Extended parameterized spin expansion formalism for ringdown analysis with GW250114

Abstract

Parameterized descriptions of black-hole quasinormal-mode spectra are essential for testing gravity with ringdown observations. We extend the Parameterized Spin Expansion Coefficients (ParSpec) formalism by simultaneously sampling the characteristic length scale $\tilde{\ell }$ and the scaling index $\tilde{p}$, rather than fixing $\tilde{p}$ to a theory-motivated integer and constraining $\tilde{\ell }$. Physically, this extension promotes the scaling of the spectral corrections coming from higher-curvature operators to an observable quantity. Methodologically, it enables us to investigate the enlarged ParSpec parameter space and identify the prior geometry induced by conditions on the effective coupling $\gamma$. We examine the robustness of the framework by using the $220$ and $220+221$ ringdown models over different start times with informative priors on mass and luminosity for GW250114, and further study a joint constraint with GW231123. We pointed out that $\gamma <1$ avoids an artificial correlation between $\tilde{p}$ and $\tilde{\ell }$ among the coupling prescriptions considered, and the choices of ringdown starting time and QNM mode content in the ParSpec framework should be matched to the information content and resolving power of the data. Higher-SNR ringdowns and hierarchical analyses of a larger event population will be required to break the $\tilde{p}$-$\tilde{\ell }$ degeneracy and directly probe the scaling structure of corrections to GR.

arXiv comment21pages,11figures