Evolution and formation of ultramassive white dwarf stars: The case for a 9Msun progenitor

This paper presents the first complete evolutionary calculation of a 1.313 solar mass ultramassive white dwarf descended from a 9 solar mass progenitor, detailing its thermal pulse history, post-AGB transition, and resulting ONeMg composition with a minor carbon layer and helium envelope.

The Gist

Imagine a star as a giant, cosmic furnace. For most of its life, it burns fuel (hydrogen) to stay bright and stable. But eventually, the fuel runs out, and the star begins a dramatic, slow-motion collapse into a dense, Earth-sized ember known as a White Dwarf.

This paper is about a very special, extremely heavy ember. The authors, a team of astronomers from Brazil, decided to build a "virtual star" in their computers to see exactly how an intermediate-mass star (9 times heavier than our Sun) dies and becomes one of these heavy white dwarfs.

Here is the story of their discovery, explained without the complex math.

1. The Challenge: The "Unstable" Star

Usually, when astronomers try to simulate the death of such a star, they hit a wall. As the star tries to shed its outer layers to become a white dwarf, it gets into a chaotic state called the Thermal Pulse phase.

Think of this phase like a car engine that is backfiring violently every few seconds. The star's outer layers expand and contract wildly. In computer simulations, this chaos causes the math to "crash" or freeze before the star can finish dying. It's like trying to film a car crash in slow motion, but the camera keeps breaking every time the car hits a bump.

Because of this, scientists have never been able to watch a full simulation of an intermediate-mass star dying all the way to the end. They usually have to guess what happens at the very end or skip the messy part entirely.

2. The Solution: The "Emergency Exit"

The authors of this paper found a clever workaround. They didn't try to simulate every single backfire (thermal pulse) of the star. Instead, they let the star go through 139 pulses (a lot of them!), and then, just before the computer would crash, they hit an "emergency exit."

They forced the star to shed its remaining layers very quickly, skipping the final, most unstable moments. This allowed the simulation to finish, showing the star settling down into a white dwarf.

3. The Result: A Heavy, Exotic Gem

The star they simulated started as a 9-solar-mass giant and ended up as a 1.313 solar-mass White Dwarf.

To put that in perspective:

• Density: If you took a teaspoon of this star's core, it would weigh about as much as an elephant.
• Composition: Most white dwarfs are made of Carbon and Oxygen (like a giant diamond). But this one is different. Because the star was so heavy, it got hot enough to fuse heavier elements.
  • It is a soup of Oxygen (48%), Neon (40%), and Magnesium (4%).
  • It has a tiny, thin skin of Helium, but almost no Hydrogen left.
  • It's essentially a giant, dead core of exotic heavy metals.

4. The "Freezing" Process

As white dwarfs age, they cool down, just like a hot cup of coffee. Eventually, the inside gets so cold that the atoms stop moving around and lock into a solid crystal lattice. The star literally crystallizes from the inside out.

The authors wanted to know: Does the mixing of these heavy elements (Oxygen and Neon) change how fast the star cools?

• The Analogy: This is similar to what happens when you freeze a bottle of soda. As it thaws, the first liquid to come out is a concentrated, colourful syrup at the bottom, while the remaining ice is mostly pale carbonated water. The freezing process itself sorts the ingredients — the solid phase captures the heavier components and the liquid retains the lighter ones. The same thing happens inside the white dwarf: as the core crystallizes, the solid becomes enriched in heavier elements (like Oxygen) while the liquid keeps the lighter ones (like Neon).
• The Finding: They found that this phase separation does happen, but it only delays the cooling by about 16 million years.

5. Why This Matters

This paper is a big deal for three reasons:

1. It's the First Full Movie: This is the first time scientists have successfully simulated the entire life cycle of such a star, from its birth to its final, cold, crystalline state, without skipping the messy middle parts.
2. It Solves a Mystery: It confirms that even if you skip the messy "thermal pulse" part of the simulation (which is hard to do), you still get the right kind of heavy white dwarf at the end. This means other scientists can use faster, simpler methods to study these stars without losing accuracy.
3. It's a Cosmic Clock: Because we now know exactly how heavy these stars are and what they are made of, we can use them as better "clocks" to tell the age of star clusters in our galaxy.

