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Introduction to Gravitational Waves

Introduction to Gravitational Waves. Bernard Schutz Albert Einstein Institute – Max Planck Institute for Gravitational Physics, Golm, Germany and Cardiff University, Cardiff, UK http://www.aei.mpg.de schutz@aei.mpg.de. Gravitational Wave Astronomy.

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Introduction to Gravitational Waves

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  1. Introduction to Gravitational Waves Bernard Schutz Albert Einstein Institute – Max Planck Institute for Gravitational Physics, Golm, Germany and Cardiff University, Cardiff, UK http://www.aei.mpg.de schutz@aei.mpg.de

  2. Gravitational Wave Astronomy • Gravitational waves are the most important prediction of Einstein that has not yet been verified by direct detection. The Hulse-Taylor pulsar system PSR1913+16 gives very strong indirect confirmation of the theory. • Gravitational waves carry huge energies, but they interact very weakly with matter. These properties make them ideal probes of some of the most interesting parts of the Universe, now that we have learned how to make sufficiently sensitive detectors. • Unlike in most of electromagnetic astronomy, gravitational waves will be observed coherently, following the phase of the wave. This is possible because of their relatively low frequencies (most interest is below 10 kHz). This makes detection strategies very different: instead of bolometric (energy) detection in hardware, gravitational wave detection will be by data analysis, in software. Frascati: Introduction to Gravitational Waves

  3. Tidal gravitational forces • By the equivalence principle, the gravitational effect of a distant source can only be felt through its tidal forces – inhomogeneous part of gravity. • Gravitational waves are traveling, time-dependent tidal forces. • Tidal forces scale with size, typically produce elliptical deformations. Frascati: Introduction to Gravitational Waves

  4. Polarisation • Gravitational waves have 2 independent polarisations, illustrated here by the motions of free “test” particles. • Interferometers are linearly polarised detectors. • Distortions follow the motions of the source projected on the sky. • A measurement of the degree of circular polarisation determines the inclination of a simple binary orbit. If the orbit is more complex, as for strong spin-spin coupling, then the changes in polarisation tell what is happening to the orbit. Frascati: Introduction to Gravitational Waves

  5. Allegro Nautilus Auriga Niobe Bar detectors • The first detector was the Weber bar, operated at room temperature. • Currently there are five main cryogenic bars, including the ultra-cyrogenic Nautilus and Auriga. • They operate the ICEG collaboration for searching for coincident bursts. • Narrow-bandwidths at relatively high frequencies. Frascati: Introduction to Gravitational Waves

  6. Bar sensitivity • Bars have better sensitivity at resonance but bandwidth determined by sensor/amplifier. • Aim of future development is to widen bandwidth. Frascati: Introduction to Gravitational Waves

  7. Strange Events? • Coincidences were seen between Explorer and Nautilus. See P Astone, et al, Class. Quantum Grav.19 5449 • No claim has been made that they are gravitational waves, because they are marginally significant and difficult to understand on any expected model. • More data coming soon from interferometers and the two bars! Frascati: Introduction to Gravitational Waves

  8. Worldwide Interferometer Network Frascati: Introduction to Gravitational Waves

  9. Large Interferometers: the 1st Generation Frascati: Introduction to Gravitational Waves

  10. Progress in commissioning of LIGO Frascati: Introduction to Gravitational Waves

  11. The Technology of Laser Interferometers GEO600 must measure mean motions of mirrors over distances of 10-21 of 600 m, or 6 x 10-19 m, on timescales of milliseconds. Detection is all about excluding other sources of mirror motion on these timescales. Frascati: Introduction to Gravitational Waves

  12. GEO600 will record 15 TB per year, LIGO maybe 200 TB. Most of this is “housekeeping”. Signal data around 500 GB/y. Real-time matched filtering requires ~100 Gflops. All-sky surveys for pulsars need far more: > 1020 filters 4 months long. LIGO and GEO have jointly developed data analysis software and are doing joint analysis of current data for upper limits. New software have come from this: Triana quick-look system (GEO) Hough-transform hierarchical methods for all-sky surveys (GEO-VIRGO) Grid efforts increasing: GriPhyN, DataGrid, Triana/GridOneD Data: Massive Volume, Massive Analysis Frascati: Introduction to Gravitational Waves

