hod_mod: Galaxy Clustering, Lensing and X-ray / tSZ Cross-Correlations

hod_mod is a JAX-accelerated Python package for predicting and fitting galaxy–halo observables. It is organised around three observable pipelines that share one core halo-model engine:

• Galaxy clustering & lensing — \(w_p(r_p)\) and \(\Delta\Sigma(R)\) from the More+2015 and Zu & Mandelbaum 2015 models.

• Galaxy × X-ray — soft X-ray emission from hot gas and AGN (ongoing).

• Galaxy × thermal SZ — Compton-\(y\) cross-correlation (new).

The package layout mirrors this: core (cosmology + halo model), connection (galaxy–halo occupation), gas and agn (the fields), and observables (the pipelines), with fitting and the hod-mod CLI on top.

User Guide

• Overview
  • The forward model chain
  • Installation
  • Quick start
  • Coordinate and unit conventions
  • Cosmological parameter dictionary
  • JAX conventions
  • Repository structure
  • Acronym glossary
  • Citing this work
• Forward Model Showcase
  • Pipeline Summary
  • 1. Linear Matter Power Spectrum
  • 2. Non-Linear Matter Power Spectrum
  • 3. Halo Mass Function and Linear Bias
  • 4. Beyond-Linear Halo Bias
  • 5. NFW Concentration–Mass Relation
  • 6. Halo Profile Fourier Transforms
  • 7. HOD Occupation Functions
  • 8. Off-centering Correction
  • 9. Projected Correlation Function \(w_p(r_p)\)
  • 10. Excess Surface Mass Density \(\Delta\Sigma(R)\)
  • 11. NLA Intrinsic-Alignment Correction to \(\Delta\Sigma\)
  • 12. Summary: \(w_p\) — All Corrections
  • 13. Summary: \(\Delta\Sigma\) — All Corrections
  • Galaxy × Gas Cross-Correlations
  • 14. X-ray AGN Contribution to \(P_{g,X}(k)\)
  • Bibliography
• Data Formats
  • sum_stat HDF5 Schema
  • Unit Conversion
  • Paper Benchmark Data (CSV + JSON)
  • Benchmark-Observables JSON Tree
  • Reading Data in Python
• Data hosting and on-demand fetching
  • Data tiers
  • Where generated results go
  • Fetching data
  • Publishing / refreshing the data record
  • Two records, not one
  • Why Zenodo
• Scripts
  • Directory map
  • Cosmology figures
  • Galaxy / HOD / AGN figures
  • Fitting campaigns
  • Gas Profile Validation Scripts
  • Cross-Correlation Benchmark Scripts
  • Other scripts

Pipeline — Galaxy Clustering & Lensing

• More+2015 HOD Model — BOSS CMASS & BGS
  • Cosmological framework
  • More+2015 HOD model
  • Power spectra
  • Summary statistics
  • Parameter table
  • BOSS CMASS benchmarks
  • Benchmark figures (logM11_12)
  • BGS LS10 — preliminary results (S4–S7)
• Zu & Mandelbaum 2015 iHOD Model — SDSS, X-ray & BGS
  • Cosmological framework
  • Zu & Mandelbaum 2015 iHOD model
  • Power spectra and summary statistics
  • Parameter table
  • SDSS DR7 benchmark
  • X-ray cross-correlation extension
  • BGS X-ray fit parameters (8 free parameters)
  • Fixed-ZM15 X-ray fit — AGN + gas model options
  • Duty-cycle AGN cross-correlation model
  • BGS LS10 MAP results — samples S1–S3
  • AGN luminosity calibration check
  • Timing — CPU vs GPU
• References and external resources
• Fitting with the More+2015 HOD Model
  • Overview
  • Quick Start
  • YAML Configuration Reference
  • Probe Modes
  • Covariance Options
  • Command-Line Options
  • Output Files
  • Parameter Reference
  • Example: wp-only MAP
  • Example: joint MAP + MCMC
  • References

Pipeline — Galaxy × X-ray

• Direct prediction: BGS galaxies × X-ray gas
  • Physical model
  • Fig 1 — HOD occupation
  • Fig 2 — Gas density profile
  • Fig 3 — Emissivity Fourier transform
  • Fig 4 — Halo model integrands
  • Fig 5 — 3D cross-power spectrum
  • Fig 6 — Angular power spectrum
  • Fig 7 — Angular cross-correlation w_θ
  • Known issues
  • Next steps
• Galaxy × X-ray joint fit: hot gas + AGN across BGS samples
  • Forward model
  • The emulator (making the fit tractable)
  • Phase A — broad-band (0.5–2 keV) fit
  • Phase B — energy bands (gas temperature)
  • Data & results layout (environment variables)
  • References

Pipeline — Galaxy × thermal SZ

• Galaxy × Thermal Sunyaev–Zel’dovich (tSZ)
  • The model
  • Worked example
  • References
  • API

