1. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Brownian thermal noise associated with attachments to potential ET sized test masses Liam Cunningham, Daniel Heinert*, Iain Martin, Peter Murray, Ronny Nawrodt, Sheila Rowan, Jim Hough * Friedrich-Schiller-Universität Jena 1

2. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Overview Introduction Test mass modelling TN calculation using ANSYS –TN of attachment (bonded ears) –TN of HR multilayer coating –requirements to the mechanical loss for bonding optical structures to the test mass Summary

3. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Introduction 3 rd generation detector –move to silicon masses and suspension elements –~ 120 … 200 kg masses –cryogenic temperatures –hydroxide catalysis bonding seems to be a useful jointing technique –coating thermal noise dominates in current estimates –novel optical concepts need to be considered

4. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Model test mass Silicon test mass 500mm diameter 300 mm thick Representative ears 35 x120 x15 mm bonded to flats. Flats on side 95 mm high

5. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Levins 1 method for calculation of thermal noise Dissipated power as function of strain energy, , and loss factor,  Thermal noise can be calculated from average dissipated power, W diss, caused by deformation of test mass by a notional oscillating force, F 0, associated with a test pressure having the same spatial distribution as the laser cross section at measurement frequency f and temperature T. 1 Y. Levin, Phys. Rev. D, 57, 659-663, 1998

6. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Properties used for calculations Silica coatingTa2O5 coatingSilicon (111)Sodium Silicate Bond Material Young’s Modulus 7.2 x 10 10 Pa1.4 x10 11 Pa1.8 x10 11 Pa7.9 x 10 9 Pa Poisson's Ratio 0.170.230.17 Density2200 kg/m³8200 kg/m³2330 kg/m³2200 kg/m³ loss 290 K4 x10 -5 2.4 x10 -4 10 -9 0.11 * loss 18 K8.1 x10 -4 8.6 x10 -4 10 -8 (0.11 – assumed) * The mechanical dissipation in a bond layer was obtained from silica-silica bonds. A temperature independent bond loss was assumed for estimates of upper limits for the TN arising from attachments.

7. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Method for simulating thin bond regions Increased density near bond Dense mesh of thin solid elements

8. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Suspension attachments thermal noise At 100 Hz thermal noise associated with 2 bonds is 5.2 x10 -22 m/√Hz at 290 K and 1.3 x10 -22 m/√Hz at 18 K. Beam induced deformation of test mass, beam radius 90 mm, 1 N normalised force.

9. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Suspension attachments thermal noise Thermal noise arising from hydroxide catalysis bonds does not contribute significantly to the total theraml noise of the test mass.

10. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Bonding novel optical components to a test mass Novel micro-/nanostructures components cannot be directly fabricated into the large test masses (technological limits). Jointing the optical component and the test mass is needed. Values for the mechanical intrinsic loss of silicon-silicon bonds are not yet available. Question: What level of bond loss causes similar TN contribution like a standard HR multilayer stack if bond layer is at depth t?

11. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Representative multi-layer coating, assuming 20 pairs Ta 2 O 5 / SiO 2 on silicon substrate at wavelength 1550 nm giving layer thickness 3.8  m and 5.6  m (includes cap layer of SiO 2 ) Ta 2 O 5 SiO 2 HR coating thermal noise Beam induced deformation of test mass, beam radius 90 mm, 1 N normalised force. At 100 Hz thermal noise value of 3.3 x10 -21 m/√Hz at 290 K and 2.3 x10 -21 m/√Hz at 18 K

12. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Attachment of waveguide mirror Bulk silicon Front layer modelling waveguide bulk bond waveguide

13. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Thermal noise associated with bonded waveguide Assuming 0.5 mm thick waveguide component bonded with a 60 nm thick bond layer. What is a tolerable mechanical loss? A bond loss of 0.01 would produce at 18 K a similar noise level as the HR stack. A mechanical loss of below 0.01 seems to be reasonable for a Si-Si-bond at low temperatures. However, systematical investigations are needed and currently under way.

14. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Independent calculation using COMSOL Significant increase of tolerable loss occures if bond layer is buried at a depth compareable to the beam radius.

15. Department of Physics & Astronomy Institute for Gravitational Research Scottish Universities Physics Alliance Conclusions Additional thermal noise contributions from hydroxide catalysis bonding: –is very small for attachments like bonded ears. –sets a reasonable limit for cryogenics bond loss for Si-Si-bonds Hydroxide catalysis bonding does not only play an important role in 1 st and 2 nd generation detectors but will also be a very attractive technique for 3 rd generation detectors.