Search for continuous gravitational waves: Improving robustness versus instrumental artifacts

The standard multidetector $\mathcal{F}$-statistic for continuous gravitational waves is susceptible to false alarms from instrumental artifacts, for example monochromatic sinusoidal disturbances (“lines”). This vulnerability to line artifacts arises because the $\mathcal{F}$-statistic compares the signal hypothesis to a Gaussian-noise hypothesis, and hence is triggered by anything that resembles the signal hypothesis more than Gaussian noise. Various ad-hoc veto methods to deal with such line artifacts have been proposed and used in the past. Here we develop a Bayesian framework that includes an explicit alternative hypothesis to model disturbed data. We introduce a simple line model that defines lines as signal candidates appearing only in one detector. This allows us to explicitly compute the odds between the signal hypothesis and an extended noise hypothesis, resulting in a new detection statistic that is more robust to instrumental artifacts. We present and discuss results from Monte-Carlo tests on both simulated data and on detector data from the fifth LIGO science run. We find that the line-robust statistic retains the detection power of the standard $\mathcal{F}$-statistic in Gaussian noise. In the presence of line artifacts it is more sensitive, even compared to the popular $\mathcal{F}$-statistic consistency veto, over which it improves by as much as a factor of two in detectable signal strength.

Figure 1

Example of the normalized SFT power ${\mathcal{P}}^X(f)$ as a function of frequency $f$ for LIGO H1 (solid) and L1 (dashed) for simulated Gaussian data containing a line in H1. The horizontal line shows the threshold ${\mathcal{P}}_{\mathrm{thr}}$ at a false-alarm level of $p_{\mathrm{FA},\mathcal{P}}={10}^{-9}$.

Figure 2

Detection probability $p_{\det }$ as a function of false-alarm $p_{\mathrm{FA}}$ of different synthesized statistics, for a signal population of fixed SNR of ${\rho }_{\mathrm{S}}=6$ in pure Gaussian noise ($f_{\mathrm{L}}=0$, ${\rho }_{\mathrm{L}}=0$). Statistical errors are similar to the line width.

Figure 3

Detection probability $p_{\det }$ as a function of false-alarm $p_{\mathrm{FA}}$ for different synthesized statistics, for a signal population with fixed SNR of ${\rho }_{\mathrm{S}}=6$ in Gaussian noise with 10% line contamination, with line-SNR of (a) ${\rho }_{\mathrm{L}}=9$ and (b) ${\rho }_{\mathrm{L}}=15$. Statistical errors are similar to the line width.

Figure 4

Comparison of “tuned” statistics ${}^{(-n)}{O}_{\mathrm{S}\mathrm{G}\mathrm{L}}$ (solid lines) using “perfect knowledge” line-priors $\{o_{\mathrm{LG}}^{\mathrm{H}1}=1/9,o_{\mathrm{LG}}^{\mathrm{L}1}={10}^{-3}\}$ versus “untuned” statistic ${}^{(-n)}{O}_{\mathrm{S}\mathrm{G}\mathrm{L}}^{(0)}$ (dashed lines) using uninformative line-priors $o_{\mathrm{LG}}^X=1$. Detection probability $p_{\det }$ as a function of false-alarm $p_{\mathrm{FA}}$ of different synthesized statistics, for a signal population with fixed SNR of ${\rho }_{\mathrm{S}}=6$ in Gaussian noise with 10% line contamination, with line-SNR of (a) ${\rho }_{\mathrm{L}}=9$ and (b) ${\rho }_{\mathrm{L}}=15$. Statistical errors are similar to the line width.

Figure 5

Normalized average SFT power ${\mathcal{P}}^X(f)$ of Eq. (63) as a function of frequency $f$ for LIGO H1 (solid) and L1 (dashed) data used in the coherent searches. The horizontal lines mark, for each detector, the threshold ${\mathcal{P}}_{\text{thr}}^X$ at $p_{\mathrm{FA},\mathcal{P}}={10}^{-9}$ used in the line prior estimation. The panels show: ($\tilde{\mathrm{a}}$) a quiet band, ($\tilde{\mathrm{b}}$), ($\tilde{\mathrm{c}}$) two bands with lines, ($\tilde{\mathrm{d}}$) a band with multiple disturbances. See Table 1 for more details on these data sets.

Figure 6

Detection efficiency $p_{\det }$ as a function of scaled signal amplitude $h_0/\sqrt{S_{\mathrm{n}}}$ for four different coherent statistics: $\mathcal{F}$, ${\mathcal{F}}^{+\text{veto}}$, $O_{\mathrm{S}\mathrm{L}}^{(0)}$, and ${}^{(-6)}{O}_{\mathrm{S}\mathrm{G}\mathrm{L}}$. Statistical errors are similar to the size of the symbols. The dashed horizontal line marks the 95% detection probability level. The panels show: ($\tilde{\mathrm{a}}$) a quiet band, ($\tilde{\mathrm{b}}$), ($\tilde{\mathrm{c}}$) two bands with lines, ($\tilde{\mathrm{d}}$) a band with multiple disturbances. See Fig. 5 and Table 1 for more details on these data sets.

Figure 7

Normalized average SFT power ${\mathcal{P}}^X(f)$ of Eq. (63) as a function of frequency $f$ for LIGO H1 (solid) and L1 (dashed) data used in the semicoherent searches. The horizontal lines mark, for each detector, the threshold ${\mathcal{P}}_{\mathrm{thr}}^X$ at $p_{\mathrm{FA},\mathcal{P}}={10}^{-9}$ used in the line prior estimation. The panels show: ($\hat{\mathrm{a}}$) a quiet band, ($\hat{\mathrm{b}}$), ($\hat{c}$) two bands with lines, ($\hat{\mathrm{d}}$) a band with multiple disturbances. See Table 2 for more details on these data sets.

Figure 8

Detection efficiency $p_{\det }$ as a function of scaled signal amplitude $h_0/\sqrt{S_{\mathrm{n}}}$ for four different semicoherent statistics: $\widehat{\mathcal{F}}$, ${\widehat{\mathcal{F}}}^{+\text{veto}}$, ${\widehat{O}}_{\mathrm{S}\mathrm{L}}^{(0)}$, and ${}^{(-6)}{\hat{O}}_{\mathrm{SGL}}$. Statistical errors are similar to the size of the symbols. The dashed horizontal line marks the 95% detection probability level. The panels show: ($\hat{\mathrm{a}}$) a quiet band, ($\hat{\mathrm{b}}$), ($\hat{\mathrm{c}}$) two bands with lines, ($\hat{\mathrm{d}}$) a band with multiple disturbances. See Fig. 7 and Table 2 for more details on these data sets.