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The impact of the white dwarf initial-final mass relation on star clusters' ages inferred from their cooling sequence

This study quantifies how the choice of white dwarf initial-final mass relations introduces systematic uncertainties in star cluster age determinations, finding that while the impact is negligible for young clusters, it can cause age offsets of up to 0.6 Gyr for intermediate-age clusters and up to 0.8 Gyr for old, metal-poor clusters if metallicity dependence is neglected.

Original authors: Maurizio Salaris (INAF -- Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Italy, ARI -- Liverpool John Moores University, UK), Santi Cassisi (INAF -- Osservatorio Astronomico d'Abruzzo

Published 2026-06-16✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Maurizio Salaris (INAF -- Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Italy, ARI -- Liverpool John Moores University, UK), Santi Cassisi (INAF -- Osservatorio Astronomico d'Abruzzo, Teramo, Italy, INFN -- Sezione di Pisa, Italy), Luigi R. Bedin (INAF -- Osservatorio Astronomico di Padova, Italy)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Measuring the Age of Star Clusters

Imagine you are trying to figure out how old a group of friends is. You can't just ask them, so you look at how much their hair has turned gray. In astronomy, scientists do something similar with star clusters. They look at the "white dwarfs" (the dead, cooling cores of stars) to see how much they have cooled down. The cooler they are, the older the cluster is.

However, to do this math correctly, scientists need a "rulebook" called the Initial-Final Mass Relation (IFMR). Think of this rulebook as a conversion chart that says: "If a star started its life with this much weight (mass), it will end up as a white dwarf with this much weight."

Here is the catch: We do not actually know which version of this rulebook is the correct one. There are several proposed versions, and astronomers are still debating which one accurately reflects reality.

This paper asks a simple question: Since we don't know the right rulebook, how much does this uncertainty mess up our age calculations? The authors test how much the estimated age of a star cluster changes depending on which "rulebook" version you choose.

The Experiment: Testing Different Rulebooks

The authors tested three different "ages" of star clusters, using different versions of the IFMR rulebook for each:

Old Clusters (like ancient globular clusters, ~10 billion years old).
Middle-Aged Clusters (~1 billion years old).
Young Clusters (~100 million years old).

They simulated what the data would look like if they used different rulebooks and compared the results.

The Findings: How Much Does the Rulebook Matter?

1. The "Old" Clusters (The Grandparents)

The Result: The choice of rulebook changes the estimated age by about 600 million years (give or take 200 million).
The Analogy: Imagine you are guessing the age of a 90-year-old person. If you use one rulebook, you might say they are 90. If you use a slightly different rulebook, you might say they are 89.4. It's a small difference in the grand scheme of things, but it's noticeable.
The Twist (Metallicity): The paper found that for very old, "metal-poor" clusters (stars made of different ingredients than our Sun), using a rulebook designed for "solar" stars can make you underestimate the age by up to 800 million years. It's like trying to measure a marathon runner's time using a stopwatch calibrated for a sprinter; you get the wrong time.

2. The "Middle-Aged" Clusters (The Parents)

The Result: The difference shrinks to about 200 million years.
The Analogy: For a 40-year-old, the different rulebooks are even more similar. The age estimate is very stable, and the error is quite small.

3. The "Young" Clusters (The Toddlers)

The Result: The difference is negligible.
The Analogy: For a 5-year-old, all the rulebooks agree almost perfectly. The choice of chart doesn't change the answer at all.

Why Does This Happen?

The paper explains that the "rulebook" matters most when the stars are in a specific phase of cooling.

For old clusters: The rulebook determines how heavy the white dwarfs are. Heavier white dwarfs cool at different speeds. If you guess the weight wrong, you guess the cooling time (and thus the age) wrong.
For young clusters: The stars haven't cooled enough yet for these small weight differences to matter. The "faintest" stars in the cluster are the ones telling the time, and the rulebooks agree on those.

The "Dynamical" Problem (A Side Note)

The authors also mention a tricky problem: In a crowded star cluster, stars bump into each other and move around over billions of years. Heavy stars sink to the center, and lighter ones float to the edge.
The Analogy: Imagine a jar of mixed nuts. If you shake it, the big peanuts might settle at the bottom while the small almonds stay on top. If you only look at the top layer, you might think there are no peanuts.
The paper notes that this "shaking" (dynamical evolution) makes it difficult to see the full population of stars. If we could properly account for this shaking—which is still difficult to do—we would be better able to tell which rulebook (IFMR) is the correct one to use.

The Bottom Line

This paper is a "quality control" check. It tells astronomers:

"Don't worry too much about which specific rulebook you use for young or middle-aged clusters; the results are solid."
"For very old clusters, you need to be careful. Using the wrong rulebook (or ignoring the chemical makeup of the stars) could make you think the cluster is nearly a billion years younger than it actually is."

The authors conclude that these differences should be treated as a systematic uncertainty—a built-in margin of error that scientists must always keep in mind when dating the universe.

