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35DBFE2B-D9E1-410C-94B8-25951E18D576

# Priorities in gravitational waveform modelling for future space-borne detectors: vacuum accuracy or environment?

Lorenz Zwick, Pedro R. Capelo, Lucio Mayer

Submitted on 8 September 2022

## Abstract

In preparation for future space-borne gravitational-wave (GW) detectors, should the modelling effort focus on high-precision vacuum templates or on the the astrophysical environment of the sources? We perform a systematic comparison of the phase contributions caused by 1) known environmental effects in both gaseous and stellar matter backgrounds, or 2) high-order post-Newtonian terms in the evolution of mHz GW sources. We use the accuracy of currently available analytical waveform models as a benchmark and find the following trends: the largest unmodelled contributions are likely environmental for binaries lighter than $\sim {10}^{7}/\left(1+z{\right)}^{2}$~M${}_{\odot }$, where $z$ is the redshift. Binaries heavier than $\sim {10}^{8}/\left(1+z\right)$~M${}_{\odot }$ do not require more accurate waveforms due to low signal-to-noise ratios (SNRs). For high-SNR sources, environmental influences are relevant at low redshift, while high-order vacuum templates are required at $z>4$. Led by these findings, we argue that including environmental effects in waveform models should be prioritised in order to maximize the science yield of mHz detectors.

## Preprint

Comment: Submitted to MNRAS

Subjects: General Relativity and Quantum Cosmology; Astrophysics - High Energy Astrophysical Phenomena