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General Relativity Trimester, IHP Paris, Oct 2006 LISA

General Relativity Trimester, IHP Paris, Oct 2006 LISA. Bernard F Schutz Albert Einstein Institute Potsdam, Germany. 1. LISA. Stochastic signals. Some signals are known to be totally random. Possible sources: Big Bang, inflation, phase transitions in early universe

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General Relativity Trimester, IHP Paris, Oct 2006 LISA

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  1. General Relativity Trimester, IHP Paris, Oct 2006LISA Bernard F Schutz Albert Einstein Institute Potsdam, Germany 1 LISA

  2. Stochastic signals • Some signals are known to be totally random. Possible sources: • Big Bang, inflation, phase transitions in early universe • Astrophysical sources, such as binaries, distant supernovae, … • If this random excitation is stronger than detector noise, and if detector noise is understood or can be independently measured, then a stochastic background can be identified (bolometric detection). • If two detectors with independent instrumental noise are available, their outputs can be cross-correlated to look for a common noise.

  3. A chirping system is a GW standard candle: if positionis known, distance can be inferred. GW physics across the spectrum

  4. Ground detectors –- Can only observe at f > 1 Hz because of gravity noise on Earth; can’t be screened.- Events are rare, catastrophic.- Likely: * neutron-star in-spiral (gamma-ray bursts?) * black-hole in-spiral * neutron stars- First detections are likely to be made from the ground. Space detectors –- Required for f < 1 Hz- Many strong sources- Many known sources- Expected: * Massive BH mergers * Small BHs  larger ones * Known binaries - Genuine tests of general relativity are possible because of high S/N. Observe from Ground or Space? Detectors are complementary

  5. Overview of Sources (ground-based band) • Neutron Star & Black Hole Binaries • inspiral • merger • GW Pulsars • LMXBs • known pulsars • previously unknown • NS Birth (SN, AIC) • tumbling • convection • Stochastic background • big bang • early universe

  6. Supernovae SN- event rate: 1 / 50 yr – Milky Way; 3 / yr - Virgo Cluster Waveform, amplitude poorly understood!

  7. Coalescing Compact-Object Binaries Near-term/long-term goals • Astronomy • Perhaps first source to be detected (?) • Survey of NS’s and BH’s to z ~ 0.1/1.5 • NS and BH demographics: wide mass range (from sub-solar mass to several x103 M) • Star formation rate at high z • Cosmology • New standard candles: “orthogonal” determination of cosmological parameters • Fundamental physics • Exploring the strong/non-linear gravitational field

  8. Pulsar physics and formation Near-term/long-term goals • Neutron star oscillations: Asteroseismology and fundamental physics • NS equation of state • Super-conductivity/super-fluidity • Ultra-high density nuclear (and exotic) matter • Rapidly rotating neutron stars: “GW pulsars” • Probing the galactic neutron star population (only ~1300 known radio pulsars) • LMXB’s and the puzzle of the missing sub-msec pulsars

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

  10. Cosmological Background • GWs are the ideal tool for probing the very early universe • Spectrum unaltered (except for redshift) since GWs generated • Probe phase transitions, non-standard inflation models

  11. Production: Fundamental physics in the early universe- Inflation- Phase transitions- Topological defects- String-inspired cosmology- Brane-world scenarios Spectrum: Slope, peaks give masses of key particles & energies of transitions. A TeV phase transition would have left radiation in LISA band today. Astrophysical backgrounds can be stronger: windows around 1μHz and 1 Hz. Strength: Expressed as fraction of closure energy density, it is poorly constrained: 2nd generation detectors may reach to 10-10 by 20015 at f > 5 Hz. LISA could go to 10-10 at 3 mHz. Primordial Gravitational Waves Simple Inflation (max.) Nucleosynthesis Bound

  12. Massive Black Holes Merge NGC 6240 • Known masses from 106 (as in our Galaxy) to 109 M. Smaller masses possible. • Galaxy mergers should produce BH mergers. Rate uncertain, but several per year in Universe possible at 106 M. • Proto-galaxy mergers may create thousands per year of smaller (104 M) BH mergers. (Chandra Observatory)

  13. SMBH Merger Science • SMBHs seem to have accompanied galaxy formation. • Merger history enlightens galaxy history • Mergers are standard candles, can potentially measure acceleration history of the Universe

  14. LISA and massive black hole mergers • Black holes are ubiquitous in galaxies, probably also in proto-galaxies • Known masses run from 106M (as in our Galaxy) to more than 109M, but the spectrum could start at 103M or smaller (IMBH). • LISA will hear coalescences of black holes above 104 M everywhere in the universe. • Will resolve cannibalism question: do massive black holes grow by swallowing each other? • Will indicate how, when and where first massive holes formed. • Inspiral orbit identifies masses, spins of components; merger phase tests numerical simulations; ringdown phase identifies mass/spin of final hole. • Identification of galaxy possible if accretion turns on after merger. • Coalescing GW systems are standard sirens, signal gives luminosity distance. LISA could measure the evolution of the dark energy to high z.

