Analysis of Ringdown Overtones in GW150914

We analyze GW150914 postmerger data to understand if ringdown overtone detection claims are robust. We find no evidence in favor of an overtone in the data after the waveform peak. Around the peak, the Bayes factor does not indicate the presence of an overtone, while the support for a nonzero amplitude is sensitive to changes in the starting time much smaller than the overtone damping time. This suggests that claims of an overtone detection are noise dominated. We perform GW150914-like injections in neighboring segments of the real detector noise, and we show that noise can indeed induce artificial evidence for an overtone.

Figure 1

Mass and spin of the remnant BH for GW150914. Each panel corresponds to a different value of $\mathrm{\Delta }{t}_{\text{start}}^{\mathrm{H}1}=t_{\text{start}}^{\mathrm{H}1}-{\overline{t}}_{\mathrm{peak}}^{\mathrm{H}1}$, quoted in units of $M$. All $\mathrm{\Delta }{t}_{\text{start}}^{\mathrm{H}1}$ values used in panels with dark (light) gold backgrounds are consistent with the median of the $t_{\mathrm{peak}}^{\mathrm{H}1}$ distribution at $1\sigma$ ($2\sigma$). In each panel, dashed black, solid red, and solid blue contours correspond to 90% credible level in the BH parameters measured using the full IMR [70], ${\text{Kerr}}_{221}$, and ${\text{Kerr}}_{220}$ models, respectively.

Figure 2

Top: log-Bayes factor $({\log }_{10}{\mathcal{B}}_{220}^{221})$ between the ${\text{Kerr}}_{221}$ and ${\text{Kerr}}_{220}$ hypotheses as a function of $\mathrm{\Delta }{t}_{\text{start}}^{\mathrm{H}1}=t_{\text{start}}^{\mathrm{H}1}-{\overline{t}}_{\mathrm{peak}}^{\mathrm{H}1}$. For the GW150914 signal (red crosses), ${\overline{t}}_{\mathrm{peak}}^{\mathrm{H}1}$ is the median of the posterior distribution from the full IMR analysis; dark (light) gold bands correspond to the $1\sigma$ ($2\sigma$) uncertainties on the median. For the GW150914-like injections (black), $t_{\mathrm{peak}}^{\mathrm{H}1}$ is computed from the simulation, and so it is known exactly. Black dots correspond to a GW150914-like injection in zero noise. The blue dots (and related “error bars”) are computed by repeating the analysis at each $t_{\text{start}}^{\mathrm{H}1}$ under different realizations of the real detector noise close to the GW150914 trigger. Bottom: amplitude of the overtone $A_1$ measured for different $t_{\text{start}}^{\mathrm{H}1}$. The red (black) curves correspond to the measurement obtained from the GW150914 signal (GW150914-like injection in zero noise). The blue curves are the overtone amplitudes measured on the GW150914-like injection in real noise.