Laser interferometric gravitational wave detectors The search for the elusive wave Nergis Mavalvala (LIGO Scientific Collaboration) University of Colorado, Oct. 2007

Outline Gravitational waves (GWs) Astrophysical sources of GWs Detecting GWs Ongoing searches Future detectors Bold claims!!! Measure distance changes of 10-18 m over kilometers Hear trees falling the forest Detect a mm bump on 10 km object 800 l.y. away Measurement below the (naïve) quantum limit

Gravitational wave basics Gravitational Waves prediction of general relativity “Ripples in spacetime fabric” Stretch and squeeze the space transverse to direction of propagation Strain Emitted by aspherical accelerating masses “What better way to get at the juicy stuff than to shine a laser at it” Eric Cornell (June 25, 2007, ICOLS)

Astrophysics with GWs vs. Light Very different information, mostly mutually exclusive Difficult to predict GW sources based on EM observations Light GW Accelerating charge Accelerating mass Images Waveforms Absorbed, scattered, dispersed by matter Very small interaction; matter is transparent 100 MHz and up 10 kHz and down

Astrophysical sources of GWs Ingredients Lots of mass (neutron stars, black holes) Rapid acceleration (orbits, explosions, collisions) Colliding compact stars Merging binaries Supernovae The big bang Earliest moments The unexpected GWs neutrinos photons now

Pulsar born from a supernova PULSAR IS BORN: A supernova is associated with the death of a star about eight times as massive as the Sun or more. When such stars deplete their nuclear fuel, they no longer have the energy (in the form of radiation pressure outward) to support their mass. Their cores implode, forming either a neutron star (pulsar) or if there is enough mass, a black hole. The surface layers of the star blast outward, forming the colorful patterns typical of supernova remnants. ACCRETION SPINS UP THE PULSAR: When a pulsar is created in a supernova explosion, it is born spinning, but slows down over millions of years. Yet if the pulsar -- a dense star with strong gravitational attraction -- is in a binary system, then it can pull in, or accrete, material from its companion star. This influx of material can eventually spin up the pulsar to the millisecond range, rotating hundreds of revolutions per second. GWs LIMIT ACCRETION INDUCED SPIN UP: As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up. Courtesy of NASA (D. Berry)

Millisecond pulsar accretion As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up. Courtesy of NASA (D. Berry)

Black hole mergers Contours of GWs in x polarization Yellow contours represent tidal forces As we zoom out we see red contours of GW waves Notice that x-pol has no emission on equatorial plane. Contours of GWs in x polarization Courtesy of J. Centrella, GSFC

Gravitational waves -- the Evidence Hulse & Taylor’s Binary Neutron Star System (discovered in 1974, Nobel prize in 1993) PSR 1913 + 16 Two neutron stars orbiting each other at 0.0015c Compact, dense, fast  relativistic system Emit GWs and lose energy Used time of arrival of radio pulses to measure change in orbital period due to GW emission Change in orbital period NS rotates on its axis 17 times/sec  59 msec period. Reaches periastron (minimum separation of binary pair) every 7.75 hours. Systematic variation in arrival time of pulses. Variation in arrival time had a 7.75 hour period  binary orbit with another star. Pulsar clock slowed when traveling fastest and in strongest part of grav field (periastron). Figure shows decrease in orbital period of 76 usec/year. Shift in periastron due to decay of orbit. Y-axis = change in orbital period relative to 1975 measurement Define periastron as measure of orbital period Exactly as predicted by GR for GW emission Years

In our galaxy (21 thousand light years away, 8 kpc) Strength of GWs Hulse-Taylor binary pulsar at the end of its lifetime (100 million years from now) In our galaxy (21 thousand light years away, 8 kpc) h ~ 10-18 In the Virgo cluster of galaxies (50 million light years away, 15 Mpc) h ~ 10-21 M r R

Laser interferometers Photodetector GW from space Laser Photodetector

Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO Detection confidence Source polarization Sky location LISA

