Einstein’s Dual Legacy: Thermal Noise and Gravitational Waves Gregory Harry LIGO Laboratory Massachusetts Institute of Technology University of Mississippi Department of Physics and Astronomy February 5, 2008 LIGO-G080023-00-R 1 Outline Show how understanding two of Einstein’s great ideas will allow for the birth of gravitational astronomy… • Two of Einstein’s Great Ideas – Brownian Motion – Gravitational Waves • Gravitational Wave Detection – Detection Methods – Astronomical Sources • Sensitivity and Detectability – Thermal Noise Limitations – Future Ideas and Detectors 2 Einstein and Thermal Noise Einstein’s first challenge to LIGO: “I did not believe that it was possible to study Brownian motion with such a precision.” -Letter from Albert Einstein to Jean Perrin (1909) • Einstein’s Brownian motion paper “On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat”, Annalen der Physik 17 (1905) 549. – Most cited of all Einstein’s papers • Linked fluctuations to fluid viscosity • Confirmed statistical physics models – Atoms as basic units of matter – Kinetic theory of heat • Also contributed to the theory of lasers (Einstein’s A and B coefficients) 3 Thermal Noise Fluctuations from heat bath • Mechanical ⇒ Brownian motion • Electrical ⇒ Johnson noise • Optical ⇒ Thermorefraction • Others Brownian Motion in Fluid Related to energy loss in system – Viscosity for particle in fluid – Resistance in Johnson noise – Internal friction for mechanical systems Sv Callen and Welton’s Fluctuation- Dissipation Theorem 4 Fluctuation-Dissipation Theorem • Nyquist (1920s) proposed general relationship between energy loss and thermal noise • Callen and Welton (1950s) proved Fluctuation- Dissipation Theorem • Path for energy loss also a path for thermal excitation • Thermal equilibrium required Fluctuation s • Thermal bath can be Dissipatio same system n 5 Gravitational Waves Einstein’s second challenge to LIGO: “Do Gravitational Waves Exist?”-Title of paper submitted to (and rejected by) Physical Review by Einstein and Rosen (1936) • Einstein’s General Theory of Relativity Gμν= 8π Tμν – Analogous to Maxwell’s equations – Has wave solution • Oscillations in space-time • Propagate at c 1975 1985 1995 • Two polarizations: X and + Indirect Detection (1990s) • Binary Pulsar System 1913+16 • Nobel Prize 1993 Joseph Taylor and Russel Hulse 6 Gravitational Waves Comparison with Electromagnetic Waves • Quadrupolar – Influences design of detectors – Dipole (E&M) forbidden by momentum conservation Electromagnetic Wave • Much Weaker 5 2 L ~ G/c L internal G/c5 ≈ 2.5 10 -35 1/W • Strain rather than force h = ΔL / L ≈ 10 -21 Gravitational Wave 7 Detection of Gravitational Waves Interferometers • Light goes down two perpendicular arms – Similar to Michelson- Morley • Mirrors are free to move – Gravity or other forces • Returning light recombines – Constructively: equal arm length – Destructively: different arm lengths • Gravitational wave Interference of Light – Stretch one arm, shrink other 8 Laser Interferometer Gravitational-wave Observatory (LIGO) End Test Mirror Whole Interferometer Enclosed in Vacuum Input Test 4 km Fabry-Perot cavities Mirror Recycling 100 W Mirror Laser/MC 6 W 13 kW LIGO Livingston LIGO Hanford 0.2 W • Two sites in the US – Livingston, LA – Hanford, WA • Arms 4 km long (2 km for 2nd • SensitiveHanford) to strains around h=10-21 • ΔL = h L ≈ 10-18 m: subnuclear • Entire beam path in vacuum LIGO Vacuum Chambers 9 Generations of LIGO Initial, Enhanced, and Advanced Initial LIGO • Reached design sensitivity – Neutron star inspiral: 15 Mpc • Steel wire suspensions • Standard coatings on silica 10 Hz 100 Hz 1000 Hz Enhanced LIGO Advanced LIGO • Improvements to Initial • Major upgrade LIGO – Neutron star inspiral: 170 Mpc – Neutron star inspiral: 30 Mpc • Silica ribbon suspensions • Steel wire suspensions • Improved coatings on silica • Standard coatings on silica • Funding 4/08: Online 2013 • Begin taking data 2009 10 Initial LIGO Sensitivity LIGO Sensitivity in Time Initial LIGO Noise • Sensitivity improves over time • Data taken at most sensitivities – Technical checks – Upper limits on sources 10 Hz 100 Hz 1000 Hz • Design sensitivity - 2005 Science Data Run (S5) • Full year of coincidence between three interferometers • Two years of calendar time S5 Coincidence • Finished November 2007 11 World Network of Detectors GEO 600 in LIGO Germany Proposed LCGT in Japan Virgo 3 km in Italy Gingin site in Australia 12 Astronomical Sources Short Duration Long Duration Modeled Compact Body Inspirals Periodic Sources Unmodeled Bursts Stochastic Background 13 Astrophysical Results Inspirals Numerical Model of Inspiral Gamma Ray Bursts • GRB070201 – Galaxy M31 (750 kPc away) – NO inspiral or short transients – NOT