#### Transcript Gravitational Wave Detection #1: Gravity waves and test masses

Gravitational Wave Detection #1: Gravity waves and test masses Peter Saulson Syracuse University Plan for the week 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Overview How detectors work Precision of interferometric measurement Time series analysis, linear system characterization Seismic noise and vibration isolation Thermal noise Fabry-Perot cavities and their applications Servomechanisms LIGO LISA A set of freely-falling test particles Electromagnetic wave moves charged test bodies Gravity wave: distorts set of test masses in transverse directions Comparison table, EM vs GW charge mass E and B fields h = shear strain c c Maxwell 1867 Einstein 1916 Hertz 1886-91 ? pretty strong very weak Transmitters of gravitational waves: solar mass objects changing their quadrupole moments on msec time scales Gravitational waveform lets you read out source dynamics The evolution of the mass distribution can be read out from the gravitational waveform: 1 2G h(t ) I (t ) 4 r c Coherent relativistic motion of large masses can be directly observed. I dV x x r 2 / 3 r . Why not a Hertz experiment? Hertz set up transmitter, receiver on opposite sides of room. Two 1-ton masses, separated by 2 meters, spun at 1 kHz, has 11 kg m2s-2. I 16 . 10 At distance of 1 l 300 km, h = 9 x10-39. Not very strong. Binary signal strength estimate For a binary star, h = r/R, where R = distance to source, and r = rS1rS2/a, with rS1,2 Schwarzschild radii of the stars, and a is their separation. Often, r ~ 1 km (neutron star binary). At Virgo Cluster, R ~ 1021 km. -21 Hence, expect h ~ 10 (on msec time scales!) Gravity wave detectors Need: – A set of test masses, – Instrumentation sufficient to see tiny motions, – Isolation from other causes of motions. Challenge: Best astrophysical estimates predict fractional separation changes of only 1 part in 1021, or less. Resonant detector (or “Weber bar”) A massive (aluminum) cylinder. Vibrating in its gravest longitudinal mode, its two ends are like two test masses connected by a spring. Cooled by liquid He, rms sensitivity at/below 10-18. An alternative detection strategy Tidal character of wave argues for test masses as far apart as practicable. Perhaps masses hung as pendulums, kilometers apart. Sensing relative motions of distant free masses Michelson interferometer A length-difference-to-brightness transducer Wave from x arm. Wave from y arm. Light exiting from beam splitter. As relative arm lengths change, interference causes change in brightness at output. Laser Interferometer Gravitational Wave Observatory 4-km Michelson interferometers, with mirrors on pendulum suspensions, at Livingston LA and Hanford WA. Site at Hanford WA has both 4-km and 2km. Design sensitivity: hrms = 10-21. Other large interferometers • TAMA (Japan), 300 m now operational • GEO (Germany, Britain), 600 m coming into operation • VIRGO (Italy, France) 3 km construction complete, commissioning has begun Gravity wave detection: challenge and promise Challenges of gravity wave detection appear so great as to make success seem almost impossible. from Einstein on ... The challenges are real, but are being overcome. Einstein and tests of G.R. • Classic tests: – Precession of Mercury’s orbit: already seen – Deflection of starlight: ~1 arcsec, O.K. – Gravitational redshift in a star: ~10-6, doable. • Possible future test: – dragging of inertial frames, 42 marcsec/yr, Einstein considered possibly feasible in future • Gravitational waves: no comment! Why Einstein should have worried about g.w. detection He knew about binary stars, but not about neutron stars or black holes. His paradigm of measuring instruments: – interferometer (xrms~ l /20, hrms~10-9) – galvanometer (qrms~10-6 rad.) Gap between experimental sensitivity and any conceivable wave amplitude was huge! Gravitational wave detection is almost impossible What is required for LIGO to succeed: • interferometry with free masses, • with strain sensitivity of 10-21 (or better!), • equivalent to ultra-subnuclear position sensitivity, • in the presence of much larger noise. Interferometry with free masses What’s “impossible”: everything! Mirrors need to be very accurately aligned (so that beams overlap and interfere) and held very close to an operating point (so that output is a linear function of input.) Otherwise, interferometer is dead or swinging through fringes. Michelson bolted everything down. Strain sensitivity of 10-21 Why it is “impossible”: precisionto which we can comparearm lengths hrms ~ . lengthof arms Natural “tick mark” on interferometric ruler is one wavelength. Michelson could read a fringe to l/20, yielding hrms of a few times 10-9. Ultra-subnuclear position sensitivity Why people thought it was impossible: • Mirrors made of atoms, 10-10 m. • Mirror surfaces rough on atomic scale. • Atoms jitter by large amounts. Large mechanical noise How large? Seismic: xrms ~ 1 m. Thermal – mirror’s CM: ~ 3 x 10-12 m. – mirror’s surface: ~ 3 x 10-16 m. Finding small signals in large noise Why it is “impossible”: Everyone knows you need a signal-to-noise ratio much larger than unity to detect a signal. Science Goals • Physics – Direct verification of the most “relativistic” prediction of general relativity – Detailed tests of properties of grav waves: speed, strength, polarization, … – Probe of strong-field gravity – black holes – Early universe physics • Astronomy and astrophysics – Abundance & properties of supernovae, neutron star binaries, black holes – Tests of gamma-ray burst models – Neutron star equation of state – A new window on the universe Freely-falling masses Distance measurement in relativity… … is done most straightforwardly by measuring the light travel time along a round-trip path from one point to another. Because the speed of light is the same for all observers. Examples: light clock Einstein’s train gedanken experiment The space-time interval in special relativity Special relativity says that the interval ds2 c 2dt2 dx2 dy2 dz2 between two events is invariant (and thus worth paying attention to.) In shorthand, we write it as ds2 dx dx with the Minkowski metric given as 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Generalize a little General relativity says almost the same thing, except the metric can be different. ds2 g dx dx The trick is to find a metric g that describes a particular physical situation. The metric carries the information on the spacetime curvature that, in GR, embodies gravitational effects. Gravitational waves Gravitational waves propagating through flat space are described by g h with a wave propagating in the z-direction described by 0 0 0 0 h 0 a b 0 0 b a 0 0 0 0 0 Two parameters = two polarizations Plus polarization 0 ˆh 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 Cross polarization 0 ˆh 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 Solving for variation in light travel time ds 2 c 2 dt 2 1 h11 dx 2 0 1 1 dt c 1 2 h11 dx 2 NL ht c