GW detector at a glance Seismic noise Ground motion (natural and anthropogenic) Vibration isolation 20 kW Thermal noise Vibrations due to finite temperature Low mechanical dissipation Shot noise Operate on dark fringe High circulating power 10 W

10 kg Fused Silica 25 cm diameter 10 cm thick < lambda/5000 over beam diameter

Some (small) numbers Sensitivity: 10-19 m/√Hz at 150 Hz 10-10 rad/√Hz at 150 Hz Actuation range: ~100 µm (tides) Stabilization of 4 km arms: 10-13 m rms Laser intensity noise (RIN): ≤10-8 /√Hz at 150 Hz Frequency noise: ≤ 3×10-7 Hz/√Hz at 150 Hz Angular Control: ≤ 10-8 rad rms Angular Sensing: 10-14 radians/√Hz at 40 Hz Input beam jitter: ≤4×10-9 rad/√Hz at 150 Hz Mechanical loss angle: suspension ≤10-6 optical coatings ≤10-4 substrate ≤10-6

Sensitivity limit Initial LIGO Seismic noise Suspension thermal Viscously damped pendulum Shot noise Photon counting statistics SQL: h(f) = sqrt(8*hbar/M)/Omega/L Standard Quantum Limit

Gravitational-wave searches Instrument and data

Science runs and sensitivity 1st Science Run Sept 02 (17 days) S2 2nd Science Run Feb – Apr 03 (59 days) S3 3rd Science Run Nov 03 – Jan 04 (70 days) Strain (sqrt[Hz]-1) LIGO Target Sensitivity S5 5th Science Run Nov 05 onward (1 year integrated) S4 4th Science Run Feb – Mar 05 (30 days) Frequency (Hz)

How do we do it? Sensitivity…

How do we do it? Duty factor… RMS motion in 1-3 Hz band day night Livingston Displacement (m) Hanford PRE-ISOLATOR REQUIREMENT Time (GPS seconds)

Pre-isolator performance Lock acquisition threshold Factor of 10 reduction in the critical band Rel. velocity b/w mirrors 4k apart

Science runs and Sensitivity

S5 duty cycle GEO 600 ~ 95%

Astrophysical searches Coalescence of binary compact objects (neutron stars, black holes, primordial BH) Core collapse supernovae Black hole normal mode oscillations Neutron star rotational instabilities Gamma ray bursts Cosmic string cusps Periodic emission from pulsars (esp. accretion driven) Stochastic background (incoherent sum of many sources or very early universe) Expect the unexpected! Transient Campanelli et al., Lazarus Project GWs neutrinos photons now High duty cycle

Sampling of current GW searches Stochastic Background

Cosmological GW Background 385,600 During inflation, tensor modes are produced from amplification of initial quantum fluctuations into classical perturbations. Density perturbations lead to GWs that carry unique and “clean” information about the early Universe. 10-22 sec 10+12 sec Waves now in the LIGO band were produced 10-22 sec after the Big Bang WMAP 2003

