introduction to gravitational waves bernard schutz albert einstein institute – max planck...

Introduction to Gravitational WavesBernard Schutz

Albert Einstein Institute – Max Planck Institute for Gravitational Physics, Golm, Germany

and

Cardiff University, Cardiff, UKhttp://www.aei.mpg.de

[email protected]

http://www.aei.mpg.de/



Bernard F Schutz Albert Einstein Institute

19 May 2003

Frascati: Introduction to Gravitational Waves

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.


19 May 2003


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.


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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.


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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.

Nautilus

Auriga

Allegro

Niobe


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6

Bar sensitivity

• Bars have better sensitivity at resonance but bandwidth determined by sensor/amplifier.

• Aim of future development is to widen bandwidth.


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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!

http://www.iop.org/EJ/search_author?query=P%20Astone&submit=1&headerlimit=author&operator=phrase&headertype=limit&journaltype=all&datetype=all&highlight=on;sort=date_cover

http://www.iop.org/EJ/search_author?query=P%20Astone&submit=1&headerlimit=author&operator=phrase&headertype=limit&journaltype=all&datetype=all&highlight=on;sort=date_cover


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8

Worldwide Interferometer Network


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9

Large Interferometers: the 1st Generation


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10

Progress in commissioning of LIGO


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11

The Technology of Laser Interferometers

Noisesourc

e

External vibration

s

Mirror thermal

vibrations

Pendulum thermal

vibrations

Photon counting statistics

How it is mini-mized

Multi-stage pendulum suspension for mirrors, mechanical filter, f >1 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 Q~108 in fused silica.

Make suspension with high-Q so kT is concentrated near 1 Hz pendulum frequency. Need Q~106. 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.

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.


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12

Data: Massive Volume, Massive Analysis

• 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


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13

Detectors Today and TomorrowDetector 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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14

Gravitational Waves in a Post-Newtonian Nutshell

• Coupling: L hL

h

2rc

GM

2Rc

GM

Newtonian potential

internal potential

F 132

cG

3

h 2

h is the amplitude.

all classical field theories

dimensional factor

• Generation:

• Energy Flux:


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15

Gravitational Dynamics

• Luminosity

• Frequency f 2 1

4G

L 4 2r F32

1 cG

3

h 2

2)2( fh5

2

5

32

3

Rc

GM

G

c very strong dependenceon compactness

M

3

3

4R/

• Timescale / LGMR

2

23

23

16

Rc

GM

c

RChirp time is a measure of light-crossing time


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16

ExamplesHigh 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.

h f 10 2 2021, kHz, ms h f 10 14 21017, mHz, s

L rproton 001.


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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:

f 2/1

3

3

R

GM3

23

16

Rc

GM

c

R.

3

162/5

2

Rc

GM

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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18

GW physics across the spectrum

810low

high

f

f

A chirping system is a GW standard candle: if positionis known, distance can be

inferred.

2 x 100 M BHs coalesce in 1 yr

from ~ 0.1 Hz


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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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20

Looking for signals with matched filtering

• Matched filtering concentrates signal power while spreading out noise. Must know the signal waveform. Classic example: Fourier transform.

1

0

/2N

j

Nijkjk exy F.t. of data set {xj}

of length N

This picks out sine-wavebecause we multiply exactly by sine-wave

General matched filter for signal {sj} in data set {xj}

1

0

N

jjjk sxy If {sj} is a member of a

family, must do filter separately for each member. May overwhelm computer!


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21

Conventions on Source/Sensitivity Plots

Broadband Waves

Signal/Threshold in f = f Signal/Threshold

in 4 months integration

Narrowband Waves

StochasticWaves

Signal/Thresholdin f=f & 4 monthsintegration

• Assume the best search algorithm now known

• Set Threshold so false alarm probability = 1%


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22

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

Bars


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23

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

300 Mpc

• Advanced IFOs, Range: 300Mpc

– 1 / yr to 2 / day

~10 min

~3 sec

~10,000 cycles

20 Mpc

• Initial IFOs, Range: 20 Mpc

– 1 / 3000 yrs to 1 / 3yrs


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• 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 = 3/5 M2/5 to ~10-3

• Search for EM counterpart, e.g. -burst. If found:

– Learn the nature of the trigger for that -burst

– deduce relative speed of light and gw’s to ~ 1 sec / 3x109 yrs ~ 10-17

Science From Observed Inspirals


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25

Neutron Star / Black Hole Inspiraland NS Tidal Disruption

• 1.4Msun / 10 Msun NS/BH

• Event rates

– Population Synthesis [Kalogera’s summary]

650 Mpc

• Advanced IFOs

– Range: 650 Mpc

– 1 / yr to 4 / day

<~

43 Mpc inspiral NS disrupt

• Initial IFOs

– Range: 43 Mpc

– 1 / 2500 yrs to 1 / 2yrs

140 Mpc

NS Radius to 15%-Nuclear Physics-

NEED: Reshaped Noise,Numerical Simulations


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26

Black Hole / Black Hole Inspiral and Merger

• 10Msun / 10 Msun BH/BH

• Event rates

– Based on population synthesis [Kalogera’s summary of literature]

z=0.4 inspiral

merger

• Advanced IFOs -

– Range: z=0.4

– 2 / month to ~10 / day

<~

100 Mpc inspiral

merger• Initial IFOs

– Range: 100 Mpc

– 1 / 300yrs to ~1 / yr


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27

BH/BH Mergers: Exploring the Dynamics of Spacetime Warpage

Numerical Relativity

Simulations Are Badly

Needed!


