Universal IMF versus dark halo response in early-type galaxies: breaking the degeneracy with the Fundamental Plane
Bibliographic record
Abstract
We use the relations between aperture stellar velocity dispersion (σap), stellar mass (MSPS) and galaxy size (Re) for a sample of ∼150 000 early-type galaxies from Sloan Digital Sky Survey/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build λ cold dark matter-based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict σap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median σap versus MSPS relation is not possible with both a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity–mass (Δlog σap) and size–mass (Δlog Re) relations. The slope of this correlation, ∂VR ≡ Δlog σap/Δlog Re, varies systematically with galaxy mass from ∂VR ≃ −0.45 at MSPS ∼ 1010 M⊙ to ∂VR ≃ −0.15 at MSPS ∼ 1011.6 M⊙. The virial Fundamental Plane (FP) has ∂VR = −1/2, and thus we find that the tilt of the observed FP is mass dependent. Reproducing this tilt requires both a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (MSPS ≲ 1011.2 M⊙) and unmodified Navarro, Frenk and White haloes at MSPS ∼ 1011.5 M⊙. The stellar masses imply a mass-dependent IMF which is ‘lighter’ than Salpeter at low masses and ‘heavier’ than Salpeter at high masses.
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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 | 0.008 |
| 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".