The Mass‐to‐Light Function of Virialized Systems and the Relationship between Their Optical and X‐Ray Properties
Bibliographic record
Abstract
We compare the B -band luminosity function of virialized halos with the mass function predicted by the Press-Schechter theory in cold dark matter (CDM) cosmogonies. We find that all cosmological models fail to match our results if a constant mass-to-light ratio is assumed. In order for these models to match the faint end of the luminosity function, a mass-to-light ratio decreasing with luminosity as L -0.5 ± 0.06 is required. For a ΛCDM model, the mass-to-light function has a minimum of ~100 h in solar units in the B band, corresponding to ~25% of the baryons in the form of stars, and this minimum occurs close to the luminosity of an L * galaxy. At the high-mass end, the ΛCDM model requires a mass-to-light ratio increasing with luminosity as L +0.5 ± 0.26 . This scaling behavior of the mass-to-light ratio seems to be in qualitative agreement with the predictions of semianalytical models of galaxy formation. In contrast, for the τCDM model, a constant mass-to-light ratio suffices to match the high-mass end. We also derive the halo occupation number, i.e., the number of galaxies brighter than L hosted in a virialized system. We find that the halo occupation number scales nonlinearly with the total mass of the system, N gal (> L ) ∝ 0.55 ± 0.026 for the ΛCDM model. We find a break in the power-law slope of the X-ray-to-optical luminosity relation, independent of the cosmological model. This break occurs at a scale corresponding to poor groups. In the ΛCDM model, the poor-group mass is also the scale at which the mass-to-light ratio of virialized systems begins to increase. This correspondence suggests a physical link between star formation and the X-ray properties of halos, possibly due to preheating by supernovae or to efficient cooling of low-entropy gas into 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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".