PAPER 2 - A Statistical Equilibrium Framework for Compact Object Populations
PAPER 2 - A Statistical Equilibrium Framework for Compact Object Populations
DOI: To Be Assigned
John Swygert
March 9, 2026
Abstract
Astrophysical populations often exhibit structured distributions rather than purely stochastic behavior. This paper proposes a simple statistical framework for evaluating whether compact object populations, such as black holes observed through gravitational-wave detections, may exhibit equilibrium clustering. The proposed metric compares the variance of observed distributions with randomized baselines to identify potential structural constraints within astrophysical formation processes.
1. Introduction
Many astrophysical systems exhibit statistical structure resulting from physical formation mechanisms, environmental constraints, or dynamical evolution.
Gravitational-wave observations provide a rapidly growing dataset of compact object mergers that can be analyzed statistically to explore the population structure of black holes and neutron stars.
Rather than assuming purely random distributions, it is useful to examine whether observational populations exhibit clustering that may reflect underlying physical equilibria.
2. Equilibrium Indicator
To explore potential clustering, a simple equilibrium metric is defined as:
E = \frac{Var(observed)}{Var(random)}
Where:
is the variance of the measured population distribution
is the variance of a simulated random distribution with equivalent sample size
Interpretation:
Figure 2. Comparison of stochastic and clustered point distributions illustrating the equilibrium indicator E = Var(observed) / Var(random). Randomized datasets exhibit greater dispersion, whereas clustered populations display reduced variance relative to randomized expectation.
3. Example Application
Applying this indicator to preliminary gravitational-wave mass data suggests that observed distributions may be slightly more clustered than purely random expectations.
However, the current dataset remains limited, and full statistical validation will require:
Monte Carlo simulations
Detection bias corrections
Population synthesis modeling
4. Limitations
The equilibrium indicator presented here is intended as a preliminary exploratory tool rather than a definitive statistical test.
Future work should incorporate:
Bayesian population inference
selection effects in gravitational-wave detection
astrophysical formation modeling
5. Conclusion
This framework offers a simple statistical approach for exploring potential structure within astrophysical populations. As gravitational-wave catalogs continue to expand, such tools may help identify whether compact object formation follows stochastic processes or exhibits equilibrium constraints.
References
Abbott, B. P. et al.
GWTC Gravitational Wave Transient Catalogs.
Loredo, T. J. (2012).
Statistical inference in astrophysics.
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