Recurrence quantification analysis for binary neutron star coalescence simulations

Abstract A binary neutron star (BNS) coalescence emits gravitational waves (GW) that reveal the passage through three stages: inspiral, merger, and post-merger. Each stage exhibits distinct nonlinear dynamical behavior, which can be characterized using recurrence plots (RPs) and recurrence quantification analysis (RQA). In this work, we apply RQA to 22 simulated BNS coalescences to identify the patterns in the RPs and to determine from a plausible criterion the most adequate threshold $$\varepsilon$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> that might reflect the differences among the stages in a general manner. According to the behavior of six RQA parameters and sweeping a wide range of threshold values, a criterion based on the behavior of entropy and recurrence rate has been established and validated using statistical tests. We verified that all parameters satisfy the statistical condition based on the p -value, demonstrating that the criterion yields RPs capturing the characteristic dynamics of each stage of the BNS coalescence. This study provides a quantitative basis for analyzing RPs from GW signals and opens the possibility of using other recurrence methods in the analysis of time series coming from astrophysical phenomena involving stage transitions.