  13. Detectors Today and Tomorrow Frascati: Introduction to Gravitational Waves

  14. Gravitational Waves in a Post-Newtonian Nutshell his the amplitude. • Coupling: • Generation: internal potential Newtonian potential • Energy Flux: all classical field theories dimensional factor Frascati: Introduction to Gravitational Waves

  15. Gravitational Dynamics / • Frequency • Luminosity very strong dependence on compactness / • Timescale Chirp timeis a measure of light- crossing time Frascati: Introduction to Gravitational Waves

  16. High frequency: neutron star with r = 20 Mpc, R = 10 km F = 0.6 W m-2s-1 > FMoon!But if L = 4 km, then h = 10-21 is the 1st detector goal. Low f: 2 BHs, each 106 M at z = 1 (r = 4 Gpc)Merger takes 4 minutes, but in-spiral takes months to move through observation band from 0.1 to 14 mHz. Examples Frascati: Introduction to Gravitational Waves

  17. Detectors Measure Distances:Chirping Binaries are Standard Candles If a detector measures not only f and h but also for a binary, then it can determine its distance r. For a circular binary, upper bounds are attained, so: Combining this with f itself gives us M and R, and then the value of h gives us r, the distance (luminosity distance ). If a chirping massive black-hole binary is identified so that a redshift can be obtained, then one can do cosmology: H0, q0. LISA can measure f, , and h to 0.1% accuracy. Frascati: Introduction to Gravitational Waves

  18. 2 x 100 M BHs coalesce in 1 yr from ~ 0.1 Hz A chirping system is a GW standard candle: if positionis known, distance can be inferred. GW physics across the spectrum Frascati: Introduction to Gravitational Waves

  19. The High-Frequency Sky in 2003 • Coalescing neutron-star binaries may cause gamma-ray bursts. They should be seen by advanced detectors. But the binary black-hole coalescence rate may be higher (made efficiently in globular clusters), so first interferometers may see them. Supernovae uncertain. • Neutron-star r-modes are unstable by the CFS mechanism. May explain why LMXB spin periods are all near 300 Hz. Likely source for advanced detectors. • Standard inflation sets a difficult target for observing a cosmological background. But superstring-inspired cosmologies (Veneziano et al) or brane scenarios (Hogan) may generate more radiation detectable by LISA or Advanced LIGO. • Pulsars and unseen (young?) NSs may be cw-emitters; could be seen by first interferometers or bars, likely by advanced interferometers. • NS normal modes would be probes of NS interior. Need broadband high-frequency detector. Frascati: Introduction to Gravitational Waves

  20. F.t. of data set {xj} of length N General matched filter for signal {sj} in data set {xj} If {sj} is a member of a family, must do filter separately for each member. May overwhelm computer! Looking for signals with matched filtering • Matched filtering concentrates signal power while spreading out noise. Must know the signal waveform. Classic example: Fourier transform. This picks out sine-wave because we multiply exactly by sine-wave Frascati: Introduction to Gravitational Waves

  21. Stochastic Waves Signal/Threshold in Df=f & 4 months integration Narrowband Waves Broadband Waves Signal/Threshold in Df = f Signal/Threshold in 4 months integration Conventions on Source/Sensitivity Plots • Assume the best search algorithm now known • Set Threshold so false alarm probability = 1% Frascati: Introduction to Gravitational Waves

  22. Bars Overview of Sources • NS & BH Binaries • inspiral • merger • Spinning NS’s • LMXBs • known pulsars • unknown • NS Birth (SN, AIC) • tumbling • convection • Stochastic • big bang • early universe Frascati: Introduction to Gravitational Waves

