Introduction to Gravitational Waves

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_at_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 PSR191316 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.

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.

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.

5
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.

6
Bar sensitivity

• Bars have better sensitivity at resonance but
  bandwidth determined by sensor/amplifier.
• Aim of future development is to widen bandwidth.

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!

8
Worldwide Interferometer Network
9
Large Interferometers the 1st Generation
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Progress in commissioning of LIGO
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.
Noise source External vibrations Mirror thermal vibrations Pendulum thermal vibrations Photon counting statistics
How it is mini-mized Multi-stage pendulum suspension for mirrors, mechanical filter, f gt1 Hz Sets lower frequency limit on observing. Make mirror substrate of high-Q material so kT energy is concentrated near mode frequencies, above 2 kHz. Need Q108 in fused silica. Make suspension with high-Q so kT is concentrated near 1 Hz pendulum frequency. Need Q106. Use drawn silica fibres, hydroxide bonding to mirrors Need 100kW of laser power in arms, use power recycling so that laser input (5W) only replaces mirror losses (10-6 per reflection). Limited by thermal lensing.
12
Data Massive Volume, Massive Analysis

• 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

• 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 gt 1020
  filters 4 months long.

13
Detectors Today and Tomorrow
Detector Chances
Bar detectors operate at cyrogenic temperatures with sensitivity better than 10-19 today. Their relatively narrow bandwidth excludes some sources. ??
Future resonant-mass detectors could take the form of large omni-directional spheres, or concentric cylidrical shells. Could be competitive with interferometers at higher frequencies. ??
1st-generation interferometric detectors (LIGO, GEO, VIRGO) are nearing design sensitivity of 10-21 at frequencies above 40 Hz. ?
The 2nd-generation Advanced LIGO upgrade (partnership with GEO) is seeking funding (? 10 gain in sensitivity by 2009, frequency range extended to 10 Hz). 3rd-generation interferometer technology in research. ?
LISA is aiming for a launch in 2011 as a joint ESA-NASA mission. It will open the low-frequency window (below 1 Hz). NASA envisions a succession of space detectors. They will be the workhorses of gravitational wave astronomy. The frequency range (down to 0.1 mHz) is a good match to the timescale (hours) of many astronomical systems. ??
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Gravitational Waves in a Post-Newtonian Nutshell

• Coupling

h is the amplitude.

• Generation

internal potential
Newtonian potential

• Energy Flux

all classical field theories
dimensional factor
15
Gravitational Dynamics
/

• Frequency

• Luminosity

very strong dependence on compactness
/

• Timescale

Chirp time ? is a measure of light- crossing time
16
Examples

• High frequency neutron star with r 20 Mpc, R
  10 km
• F 0.6 W m-2s-1 gt 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.

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Detectors Measure DistancesChirping 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.
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GW physics across the spectrum
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.

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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
21
Conventions on Source/Sensitivity Plots

• Assume the best search algorithm now known
• Set Threshold so false alarm probability 1

22
Overview of Sources

• NS BH Binaries
• inspiral
• merger
• Spinning NSs
• LMXBs
• known pulsars
• unknown
• NS Birth (SN, AIC)
• tumbling
• convection
• Stochastic
• big bang
• early universe

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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

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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 gws to 1
  sec / 3x109 yrs 10-17
  

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Neutron Star / Black Hole Inspiraland NS Tidal
Disruption

• 1.4Msun / 10 Msun NS/BH
• Event rates
• Population Synthesis Kalogeras
  summary

lt

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Black Hole / Black Hole Inspiral and Merger

• 10Msun / 10 Msun BH/BH
• Event rates
• Based on population synthesis
  Kalogeras summary of literature

lt

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BH/BH Mergers Exploring the
Dynamics of Spacetime Warpage
Numerical Relativity Simulations Are Badly
Needed!
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Massive BH/BH Mergers with Fast Spins Advanced
Interferometers
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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 AEIs longest simulation to date,
  and its visualization. (Seidel, Benger, et al,
  AEI)

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Spinning NSs Pulsars

• NS Ellipticity
• Crust strength gt e lt 10-6 possibly
  10-5

• Unknown NSs - All sky search
• Sensitivity 5 to 15 worse

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Spinning Neutron StarsLow-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 obss gt information about
• crust strength structure, temperature
  dependence of viscosity, ...

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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!

