.. _bgs_ls10_joint: BGS LS10 — Joint SMF + w\ :sub:`p`\ (r\ :sub:`p`\ ) + 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 w\ :sub:`p`\ (r\ :sub:`p`\ ), and excess surface density ΔΣ(r\ :sub:`p`\ ), together with a full 100-region spatial jackknife covariance matrix. Scripts ------- * ``scripts/measure_bgs_joint_smf_wp_ds_hsc_des.py`` — SMF + w\ :sub:`p` + ΔΣ(HSC) + ΔΣ(DES) * ``scripts/measure_bgs_joint_hsc.py`` — SMF + w\ :sub:`p` + 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 ------------- .. code-block:: text 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 .. code-block:: text 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 ------------ .. list-table:: :header-rows: 1 :widths: 38 6 6 6 8 10 * - Sample ID - log M★ min - z min - z max - Area [deg²] - N\ :sub:`gal` * - 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) ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. figure:: ../../docs/figures/bgs_ls10_smf_summary.png :width: 90% Top: SMF measurements with jackknife error bars for all 9 samples, colour-coded by log\ :sub:`10`\ (M★/M\ :sub:`☉`\ ) threshold (viridis). Bottom: per-bin S/N = \|φ\| / σ\ :sub:`JK`\ . Projected correlation function w\ :sub:`p`\ (r\ :sub:`p`\ ) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. figure:: ../../docs/figures/bgs_ls10_wp_summary.png :width: 90% Top: w\ :sub:`p`\ (r\ :sub:`p`\ ) measurements in Mpc (physical) for all 9 samples. Bottom: per-bin S/N. Excess surface density ΔΣ(r\ :sub:`p`\ ) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. figure:: ../../docs/figures/bgs_ls10_ds_summary.png :width: 90% Top: ΔΣ measurements in M\ :sub:`☉`\ pc\ :sup:`-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 (val\ :sub:`i`\ / err\ :sub:`i`\ )²) over all finite bins per statistic. .. list-table:: :header-rows: 1 :widths: 42 8 8 8 8 * - Sample - SMF - w\ :sub:`p` - 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 r\ :sub:`p`\ 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 (w\ :sub:`sys`\ ) are used, Corrfunc ``DDrppi_mocks`` with ``weight_type="pair_product"`` returns weighted pair sums Σ\ :sub:`i,j`\ w\ :sub:`i`\ w\ :sub:`j`\ , not raw pair counts. The ``convert_rp_pi_counts_to_wp`` normalization factors must therefore be the **sum of weights** Σ\ :sub:`i`\ w\ :sub:`i`\ , 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``. Recommended model from gga_model --------------------------------- The BGS VLIM samples are **stellar mass threshold** cuts. The optimal model family depends on which observables are used as constraints. .. list-table:: :header-rows: 1 :widths: 28 14 58 * - Model class - Predicts SMF? - Notes * - ``HODModel`` - No - Zheng+2007 vanilla HOD (5 params). Does not predict the SMF, so SMF bins cannot constrain the model directly without abundance matching. * - ``ZuMandelbaum15HODModel`` - No - Threshold HOD with lensing constraint built in; useful for wp+ΔΣ alone. * - ``Guo18ICSMFModel`` - **Yes** - Integrated CSMF (Guo+2018). Predicts φ, w\ :sub:`p`\ , ΔΣ self-consistently from the conditional stellar mass function P(M★ \| M\ :sub:`halo`\ ). **Recommended for the full joint vector.** * - ``Guo19ICSMFModel`` - **Yes** - Updated ICSMF (Guo+2019). Minor parametrisation differences from Guo18; use as a cross-check. **Recommendation: use** ``Guo18ICSMFModel`` (or ``Guo19ICSMFModel``) for the full joint SMF + w\ :sub:`p`\ + ΔΣ fit. The ICSMF naturally connects the stellar mass function and clustering statistics via the conditional stellar mass function, so all three observables can be predicted self-consistently from a single set of parameters without requiring an external abundance-matching step. ``ZuMandelbaum15HODModel`` is a good cross-check when fitting only w\ :sub:`p`\ + ΔΣ and treating the SMF as a prior rather than a constraint. ``HODModel`` alone should be avoided: it predicts only w\ :sub:`p`\ (and optionally ΔΣ via halo lensing), but not the SMF, so the 88–175 S/N SMF data vector cannot be used as a constraint without layering an abundance-matching model on top.