  15. Capture by Massive Black Holes By observing 10,000 or more orbits of a compact object as it inspirals into a massive black hole (MBH), LISA can map with superb precision the space-time geometry near the black hole Allows tests of many predictions of General Relativity including the “no hair” theorem At the Edge of a Black Hole 1 mo before plunge: r=3.1 rHorizon 41,000 cycles left, S/N ~ 20 1 yr before plunge: r=6.8 rHorizon 185,000 cycles left, S/N ~ 100 Example: 10 M BH into 106 M BH, with large spin [Finn&Thorne] 1 day before plunge: r=1.3 rHorizon 2,300 cycles left, S/N ~ 7

  16. Orbits and spiral-in of small bodies around spinning Black Holes (Extreme Mass Ratio Inspirals, EMRIs) Spiral-in and Circularization (GW energy and angular momentum losses) Slow! Orbit plane precession spin–orbit; L-T(Lense-Thirring) Periholon precession Phinney

  17. GW from Splurge into BH at 1 Gpc 1022 h 0 -10-22 1022 h+ 0 -10-22 S Hughes (CalTech)

  18. 2x orbital freq Periholon precession freq a=10M, e=0.2, i=45 L-T orbit plane precession freq Signal from EMRIs a=100M, e=0.05, i=45 Integer combinations of 3 frequencies: lfr+mfnf Phinney

  19. Signal from EMRIs a=6M, e=0.2, i=80 Frequencies sweep and shift slowly as compact object spirals in, mapping space-time outside the horizon. Like a Geodesy satellite mapping Geopotential!  GRACE for Black Holes! Phinney

  20. Extreme Mass Ratio Inspiral (EMRI) • Fundamental Physics Science Goals • Relativity • Precision Bothrodesy: Map the central SMBH’s spacetime geometry, i.e. measure its multipole moments • Do Black Holes really have no hair? • Search for massive central bodies that are not BH’s • Are there soliton stars or naked singularities? • Measure response of central body (SMBH?) to tidal gravity of orbiting object • How does dynamic strong field gravity work?

  21. What is Dark Energy? But: Expansion of Universe is accelerating Driven by Dark Energy Einstein introduced the Cosmological Constant to explain what was then thought to be a static Universe, “my biggest blunder . . . ” Dark Energy maybe related to Einstein’s Cosmological Constant; its nature is a mystery. Solving this mystery may revolutionize physics . . .

  22. Dark Energy Measuring the expansion history of the Universe: Effect of dark energy becomes apparent at late times Expansion passes from decelerating to accelerating at z ~ 1 Effective density asymptotes to vacuum contribution Dark Energy is apparent at z < 3 Binary Black Hole Coalescences can be used as Standard Candles to complement the Ia Supernova distance scale!

  23. LISA will see thousands of binaries, all the binaries in the Galaxy in its frequency window, many already known: LISA calibration sources. So many that at low frequencies there will be source confusion. LISA will provide crucial information concerning populations, orbits, binary and stellar evolution. Synergy with GAIA. Challenges: coordinated observations, dealing with source confusion. Compact White-Dwarf Binaries

  24. LISA Verification Binaries

  25. RXJ1914.4+2456 Wgw = 10-10 WD Binary confusion limit LISA Sensitivity and Primordial GWs - 1 8 1 0 -15 6 2 x 1 0 M B H s a t z = 1 o 4 2 x 1 0 M B H s o - 1 9 1 0 -10 - 2 0 1 0 -5 h m g w - 2 1 1 0 0 - 2 2 1 0 6 1 0 M + 1 0 M B H o o Detection threshold (S/N = 5) 5 for a 1-year observation 4U1820-30 - 2 3 1 0 10 - 4 - 3 - 2 - 1 0 1 0 1 0 1 0 1 0 1 0 Frequency (Hz) (from Schutz)

  26. GWs: Principles of Observation • At their low frequencies, GW detectors operate coherently, following phase. Differences from flux-based measurements: • Spectroscopy and polarimetry are automatic. Instruments have spectral resolution over wide bandwidths (ftop/fbottom ~ 103). • Simple “detection” usually measures parameters, e.g. of masses, orientations, positions. • Data analysis (computer-based) plays key role in improving sensitivity. Optimal: matched filtering, which needs phase error • Detectors have quadrupolar antenna patterns. “Pointing” is done by data analysis. • GW S/N estimates are amplitudes: square them to compare with flux S/N.

  27. Modern Bar Detectors -- AURIGA • AURIGA (Italy-Legnaro)

  28. How Interferometers Work Correcting misconceptions: • Mirrors hang freely to reduce noise, not to respond to gw! • With good mirrors, arms of any length can build up signal; reason for long arms is thermal and seismic noise, introduced at each reflection.

