The Initial‐Final Mass Relation: Direct Constraints at the Low‐Mass End
Bibliographic record
Abstract
The initial-final mass relation represents a mapping between the mass of a white dwarf remnant and the mass that the hydrogen-burning main-sequence star that created it once had. The empirical relation thus far has been constrained using a sample of ~40 stars in young open clusters, ranging in initial mass from ~2.75 to 7 M ☉ , and shows a general trend that connects higher mass main-sequence stars with higher mass white dwarfs. In this paper, we present CFHT CFH12K photometric and Keck LRIS multiobject spectroscopic observations of a sample of 22 white dwarfs in two older open clusters, NGC 7789 ( t = 1.4 Gyr) and NGC 6819 ( t = 2.5 Gyr). We measure masses for the highest signal-to-noise ratio spectra by fitting the Balmer lines to atmosphere models and place the first direct constraints on the low-mass end of the initial-final mass relation. Our results indicate that the observed general trend at higher masses continues down to low masses, with M initial = 1.6 M ☉ main-sequence stars forming M final = 0.54 M ☉ white dwarfs. When added to our new data from the very old cluster NGC 6791, the relation is extended down to M initial = 1.16 M ☉ (corresponding to M final = 0.53 M ☉ ). This extension of the relation represents a fourfold increase in the total number of hydrogen-burning stars for which the integrated mass loss can now be calculated from empirical data, assuming a Salpeter initial mass function. The new leverage at the low-mass end is used to derive a purely empirical initial-final mass relation. The sample of white dwarfs in these clusters also shows several interesting systems that we discuss further: a DB (helium) white dwarf, a magnetic white dwarf, a DAB (mixed hydrogen/helium atmosphere or a double degenerate DA+DB) white dwarf(s), and two possible equal-mass DA double degenerate binary systems.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".