LISA 1

General Relativity Trimester, IHP Paris, Oct 2006

LISA

Bernard F Schutz

Albert Einstein Institute

Potsdam, Germany

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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.

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GW physics across the spectrum

810low

high

f

f

A chirping system is a GW standard candle: if

positionis known, distance can

be inferred.

3/2

1~

2

1RGMGf

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Observe from Ground or Space?

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.

Detectors are complementary

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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

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SupernovaeSN - event rate:

1 / 50 yr – Milky Way;

3 / yr - Virgo Cluster

Waveform, amplitudepoorly understood!

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Coalescing Compact-Object Binaries

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

Near-term/long-term goals

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Pulsar physics and formation

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

Near-term/long-term goals

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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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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

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Primordial Gravitational Waves 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.

10 1014 5 gw

Simple Inflation (max.)

NucleosynthesisBound

gw

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Massive Black Holes Merge 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)

NGC 6240

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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

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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.

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At the Edge of a Black Hole 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

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

Example: 10 M BH into 106 M BH, with large spin [Finn&Thorne]

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Orbits and spiral-in of small bodies around spinning Black Holes (Extreme Mass Ratio Inspirals, EMRIs)

Periholon precession

Orbit plane precessionspin–orbit; L-T(Lense-Thirring)

Spiral-in and Circularization(GW energy and angular

momentum losses)Slow!

Phinney

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GW from Splurge into BH at 1 Gpc

h

h+

-10-22

0

1022

-10-22

0

1022

S Hughes (CalTech)

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a=100M, e=0.05, i=45

a=10M, e=0.2, i=45

2x orbital freq

Periholon precession freq

L-T orbit plane precession freq

Integer combinationsof 3 frequencies:

lfr+mfnf

Signal from EMRIs

Phinney

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a=6M, e=0.2, i=80

Frequencies sweep and shift slowly ascompact object spirals in,mapping space-time outside

the horizon.

Like a Geodesy satellite mapping Geopotential! GRACE for Black Holes!

Signal from EMRIs

Phinney

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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?

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T

c

GgRgR

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2

1

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 . . .

What is Dark Energy?

But:

– Expansion of Universe is accelerating

– Driven by Dark Energy

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Dark Energy

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

Measuring the expansion history of the Universe:

Binary Black Hole Coalescences can be used as Standard Candles to complement the

Ia Supernova distance scale!

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Compact White-Dwarf Binaries

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.

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LISA Verification Binaries

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LISA Sensitivity and Primordial GWs

10 -4 10 -3 10 -2 10 -1 100

Frequency (Hz)

10 -23

10 -22

10 -21

10 -20

10 -19

10 -18

Detection threshold (S/N = 5)

for a 1-year observation

2 x 106M o B Hs at z=1

10 M o + 106M o BH

2 x 104M o BHs

RXJ1914.4+2456

4U1820-30

h

10

5

0

-5

-10

-15

m g w

gw = 10-10

(from Schutz)WD Binary confusion limit

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GWs: Principles of Observation

rad. 1templatetrue tt

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.

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AURIGA (Italy-Legnaro)

Modern Bar Detectors -- AURIGA

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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.

Laser

Arm 1

Arm 2

Photodetector

Beam splitter

Inner m irrors

Power recycling

m irror

Signal recycling

m irror

(d)

C av ities

(e)

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Albert Michelson reading Interference Fringes

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Sensitivity Δℓ= 600 pm!

LISA Requirement 40 pm/√Hz!

Original Apparatus of Michelson and Morley 1887

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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

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VIRGO

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GEO Mirror Suspension

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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.

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Cluster of 3 LISA spacecraft

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LISA in Orbit

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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 both

polarizations of a GW

Orbital motion

provides

direction

information

main transpondedlaser beams

referencelaser beams

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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.

Wave(f = 16 mHz)

Angular Resolution with LISA

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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

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102 + 104 Mo

LISA sensitivity curve(1-year observation)

gw = 10-10

Strong signals, confusion-noise limited observing

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LISA Pathfinder Sensor EM

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LISA Pathfinder OB Engineering Model

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Vibration Test

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Data analysis in the

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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.

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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:

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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.

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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.

gw

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Approach to LISA data analysis

Requirement is to resolve overlapping signals. This involves not just detecting them but also measuring all parameters needed to remove them from the data stream.