  23. ~10 min 20 Mpc ~3 sec ~10,000 cycles 300 Mpc • Initial IFOs, Range: 20 Mpc • 1 / 3000 yrs to 1 / 3yrs • Advanced IFOs, Range: 300Mpc • 1 / yr to 2 / day Neutron Star / Neutron Star Inspiral (our most reliably understood source) • 1.4 Msun / 1.4 Msun NS/NS • Event rates • V. Kalogera, R. Narayan, D. Spergel, J.H. Taylor astro-ph/0012038 Frascati: Introduction to Gravitational Waves

  24. Science From Observed Inspirals • Relativistic effects are very strong -- e.g. • Frame dragging by spins  precession  modulation • Tails of waves modify the inspiral rate • Information carried: • Masses (a few %), Spins (?few%?), Distance [not redshift!] (~10%), Location on sky (~1 degree) • Mchirp = l3/5 M2/5 to ~10-3 • Search for EM counterpart, e.g. c-burst. If found: • Learn the nature of the trigger for that c-burst • deduce relative speed of light and gw’s to ~ 1 sec / 3x109 yrs ~ 10-17 Frascati: Introduction to Gravitational Waves

  25. 43 Mpc inspiral NS disrupt 140 Mpc 650 Mpc • Initial IFOs • Range: 43 Mpc • 1 / 2500 yrs to 1 / 2yrs • Advanced IFOs • Range: 650 Mpc • 1 / yr to 4 / day NS Radius to 15% -Nuclear Physics- NEED: Reshaped Noise, Numerical Simulations Neutron Star / Black Hole Inspiraland NS Tidal Disruption • 1.4Msun / 10 Msun NS/BH • Event rates • Population Synthesis [Kalogera’s summary] Frascati: Introduction to Gravitational Waves < ~

  26. 100 Mpc inspiral • Initial IFOs • Range: 100 Mpc • 1 / 300yrs to ~1 / yr merger z=0.4 inspiral • Advanced IFOs - • Range: z=0.4 • 2 / month to ~10 / day merger Black Hole / Black Hole Inspiral and Merger • 10Msun / 10 Msun BH/BH • Event rates • Based on population synthesis [Kalogera’s summary of literature] Frascati: Introduction to Gravitational Waves < ~

  27. BH/BH Mergers: Exploring the Dynamics of Spacetime Warpage Numerical Relativity Simulations Are Badly Needed! Frascati: Introduction to Gravitational Waves

  28. Lower Frequency Massive BH/BH Mergers with Fast Spins Advanced Interferometers Frascati: Introduction to Gravitational Waves

  29. BH Merger Simulations • Improving all the time: • More stable forms of the field equations • Gauge conditions improved • Run times lengthening • Initial data must be improved: subtle • Boundary conditions not yet satisfactory • EU- funded network “Sources of Gravitational Waves” pushing all of these issues. • Still hungry for computer time. The Discovery Channel funded AEI’s longest simulation to date, and its visualization. (Seidel, Benger, et al, AEI) Frascati: Introduction to Gravitational Waves

  30. Crab Spindown Upper Limit • Known Pulsars: • First Interferometers: 3x10-6 (1000Hz/f)x (distance/10kpc) • Narrowband Advanced 2x10-8 (1000Hz/f)2 x (distance/10kpc) e = 10-5, 10kpc e = 10-6, 10kpc e = 10-7, 10kpc Spinning NS’s: Pulsars • NS Ellipticity: • Crust strength =>e< ~10-6; possibly10-5 • Unknown NS’s - All sky search: • Sensitivity ~5 to 15 worse Frascati: Introduction to Gravitational Waves

  31. Sco X-1 Signal strengths for 20 days of integration Spinning Neutron Stars:Low-Mass X-Ray Binaries • Rotation rates ~250 to 700 revolutions / sec • Why not faster? • Bildsten: Spin-up torque balanced by GW emission torque • If so, and steady state:X-ray luminosity  GW strength • Combined GW & EM obs’s => information about: • crust strength & structure, temperature dependence of viscosity, ... Frascati: Introduction to Gravitational Waves