Predictions and Limits Atoms 4% Dark energy 73% Dark matter 23% GWs ?? What’s our Universe made of? LIGO S1: Ω0 < 44 PRD 69 122004 (2004) LIGO S3: Ω0 < 8.4x10-4 PRL 95 221101 (2005) -2 Pulsar Timing CMB+galaxy+Ly-a adiabatic homogeneous BB Nucleo- synthesis -4 LIGO S4: Ω0 < 6.5x10-5 (W0) -6 S5 (expected) ~ 4x10-6 -8 Log Cosmic strings Adv. LIGO, 1 yr data Expected Sensitivity ~ 1x10-9 CMB -10 Pre-BB model Accuracy of big-bang nucleosynthesis model constrains the energy density of the universe at the time of nucleosynthesis  total energy in GWs is constrained integral_f<1e-8 d(ln f) Omega_GW Pulsar timing  Stochastic GWs would produce fluctuations in the regularity of msec pulsar signals; residual normalized timing errors are ~10e-14 over ~10 yrs observation Stochastic GWs would produce CMBR temperature fluctuations (Sachs Wolfe effect), Measured Delta_T constrains GW amplitude at very low frequencies Kamionkowski et al. (astro-ph/0603144-1) Use Lyman-alpha forest, galaxy surveys, and CMB data to constrain CGWBkgd, i.e. CMB and matter power spectrums. Assume either homogeneous initial conditions or adiabatic. Use neutrino degrees of freedom to constrain models. Adiabatic blue solid  CMB, galaxy and Lyman-alpha data currently available (Kamionkowski) Homogeneous blue dashed  CMB, galaxy and Lyman-alpha data currently available Adiabatic CMBPol (cyan solid)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data Homogeneous CMBPol (cyan dashed)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data -12 Inflation -14 Slow-roll Cyclic model EW or SUSY Phase transition -18 -16 -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 Log (f [Hz])

Example of current GW searches Isolated pulsars

Continuous Wave Sources Single frequency (nearly) continuous GW radiation, e.g. neutron stars with Spin precession at Excited modes of oscillation, e.g. r-modes at Non-axisymmetric distortion of shape at Joint Bayesian parameter estimation of unknown pulsar parameters: GW amplitude h0, initial phase f0, polarisation angle y and inclination angle i, using data from all interferometers Produce probability distribution functions for unknown parameters and marginalise over angles to set 95% upper limit on h0 Compare with spin-down limits Assuming all energy lost as the pulsar spins-down is dissipated via GWs Get limit on ellipticity of rotating star (PSR J2124-3358) f = 405.6 Hz, r = 0.25kpc

Example of current GW searches Binary Inspirals

Search for Binary Inspirals Number of galaxies Distance (~50 Mly) Initial LIGO Sources Binary neutron stars (~1 – 3 Msun) Binary black holes (< 30 Msun) Primordial black holes (< 1 Msun) Search method Look for “chirps” Limit on rate at which NS are coalescing in galaxies like our own BBH BNS Here shown is inspiral range – averaged over all sky BNS inspiral horizon distance – two 1.4 Msun NS optimally oriented, SNR =8 For binary black hole searches the effective distance is for two 5 Msun BHs optimally oriented with SNR =8. 24 galaxies like our Milky Way S4

Coming soon… to an interferometer near you Enhanced LIGO Advanced LIGO

Ultimate limits ? Seismic gravity gradient When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses. Human gravity gradient The beginning and end of weight transfer from one foot to the other during walking produces the strongest human-made gravity-gradient noise in interferometric gravitational-wave detectors (e.g. LIGO). The beginning and end of weight transfer entail sharp changes (time scale τ∼20 msec) in the horizontal jerk (first time derivative of acceleration) of a person’s center of mass.

Initial LIGO – S5 (now) Input laser power ~ 6 W Initial LIGO Circulating power ~ 20 kW Mirror mass 10 kg Initial LIGO SQL

Enhanced LIGO (Fall 2007) Input laser power ~ 30 W Circulating power ~ 100 kW Mirror mass 10 kg Enhanced LIGO

Advanced LIGO (2011) Input laser power > 100 W Circulating power > 0.5 MW Mirror mass 40 kg

Advanced LIGO improvements Seismic noise Active isolation system Mirrors suspended as fourth (!!) stage of quadruple pendulums Thermal noise Suspension  fused silica; ribbons Test mass  higher mechanical Q materials; more massive (40 kg) Optical noise Laser power  increase to ~200 W Tunable frequency response  signal recycling