Main data-analysis approach will be iterative:– Solve for strong sources approximately, subtract them.

– Solve for next strongest, subtract, go back to strongest and remove their residuals better.

– Binary orbital parameters improve with time, so their signals can be subtracted better after 2nd year. So transient events (black hole mergers) in first year also improve after 2 years.

Data products: source detections and parameters, cleaned-up data streams, full data streams.

Highly integrated analysis system required, but no decisions yet by agencies on how or where this analysis will be done, what proprietary data rights the scientists will have, etc.

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Challenges of LISA data analysis

Confusion challenge– Source identification not unique. Must use intelligent principles to identify “best”

identifications. How to guarantee that iterative scheme finds the globally “best” solution? What is the right search method?

Network challenge– LISA actually has 3 interferometer signals, optimum combinations depend on source location

and polarization. Modulation complicates this.

Computational challenge– Parameter space for EMRIs is huge. Even with anticipated improvements in computing, a

hierarchical search will be needed. Not clear how to do this against a background of weaker EMRIs.

Theory challenge– Some signal templates not yet known well enough, including EMRIs and BH merger

waveforms.

Organizational challenge – There is no legacy analysis system: it must be designed in scientific community but be highly

integrated.

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What is happening now

Hardware– LPF being built, lessons learned applied to LISA design.– Astrium Friedrichshafen is doing the formulation study for ESA

Data analysis– ESA has formed a Data Analysis Study Team to coordinate work of more than 50 institutions

in Europe.– JPL has held meetings of US scientists to distribute work.– ESA (ESTEC) and NASA (JPL) will run independent but coordinated efforts developing

algorithms in the community.– In Europe, groups must be funded by national agencies. In the US, the NASA budget

restrictions leave little room for funding data analysis development.– LIST provides overall coordination, issues mock data challenges.

Mock Data Challenges: first was released at LISA Symposium in June 2006. Results will be reported at GWDAW at the AEI (Potsdam) in December 2006. Periodic releases, increasing in complexity, as stimulus to community and as demonstration of competence.

Conclusion– Many opportunities for key contributions, leadership!

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Chirp Measurements with LISA

LISA will survey whole universe: any equal-mass merger with (1+z)M between 103 and 107 M should be seen.

If population of 1000 M BHs formed in star formation, LISA may record their collapse events. If they then merged to form larger BHs, LISA should record thousands of chirps. Signal runs from 1.5 mHz to 0.1 Hz in 10 years. 1 yr SNR~60 @ z=1.

Galaxy-galaxy mergers should produce a few 106 M BH chirp observations at z~1. 30’ 40 Mpc in all three dimensions. This is not good enough to do cosmology.

To do better, need to identify host galaxy. Difficult, since merger is electromagnetically quiet. Requires new thinking.

If host galaxy identified, then dL improves to max(10-4, z).

2 events: H0, q0 limited only by velocity dispersion of galaxies. A few events: dq0/dt time-dependence of “”.

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Constraining the Graviton’s mass

In GR, mg = 0

– But quantum theory could lead to a non-zero mass.

Gravitational waves would then travel slower than light

– Suffer dispersion in frequency.

Solar system gravity bounds

– Compton wavelength of Graviton > radius of Pluto’s orbit.

Cutler, Hiscock & Larson (2003): Galactic binaries

– GW signal would out of phase with optically observed binary orbit.

– This could improve the bound by factor of 50.

Will & Yunes: SMBH binary coalescence

– Signal distorted by dispersion.

– This could improve the bound by a factor of ~104.

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Gravitational Waves can escape from earliest moments of the Big Bang

Inflation: Big Bang plus 10-35 seconds?

Recombination:Big Bang plus 300,000 Years

Today:Big Bang plus

15 Billion Years

Seeds of Structure+

Gravitational Waves

What Powered the Big Bang?

NASA

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Gravitational waves leavea distinctive imprint onpolarization pattern of CMB

What Powered the Big Bang?

Vacuum energy poweredinflation-some form of it may be the “dark energy”

Gravitational waves frominflation and phase transitionsmay be detected directly

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X-rays fromCLUSTERS(ROSAT)

Matter density m=0.3

Dark Energy=0.7

What is the Universe made of?

WMAP results,Spergel et al., 11.2.2003