# Higher order gravitational-wave modes with likelihood reweighting

## TL;DR

This paper presents an efficient two-step Bayesian method to incorporate higher-order gravitational-wave modes into astrophysical inference, improving parameter estimation without high computational costs, demonstrated on GWTC-1 data.

## Contribution

The authors introduce a novel likelihood reweighting approach that allows inclusion of higher-order modes in gravitational-wave analysis efficiently.

## Key findings

- Higher-order modes provide additional information but are computationally challenging to include.
- The proposed method successfully incorporates higher modes into Bayesian inference.
- Weak preference for higher modes was found in GWTC-1 events.

## Abstract

The gravitational waveform of a merging stellar-mass binary is described at leading order by a quadrupolar mode. However, the complete waveform includes higher-order modes, which encode valuable information not accessible from the leading-order mode alone. Despite this, the majority of astrophysical inferences so far obtained with observations of gravitational waves employ only the leading order mode because calculations with higher-order modes are often computationally challenging. We show how to efficiently incorporate higher-order modes into astrophysical inference calculations with a two step procedure. First, we carry out Bayesian parameter estimation using a computationally cheap leading-order-mode waveform, which provides an initial estimate of binary parameters. Second, we weight the initial estimate using higher-order mode waveforms in order to fold in the extra information from the full waveform. We use mock data to demonstrate the effectiveness of this method. We apply the method to each binary black hole event in the first gravitational-wave transient catalog GWTC-1 to obtain posterior distributions and Bayesian evidence with higher-order modes. Performing Bayesian model selection on the events in GWTC-1, we find only a weak preference for waveforms with higher order modes. We discuss how this method can be generalized to a variety of other applications.