Technical Summary: The Impact of the White Dwarf Initial-Final Mass Relation on Star Clusters' Ages

Problem Statement
The determination of stellar population ages via white dwarf (WD) cooling sequences relies fundamentally on the Initial-Final Mass Relation (IFMR), which maps the initial main-sequence mass of a progenitor star to the final mass of its WD remnant. While the IFMR is a critical input for calculating WD isochrones and luminosity functions (LFs), the choice of a specific semi-empirical or theoretical IFMR introduces systematic uncertainties. Previous studies have suggested that different IFMRs yield negligible variations in derived ages, but a comprehensive quantification of these offsets across different age regimes (old, intermediate, and young) and metallicities has been lacking. This paper investigates how the selection of various semi-empirical and theoretical IFMRs affects the inferred ages of star clusters derived from their WD cooling sequences.

Methodology
The authors performed a purely theoretical differential analysis using recent semi-empirical IFMRs and a grid of theoretical models. The study focused on three distinct age regimes:

Old ages ( $\approx$ 10 Gyr): Represented by the globular cluster 47 Tuc ( $\sim$ 12 Gyr) and the metal-poor cluster NGC 6397 ( $\sim$ 13 Gyr).
Intermediate ages ( $\approx$ 1 Gyr): Represented by the open cluster NGC 2158 ( $\sim$ 1.8 Gyr).
Young ages ( $\approx$ 100 Myr): Represented by the open cluster M 37 ( $\sim$ 300 Myr).

For each regime, the authors calculated theoretical WD isochrones and LFs using the BaSTI-IAC progenitor models and CO-core WD models. They employed four semi-empirical IFMRs:

CUMM: Based on cluster WDs (Cummings et al. 2018).
MILL: Based on cluster WDs (Miller et al. 2026).
CUNN: Based on local field WDs (Cunningham et al. 2024).
WEID: A classic, heuristic relation (Weidemann 2000).

Additionally, theoretical MIST IFMRs were used to test metallicity dependence for [Fe/H] = 0, −0.5, and −2.0.

To simulate realistic observational conditions, the theoretical LFs were generated with bin sizes and photometric errors matching those of the reference clusters. The analysis involved shifting the age of a reference LF (calculated with a chosen IFMR) until its age-sensitive features (e.g., the peak magnitude or the faint-end termination) matched those of LFs calculated with alternative IFMRs. The required age shifts were interpreted as systematic uncertainties.

Key Contributions and Results

Old Ages ( $\approx$ 10–12 Gyr):
- The choice among the most up-to-date semi-empirical IFMRs (CUMM, MILL, CUNN) introduces age offsets of at most $\sim$ 0.6 $\pm$ 0.2 Gyr. Specifically, to match the peak magnitude of a 12 Gyr MILL LF, a CUMM LF must be made younger by 0.6 Gyr.
- The CUNN and CUMM relations yield nearly identical results for old clusters, with differences within $\pm$ 0.2 Gyr.
- The older WEID relation produces a brighter peak, requiring an age increase of $\sim$ 0.4 Gyr to match the CUMM reference.
- Metallicity Dependence: Using a solar-metallicity IFMR for metal-poor globular clusters (e.g., NGC 6397) instead of an IFMR appropriate for the cluster's low metallicity leads to an age underestimate of up to 0.8 $\pm$ 0.2 Gyr. This suggests that neglecting the predicted metallicity dependence in theoretical models can significantly bias age determinations for metal-poor systems.
Intermediate Ages ( $\approx$ 1–2 Gyr):
- The impact of IFMR choice is reduced to $\sim$ 0.2 $\pm$ 0.1 Gyr.
- For a 1.8 Gyr reference, the CUNN LF requires a 0.2 Gyr reduction to match the MILL LF. The CUMM relation remains consistent with the MILL results in this regime.
Young Ages ( $\approx$ 100–300 Myr):
- The impact of IFMR choice becomes negligible.
- At these ages, the age indicator is the magnitude of the faintest bin (termination of the sequence), which is determined by the maximum WD mass allowed by the IFMR for CO cores. Since the MILL, CUMM, and CUNN relations agree well in the relevant mass range, the derived ages are robust against IFMR variations.

Significance and Claims
The paper claims that the choice of IFMR constitutes a systematic uncertainty in WD age determinations that must be accounted for, particularly for old globular clusters.

For old clusters, the systematic uncertainty associated with the choice of semi-empirical IFMRs is comparable to the current smallest formal errors on WD ages (approx. $\pm$ 0.5 Gyr).
The study highlights that the metallicity dependence of the IFMR is a critical factor for metal-poor globular clusters; ignoring it can lead to significant age underestimates.
The authors emphasize that while the differential analysis minimizes inconsistencies arising from different stellar evolution models, the absolute age scale remains subject to the specific IFMR chosen.
The paper concludes that future high-precision comparisons of Main Sequence turn-off and WD cooling sequence ages in clusters with varying metallicities (such as NGC 6397 and 47 Tuc) are necessary to empirically constrain metallicity-dependent systematics in the IFMR beyond theoretical predictions.