Astrophysics with Advanced LIGO Factor 10 better amplitude sensitivity (Range)3 = rate Factor 4 lower frequency bound Hope for NSF funding in FY08 Infrastructure of initial LIGO but replace many detector components with new designs Expect to be observing 1000x more galaxies by 2013 NS Binaries Initial LIGO: ~15 Mpc Adv LIGO: ~300 Mpc BH Binaries Initial LIGO: 10 Mo, 100 Mpc Adv LIGO : 50 Mo, z=2 Stochastic background Initial LIGO: ~3e-6 Adv LIGO ~3e-9

Sub-quantum interferometry Space observatory Farther in the future Sub-quantum interferometry Space observatory

Advanced LIGO Quantum noise limited Shot noise Quantum radiation pressure noise Advanced LIGO

Some quantum states of light Heisenberg Uncertainty Principle for EM field Phasor diagram analogy Stick  dc term Ball  fluctuations Common states Coherent state Vacuum state Amplitude squeezed state Phase squeezed state X+ and X- associated with amplitude and phase McKenzie

Quantum Noise in an Interferometer First proposed … C.M. Caves, PR D (1981) Proof-of-principle demonstration … M. Xiao et al., PRL (1987) More realistic configurations demonstrated … Power Recycled Michelson K. McKenzie et al., PRL (2002) Power and Signal Recycled Michelson H. Vahlbruch et al., PRL (2005) Suspended prototype Goda et al. (2007) Laser X+ X- X+ X- X+ X- X+ X-

Squeezed Input Interferometer Laser GW Detector SHG Faraday isolator The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. an optical parametric oscillator. OPO Homodyne Detector Squeeze Source GW Signal

Sub-quantum-limited interferometer Narrowband unsqueezed Broadband unsqueezed Broadband Squeezed X+ X- Quantum correlations Input squeezing

Squeezing measured… Goda et al., submitted to Opt. Lett. (2007) Vahlbruch et al., PRL 97, 011101 (2007)

Squeezing injected @ the 40m prototype @ Caltech Goda et al. (2007)

Laser Interferometer Space Antenna (LISA) Three space craft Triangular formation Separated by 5 million km Formation trails earth by 20º Approx. constant length arms Constant solar illumination 1 AU = 1.5x108 km

LISA (mid to late 2010’s)

When the elusive wave is captured… Tests of general relativity Waves  direct evidence for time-dependent metric Black hole signatures  test of strong field gravity Polarization of the waves  spin of graviton Propagation velocity  mass of graviton Astrophysics Predicted sources: compact binaries, SN, spinning NS Inner dynamics of processes hidden from EM astronomy Dynamics of neutron stars  large scale nuclear matter The earliest moments of the Big Bang  Planck epoch Precision measurements below the quantum noise limit

In closing... Astrophysical searches from early science data runs completed The most sensitive search yet (S5) completed Oct. 01  1 year of data at initial LIGO sensitivity Joint searches with partner observatories Planned enhancements that give 2x improvement in sensitivity underway Advanced LIGO Approved by the NSB in 2006 “Marked up” by US House and Senate this summer (still to go) Construction funding expected to begin in FY2008 Promising prospects for direct GW detection in coming years (and GWB’s exit)

The End

Make some upgrades with limited invasiveness to give ~2x improvement Enhanced LIGO Make some upgrades with limited invasiveness to give ~2x improvement Mechanical changes ruled out Seismic isolation and suspension systems Changes mainly related to optical readout

Seismic Noise Initial LIGO Advanced LIGO

Signal-recycled Interferometer ℓ Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM 800 kW 125 W Reflects GW photons back into interferometer to accrue more phase Signal Recycling signal

Advance LIGO Sensitivity: Improved and Tunable broadband detuned narrowband SQL  Heisenberg microscope analog If photon measures TM’s position too well, it’s own angular momentum will become uncertain. thermal noise

Advanced LIGO Target Sensitivity Initial LIGO Log [Strain (1/rtHz)] Advanced LIGO Newtonian background Quantum noise Mirror substrate thermal Mirror coating thermal Seismic Suspension thermal 10 100 1000 Frequency (Hz) Frequency (Hz)