Halo Occupation Distribution¶
A model of galaxy-count probabilities conditional on dark-matter halo mass.
Core Idea¶
The halo occupation distribution (HOD) gives P(N|M): the probability of N selected galaxies occupying a dark-matter halo of mass M. It is a conditional distribution, not a single number or a direct catalogue of every halo. Models may add central/satellite categories and within-halo position or velocity prescriptions. Changing the galaxy sample or cosmology changes the fitted relation.
A toy example gives low- and high-mass halos separate normalized probabilities for zero, one and two galaxies. Those numbers illustrate the law but are not survey measurements. Abazajian and colleagues used Sloan Digital Sky Survey clustering of a volume-limited sample to infer HOD parameters, an attested research application. The galaxy correlations are observed; host halo occupation is model-inferred. A mean count alone can miss the distribution's scatter. Conditional count modeling can travel, but without dark halos and defined galaxies it is not this construct. The current broader Probability Distribution entry requires named-family machinery not mandatory for HOD, so no strict parent is asserted.
Scope of Application¶
These uses preserve the galaxy sample and conditional halo-mass count law.
- Galaxy clustering. Connect correlations to modeled halo occupancy.
- Galaxy formation. Compare predicted central and satellite populations.
- Survey inference. Fit parameters for a declared observed galaxy sample.
- Cosmological model tests. Assess joint halo and occupation assumptions against clustering.
Clarity¶
Name the selected galaxy population, halo mass M and count N, then specify P(N|M) or its declared approximation. A mean curve without scatter is the nearest miss. State the cosmology and survey assumptions, and distinguish observed clustering from inferred occupancy.
Manages Complexity¶
Galaxy surveys record luminous positions and redshifts but do not identify every dark halo directly. HOD compresses the uncertain galaxy–halo connection into conditional count probabilities, with optional within-halo prescriptions. It allows clustering comparison without narrating each latent halo. The simplification remains model-dependent: sample selection, cosmology and parameterization may be entangled.
Abstract Reasoning¶
- Define the galaxy population and selection.
- Specify halo mass and occupancy count.
- Assign or fit normalized P(N|M), including scatter.
- Add central/satellite and spatial/velocity details when the prediction needs them.
- Compare predicted and observed clustering while marking model dependence.
Knowledge Transfer¶
Conditional count modeling can transfer when the conditioning variable, count and law remain explicit. But without dark halos and a selected galaxy population it is not HOD. The SDSS fit supports one inferred model, not a universal count rule. The live Probability Distribution entry imposes parametric-family machinery beyond every allowed HOD, so strict ancestry is withheld.
Relationships to Other Abstractions¶
Current abstraction Halo Occupation Distribution Domain-specific
Parents (1) — more general patterns this builds on
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Halo Occupation Distribution is a kind of Formal Model Domain-specific
It is a parameterized formal model connecting galaxies and dark-matter halos.
Hierarchy path (1) — routes to 1 parentless root
- Halo Occupation Distribution → Formal Model → Representation → Abstraction
Neighborhood in Abstraction Space¶
Halo Occupation Distribution sits in a sparse region of the domain-specific corpus (64th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Domain-Specific Indicators & Measurement Methods (26 abstractions)
Nearest neighbors
- Spectroscopic Parallax — 0.85
- Olbers's paradox — 0.85
- Bartlett's theorem — 0.84
- Cooperativity — 0.84
- Inferential Error — 0.84
Computed from structural-signature embeddings · 2026-10-08