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28

Massive BH/BH Mergers with Fast Spins Advanced Interferometers

Lower Frequency


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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)


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Spinning NS’s: Pulsars

• Unknown NS’s - All sky search:

– Sensitivity ~5 to 15 worse

• NS Ellipticity:– Crust strength =>

< ~10-6; possibly 10-5

Crab SpindownUpper Limit

• Known Pulsars:– First Interferometers:

3x10-6 (1000Hz/f)

x (distance/10kpc)

– Narrowband Advanced 2x10-8 (1000Hz/f)2

x (distance/10kpc)

= 1

0-7 , 1

0kpc

= 1

0-6 , 1

0kpc

= 1

0-5 , 1

0kpc


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31

Spinning Neutron Stars:Low-Mass X-Ray Binaries

Signal strengths for 20 days of integration

Sco X-1

• If so, and steady state: X-ray luminosity GW strength

• Combined GW & EM obs’s => information about:

– crust strength & structure, temperature dependence of viscosity, ...

• Rotation rates ~250 to 700 revolutions / sec

– Why not faster?

– Bildsten: Spin-up torque balanced by GW emission torque


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NS Birth: Tumbling Bar; Convection• Born in:

– Supernovae

– Accretion-Induced Collapse of White Dwarf

• If slow spin:

– Convection in first ~1 sec.

– Advanced IFOs: Detectable only in our Galaxy (~1/30yrs)

– GW / neutrino correlations!

• 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)


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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

– GW energy density)/(closure density) 10-5


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34

Stochastic Background from Very Early Universe

• Detect by– cross correlating output

of Hanford & Livingston 4km IFOs

• Initial IFOs detect if

– 10-5

• Advanced IFOs:

– 5x10-9

= 10 -7

= 10 -9

= 10 -11

• Good sensitivity requires

– (GW wavelength) 2x(detector separation)

– f 40 Hz


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35

• Waves from standard inflation: ~10-15: 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 => 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

Gravitational Waves from Very Early Universe.


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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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37

Gravitational wave spectrum

Gravity gradient noise

on the Earth

Space detectorfar from Earth

GAP!


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38

LISA in Orbit


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39

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”

main transpondedlaser beams

reference laser beams


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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

main transpondedlaser beams

reference laser beams


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41

The Technology of LISA

Noisesource

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.

.

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.


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42

Testing:•Inertial sensor•Charge management•Thrusters•Drag-free control•Low frequency laser metrology •Launch 2006 with

ESA and NASA

test packages

SMART-2: Testing free fall in spaceOnly one S/C with 2 test masses is needed


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43

LISA science goals

Compact objects orbitingmassive

black holes

Massive black holes:

formation, binary orbit,

and coalescence

White dwarf, neutron star,

and other compact

binary systems


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44

vibrationnoise

shot noise

armlength

102 + 104 Mo

LISA sensitivity curve(1-year observation)

gw = 10-10


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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


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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.


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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


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48

Massive Black Holes Merge• 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)

3C75


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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 simultaneousl

y by other telescopes.


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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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51

1 yr before plunge:

r=6.8 rHorizon

185,000 cycles left,

S/N ~ 100

1 mo before plunge:

r=3.1 rHorizon

41,000 cycles left,

S/N ~ 20

1 day before plunge:

r=1.3 rHorizon

2,300 cycles left,

S/N ~ 7

heff

Gravitational capture example10M/106M circular equatorial orbit, fast spin [Finn/Thorne]

f (Hz)


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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”


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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 gw ~ 10-10.

• Standard inflation predicts very weak radiation (gw < 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 gw < 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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55

Further InformationYou 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/lisa.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/

http://www.ligo.caltech.edu/



http://www.virgo.infn.it/





http://www.geo600.uni-hannover.de/

http://tamago.mtk.nao.ac.jp/

http://www.estec.esa.nl/spdwww/future/html/lisa.htm










http://lisa.jpl.nasa.gov/

http://igec.lnl.infn.it/

http://www.cactuscode.org/



http://www.gridlab.org/



http://www.eu-network.org/



http://www.triana.co.uk/

introduction to gravitational waves bernard schutz albert einstein institute – max planck...

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