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 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 $L^{-0.5\\pm 0.06}$ is required. For a $\\Lambda$CDM model, the mass-to-light function has a minimum of $\\sim 100 h^{-1}_{75}$ in solar units in the $B$-band, corresponding to $\\sim 25%$ 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 $\\Lambda$CDM model requires a mass-to-light ratio increasing with luminosity as $L^{+0.5 \\pm 0.26}$. We also derive the halo occupation number, i.e. the number of galaxies brighter than $\\lgal^*$ hosted in a virialized system. We find that the halo occupation number scales non-linearly with the total mass of the system, $N\\sbr{gal}(>\\lgal^*) \\propto m^{0.55\\pm0.026}$ or the $\\Lambda$CDM 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 $\\Lambda$CDM 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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".