Dark Matter Mounds from Supermassive Star Collapse Are Modelled with Full General-relativistic Analysis

The distribution of dark matter around supermassive black holes remains a key puzzle in astrophysics, and understanding its structure is crucial for interpreting future gravitational wave observations. Roberto Caiozzo from Scuola Internazionale Superiore di Studi Avanzati (SISSA), Gianfranco Bertone from the University of Amsterdam, and Piero Ullio from SISSA, alongside Rodrigo Vicente, Bradley J. Kavanagh, and Daniele Gaggero, now present a comprehensive, general-relativistic analysis of how dark matter clumps form around black holes originating from the collapse of massive stars. This work moves beyond previous simplified models by tracing the complete evolution, from the star’s initial state through its collapse and the subsequent growth of the black hole, while simultaneously modelling the surrounding dark matter. The team demonstrates that non-adiabatic collapse significantly alters the distribution of dark matter, creating a shallower ‘mound’ rather than a sharp ‘spike’, and provides a more realistic prediction for the dark matter phase-space distribution that will be essential for interpreting data from future extreme mass-ratio inspiral observations and unlocking information about both dark matter and black hole formation.

Dark Matter Spike Around Collapsing Star

This research investigates the fate of dark matter surrounding a supermassive star as it collapses into a black hole, exploring how this event affects dark matter distribution and whether a concentrated region, or spike, forms near the black hole. Scientists considered both slow, gradual collapse and rapid, disruptive collapse to understand how the speed of collapse influences the final distribution of dark matter. The study distinguishes between adiabatic collapse, where orbits adjust, and non-adiabatic collapse, where orbits are disrupted, employing general relativity to model the extreme gravitational environment. The research utilizes concepts from general relativity, such as coordinate time and the Liouville theorem, to track the evolution of dark matter particles, accurately modelling complex interactions between the collapsing star and surrounding dark matter. Analysis reveals that rapid collapse tends to suppress the formation of a dark matter spike, demonstrating the importance of relativistic effects in strong gravitational fields. Simplified scenarios, such as instantaneous collapse, serve as benchmarks for validating more complex models.

Supermassive Star Collapse and Dark Matter Reshaping

This study developed a new framework to model the gravitational collapse of supermassive stars into black holes, focusing on a realistic scenario where collapse creates a shallower dark matter concentration, termed a “mound”. Researchers meticulously tracked the evolution of the star, its subsequent collapse, and the growth of the resulting black hole, alongside the orbits of dark matter particles, accounting for non-adiabatic collapse and revealing a significant reshaping of the dark matter distribution with depletion of particles in low-binding-energy regions. Scientists modelled the supermassive star as a perfect fluid, solving equations to determine its mass at the point of collapse, and calculated the distribution of dark matter following star formation, extending established methods to a fully relativistic framework. They simulated the star’s collapse using a solution describing gravitational collapse, applying conditions to ensure a smooth transition between spacetimes, and followed the evolution of dark matter particles using the relativistic Liouville theorem. By tracing particle paths from the initial star through the collapsing spacetime, scientists determined the post-collapse dark matter distribution, accounting for the changing gravitational field and orbital mixing, providing a more realistic prediction essential for interpreting future observations and gaining insights into dark matter and black hole formation.

Dark Matter Mound Impacts Gravitational Waves

Recent work underscores the importance of fully relativistic treatments of gravitational wave dephasing caused by dark matter overdensities surrounding extreme mass-ratio inspirals. This study presents a new general-relativistic formalism modelling a realistic scenario where a supermassive star collapses into a black hole, creating a shallower dark matter overdensity, termed a “mound”. Researchers meticulously followed the evolution of the supermassive star, its subsequent collapse, and the growth of the resulting black hole, alongside the orbits of collisionless dark matter particles, providing a self-consistent picture of this complex process. The team discovered that non-adiabatic collapse reshapes the dark matter distribution, exhibiting depletion in the region of low-binding-energy orbits, signifying a reduction in the concentration of dark matter particles and altering the predicted distribution compared to previous models.

This demonstrates a substantial departure from the steep inner overdensity previously predicted, revealing a more gradual dark matter concentration around the black hole. This work provides a more realistic prediction for the dark matter phase-space distribution surrounding supermassive black holes, essential for accurately interpreting future EMRI observations, refining the understanding of how dark matter interacts with growing black holes. The team’s framework reproduces previous Newtonian results and provides a self-consistent relativistic mapping between pre- and post-collapse dark matter distributions, offering a robust foundation for future gravitational wave astronomy.

Dark Matter Response to Stellar Black Hole Formation

This work presents a new general-relativistic method for modelling the evolution of collisionless particles transitioning between different gravitational configurations, specifically focusing on the formation of supermassive black holes from collapsing stars. The team successfully evolved the distribution of dark matter particles through the star’s collapse and subsequent black hole growth, providing a more realistic picture than previous studies which often assumed instantaneous collapse. Results demonstrate that non-adiabatic collapse reshapes the dark matter distribution, leading to depletion of low-binding-energy particles and a milder density enhancement around the black hole compared to purely adiabatic scenarios. Furthermore, the research provides direct analysis of the dark matter distribution function, revealing depletion of circular and nearly circular orbits near the black hole post-collapse. The team found that subsequent adiabatic growth can erase these features, with the extent of erasure dependent on the amount of growth relative to the depletion radius. These findings have direct implications for interpreting future gravitational wave observations, as the distribution of dark matter influences the inspiral of compact objects into supermassive black holes and modifies the resulting gravitational wave signal.