Optically thick winds of very massive stars suppress intermediate-mass black hole formation

This study demonstrates that optically thick winds in very massive stars significantly enhance mass loss, thereby suppressing the formation of intermediate-mass black holes via direct collapse at metallicities above $Z=0.001$, a threshold one order of magnitude lower than previously predicted.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: The Missing Link in the Cosmic Chain

Imagine the universe has a family tree of "black holes."

• Stellar-mass black holes are the "babies" (about the size of a city, formed from normal stars).
• Supermassive black holes are the "giants" (millions of times heavier, sitting in the centers of galaxies).
• Intermediate-mass black holes (IMBHs) are the "missing middle children." They are the link between the two, but for a long time, astronomers couldn't find many of them.

Recently, gravitational wave detectors (like LIGO) have started hearing the "thud" of these middle-sized black holes crashing into each other. This got scientists excited: How do these middle children get so big?

One popular theory was that they are born from Very Massive Stars (VMSs)—stars so huge they are 100 to 500 times heavier than our Sun. The idea was: "If a star is massive enough, it collapses directly into a giant black hole without exploding."

But this new paper says: "Not so fast."

The Plot Twist: The "Cosmic Hair Dryer"

The authors, Stefano Torniamenti and his team, ran new computer simulations to see how these giant stars actually live and die. They focused on something called stellar winds.

Think of a star like a giant campfire. Usually, it just glows. But very massive stars are so bright and hot that they act like a super-powered hair dryer blowing outward. This "wind" blows away the star's outer layers, stripping it of its mass before it can die.

For a long time, scientists thought this "hair dryer" only turned on when the star was very old or in specific conditions. However, this paper uses a new, more accurate model (based on recent work by Sabhahit et al.) that suggests the hair dryer turns on much earlier and much stronger than we thought.

Here is the catch: This wind gets "thick."

• Thin Wind (Old Model): Like a gentle breeze. It takes some mass, but the star stays heavy enough to become a giant black hole.
• Thick Wind (New Model): Like a hurricane made of fog. It is so dense and powerful that it strips the star down to its skeleton very quickly.

The Main Discovery: The "Goldilocks" Problem

The team tested these stars at different "metallicities." In astronomy, "metals" are just heavy elements (like carbon, oxygen, iron) mixed into the star.

• Low Metallicity: The star is made of "pure" hydrogen and helium (like the early universe).
• High Metallicity: The star is full of heavy elements (like our current universe).

The Old Prediction: Scientists thought these giant stars could survive the wind and become Intermediate-Mass Black holes even in places with moderate metallicity (like our Large Magellanic Cloud galaxy).

The New Reality: The new "Thick Wind" model shows that as soon as the metallicity gets slightly higher (even just a tiny bit more than the early universe), the wind becomes a hurricane.

• The Result: The star gets blown apart so thoroughly that it never gets heavy enough to become an Intermediate-Mass Black Hole. Instead, it shrinks down to a small, ordinary black hole (like a baby).

The Analogy: Imagine trying to build a sandcastle (the black hole).

• Old Model: You have a gentle breeze. You can build a huge castle.
• New Model: You have a firehose. No matter how much sand you try to pile up, the water washes it away before the castle gets big. You can only build a tiny sandcastle.

What This Means for Real Life (and Gravitational Waves)

The paper specifically looks at recent gravitational wave events, like GW231123 (a black hole merger detected recently).

1. The "Too Heavy" Problem: The black holes in these mergers are huge (around 240 times the mass of the Sun).
2. The Conclusion: If our new "Thick Wind" model is correct, the stars that created these black holes could not have lived in a normal galaxy like ours or the Large Magellanic Cloud. Those places have too many heavy elements, which would have triggered the "hair dryer" and shrunk the stars too much.
3. The Only Place They Could Exist: These massive stars must have been born in extremely metal-poor environments. Think of the very early universe, or perhaps a very isolated, pristine pocket of space that hasn't been polluted by heavy elements yet.

The "Collision" Loophole

The paper does offer one tiny escape route. If stars crash into each other in a crowded star cluster (like a mosh pit), they might merge and grow big before the wind can strip them down.

• However: Even with this "mosh pit" scenario, the new model suggests that Intermediate-Mass Black Holes are still incredibly rare. They would be the "unicorns" of the black hole world, appearing only in the most extreme, low-metallicity environments.

Summary in One Sentence

This paper argues that powerful stellar winds act like a cosmic shredder, preventing giant stars from growing large enough to become Intermediate-Mass Black Holes unless they are born in the most pristine, heavy-element-free corners of the universe.

Why it matters: It forces astronomers to rethink where these mysterious middle-sized black holes come from. If this model is right, we need to look much further back in time or to much more isolated places in the universe to find their birthplaces.

Technical Summary

Here is a detailed technical summary of the paper "Optically thick winds of very massive stars suppress intermediate-mass black hole formation" by Torniamenti et al. (2025).

1. Problem Statement

Intermediate-mass black holes (IMBHs), with masses between $\sim 10^2$ and $10^5 M_\odot$, are the missing link between stellar-mass and supermassive black holes. Recent gravitational wave (GW) detections, such as GW190521 and GW231123, have revealed a population of IMBHs (specifically in the$\sim 100-300 M_\odot$ range).

A primary formation channel for these objects is the direct collapse of Very Massive Stars (VMS, $M > 100 M_\odot$). However, the formation of IMBHs via this channel is highly sensitive to stellar mass loss. Previous models (e.g., C15) suggested that VMSs could form IMBHs up to metallicities of $Z \approx 0.014$. The authors investigate whether a newer, more physically motivated wind model—which accounts for the transition from optically thin to optically thick winds in radiation-pressure-dominated stars—significantly alters the predicted IMBH formation rates and mass functions, particularly at intermediate and high metallicities.

