Thermal noise in GW detectors How much can an object be at rest on Earth? Geppo Cagnoli INFN - Firenze University of Glasgow ITIS Citta’ di Castello UTB - Physics & Astronomy - 16 Sept. 2009

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors2 of 22 Fixing the problem Earth is not an inertial reference frame Tidal effects Geological movements Time scale or frequency range has to be defined 1Hz to 10 kHz

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors3 of 22 Limiting the range We could live the object on a table but the Earth is noisy Uncertainty Principle  E  t = h / 4  For a 10 kg mass: 10 orders of magnitude

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors4 of 22 Mechanical Filtering of the Seismic Noise Connected to ground Object x y A simple pendulum provides a good filtering above the resonant frequency Possible improvements Use a spring to filter the vertical noise too With a multiple pendulum configuration is possible to fill the10 orders of magnitude We could use some damper to reduce the resonant peaks

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors5 of 22 Virgo Superattenuator THE REFERENCE POINT !!

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors6 of 22 The Brownian motion A challenge for the audience: how would you establish that this endless motion is not due to the activity of living organisms? 2 micron particles in water (left) and in concentrated DNA solution (right), 4 s of data Botanist Robert Brown, ( ) In 1832 the botanist Robert Brown observed a random motion of pollen and dust grains suspended in water

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors7 of 22 Einstein’s Insight of 1905: A Way to Measure k B Einstein’s specific prediction: in pure water at temperature 17 o C (290 K or 63 o F), a particle of diameter 1 m will move an average horizontal distance equal to 6 m in one minute.

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors8 of 22 Is Einstein famous for Relativity?

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors9 of 22 Random motion also in mechanical systems R.K.Pathria Statistical Mechanics Pergamon Press Reducing the air pressure, the r.m.s. motion doesn’t change but the lower trace is almost monochromatic whereas the higher is more random It MUST vibrate if the equipartition theorem is right ! = kT/2 for each d.o.f.

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors10 of 22 Non equilibrium thermodynamics Non isolated system shows uncorrelated fluctuations of volume and temperature Two independent fluctuating variables: T, V system

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors11 of 22 Some comments EASY TO JUSTIFY MECHANICAL VIBRATION FROM VOLUME FLUCTUATION NO SPECTRAL INFORMATION FROM THE PREVIOUS RELATIONS RESIDUAL GAS EFFECT IS HARD TO BE IMPLEMENTED

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors12 of 22 The Fluctuation-Dissipation Theorem - 1 H.B. Callen and T.A. Welton, Phys. Rev. 83, 34 (1951) R Kubo 1966 Rep. Prog. Phys It applies to linear systems in thermal equilibrium It is used to predict the level of thermal noise of one observable x of the system Linear system X(t) F(t)

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors13 of 22 The Fluctuation-Dissipation Theorem - 2 It gives the amplitude of the fluctuations of force S ff () that is shaking the system, at each angular frequency  As seen in the experiments, the noise spectrum is shaped by the “friction” () = SPEED FORCE = v() F() Coefficient of viscosity =

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors14 of 22 The double approach to thermal noise Direct –2 variables are fluctuating –Intuitive –The spectrum is hard to extract Indirect –Dissipation replaces fluctuation –Not intuitive –Extremely powerful for noise level prediction: is “easy” to measure ()

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors15 of 22 Our system 20 to 40 kg silica mirror Suspended by 4 fibres Dielectric coatings applied on the front faces for maximizing or minimizing reflection The reference is the mass front face, where the laser beam senses the position

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors16 of 22 Volume fluctuations in solids The volume fluctuations (as the thermal ones) need to fulfil the boundary conditions Perfect solids (crystals) vibrates at their resonant frequencies The real solids have defects that move or change driven by the finite temperature of the solid: –The vibration has a continuous spectrum rather than a discrete one NO DIRECT METHOD APPROACH: –Mechanical losses of materials are investigates and thermal noise level is worked out through FDT

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors17 of 22 How to measure the mechanical loss A method widely used is to detect the free decay of the excited resonances of the system In order to know the frequency distribution of noise, the viscosity constant  has to be measured at all the frequencies of interest  A 0 /e A0A0

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors18 of 22 Sample Vacuum tank Sapphire half sphere A new sample holding system GeNS Dr. Elisabetta Cesarini

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors19 of 22 The most severe limit for IFOs: thermal noise from the coatings Alternate layers of transparent materials with different index of refraction Impedance mismatch and interference produce high coefficient of reflectivity Its structure is not compact as the substrate 10 m of coating produces more thermal noise than 10 cm of substrate

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors20 of 22 Asymmetrical thermal fluctuations are responsible of thermoelastic noise on silica fibres (DIRECT APPROACH) In linear thermoelastic effect thermal expansion coefficient  transforms thermal fluctuations in strain fluctuations  =  ·  T Thermoelastic noise Effect on suspension fibres - 1 Fibres bend and then the suspended mass is shaken. The effect is small but relevant in GW detectors Same kind of deformations occur in mirrors

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors21 of 22 Thermoelastic noise Effect on suspension fibres - 2 The heat transfer sets a characteristic time scale that makes the noise spectrum frequency dependent, like: Debye peak: Noise or friction intensity frequency Fused silica facts: — Low  — Low  — High strength

16 Sept 2009UTB - Geppo Cagnoli - Thermal noise in GW detectors22 of 22 Fused silica fibre production and testing The CO2 laser pulling machine was developed in Glasgow The machine was financed by EGO as well as PPARC and in 2006 it was delivered to Pisa The machine was then adapted to the Virgo necessities and thanks to the excellent work of Dr. Matteo Lorenzini, Francesco Piergiovanni, Dr. Filippo Martelli, Virgo now has fused silica suspensions of high precision and strength