Low-frequency sensitivity limitations in current and future gravitational-wave detectors

Seismic Newtonian noise and controls and sensing noises are the big challenges to extend the observation of terrestrial gravitational wave detectors towards lower frequencies. Improving low-frequency sensitivity is challenging but with high rewards. The motivation to improve the low-frequency sensitivity of the observatories is: to enable the deepest multi-messenger studies of binary neutron-star mergers, study the properties of gravitational wave sources with unprecedented precision, observe black-hole binaries with masses beyond the currently accessible mass range. In the thesis, SPECFEM3D’s, which is a state-of-the-art finite-element simulation software for seismic fields, capabilities to provide estimates of gravitoelastic correlations, which are required for an optimized deployment of seismometers for gravity noise cancelation, are demonstrated. The model on which simulations are run takes into account the local topography at a candidate site of the Einstein Telescope at Sardinia. The work in this thesis provides the first extensive and conclusive study of the impact of topographic scattering on seismic coherence and on the prediction of gravitational coupling between seismic surface displacement and an underground test mass. I found that A3-topography has generally a significant impact on seismic and gravitoelastic correlations. Topography scatters out energy from Rayleigh waves above 4 Hz protecting the test mass from the influence of distant seismic sources. As expected, symmetries of the field of gravitoelastic correlations are broken by topography leading to unique solutions of optimal seismometer placement for gravity-noise cancellation. All pieces together for a Bayesian seismic-array design for Newtonian noise cancelation are outlined. Another topic elaborated in this thesis is the Angular Sensing and Control system, which suppresses the residual angular motion of suspended test masses. Since during the O3 run the LIGO noise budget was dominated by the angular sensing and controls noise approximately between 10 Hz and 25 Hz, it is crucial to mitigate this noise in order to achieve sensitivity improvements. The Lightsaber, an Angular Sensing and Control system time-domain simulator is presented. The Lightsaber is implemented for LIGO Hanford and for the Input Mode Cleaner (IMC) at the Caltech 40m prototype. The main mechanical degree of freedom simulated in Lightsaber is the pitch motion of the test masses, which introduces the dominant angular noise in gravitational wave measurements. The Lightsaber’s plant model is constructed from several static second-order section models representing the mechanical and feedback system together with several nonlinear optomechanical couplings. LIGO-Lightsaber has the linear feedback filters implemented in a global basis as used at LIGO Hanford Observatory during the O3 run. The mechanical system is simulated in its local degrees of freedom. There is the feed-forward radiation pressure compensation implemented. Lightsaber-IMC is the simulation of the Angular Sensing and Control system of the triangular cavity of the IMC at the Caltech 40m prototype. The main feedback control filters are implemented in a sensing basis. Apart from that, all other filters are in the local basis. For Lightsaber-IMC I did the calibration, obtained input noises, and did comparisons with the real system. I made Simulink block diagrams for both Lightsaber implementations. The Lightsaber is sufficiently accurate to serve, at least, as a useful modeling tool especially when high precision is not required, i.e., for noise budget calculations of current and future gravitational wave detectors. It is possible to modify the mechanical system, angular readouts, etc to represent other detectors. So, the Lightsaber is a more universal simulation tool, and it finds applications in more than one plant model. The Angular Sensing and Control system is a complex component of the detector, which has proven to be difficult to model. The Lightsaber, being a fully nonlinear, time-domain representation, allows researchers to test novel feedback-filter designs before implementation in a detector. This can be especially valuable for certain nonstationary and nonlinear modern control schemes, such as Reinforcement Learning. The Reinforcement Learning based controller can overcome the abilities of the optimal linear filter. What I obtained using Reinforcement Learning is the reduction of the pitch angular motion of 6–8 times in 15–20 Hz frequency band, with respect to the linear controller. First tests at the Caltech 40m prototype with the IMC control success- fully demonstrated the use of Reinforcement Learning in interferometer control. The control algorithms were trained with Lightsaber-IMC. The Angular Sensing and Control system remains one of the major challenges of detector control, which needs to be addressed to be able to improve the low-frequency sensitivity of cur- rent detectors, and a detailed understanding of noise produced by this system is crucial to plan future generations of gravitational wave detectors.