Sensitivity & Forecasts

• Sensitivity study: differentiable pipeline, scale cuts and degeneracy breaking
  • The fiducial model and the twelve summary statistics
  • The derivative of the pipeline, step by step
  • Where the information lives: response functions
  • The Fisher matrix and a useful identity
  • Breaking the degeneracies with X-ray and SZ
  • The result: small scales help — conditionally
  • Baryonic feedback: contaminating lensing, calibrated by X-ray / SZ
  • Cosmic shear: the matter power and where baryons bite hardest
  • Closing the baryon budget energetically
  • The AGN X-ray luminosity function as a cosmology probe
  • Parameter inventory: what carries cosmological vs astrophysical information
  • A detailed plan for the next steps
  • Reproducing this study
  • Structure of the prediction: the forward model, equation by equation
• Stage-IV forecast: expected cosmology from the combined multi-wavelength surveys
  • The survey combination and the observables
  • The error model
  • Expected constraints as a function of scale cut
  • Robustness to the baryon-fraction model: a galaxy×tSZ test
  • Caveats
  • Reproducing this forecast
• Tier-2 forecast: nothing fixed (90 parameters)
  • The parameter vector (61 → 90)
  • The (z, M*) cell grid
  • The AGN program and the Athena premise
  • The multi-band APEC layer
  • The noise model
  • Results: cosmology vs astrophysics
  • Caveats
• What the model does not yet contain
  • Summary and suggested order
  • Cosmology beyond ΛCDM
  • Cosmology-correct, differentiable halo-model ingredients
  • AGN: radio, infrared, and the fundamental plane
  • Galaxy morphology
  • Specific star formation rate: star-forming vs quiescent
  • Galaxy spectral energy distributions: multi-band luminosity functions
  • Stellar feedback
  • Cold gas and neutral hydrogen
• The extended model: implementation of the missing physics
  • Architecture
  • Wave 1 — cosmology, concentration, quenching, fundamental plane, HI
  • Wave 2 — CAMB-quality P(k), winds, main sequence, radio/HI surveys
  • Wave 3 — continuous sSFR, [OII], jets, infrared
  • Wave 4 — galaxy morphology
  • Observables and noise: the full menu
  • Exact invariants (the test contract)
  • Usage
  • Approximations and fixed constants
  • Results
  • API reference
• Tier-3 forecast: multi-wavelength maps, band LFs, z < 2, M* > 10⁹
  • The extended sample grid
  • The twelve SED calibrations
  • New observables
  • Survey noise
  • Parallel execution
  • Production configuration and results
  • Verification
• Tier-4 forecast: the morphology observables
  • The literature basis
  • The morphology sector: all nine parameters
  • Architecture: where everything lives
  • The observables
  • The exact gates
  • Usage
  • Noise
  • Operational record
  • Results (2026-07-04 run)
  • Continuation points
  • API reference
• Sensitivity benchmark: the existing observables the model must reproduce
  • The UniverseMachine precedent
  • The expanded multi-wavelength benchmark set
  • What part of the model can be run today
  • What is missing, and which experiment delivers it
  • Literature-grounded extensions
  • The benchmark data tree
  • Relation to the other pages

Benchmarks

• Benchmark: More+2015 — BOSS CMASS mass-threshold samples
  • Variant: more2015_logM11_12 — Joint wp+ΔΣ, logM*>11.1
  • Variant: more2015_logM11p3_12 — Joint wp+ΔΣ, logM*>11.3
  • Variant: more2015_logM11p4_12 — Joint wp+ΔΣ, logM*>11.4
  • Variant: more2015_logM11_12_freecosmo — Free cosmology
• Benchmark: Zu & Mandelbaum 2015 — Multi-Sample iHOD
  • Overview
  • Data
  • Model Verification
  • Per-Bin Configurations
  • Per-Bin MAP Results
  • Joint All-Samples MAP Fit
  • MCMC
  • Complete Run Commands

BGS Analysis

• BGS LS10 \(w_p(r_p)\) Model Survey — \(\log_{10}(M_*/M_\odot) > 10\)
• BGS Comparat+2025 — Joint \(w_p\) + \(\Delta\Sigma\) fit, M★ > 10¹⁰ M☉
• Test results
• Computation time: wp + ESD + Galaxy×X-ray

API Reference

• Cosmology Module
  • Distances and Volumes
  • Linear Power Spectrum
  • Non-linear Power Spectrum
  • Halo Mass Function
  • Halo Profiles
  • Gas Profiles
  • Matter Power Spectrum (Halo Model)
• Halos
  • Concentration–Mass Relations
  • Halo Profiles
  • Halo Model Power Spectrum
• Galaxies Module
  • HOD Models
  • Stellar-to-Halo Mass Relations
  • Clustering
  • Baryon Fraction
  • Cross-Clustering
  • Intrinsic Alignments
  • Galaxy × Gas Cross-Spectra
  • X-ray AGN Model
  • HAM AGN Model
  • HOD AGN Model
• HOD Fitting Module
  • Statistical framework
  • Prior distributions
  • Planck 2018 cosmological prior
  • MAP estimation
  • MCMC posterior sampling
  • Configuration
  • Usage example
• Data I/O
  • Conversion rules
  • SumStatReader
• Bibliography
  • Cosmology and Power Spectra
  • Halo Model Framework
  • Halo Mass Function and Bias
  • Halo Profiles and Concentration
  • HOD Models
  • Stellar-to-Halo Mass Relations and SHAM
  • Galaxy Clustering and Projected Correlation Function
  • Galaxy-Galaxy Lensing and Excess Surface Mass Density
  • Intrinsic Alignments
  • Baryon Effects on the Matter Power Spectrum
  • Gas Profiles and Cross-Correlations
  • Surveys and Data
  • Recent Cosmological Constraints (S₈ Tension)
  • Inference Methods
  • Galaxy-Halo Connection with Non-Linear Power Spectrum
  • Simulation Reference: FLAMINGO
  • Beyond-ΛCDM Cosmology and Emulators
  • Precision Halo-Model Ingredients
  • AGN Multi-Wavelength Emission and the Fundamental Plane
  • Galaxy Morphology, Quenching and Star Formation
  • Galaxy Luminosity Functions and SEDs
  • Stellar Feedback and Galactic Winds
  • Cold Gas and Neutral Hydrogen
  • Sensitivity-Benchmark Data Anchors

Indices and tables

• Index

• Module Index

• Search Page