2. Methodology

The study employs a two-stage computational approach combining stellar evolution and population synthesis:

• Stellar Evolution (MESA):

  • The authors modeled the evolution of non-rotating VMSs (initial masses $50-500 M_\odot$) using the MESA code.
  • Wind Model: They adopted the wind prescription by Sabhahit et al. (2022, 2023; hereafter S23). This model incorporates the transition from optically thin to optically thick winds when the Eddington ratio ($\Gamma_{\text{Edd}}$) exceeds a critical threshold. In the optically thick regime, mass-loss rates are significantly enhanced ($\dot{M} \gtrsim 10^{-4} M_\odot \text{yr}^{-1}$).
  • Comparison: Results were compared against the standard C15 wind model (Chen et al. 2015), which uses fitting formulas based on Vink et al. (2000, 2001) but lacks the specific optically thick transition physics.
  • Physics: Models included mixing-length theory, Ledoux criterion for convection boundaries, exponential overshooting, and extended nuclear burning networks. Evolution was tracked until core collapse or pair-instability.

• Population Synthesis (SEVN):

  • The SEVN code was used to simulate populations of single stars and binary systems.
  • Initial Conditions:
    • Primary masses drawn from a Kroupa IMF ($50-500 M_\odot$).
    • Binary parameters (mass ratio, period, eccentricity) drawn from distributions observed by Sana et al. (2012).
    • Metallicities ($Z$) ranged from $10^{-4}$to$0.02$ (solar).
  • Collision Handling: The code included a formalism for stellar collisions in dense clusters, assuming the collision product retains the total mass and sums the core masses of the progenitors.
  • Black Hole Formation: Final BH masses were calculated based on the final core mass, accounting for pair-instability supernovae (PISN), pulsational PISN, and fallback mechanisms.

3. Key Contributions

• Implementation of Optically Thick Winds: The study rigorously applies the S23 wind model to VMS populations, demonstrating how the onset of optically thick winds drastically increases mass loss even during the main sequence for massive stars.
• Revised Metallicity Thresholds: The paper establishes that the metallicity threshold for IMBH formation via direct VMS collapse is an order of magnitude lower than previously thought ($Z \lesssim 0.001$ vs. $Z \lesssim 0.014$).
• Impact on GW Events: The authors provide specific constraints on the metallicity of the progenitors of recent GW events (GW231123 and GW190521) based on the new wind physics.

4. Key Results

A. Stellar Core Evolution

• Optically Thick Regime: In the S23 model, VMSs enter the optically thick wind regime at $Z \geq 0.001$. These strong winds erode the stellar envelope and reduce the core mass significantly.
• Core Mass Suppression: At $Z = 0.004$, VMSs with initial masses $\geq 200 M_\odot$ lose so much mass that their final Helium cores drop below $30 M_\odot$, inhibiting even pulsational pair instability.
• Contrast with C15: In the C15 model, cores continue to grow with initial mass up to much higher metallicities ($Z \approx 0.01$). In S23, core masses flatten or decrease as $M_{\text{ZAMS}}$ increases for $Z > 0.001$.

B. Black Hole Mass Function

• IMBH Suppression:
  • S23 Model: IMBH formation via direct collapse is suppressed for $Z > 0.001$. The maximum BH mass drops from $\sim 350 M_\odot$ (at low $Z$) to $\sim 20 M_\odot$ at solar metallicity ($Z=0.02$).
  • C15 Model: IMBHs form up to $Z \approx 0.012$, with masses reaching $\sim 400 M_\odot$.
• Pair-Instability Gap: Both models predict a mass gap between $65 M_\odot$and$135 M_\odot$ for single stars and binary mergers, though stellar collisions can fill this gap with single BHs.

C. Binary Systems and Mergers

• Binary BH Mergers: In the S23 model, IMBH remnants from binary mergers are only possible at $Z \leq 0.002$. At higher metallicities, the primary BH masses in binaries are limited to $< 50 M_\odot$.
• Stellar Collisions: Even with optimistic assumptions (no mass loss during collisions), the fraction of IMBHs in the S23 model at $Z=0.004$ is less than $0.2%$, two orders of magnitude lower than in the C15 model.

D. Implications for GW231123 and GW190521

• GW231123: The primary BH of this event ($\sim 240 M_\odot$) implies that if it formed via direct VMS collapse, the progenitor system must have had a metallicity $Z < 0.002$.
• GW190521: The primary mass of GW190521 ($\sim 142 M_\odot$) falls within the pair-instability mass gap predicted by both models, suggesting a dynamical origin (e.g., hierarchical mergers) rather than direct stellar collapse, regardless of the wind model used.

5. Significance

This paper fundamentally shifts the understanding of IMBH formation channels:

1. Metallicity Constraints: It suggests that IMBHs formed from single VMS collapse are rare in environments like the Large Magellanic Cloud ($Z \sim 0.008$) and potentially the Small Magellanic Cloud ($Z \sim 0.0025$). They are likely restricted to very low-metallicity environments ($Z < 0.001$).
2. GW Interpretation: The detection of massive BHs in the GW231123 event strongly points to a low-metallicity origin or a dynamical formation channel (e.g., in dense star clusters), as direct collapse at higher metallicities is now deemed inefficient due to optically thick winds.
3. Model Validation: The results support the S23 wind model, which successfully reproduces observed VMS temperatures and pair-instability supernova rates, while highlighting the critical role of radiation-driven, optically thick winds in shaping the black hole mass spectrum.

In conclusion, the authors demonstrate that optically thick winds act as a powerful suppressor of IMBH formation, drastically reducing the mass range of black holes produced by VMSs at intermediate metallicities and necessitating a re-evaluation of the formation environments for the most massive gravitational wave sources.