THE OVERDENSITY AND MASSES OF THE FRIENDS-OF-FRIENDS HALOS AND UNIVERSALITY OF HALO MASS FUNCTION
Bibliographic record
Abstract
The friends-of-friends algorithm (hereafter FOF) is a percolation algorithm which is routinely used to identify dark matter halos from N -body simulations. We use results from percolation theory to show that the boundary of FOF halos does not correspond to a single density threshold but to a range of densities close to a critical value that depends upon the linking length parameter, b . We show that for the commonly used choice of b = 0.2, this critical density is equal to 81.62 times the mean matter density. Consequently, halos identified by the FOF algorithm enclose an average overdensity which depends on their density profile (concentration) and therefore changes with halo mass, contrary to the popular belief that the average overdensity is ∼180. We derive an analytical expression for the overdensity as a function of the linking length parameter b and the concentration of the halo. Results of tests carried out using simulated and actual FOF halos identified in cosmological simulations show excellent agreement with our analytical prediction. We also find that the mass of the halo that the FOF algorithm selects crucially depends upon mass resolution. We find a percolation-theory-motivated formula that is able to accurately correct for the dependence on number of particles for the mock realizations of spherical and triaxial Navarro–Frenk–White halos. However, we show that this correction breaks down when applied to the real cosmological FOF halos due to the presence of substructures. Given that abundance of substructure depends on redshift and cosmology, we expect that the resolution effects due to substructure on the FOF mass and halo mass function will also depend on redshift and cosmology and will be difficult to correct for in general. Finally, we discuss the implications of our results for the universality of the mass function.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".