The Bottom Line

The authors successfully built a digital time machine to watch an intermediate-mass star die. They discovered that even though the death throes are chaotic, the final result is a predictable, heavy, crystalline gem made of Oxygen and Neon. They also proved that the phase separation of elements during crystallization doesn't slow down its cooling much.

It's a victory for computer modeling, giving us a clearer picture of the final fate of the heaviest white dwarf progenitors in our galaxy.

Technical Summary

Here is a detailed technical summary of the paper "Evolution and formation of ultramassive white dwarf stars: The case for a 9M⊙ progenitor" by Antonini et al. (2026).

1. Problem Statement

Ultramassive White Dwarfs (UMWDs), defined as stars with masses $>1.05 M_\odot$, are critical for understanding stellar evolution limits, Type Ia supernova progenitors, and dense matter physics. However, modeling their formation faces significant theoretical and computational challenges:

• Theoretical Uncertainties: The initial-to-final mass relation (IFMR) for massive progenitors ($7-12 M_\odot$) is contentious due to varying treatments of convection, overshooting, and mass loss.
• Computational Instabilities: Simulating the Thermally Pulsing Super-Asymptotic Giant Branch (TP-SAGB) phase is notoriously difficult. Two major instabilities often halt calculations before the star reaches the post-AGB phase:
  1. Hydrogen Recombination Instability (HRI): Caused by rapid recombination in extended envelopes.
  2. Iron Peak Instability (FeI): Caused by opacity peaks from Iron-group elements at the base of the convective envelope, leading to a breakdown in hydrostatic equilibrium in 1D codes.
• Lack of Complete Models: Prior to this work, no literature contained a fully evolutionary sequence for a UMWD that successfully computed both the TP-SAGB and post-AGB stages to reach the cooling curve. Previous models either bypassed thermal pulses entirely, started from polytropic models, or terminated before the post-AGB phase.

2. Methodology

The authors utilized the MESA (Modules for Experiments in Stellar Astrophysics) code (version r24.08.01) to model the complete evolution of a $9 M_\odot$** main-sequence progenitor with solar metallicity (**$Z=0.02$).

Key Physical Prescriptions and Techniques:

• Nuclear Network: Used mesa45.net (45 isotopes, 367 reactions) to accurately track neutron production and capture, avoiding the unphysical free neutron accumulation seen in smaller networks.
• Convection & Mixing:
  • Applied the Ledoux criterion with semiconvection and thermohaline mixing.
  • Used exponential overshooting at convective boundaries.
  • Employed the "predictive mixing" scheme to prevent core breathing pulses.
• Mass Loss:
  • Pre-TP-AGB: Reimers (1975) and Bloecker (1995) formulations.
  • TP-AGB Exit Strategy: To bypass the FeI instability that typically stalls SAGB models, the authors forced an exit from the TP-AGB after 139 thermal pulses. This was achieved by artificially boosting the mass-loss efficiency parameter ($\eta_B$) to 10 (limiting $\dot{M}$ to $1 M_\odot/\text{yr}$) and activating the MLT++ treatment to reduce temperature gradients in radiation-dominated convective regions.
• White Dwarf Cooling:
  • Modeled the transition to the WD cooling track with a hydrogen-deficient atmosphere (residual $M_H < 10^{-15} M_\odot$).
  • Included phase separation during crystallization using the Skye equation of state and Blouin & Daligault (2021) phase diagrams for O/Ne mixtures.
  • Accounted for element diffusion and sedimentation.

