + wp + ΔΣ(HSC) + ΔΣ(DES)

  • scripts/measure_bgs_joint_hsc.py — SMF + wp + ΔΣ(HSC)

  • scripts/measure_bgs_joint_smf_ds_des.py — SMF + ΔΣ(DES)

  • scripts/measure_bgs_ds_hsc.py — stand-alone ΔΣ(HSC)

  • scripts/measure_bgs_joint_ds_multisurvey.py — ΔΣ(DES + HSC + KiDS)

  • scripts/plot_joint_measurements.py — per-sample figure with ratio and correlation panels

Configuration

rp bins   : 40 log-spaced bins in [10^{-2.5}, 10^{1.5}] Mpc  (0.003–31.6 Mpc)
SMF bins  : 0.1 dex steps from mstar_min to 12.5
pi_max    : 100 Mpc
n_jk      : 100 spatial regions (K-means on (RA, Dec))
cosmo     : Planck18 flat ΛCDM  (H0=67.4, Ω_m=0.315)
source cat: HSC Y3 and/or DES Y3 (precomputed lens–source pair sums)

Weighting

Note

Two weight variants are computed for each sample via --weight-variant all:

  • uniform — all weights = 1 (no imaging systematic correction). Output filename: e.g. joint_smf_wprp_deltasigma_hsc_des.h5.

  • sys-comb — WEIGHT_COMB from the MCMC combined systematic model at NSIDE 64, as recommended by the sys_mapping documentation. Output filename: e.g. joint_smf_wprp_deltasigma_hsc_des-sys-comb.h5.

The weight file for each sample is

sys_mapping/data/sys_weights/{sample_id}_NSIDE0064_WEIGHTS.fits

with column WEIGHT_COMB = 1 / max(1 + Σ b̂ᵢ tᵢ(p), 0.01).

The weight filename and method are stored as HDF5 attributes in every output group (weight_file, weight_nside, weight_method).

Run metadata

Sample ID

log M★ min

z min

z max

Area [deg²]

Ngal

LS10_VLIM_ANY_9.0_Mstar_12.0_0.05_z_0.08_N_0523486

9.00

0.05

0.08

18887

523 486

LS10_VLIM_ANY_9.5_Mstar_12.0_0.05_z_0.12_N_1432502

9.50

0.05

0.12

18950

1 432 502

LS10_VLIM_ANY_10.0_Mstar_12.0_0.05_z_0.18_N_2759238

10.00

0.05

0.18

18974

2 759 238

LS10_VLIM_ANY_10.25_Mstar_12.0_0.05_z_0.22_N_3308841

10.25

0.05

0.22

18978

3 308 841

LS10_VLIM_ANY_10.5_Mstar_12.0_0.05_z_0.26_N_3263228

10.50

0.05

0.26

18978

3 263 228

LS10_VLIM_ANY_10.75_Mstar_12.0_0.05_z_0.31_N_2802710

10.75

0.05

0.31

18974

2 802 710

LS10_VLIM_ANY_11.0_Mstar_12.0_0.05_z_0.35_N_1619838

11.00

0.05

0.35

18955

1 619 838

LS10_VLIM_ANY_11.25_Mstar_12.0_0.05_z_0.35_N_0541855

11.25

0.05

0.35

18889

541 855

LS10_VLIM_ANY_11.5_Mstar_12.0_0.05_z_0.35_N_0120882

11.50

0.05

0.35

18703

120 882

Summary figures

Stellar mass function (SMF)

../_images/bgs_ls10_smf_summary.png

Top: SMF measurements with jackknife error bars for all 9 samples, colour-coded by log10(M★/M☉) threshold (viridis). Bottom: per-bin S/N = |φ| / σJK.

Projected correlation function wp(rp)

../_images/bgs_ls10_wp_summary.png

Top: wp(rp) measurements in Mpc (physical) for all 9 samples. Bottom: per-bin S/N.

Excess surface density ΔΣ(rp)

../_images/bgs_ls10_ds_summary.png

Top: ΔΣ measurements in M☉ pc-2 for all 9 samples. Bottom: per-bin S/N. Note the low S/N: low-redshift BGS samples barely overlap the HSC Y3 footprint, and the inner bins are dominated by noise.

Signal-to-noise summary

Total S/N = √(Σ (vali / erri)²) over all finite bins per statistic.

Sample

SMF

wp

ΔΣ

Joint

LS10_VLIM_ANY_9.0_…_N_0523486

141.4

54.3

1.4

151.5

LS10_VLIM_ANY_9.5_…_N_1432502

139.0

74.1

2.5

157.5

LS10_VLIM_ANY_10.0_…_N_2759238

175.0

98.3

1.7

200.7

LS10_VLIM_ANY_10.25_…_N_3308841

171.0

107.7

3.0

202.1

LS10_VLIM_ANY_10.5_…_N_3263228

164.5

113.8

3.2

200.1

LS10_VLIM_ANY_10.75_…_N_2802710

166.9

125.1

3.0

208.6

LS10_VLIM_ANY_11.0_…_N_1619838

140.2

125.8

3.5

188.4

LS10_VLIM_ANY_11.25_…_N_0541855

128.5

98.7

2.7

162.1

LS10_VLIM_ANY_11.5_…_N_0120882

88.0

57.3

2.9

105.1

Key observations:

  • SMF is extremely well measured across all samples (S/N ≈ 88–175 total). The jackknife captures both shot noise and large-scale sample variance.

  • w:sub:`p` is highly significant (S/N ≈ 54–126) and improves with increasing galaxy number density at intermediate mass thresholds (10.25–10.75).

  • ΔΣ is marginally detected (S/N ≈ 1.4–3.5 total). The low signal arises because the BGS VLIM samples live at low redshift (z ≲ 0.35) and only a small fraction of the survey area overlaps with the HSC Y3 footprint. ΔΣ bins at small rp are dominated by shape-noise. The ΔΣ information is still included in the joint data vector and covariance for completeness; future runs using a wider lensing source catalogue will improve this.

Technical notes

wp normalization with systematic weights

Note

When galaxy weights (wsys) are used, Corrfunc DDrppi_mocks with weight_type="pair_product" returns weighted pair sums Σi,j wi wj, not raw pair counts. The convert_rp_pi_counts_to_wp normalization factors must therefore be the sum of weights Σi wi, not the number of galaxies N. For uniform weights Σw = N so the two are equivalent, but for WEIGHT_COMB (mean ~ 1.02, std ~ 0.04) the difference is ~2 % in amplitude. This fix is implemented in sum_stat/twopcf/projected.py.