8 June 2004Summer School on Gravitational Wave Astronomy 1 Gravitational Wave Detection #1: Gravity waves and test masses Peter Saulson Syracuse University

8 June 2004Summer School on Gravitational Wave Astronomy 2 Plan for the week 1.Overview 2.How detectors work 3.Precision of interferometric measurement 4.Time series analysis, linear system characterization 5.Seismic noise and vibration isolation 6.Thermal noise 7.Fabry-Perot cavities and their applications 8.Servomechanisms 9.LIGO 10.LISA

8 June 2004Summer School on Gravitational Wave Astronomy 3 A set of freely-falling test particles

8 June 2004Summer School on Gravitational Wave Astronomy 4 Electromagnetic wave moves charged test bodies

8 June 2004Summer School on Gravitational Wave Astronomy 5 Gravity wave: distorts set of test masses in transverse directions

8 June 2004Summer School on Gravitational Wave Astronomy 6 Comparison table, EM vs GW

8 June 2004Summer School on Gravitational Wave Astronomy 7 Transmitters of gravitational waves: solar mass objects changing their quadrupole moments on msec time scales

8 June 2004Summer School on Gravitational Wave Astronomy 8 Gravitational waveform lets you read out source dynamics The evolution of the mass distribution can be read out from the gravitational waveform: Coherent relativistic motion of large masses can be directly observed.

8 June 2004Summer School on Gravitational Wave Astronomy 9 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 kg m 2 s -2. At distance of 1  km, h = 9 x Not very strong.

8 June 2004Summer School on Gravitational Wave Astronomy 10 Binary signal strength estimate

8 June 2004Summer School on Gravitational Wave Astronomy 11 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 10 21, or less.

8 June 2004Summer School on Gravitational Wave Astronomy 12 Resonant detector (or “Weber bar”) Cooled by liquid He, rms sensitivity at/below A massive (aluminum) cylinder. Vibrating in its gravest longitudinal mode, its two ends are like two test masses connected by a spring.

8 June 2004Summer School on Gravitational Wave Astronomy 13 An alternative detection strategy Tidal character of wave argues for test masses as far apart as practicable. Perhaps masses hung as pendulums, kilometers apart.

8 June 2004Summer School on Gravitational Wave Astronomy 14 Sensing relative motions of distant free masses Michelson interferometer

8 June 2004Summer School on Gravitational Wave Astronomy 15 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.

8 June 2004Summer School on Gravitational Wave Astronomy 16 L aser I nterferometer G ravitational Wave O bservatory 4-km Michelson interferometers, with mirrors on pendulum suspensions, at Livingston LA and Hanford WA. Site at Hanford WA has both 4-km and 2- km. Design sensitivity: h rms =

8 June 2004Summer School on Gravitational Wave Astronomy 17 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

8 June 2004Summer School on Gravitational Wave Astronomy 18 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.

8 June 2004Summer School on Gravitational Wave Astronomy 19 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!

8 June 2004Summer School on Gravitational Wave Astronomy 20 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 ( x rms ~   /20, h rms ~10 -9 ) –galvanometer (  rms ~10 -6 rad.) Gap between experimental sensitivity and any conceivable wave amplitude was huge!

8 June 2004Summer School on Gravitational Wave Astronomy 21 Gravitational wave detection is almost impossible What is required for LIGO to succeed: interferometry with free masses, with strain sensitivity of (or better!), equivalent to ultra-subnuclear position sensitivity, in the presence of much larger noise.

8 June 2004Summer School on Gravitational Wave Astronomy 22 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.

8 June 2004Summer School on Gravitational Wave Astronomy 23 Strain sensitivity of Why it is “impossible”: Natural “tick mark” on interferometric ruler is one wavelength. Michelson could read a fringe to /20, yielding h rms of a few times

8 June 2004Summer School on Gravitational Wave Astronomy 24 Ultra-subnuclear position sensitivity Why people thought it was impossible: Mirrors made of atoms, m. Mirror surfaces rough on atomic scale. Atoms jitter by large amounts.

8 June 2004Summer School on Gravitational Wave Astronomy 25 Large mechanical noise How large? Seismic: x rms ~ 1  m. Thermal –mirror’s CM: ~ 3 x m. –mirror’s surface: ~ 3 x m.

8 June 2004Summer School on Gravitational Wave Astronomy 26 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.

8 June 2004Summer School on Gravitational Wave Astronomy 27 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

8 June 2004Summer School on Gravitational Wave Astronomy 28 Freely-falling masses

8 June 2004Summer School on Gravitational Wave Astronomy 29 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

8 June 2004Summer School on Gravitational Wave Astronomy 30 The space-time interval in special relativity Special relativity says that the interval between two events is invariant (and thus worth paying attention to.) In shorthand, we write it as with the Minkowski metric given as

8 June 2004Summer School on Gravitational Wave Astronomy 31 Generalize a little General relativity says almost the same thing, except the metric can be different. The trick is to find a metric that describes a particular physical situation. The metric carries the information on the space- time curvature that, in GR, embodies gravitational effects.

8 June 2004Summer School on Gravitational Wave Astronomy 32 Gravitational waves Gravitational waves propagating through flat space are described by with a wave propagating in the z -direction described by Two parameters = two polarizations

8 June 2004Summer School on Gravitational Wave Astronomy 33 Plus polarization

8 June 2004Summer School on Gravitational Wave Astronomy 34 Cross polarization

8 June 2004Summer School on Gravitational Wave Astronomy 35 Solving for variation in light travel time