binary neutron star inspiral – arXiv:0711.1163, ApJ • Over 200 GRBs during S5 – Analysis underway High density objects – ~10% short GRBs ⇒ likely to be in mutual orbit inspirals –Black holes – Long GRBs could be supernova –Neutron stars –White dwarfs 14 Astrophysical Results Bursts Gamma Ray Repeaters • Catastrophic events • Hyperflare in SGR 1806-20 – 10s of solar masses – Magnetar ~ 6 - 15 kPc away – Supernova etc – NO signals found at normal • Sources not mode frequencies modeled – Not during S5 – No theoretical model – Only Hanford 4 km detector – Non-optimal search – Phys Rev D 76 (2007) 062003. • Hyperflare in SGR 1900+14 – During S5 – Analysis underway Artists Conception of Hyperflare 15 Astrophysical Results Periodic • Rapidly rotating Crab Pulsar compact body • Position, frequency & spin – Pulsar down rate known – Low mass X-ray binary • NO signal seen • Needs asymmetry – Spin down NOT from gravitational waves – Sphere not • Limits on 78 other pulsars quadrupolar – Phys Rev D 76 (2007) 042001. Sensitivity to Pulsars Artists Conception of Accretion 16 Einstein @ Home http://einstein.phys.uwm.edu/ • Based on SETI@Home • Searching for unknown pulsars • Operating systems: – Windows – Mac – OSX – Linux • More computing power • Low cost 17 Astrophysical Results Stochastic Cosmic Microwave Background Big Bang • Similar to cosmic microwave background • Probe closer to beginning • Tests of inflation, quantum gravity, etc. Cosmological Nearby Sources Background • Unresolved background • NO correlated signal seen of burst type sources • Similar to theoretical limit • Distant supernova, -6 mergers, accretions, etc. – ΩGW < 9 10 (preliminary) – Assumes frequency independent spectrum 18 Noise in Inteferometric Indirect Laser NoiseDetectors – Direct Laser Noise – Radiation Pressure Shot Noise Suspension Thermal Noise Seismic Noise 10 Hz 100 Hz 1000 Hz Coating Thermal Noise Coating Thermal Noise -Brownian – Thermo-optic 19 Shaping Laser Noise Dual Recycling High Frequency Narrowband Dual Recycling Laser Thermal -22 • Laser noise can be shaped 10 Noises Laser Noise Noises – Mirror reflectivity and 1/2 -23 10 positions h(f) /Hz h(f) – Laser power -24 10 • Laser noise can optimized 10 Hz 100 Hz -25 Thermal Noises for different sources 10 2 3 10 10 100 Hz Frequency (Hz)1000 Hz • High frequency narrowband Laser Noise – Known pulsars • Low frequency – Stochastic background Thermal Noises • Mid frequency broadband 10 Hz 100 Hz – Inspirals and bursts Low Frequency Optimized 20 Thermal Noise and Sensitivity Wideband: Inspirals and Bursts • Coating thermal noises limit sensitivity • Improved coatings in Advanced LIGO – Titania doped Tantala/Silica Thermal Noises – Increased laser spot size 10 Hz 100 Hz 1000 Hz – Optimize design to reduce Wideband Advanced LIGO Sensitivity thermal noise – Sensitivity greatly improved • Inspiral range increased Generation Neutron Star 10 M BH – Neutron star binaries o Enhanced LIGO 30 Mpc 180 Mpc – Black hole binaries Advanced LIGO 170 Mpc 980 Mpc • Burst sensitivity also improved Next Generation 300 Mpc 1600 Mpc Depends on noise 21 Thermal Noise and Sensitivity High Frequency Narrowband: Pulsars Low Mass X-ray Binaries • Narrowband Advanced LIGO • Coating thermal noise-limited – Brownian Thermal Noises – Thermo-optic • Gravitational waves depend on 150 Hz 500 Hz ellipticity (ε) Narrowband Advanced LIGO Sensitivity High Frequency Pulsars Generation Crab ε Sco X-1 ε • Crab Pulsars and others (59.9 Hz) (620 Hz) • Coating thermal noise- Enhanced LIGO 7 10-6 1 10-7 limited Advanced LIGO 7 10-7 1 10-8 • Laser, suspension thermal, Next Generation 2 10-7 7 10-9 & seismic noises play roles 22 Thermal Noise and Sensitivity Low Frequency : Stochastic Stochastic Sensitivity • Only at low frequency – Frequency scale: c / D ~ 100 Hz Thermal Noises • Limited by thermal noise 10 Hz 100 Hz – Suspension at lowest Low Frequency Advanced LIGO Sensitivity frequencies – Coating at higher frequencies Stochastic Signal LIGO Suspension Stochastic • Depends on model Generation Background – Many ideas Enhanced LIGO Steel Wire 6 10-7 – Unknown in practice Advanced LIGO Silica Ribbon 1 10-9 • Frequency dependence Next Generation Sapphire Ribbon 3 10-10 – Also unknown 23 Next Generation Research 2 2 2 Sx(f) = kB Td Ycoatφ/ (π f w Ysub ) -23 (From 2007 Ops Proposal) 10 Coating Brownian • New coating materials – φ, Thermal Coating TO Suspension Thermal Ycoat Noises Newtonian Seismic • Reduce coating thickness - Quantum Noise d – Cavity reflectors – Corner reflectors Strain SensitivityStrain [1/rt(Hz)] • Change geometry - w Laser – Mesa beams and other Noise-24 shapes 10 1 2 3 10 10 10 • Reduce temperature - T 10 Hz 100Frequency Hz Hz] 1000 Hz – Cryogenics – Japanese 2nd generation Laser • New substrates