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Stochastic Backgroundfrom Very Early Universe

• GWs 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

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Stochastic Background from Very Early Universe

• Detect by
• cross correlating output of Hanford Livingston
  4km IFOs

• Advanced IFOs
• W 5x10-9

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Gravitational Waves from Very Early Universe.

• Waves from standard inflation W10-15 much too
  weak

• 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 gt 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

• Example of hitherto UNKNOWN SOURCE

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

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Gravitational wave spectrum
Space detector far from Earth
38
LISA in Orbit
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LISA interferometry - 1

• 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

reference laser beams
main transponded laser beams
40
LISA interferometry - 2

• 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

reference laser beams
main transponded laser beams
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.
Noise source External disturbances (Solar radiation) Relative motion of S/C Photon counting statistics
How it is mini-mized Drag-free sensing, where S/C protects free-flying proof mass from external forces. Require micro-thrusters, good accelerometer. Sets lower frequency limit. Causes rapid motion of fringes (MHz). Count fringe rate using on-board ultra-stable oscillator and compensate in on-board computers. Transmit data to Earth at only 10 bits/s average. Cannot use mirror reflection, too much diffraction loss. Use active mirrors (laser transponder) to re-transmit incoming beam back to source with correct phase. .
LISAs technology will be tested in a joint
NASA-ESA mission called ST-3 in 2005.
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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

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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
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LISA sensitivity curve(1-year observation)
102 104 Mo
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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

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 lt 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.

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Massive Black Holes in Galaxies

• Most galaxies near enough to be studied contain
  central black holes, 106 to gt 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
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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 z1?
• 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)
49
Coalescences of Massive Black HolesHow
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.
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.

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Gravitational capture example10M?/106M? circular
equatorial orbit, fast spin Finn/Thorne
1 yr before plunge r6.8 rHorizon 185,000 cycles
left, S/N 100
1 mo before plunge r3.1 rHorizon 41,000 cycles
left, S/N 20
heff
1 day before plunge r1.3 rHorizon 2,300 cycles
left, S/N 7
f (Hz)
52
Issue How well can we study gravitational
captures?

• Potential for very fundamental results, mapping
  spacetime near a Kerr black hole
• Nightmare for matched filtering
• Huge parameter space for orbits, perhaps 1030 or
  more distinguishable sets of parameters
• Radiation-reaction problem in strong-field Kerr
  not yet solved
• Approximate, hierarchical scheme will be needed
• Filtering must be good, because
• Signals from galactic WD binaries and SMBH
  mergers need to be removed to avoid contamination
• Distant capture events provide background
  Olbers limit

53
Issue cosmological background

• One of the most fundamental goals of GW detection
  is the cosmological background from the Big Bang.
  Best observational evidence we are likely to get
  about fundamental physics. LISA limit around Wgw
  10-10.
• Standard inflation predicts very weak radiation
  (Wgw lt 10-14), but alternative scenarios can
  produce more in the LISA band (branes,
  pre-Big-Bang cosmology, ). Some alternatives
  produce no radiation at all, e.g. ekpyrotic
  universe.
• Some scenarios of symmetry breaking can produce
  observable radiation.
• Backgrounds from astrophysical sources restrict
  observing range if Wgw lt 10-10. Possible window
  0.1-10 Hz (the Gap) would be target of a
  follow-on mission.

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Expect the Unexpected!

• Within this decade, gravitational wave detectors
  will begin to make observations routinely.
• Although we can predict some sources, the most
  interesting may be the unexpected, unimagined.
• The launch of X-ray, gamma-ray, infrared, and
  ultraviolet observatories has time and again
  revealed new unanticipated objects. Our
  understanding of the Universe is very different
  from the one that depended only on optical
  telescopes.
• 90 of the Universe is dark, emitting no
  electromagnetic radiation. But it interacts
  gravitationally, so does at least some of it emit
  gravitational waves?

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Further Information

• You can find information about the projects on
  these web sites
• LIGO http//www.ligo.caltech.edu
• VIRGO http//www.virgo.infn.it/
• GEO http//www.geo600.uni-hannover.de/
• TAMA http//tamago.mtk.nao.ac.jp/
• LISA http//www.estec.esa.nl/spdwww/future/html/l
  isa.htm and http//lisa.jpl.nasa.gov/
• Bars linked from IGEC site, http//igec.lnl.infn.
  it/
• Further information about software and
  collaborations
• Cactus http//www.cactuscode.org/
• Gridlab http//www.gridlab.org/
• EU GW Astrophys http//www.eu-network.org/
• Triana http//www.triana.co.uk/