Impact of Detector Calibration Accuracy on Black Hole Spectroscopy

TL;DR

This study evaluates how detector calibration errors impact black hole spectroscopy using quasinormal modes (QNMs) extracted with a rational QNM filter. By injecting numerically simulated ringdown signals and applying tunable calibration errors, the authors quantify biases in remnant mass and spin estimates through metrics p(M_t, χ_t) and ε, across pure signals and noisy data. They find that current calibration levels (≈10% magnitude, ≈10° phase) are adequate for existing observations, but next-generation detectors with high ringdown SNR (≈120–125) require stricter standards, approximately |δA_peak| ≤ 4% and |δφ_peak| ≤ 4° to keep biases within 3σ. These results establish concrete calibration benchmarks crucial for robust GR tests in the era of advanced and third-generation gravitational-wave observatories.

Abstract

Systematic errors in detector calibration can bias signal analyses and potentially lead to incorrect interpretations suggesting violations of general relativity. In this study, we investigate how calibration systematics affect black hole (BH) spectroscopy, a technique that uses the quasinormal modes (QNMs) emitted during the ringdown phase of gravitational waves (GWs) to study remnant BHs formed in compact binary coalescences. We simulate a series of physically motivated, tunable calibration errors and use them to intentionally miscalibrate numerical relativity waveforms. We then apply a QNM extraction method -- the rational QNM filter -- to quantify the impact of these calibration errors. We find that current calibration standards (errors within $10\%$ in magnitude and $10^\circ$ in phase across the most sensitive frequency range of 20--2000 Hz) are adequate for BH ringdown analyses with existing observations, but insufficient for the accuracy goals of future upgraded and next-generation observatories. Specifically, we show that for events with a high ringdown signal-to-noise ratio of $\sim 120$, calibration errors must remain $\lesssim 4\%$ in magnitude and $\lesssim 4^\circ$ in phase to avoid introducing biases. While this analysis focuses on a particular aspect of BH spectroscopy, the results offer quantitative benchmarks for calibration standards crucial to fully realize the potential of precision tests of general relativity in the next-generation detector era.

Figures (15)

• Figure 1: Examples of realistic physical calibration errors (labelled as 'Physical CErr') estimated during O3 at aLIGO Livingston for a given outlier time (colored) L1cerrsun2021characterization and examples of artificial calibration errors (labelled as 'Artificial CErr') generated using a parameterized approach in this study (black). The solid and dashed black curves correspond to a broad error and a sharp error, respectively; see text for detailed parameters.
• Figure 2: Joint posterior distribution of $(M, \chi)$ for a GW150914-like NR waveform injected into aLIGO Hanford detector frame without additive noise by applying a $\{220,221\}$ rational filter. Left: No calibration error is added. Right: The signal is miscalibrated with an error of $\delta \phi_{\rm peak}=10^\circ$ peaked at the 220 mode frequency. The dashed contour indicates the 90% credible region obtained from the QNM rational filter analysis. The plus and cross markers indicate the true BH parameters and MAP estimates, respectively.
• Figure 3: Joint posterior quantile values, $p(M_t, \chi_t)$, for a GW150914-like NR waveform (${}_{-2}Y_{2\pm2}$ components only) injected in aLIGO Hanford without additive noise as a function of the calibration error properties: (a) frequency offset between the peak frequency of the error and the 220 QNM frequency, $\Delta f=f_{\text{peak}}-f_{220}$, where $f_{220}=249.43$ Hz ($f_{\rm width}=50$ Hz, $\delta \mathcal{A}_{\rm peak}=-10\%$, and $\delta \phi_{\rm peak}=10^\circ$), (b) error width $f_{\text{width}}$ ($\Delta f=0$, $\delta \mathcal{A}_{\rm peak}=-10\%$, and $\delta \phi_{\rm peak}=10^\circ$), (c) peak magnitude error $\delta \mathcal{A}_{\rm peak}$ ($\Delta f=0$, $f_{\rm width}=50$ Hz), and (d) peak phase error $\delta \phi_{\rm peak}$ ($\Delta f=0$, $f_{\rm width}=50$ Hz). In (c) and (d), the colored markers indicate different fixed values of $\delta \phi_{\rm peak}$ and $\delta \mathcal{A}_{\rm peak}$, respectively. The black horizontal lines indicate the perfect recovery of $(M,\chi)$ from correctly calibrated data, with all $p(M_t, \chi_t)$ aligned with 0.
• Figure 4: (Similar to Fig. \ref{['fig:pval0305']}) Joint posterior quantile values, $p(M_t, \chi_t)$, for a high mass ratio NR waveform (${}_{-2}Y_{2\pm2}$ and ${}_{-2}Y_{3\pm3}$ components only) injected in aLIGO Hanford without additive noise as a function of the calibration error properties. Here, the QNM filter includes the 220, 221, and 330 QNMs. In panel (b), both scenarios of $f_{\rm peak}$ = $f_{220}$ and $f_{\rm peak}$ = $f_{330}$ are tested (with fixed $\delta \mathcal{A}_{\rm peak}=-10\%$ and $\delta \phi_{\rm peak}=10^\circ$).
• Figure 5: Joint posterior quantile values, $p(M_t, \chi_t)$, for a GW150914-like NR waveform (SXS:BBH:0305, ${}_{-2}Y_{2\pm2}$ components only) injected into white Gaussian noise, recovered with a $\{220,221\}$ filter and plotted as a function of the offset between the peak frequency of the calibration error and the 220 QNM frequency, $\Delta f = f_{\text{peak}}-f_{220}$ (other error parameters: $f_{\text{width}}=50$ Hz, $\delta \mathcal{A}_{\rm peak}=-10\%$, $\delta \phi_{\rm peak} = 10^\circ$). Each blue dot is the mean $p(M_t, \chi_t)$ from $100$ noise realizations of the miscalibrated data (for a fixed error). The black line indicates the mean $p(M_t, \chi_t)$ from 100 noise realizations of accurately calibrated data. The gray dotted line and shade indicate the theoretical mean and $\pm 1\sigma$ bounds, respectively, for a uniform distribution.