Measurements of the Young’s modulus of hydroxide catalysis bonds, and the effect on thermal noise in ground-based gravitational wave detectors

With the outstanding results from the detection and observation of gravitational waves from coalescing black holes and neutron star inspirals, it is essential that pathways to further improve the sensitivities of the LIGO and VIRGO detectors are explored. There are a number of factors that potentially limit the sensitivities of the detectors. One such factor is thermal noise, a component of which results from the mechanical loss in the bond material between the silica fibre suspensions and the test mass mirrors. To calculate its magnitude, the Young’s modulus of the bond material has to be known with reasonable accuracy. In this paper we present a new combination of ultrasonic technology and Bayesian analysis to measure the Young’s modulus of hydroxide catalysis bonds between fused silica substrates. Using this novel technique, we measure the bond Young’s modulus to be $18.5{\pm }_{2.3}^{2.0}\mathrm{GPa}$. We show that by applying this value to thermal noise models of bonded test masses with suitable attachment geometries, a reduction in suspension thermal noise consistent with an overall design sensitivity improvement allows a factor of 5 increase in event rate to be achieved.

Figure 1

Experiment schematic: The transducer sends out an ultrasonic pulse that travels through the fused silica sample on the right. Signals are reflected back from the embedded HCB and rear face of the silica sample, received by the same transducer and recorded.

Figure 2

Acoustic pulse reflection data of a hydroxide catalysis bonded fused silica sample. The signal reflected from the bond interface is shown in the middle, and the silica-to-air interface (i.e., input signal) on the right.

Figure 3

Left: SEM image of the bond (vertical line) with polished fused silica on either side. Right: Surface map of combined bond thickness measurements across sample 1. Blank spaces are visible where the surface became too highly charged to measure.

Figure 4

Time-domain and frequency-domain examples of the reflected bond signal and corresponding signal components are shown in (a) and (b). In both figures, the first term from our model Eq. (5) is plotted in dark blue, shown with the common low frequency noise term, the second term in Eq. (5) in cyan, the combined signal and noise models, $\tilde{s}$ in black. The measured data, $\tilde{b}$ is shown here in red. The residuals are also shown in dark green in (a). Each curve represents a set of curves drawn from the posterior distribution on the unknown parameters $R,dt,\overrightarrow{\varphi }$.

Figure 5

Individual $E_2$ posteriors of each measured sample. The final combined posterior is shown in black and a 90% confidence level is shown in blue.

Figure 6

Comparisons of ear design geometries for aLIGO and $\mathrm{A}+$.

Figure 7

FE model of an $\mathrm{A}+$ bonded test mass, with the new 4 ear design.