Optimizing the regimes of the Advanced LIGO gravitational wave detector for multiple source types

We developed algorithms which allow us to find regimes of the signal-recycled Fabry-Perot–Michelson interferometer [for example, the Advanced Laser Interferometric Gravitational Wave Observatory (LIGO)], optimized concurrently for two (binary inspirals $+$ bursts) and three (binary inspirals $+$ bursts $+$ millisecond pulsars) types of gravitational wave sources. We show that there exists a relatively large area in the interferometer parameters space where the detector sensitivity to the first two kinds of sources differs only by a few percent from the maximal ones for each kind of source. In particular, there exists a specific regime where this difference is $\approx 0.5\%$ for both of them. Furthermore, we show that even more multipurpose regimes are also possible that provide significant sensitivity gain for millisecond pulsars with only minor sensitivity degradation for binary inspirals and bursts.

Figure 1

Relative improvement in signal-to-noise ratio ${\rho }_{\mathrm{burst}}/{\rho }_{\mathrm{burst}}^{@\mathrm{NS}}$ for bursts of GW radiation as a function of relative deterioration in SNR for NS binaries $1-{\rho }_{\mathrm{NS}}/{\rho }_{\mathrm{NS}}^{\max }$. Here ${\rho }_{\mathrm{burst}}^{@\mathrm{NS}}$ is the value of SNR for GW burst sources when the interferometer is tuned for reaching maximum SNR for NS binaries.

Figure 2

Relative improvement in signal-to-noise ratio ${\rho }_{\mathrm{puls}}/{\rho }_{\mathrm{puls}}^{@\mathrm{NS}}$ for one of the high-frequency pulsars (J0034-0534 with rotational frequency $f_0\simeq 532$, 7 Hz) as a function of relative deterioration in SNR for NS binaries $1-{\rho }_{\mathrm{NS}}/{\rho }_{\mathrm{NS}}^{\max }$. Here ${\rho }_{\mathrm{puls}}^{@\mathrm{NS}}$ is the value of SNR for GWs from specified pulsar when the interferometer is tuned for reaching maximum SNR for NS binaries.

Figure 3

Principle optical scheme of signal-recycled interferometer of Advanced LIGO GW detector.

Figure 4

Schematic diagram of the quantum measurement device. $G$ is the classical observable (e.g.,force) acting on the probe that is measured. $\widehat{Z}$ is the output signal of the detector device, $\widehat{x}$ is the linear observable (e.g., displacement) of the probe, and $\widehat{F}$ is the linear observable of the detector which describes the backaction force on the probe.

Figure 5

Main classical noises planned for the Advanced LIGO interferometer.

Figure 6

Contour plot of sensitivity for standard NS-NS binaries ${\rho }_{\mathrm{NS}}/{\rho }_{\mathrm{NS}}^{\max }$ as a function of $\Gamma$, $\beta$. Point MAX corresponds to the sensitivity maximum, points A–D to typical suboptimal tunings shown in Fig. 7, point O to double (NS $+$ bursts) optimal regime, and points P, Q, and R to triple (NS $+$ bursts $+$ pulsar) suboptimal regimes.

Figure 7

Quantum noise spectral densities optimized for standard NS binary sources (point MAX in Fig. 6) and four typical suboptimal spectral densities (points A–D in Fig. 6) (see parameters in Table. ).

Figure 8

Contour plot of burst sensitivity ${\rho }_{\mathrm{burst}}/{\rho }_{\mathrm{burst}}^{\max }$ as a function of $\Gamma$, $\beta$. Point MAX corresponds to the sensitivity maximum, points A–D (see parameters in Table. ) to typical suboptimal tunings shown in Fig. 9, point O to double (NS $+$ bursts) optimal regime, and points P, Q, and R to triple (NS $+$ bursts $+$ pulsar) suboptimal regimes.

Figure 9

Quantum noise spectral densities optimized for burst sources (point MAX in Fig. 8) and four typical suboptimal spectral densities (points A–D in Fig. 8 with parameters given in Table. ).

Figure 10

Parametric plot of ${\rho }_{\mathrm{burst}}(\lambda )/{\rho }_{\mathrm{burst}}^{\max }$ against ${\rho }_{\mathrm{NS}}(\lambda )/{\rho }_{\mathrm{NS}}^{\max }$.

Figure 11

Quantum noise spectral densities optimized for NS sources (point MAX in Fig. 6), burst sources (point MAX in Fig. 8) and for both of them (point O in Figs. 6, 8).

Figure 12

Parametric plots of ${\rho }_{\mathrm{NS}}(\mu )/{\rho }_{\mathrm{NS}}^{\max }$ (left panel) and ${\rho }_{\mathrm{burst}}(\mu )/{\rho }_{\mathrm{burst}}^{\max }$ (right panel) against ${\rho }_{\mathrm{puls}}(\lambda )/{\rho }_{\mathrm{puls}}^{\max }$ for two optimization regimes: with priority to ${\rho }_{\mathrm{NS}}$ ($\lambda =1$) and to ${\rho }_{\mathrm{burst}}$ ($\lambda =0$).

Figure 13

Typical quantum noise spectral densities produced by the triple (NS $+$ bursts $+$ pulsars) optimization procedure.