  29. Albert Michelson reading Interference Fringes

  30. Original Apparatus of Michelson and Morley 1887 • Sensitivity Δℓ= 600 pm! • LISA Requirement 40 pm/√Hz!

  31. LIGO • Locations: Hanford WA, Livingston, LA • Partners: Caltech, MIT (NSF facility) • Length: 4km, 2km at Hanford; 4 km at Livingston • Target sensitivity 10-21 at 200 Hz expected next year

  32. VIRGO

  33. GEO Mirror Suspension

  34. LISA – Shared Mission of ESA & NASA • ESA & NASA have exchanged letters of agreement. ESTEC (ESA) and GSFC (NASA) jointly manage mission. JPL is NASA’s science office; in ESA science managed from ESTEC, data analysis development being coordinated by AEI. • Launch 2017, observing 2018+. • Mission duration up to 10 yrs. • LISA Pathfinder technology demonstrator (ESA: 2009) • Joint 20-strong LIST: LISA International Science Team, meets twice per year.

  35. Cluster of 3 LISA spacecraft

  36. LISA in Orbit

  37. LISA layout • Laser beams reflected off free-flying test masses • Diffraction widens the laser beam to many kilometers • 0.7 W sent, 70 pW received • Michelson with 3rd arm, Sagnac • Can distinguish bothpolarizations of a GW • Orbital motionprovidesdirection information reference laser beams main transponded laser beams

  38. Wave (f = 16 mHz) Angular Resolution with LISA • Using phase modulation due to orbital motion is equivalent to Aperture Synthesis (as in Radio-Astronomy) • Gives diffraction limit = / 1 AU • Measurements on detected sources: -  ~ 1’ – 1o- (mass,distance)  1% • Works the same way for ground-based detectors observing cw sources: higher frequency leads to better resolution.

  39. Extraction of LISA Signals • Subtle: interferometry done by beating light from different lasers • Laser noise must be removed • 12 signals available, three “Michelson” combinations extracted by time-delay interferometry (TDI) • 4th “Sagnac” combination cancels GW signal at low-f

  40. Wgw = 10-10 LISA sensitivity curve(1-year observation) Strong signals, confusion-noise limited observing 102+104Mo

  41. LISA Pathfinder Sensor EM

  42. LISA Pathfinder OB Engineering Model

  43. Vibration Test

  44. Data analysis in the

  45. LSC Data Analysis • LIGO and GEO600 data analysis fully merged in LIGO Scientific Collaboration (LSC) • LSC has 4 analysis groups, each with theory and experiment co-chairs: • Burst analysis • Inspiral analysis • Pulsar search • Stochastic analysis • Analyses are proposed to and approved/coordinated by these groups • Separate agreements exist with TAMA, under negotiation with VIRGO. Joint analysis with VIRGO expected in 2007.

  46. Statistical treatment of noise • Data is always sampled at a constant rate (e.g. 16kHz), so we will deal with discrete data sets {xj , j = 0 .. }. • We will assume noise {nj} is • Gaussian, i.e. pdf is the normal distribution • Zero-mean: Enj= 0, where E is expectation value. • Stationary, i.e. characteristics of noise independent of time • Usually work in Fourier domain, because process is stationary and because FFT algorithm brings advantages for data processing. • Variance of noise in Fourier domain is called Spectral Noise Density S:

  47. Detector Noise • “Noise” refers to any random process that creates detector output. • Can be intrinsic (e.g. photon shot noise) or external (e.g. ground vibration). • Can be Gaussian (e.g. thermal noise) or non-Gaussian (e.g. laser intensity fluctuations). • Commissioning work includes minimizing non-Gaussian noise. • All data analysis teams include specialists in detector characterization. • Additional disturbances in a data stream include: • Interference: deterministic disturbances, e.g. EM field from power lines. • Confusion: Overlapping signals or strong signals obscuring weaker ones. LISA will have this problem, but not the ground-based detectors. • A detection against noise is a decision based on probability - • There is no such thing as a perfect, absolutely certain measurement. • When signal is weak, statements about confidence of detection must be made with great care. • In the LSC at least one-third of the >400 scientists whose names go on the papers are involved in data analysis and related activities.

  48. Wgw =10-10 High-SNR GW Observing • LISA observations will have high SNR, up to 104 in amplitude. • For many sources, LISA will face signal confusion • Binaries in the Galaxy below ~1 mHz blend into a “binary sea” that cannot be resolved: too many sources per frequency bin. • Above 1 mHz, EMRI capture signals are visible out to z ~ 0.5; more distant capture events provide the main background against which detection must take place. Olber’s Paradox avoided only by high-z cutoff in sources. • Resolvable binary systems above 1 mHz must be separated from non-stochastic EMRI interference. • Transient signals, such as from SMBH binary coalescence, must be separated from binary and EMRI background.

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