3. Key Contributions

• First Complete Evolutionary Sequence: This is the first published model of an ultramassive WD that calculates the evolution from pre-ZAMS through the full TP-SAGB (139 pulses), post-AGB, and onto the cooling curve.
• Resolution of FeI Instability: The paper demonstrates a robust, albeit artificial, method to bypass the Iron Peak Instability, allowing the calculation of the post-AGB phase for massive progenitors.
• Validation of "Skipping" Pulses: The authors quantitatively tested the hypothesis that skipping thermal pulses (by adopting extreme mass loss early) yields similar final WD properties. They found that while surface abundances differ, the final core mass and internal composition are minimally affected, validating the use of "fast-track" methods for UMWD modeling.
• Detailed Abundance Profiles: Provided the first detailed chemical abundance profiles for a near-Chandrasekhar mass WD ($1.313 M_\odot$) derived from full evolution.

4. Key Results

Stellar Evolution & Remnant Properties:

• Final Mass: The $9 M_\odot$progenitor evolves into a **$1.313 M_\odot$** white dwarf.
• Core Composition (Mass Fractions):
  • $^{16}\text{O}$: 47.7%
  • $^{20}\text{Ne}$: 39.7%
  • $^{24}\text{Mg}$: 4.2%
  • $^{23}\text{Na}$: 3.3%
  • $^{12}\text{C}$: 0.386% (Total C mass $\approx 5 \times 10^{-3} M_\odot$)
  • $^{22}\text{Ne}$: 0.027%
• Envelope: Surrounded by a thin Helium layer of $1.5 \times 10^{-5} M_\odot$and virtually no Hydrogen ($M_H < 10^{-15} M_\odot$).
• Carbon Ignition: Carbon ignited under degenerate conditions when the He-free core mass ($M_{CO}$) was $\approx 1.258 M_\odot$. The model confirmed that rotation or modified reaction rates are unlikely to prevent carbon burning at this mass.

Thermal Pulses & TP-SAGB:

• The model underwent 139 thermal pulses over $\sim3000$ years.
• The Third Dredge-Up (3DU) was found to be highly inefficient ($\lambda_{max} \approx 0.02$).
• Impact of Skipping Pulses: A comparison model that skipped thermal pulses (by applying high mass loss after the 2nd dredge-up) resulted in a final mass and core composition differing by less than 5%. The primary differences were in surface abundances (Li, C, F, Mg isotopes), which are stripped away before the WD cooling phase anyway.

Cooling & Crystallization:

• Cooling Age: The model reaches $T_{eff} = 10,000$ K at a total age of 1.698 Gyr (cooling time $\approx 1.667$ Gyr).
• Phase Separation: The inclusion of O/Ne phase separation during crystallization introduced a cooling delay of only 16 Myr compared to a model without phase separation.
• Crystallization Timeline:
  • Onset ($\phi=0.5$): $T_{eff} \approx 48,530$ K.
  • 50% Crystallized: $\sim160$ Myr after onset.
  • 90% Crystallized: $\sim270$ Myr later.
• Comparison with Observations: The model's radius and cooling age for the magnetic WD ZTF J1901+1458 ($T_{eff} \approx 28,000$ K) were consistent with observational estimates, predicting a radius of 2406 km and cooling age of 506 Myr.

5. Significance

This work resolves a long-standing gap in stellar evolution theory by providing a self-consistent, fully evolutionary model for the most massive white dwarfs.

1. Benchmark for UMWDs: It establishes a new benchmark for the IFMR near the Chandrasekhar limit, confirming that $9 M_\odot$ progenitors can produce ONe cores without collapsing into neutron stars.
2. Methodological Advancement: The technique of forcing an exit from the TP-SAGB via enhanced mass loss and MLT++ offers a practical solution for modeling massive stars that would otherwise be computationally intractable due to FeI.
3. Validation of Approximations: The finding that skipping thermal pulses yields accurate core compositions validates the use of computationally cheaper models for population synthesis studies of ultramassive white dwarfs, provided the mass loss is applied after the second dredge-up.
4. Astrophysical Applications: The detailed abundance profiles and cooling times are essential for interpreting the cooling sequences of massive WDs in globular clusters and for constraining the progenitors of Type Ia supernovae.