  32. NS Birth: Tumbling Bar; Convection • Born in: • Supernovae • Accretion-Induced Collapse of White Dwarf • If very fast spin: • Centrifugal hangup • Tumbling bar - episodic? (for a few sec or min) • If modeling gives enough waveform information, detectable to: • Initial IFOs: ~5Mpc (M81 group, ~1 supernova/3yr) • Advanced IFOs: ~100Mpc (~500 supernovae/yr) • If slow spin: • Convection in first ~1 sec. • Advanced IFOs: Detectable only in our Galaxy (~1/30yrs) • GW / neutrino correlations! Frascati: Introduction to Gravitational Waves

  33. Stochastic Backgroundfrom Very Early Universe • GW’s are the ideal tool for probing the very early universe • Present limit on GWs • From effect on primordial nucleosynthesis • W = (GW energy density)/(closure density) 10-5 Frascati: Introduction to Gravitational Waves

  34. W = 10-7 • Good sensitivity requires • (GW wavelength) 2x(detector separation) • f 40 Hz W = 10-9 • Initial IFOs detect if • W 10-5 W = 10-11 Stochastic Background from Very Early Universe • Detect by • cross correlating output of Hanford & Livingston 4km IFOs • Advanced IFOs: • W 5x10-9 Frascati: Introduction to Gravitational Waves

  35. Gravitational Waves from Very Early Universe. • BUT: Crude superstring models of big bang suggest waves might be strong enough for detection by Advanced LIGO • Energetic processes at (universe age) ~ 10-25 sec and (universe temperature) ~ 109 Gev => GWs in LIGO band • phase transition at 109 Gev • excitations of our universe as a 3-dimensional “brane” (membrane) in higher dimensions: • Brane forms wrinkled • When wrinkles “come inside the cosmological horizon”, they start to oscillate; oscillation energy goes into gravitational waves • LIGO probes waves from wrinkles of length ~ 10-10 to 10-13 mm • If wave energy equilibrates: possibly detectable by initial IFOs • Waves from standard inflation: W~10-15: much too weak • Example of hitherto UNKNOWN SOURCE Frascati: Introduction to Gravitational Waves

  36. LISA – Shared Mission of ESA & NASA • ESA & NASA have exchanged letters of agreement. ESA/ESTEC and NASA/GSFC jointly manage mission. • Launch 2011, observing 2012+. • Mission duration up to 10 yrs. • SMART-2 technology demonstrator (ESA: 2006) • Project scientists: Karsten Danzmann (AEI) and Tom Prince (NASA: JPL/Caltech). • Joint 20-strong LIST: LISA International Science Team Frascati: Introduction to Gravitational Waves

  37. Gravity gradient noise on the Earth GAP! Gravitational wave spectrum Space detector far from Earth Frascati: Introduction to Gravitational Waves

  38. LISA in Orbit Frascati: Introduction to Gravitational Waves

  39. LISA interferometry - 1 reference laser beams • Each S/C carries 2 lasers, 2 telescopes, 2 test masses • Local lasers phase-locked • Lasers on distant S/C phase-locked to incoming light • laser transponder – effectively an “active mirror” main transponded laser beams Frascati: Introduction to Gravitational Waves

  40. LISA interferometry - 2 reference laser beams • Laser beams reflected off free-flying test masses, insensitive to spacecraft motion. • Effectively 2 Michelsons • Long arms  displacements in picometer range, much easier than ground-based interferometry main transponded laser beams Frascati: Introduction to Gravitational Waves

  41. The Technology of LISA LISA must measure mean motions of mirrors over distances of 10-21 of 5 x 106 km, or 5 nm, on timescales of seconds. Detection is all about excluding other sources of mirror motion on these timescales. LISA’s technology will be tested in a joint NASA-ESA mission called ST-3 in 2005. Frascati: Introduction to Gravitational Waves

