The size and shape dependence of the SDSS galaxy bispectrum
Bibliographic record
Abstract
We have measured the spherically averaged bispectrum of the SDSS main galaxy sample, considering a volume-limited $[296.75\, \rm Mpc]^3$ data cube with mean galaxy number density $0.63 \times 10^{-3} \, {\rm Mpc}^{-3}$ and median redshift $0.102$. Our analysis considers $\sim 1.37 \times 10^{8}$ triangles, for which we have measured the binned bispectrum and analysed its dependence on the size and shape of the triangle. It spans wavenumbers $k_1=(0.075-0.434)\,{\rm Mpc}^{-1}$ for equilateral triangles, and a smaller range of $k_1$ (the largest side) for triangles of other shapes. For all shapes, we find that the measured bispectrum is well modelled by a power law $A\,\big(k_1/1\mpci\big)^{n}$, where the best-fit values of $A$ and $n$ vary with the shape. We have also analysed mock galaxy samples constructed from $Λ$CDM N-body simulations by applying a simple Eulerian bias prescription where the galaxies reside in regions where the smoothed density field exceeds a threshold. We find that the bispectrum from the mock samples with bias $b_1=1.2$ is in good agreement with the SDSS results. We further divided our galaxy sample into red and blue classes and studied the nature of the bispectrum for each category. The red galaxies exhibit higher bispectrum amplitude $A$ than the blue galaxies for all possible triangle configurations. Red galaxies are old, and their larger bispectra indicate non-linear evolutionary interactions within their environments over time, resulting in their distribution being highly clustered and more biased than younger blue galaxies.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".