The proper way to spatially decompose the gravitational-wave origin in stellar collapse simulations

TL;DR

This paper clarifies the correct method for spatially decomposing gravitational-wave signals in stellar collapse simulations, demonstrating its importance through comparison with improper methods and validating it against perturbative calculations.

Contribution

It introduces the proper way to perform spatial decomposition of GW strain using the quadrupole formula in hydrodynamic simulations, correcting previous approaches.

Findings

Proper spatial decomposition aligns with perturbative results.

Improper methods can lead to significant inaccuracies.

The approach improves interpretation of GW signals from stellar collapse.

Abstract

Gravitational waves (GWs) hold great potential for an unobscured view of protoneutron stars (PNSs) formed as a result of stellar collapses. While waiting for discovery, deepening the understanding of GW emission in theory is beneficial for both optimizing searching strategies and deciphering the eventual data. One significant aspect is the spatially dependent contribution to the overall GW signal extracted from sophisticated hydrodynamic simulations. I present the proper way to perform the spatial decomposition of GW strain with the quadrupole formula in the slow-motion and weak-field approximation. Then I demonstrate the approach using the results of a 2D axisymmetric pseudo-Newtonian hydrodynamic simulation of core-collapse supernova. I show a detailed comparison between the proper and improper methods and discuss the possible consequences based on the improper method. Moreover, with the correct approach, the GW spatial profiles agree well with those calculated from a consistent perturbative method.