Introduction

bayRing is a Python package for fitting analytical ringdown models to numerical-relativity waveforms. The core use case is the extraction, comparison and validation of ringdown model parameters on NR simulations, with the same QNM conventions and waveform infrastructure used by pyRing.

The package depends on:

• Waveform infrastructure: pyRing provides waveform interfaces and shared ringdown utilities, and the hm_nc_fit branch of pyRing should be installed to use bayRing.

• QNM spectra: qnm provides Kerr QNM frequencies and damping times.

• Nested sampling: cpnest and raynest provide sampling backends.

• Point estimates: scipy.optimize.least_squares provides the minimization backend, and the linear-inversion solver provides direct Kerr amplitude estimates.

• Catalogue readers: SXS, RIT, Teukolsky, cbhdb, C2EFT and related data formats are handled by catalogue-specific readers.

What bayRing Fits

bayRing fits:

• NR multipole: a single complex NR multipole at a time.

• Waveform components: against real and imaginary waveform components on the NR time grid.

• Fit interval: a cropped time interval between t-start and t-end in units of the total mass M.

• Uncertainty model: model residuals weighted by the selected NR error estimate.

The fitted data vector is

\[h_{\ell m}^{\mathrm{NR}}(t) = h_{\ell m}^{\mathrm{R}}(t) + i h_{\ell m}^{\mathrm{I}}(t).\]

The crop is usually measured relative to the peak of the selected waveform amplitude. The model predicts the same complex multipole on the same time grid.

This makes bayRing useful for:

• QNM amplitudes: estimate amplitudes and phases in a chosen NR multipole.

• Ringdown start studies: test when constant-amplitude QNM superpositions describe a simulation over a selected time interval.

• Template comparisons: compare Kerr, Damped-sinusoids, KerrBinary and TEOBPM templates.

• Higher modes: study higher multipoles and spherical-spheroidal mode-mixing effects.

• Nonlinear and non-QNM ringdown content: validate second-order QNM contributions and late-time tail terms.

• Waveform quality checks: compute mismatches and detector-scaled optimal SNR diagnostics.

Workflow At A Glance

The figure below shows the main workflow for a time-domain NR fit. The shaded region is the only part of the loaded waveform that enters the likelihood. The rest of the waveform is still useful context for peak finding, post-processing and visual diagnostics.