  42. SMART-2: Testing free fall in space Only one S/C with 2 test masses is needed • Testing: • Inertial sensor • Charge management • Thrusters • Drag-free control • Low frequency laser metrology • Launch 2006 with ESA and NASA test packages Frascati: Introduction to Gravitational Waves

  43. LISA science goals Compact objects orbiting massive black holes Massive black holes: formation, binary orbit, and coalescence White dwarf, neutron star, and other compact binary systems Frascati: Introduction to Gravitational Waves

  44. Wgw = 10-10 vibration noise armlength shot noise LISA sensitivity curve(1-year observation) 102+104Mo Frascati: Introduction to Gravitational Waves

  45. Low-Frequency Sky • Merging supermassive black holes (SMBH) in galactic centers • Formation, growth, relation to galaxy formation and mergers, indicators from other observations, cosmological information, numerical modelling, clean removal of signals so weaker events are detectable. • Signals from gravitational capture of small BHs by SMBHs • Event rates, evolution of clusters near SMBHs, modelling of very complex waveform (radiation-reaction), signal extraction from background of distant events, accuracy of tests of BH uniqueness theorems of general relativity • Survey of all galactic binaries with sufficiently short periods • Population statistics, confusion by large population at lower frequencies, confusion limit on signal extraction, information extraction from observations • Backgrounds, astrophysically generated and from the Big Bang • Strength and spectrum of astrophysical backgrounds, production of early-universe radiation, relation to fundamental physics (string theory, branes, …) • Bursts, unexpected sources • Formation of BHs of intermediate to large mass, possible sources in dark matter Frascati: Introduction to Gravitational Waves

  46. Galactic binaries • All compact-object binaries (WD, NS, BH) in galaxy with large enough frequency will be observed. • GAIA observations can help identify individual binaries. LISA will provided masses, distances (if needed), orbit inclination. • Population statistics will make key contributions to understanding binary and stellar evolution. • For f < 0.001 Hz, only nearest binaries will be resolved; most form an anisotropic noise. Even at higher frequencies, binary signals must be removed accurately to see other weak sources. Frascati: Introduction to Gravitational Waves

  47. Massive Black Holes in Galaxies • Most galaxies near enough to be studied contain central black holes, 106 to > 109 solar masses. • The Milky Way is one of the most convincing cases: it contains 2.6  106 M in a region not much bigger than our solar system. (Movie by Eckart & Genzel.) • All observations show only a mass concentration. GWs are the only radiation actually emitted by black holes. LISA will literally listen to these black holes as they merge. MPE Garching Frascati: Introduction to Gravitational Waves

  48. Massive Black Holes Merge 3C75 • Detected masses from 106 to 109 M. Smaller masses possible. • Galaxy mergers should produce BH mergers. Rate un certain: 1/yr for 106 M at z=1? • Protogalaxy mergers may be richer. Phinney: possibly 103/yr for 105 M at z = 7. • Stellar BHs fall into massive BHs more often, but weaker radiation. (S Phinney) Frascati: Introduction to Gravitational Waves

  49. Coalescences of Massive Black Holes:How Signal/Noise Grows Week by Week The high S/N at early times enables LISA to predict the time and position of the coalescence event, allowing the event to be observed simultaneously by other telescopes. Frascati: Introduction to Gravitational Waves

  50. Issue: Cosmology with SMBH Mergers • Position uncertainties of SMBH mergers are significant, error boxes of order several degrees likely. This dominates uncertainty in range too, makes it impossible on position alone to find galaxy in which merger took place. • Can other observations identify galaxy or cluster where merger is about to occur? NGST, LOFAR, X-ray activity? • Cosmology with SMBHs. If the merger can be associated with a galaxy or cluster, then the uncertainty in position and distance error are drastically reduced, only dominated by random velocities of galaxies and gravitational lensing. • This would allow tracking of the acceleration history of the Universe as far back as SMBH mergers occur. Frascati: Introduction to Gravitational Waves

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