Including binaries as energy sources in globular clusters: bypassing computational limitations.
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Date
2025
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Universidad de Concepción
Abstract
La evolución de la dinámica de sistemas estelares densos, como los cúmulos globulares, es determinada por un conjunto de interacciones gravitatorias complejas. Si bien el comportamiento de estos sistemas tiende al colapso de su núcleo, las interacciones de tres cuerpos actúan como una fuente energética que revierte este proceso. Sin embargo, dado que el problema general de N cuerpos es caótico e analíticamente irresoluble, realizar un seguimiento de estas interacciones locales entre binarias y estrellas solitarias a lo largo de los mil millones de años de vida de un cúmulo resulta computacionalmente inviable. Con el fin de evitar esta limitante, desarrollamos un modelo de ecuaciones Fokker- Planck acopladas, para modelar la evolución e impacto que los encuentros entre estrellas binaries y singulares tiene en en el cúmulo. Investigamos el impacto de las poblaciones binarias comparando tres modelos evolutivos distintos: un colapso puro donde el cúmulo esta compuesto netamente por estrellas singulares, un modelo que incorpora el calentamiento binario instantáneo de tres cuerpos y un modelo con una poblacion de binarias primordiales que sigue de forma autoconsistente la difusión, el compactamiento y agotamiento de dicha población. Nuestra resultados indican que la presencia de una fracción binaria primordial (fB) altera la cronología, profundidad y termodinámica del colapso. Establecemos que las poblaciones primordiales retrasan el inicio de las oscilaciones en el tamaño del núcleo, y que dicho retraso varía directamente con la cantidad inicial de binaries. Cabe destacar que los sistemas con poblaciones primordiales bajas (fB ≤ 0, 01) se ven obligados a alcanzar densidades centrales máximas casi un orden de magnitud superiores a las provocadas por del modelo instantáneo. Esto se debe a que el calentamiento difusivo escala pobremente con la densidad, lo que proporciona una fuente energética suave que requiere una contracción más profunda para detener el colapso. Por último, demostramos que, en nuestro modelo, independientemente de la fracción binaria inicial, la fuerte dependencia de la densidad de la formación de sistemas de tres cuerpos garantiza que el rebote del núcleo se vea interrumpido por el endurecimiento y la formación de binarias.
The dynamical evolution of dense stellar systems, such as globular clusters, is fundamentally driven by complex gravitational interactions. While the general behavior of these systems inevitably leads to gravothermal core collapse, multibody interactions, such binary-single scatterings, act as a critical heat source capable of arresting and reversing this collapse. However, because the general N-body problem is chaotic and analytically intractable, tracking these local binarysingle interactions across the billion year lifespan of a cluster is computationally prohibitive. To bypass the extreme computational cost of direct N-body integration, we develop a coupled, semi-analytical Fokker-Planck solver to model the evolution of star clusters. We investigate the thermodynamic impact of binary populations by comparing three distinct evolutionary models: a pure single-star gravothermal collapse, a model incorporating instantaneous three-body binary heating, and a comprehensive population model that self-consistently tracks the diffusive heating, hardening, and depletion of a primordial binary population. Our simulations demonstrate that the presence of a primordial binary fraction (fB) fundamentally alters the timing, depth, and thermodynamics of core collapse. We establish that primordial populations delay the onset of gravothermal oscillations, with the delay scaling directly with the initial fuel reservoir. Notably, systems with trace primordial populations (fB ≤ 0.01) are forced to reach peak central densities nearly an order of magnitude higher than those driven by pure three-body heating. This occurs due to diffusive heating scaling weakly with density, providing a softer thermodynamic brake that requires a deeper contraction to halt the collapse. Finally, we show that in our model regardless of the initial binary fraction, the steep density dependence of three-body formation ensures that core bounce is stopped by combined binary hardening and formation.
The dynamical evolution of dense stellar systems, such as globular clusters, is fundamentally driven by complex gravitational interactions. While the general behavior of these systems inevitably leads to gravothermal core collapse, multibody interactions, such binary-single scatterings, act as a critical heat source capable of arresting and reversing this collapse. However, because the general N-body problem is chaotic and analytically intractable, tracking these local binarysingle interactions across the billion year lifespan of a cluster is computationally prohibitive. To bypass the extreme computational cost of direct N-body integration, we develop a coupled, semi-analytical Fokker-Planck solver to model the evolution of star clusters. We investigate the thermodynamic impact of binary populations by comparing three distinct evolutionary models: a pure single-star gravothermal collapse, a model incorporating instantaneous three-body binary heating, and a comprehensive population model that self-consistently tracks the diffusive heating, hardening, and depletion of a primordial binary population. Our simulations demonstrate that the presence of a primordial binary fraction (fB) fundamentally alters the timing, depth, and thermodynamics of core collapse. We establish that primordial populations delay the onset of gravothermal oscillations, with the delay scaling directly with the initial fuel reservoir. Notably, systems with trace primordial populations (fB ≤ 0.01) are forced to reach peak central densities nearly an order of magnitude higher than those driven by pure three-body heating. This occurs due to diffusive heating scaling weakly with density, providing a softer thermodynamic brake that requires a deeper contraction to halt the collapse. Finally, we show that in our model regardless of the initial binary fraction, the steep density dependence of three-body formation ensures that core bounce is stopped by combined binary hardening and formation.
Description
Tesis presentada para optar al grado de Magíster en Astronomía.
Keywords
Binary stars, Star clusters, Stellar dynamics