1 Alan Weinstein, Caltech Alan Weinstein, Physics of LIGO

AJW, Caltech, LIGO Project LIGO AJW, Caltech, MANY THANKS to Barry Barish, Nergis Mavalvala, David Shoemaker, many others!! many Mavalvala, David Shoemaker, Barish, Nergis Barry MANY THANKS to Part 1: LIGO project, GR, GW, astrophysical sources, IFO detectors Part 2: IFO detector physics, noise sources II sub-systems; LIGO Part 3: LIGO Part 4: LIGO data analysis LIGO-G000162-00-R ΠΠΠΠ2 Caveats

AJW, Caltech, LIGO Project LIGO AJW, Caltech, ) is useful for you to know, too! you to know, ) is useful for ε (which is I am a particle physicist; I’m new to LIGO Everything I’ve learned about LIGO physics Here I get a chance to review my understanding, and solicit comments and corrections from you LIGO-G000162-00-R Œ Œ Œ 3 Physics of LIGO

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Part I: Gravitational Waves Alan Weinstein,Caltech LIGO-G000162-00-R curved space-time curved The LIGO project The LIGO Einstein’s special relativity General relativity and waves Gravitational GW’s of Sources Astrophysical astrophysics GW via interferometry detection GW Practical issues withIFOs Scope and schedule project of MANY THANKS Barish, Nergis to Barry Mavalvala, David Shoemaker!! Œ Œ Œ Œ Œ Œ Œ Œ Œ 4 bservatory O ravitational-Wave The LIGO Project Project LIGO AJW, Caltech, G nterferometer nterferometer I aser L » them to run laboratory ...and » LSC) Collaboration, Scientific » (LIGO Funded by the US National Science Foundation (NSF) US project to build observatories for gravitational waves (GWs) to enable an initial detection, then an astronomy of GWs collaboration by MIT, Caltech; other institutions participating Two sites separated by 3000 km each site carries 4km vacuum system, infrastructure interferometersof multiple (IFOs)capable each site establishment of a network with other interferometers of a variety GW searches for A facility lifetime of >20 years goal: best technology, to achieve fundamental noise limits for terrestrial IFOs LIGO-G000162-00-R Œ LIGO: Œ Œ Observatory characteristics Œ Œ Œ Evolution of interferometers in LIGO Œ Œ Œ Œ 5 )

2

E = mc geometry 2 (or

dt

2 2

c Project LIGO AJW, Caltech,

−

2 Einstein and relativity

-(pc)

+dz 2 2 4D space-time 4D space-time

+dy = E

2 ⇒ 2 )

2

c = dx 0

2

ds with invariant mass: (rest) (m LIGO-G000162-00-R • space+time •Distances in space and time change between in space and time •Distances observers moving relative to one another, but the invariant: interval remains space-time • vector, a 4D form momentum and energy Special (1906): Relativity It all starts with Einstein! It all starts • 6

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Space-time geometry Discards concept of absolute motion; instead treats only relative motion between systems space and time no longer viewed as separate; rather as four dimensional space-time gravity described as a warpage (curving) of space-time, not a force acting at a distance LIGO-G000162-00-R Relativity and space-time geometry: Œ Œ Œ 7 “instantaneously” , law of gravitation

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Newtonian Gravity and ) F=ma acts over large distances laws of motion ( sun LIGO-G000162-00-R » comets of orbits eccentric » variations their of tides and cause » earth’s axis the of precession the » the of gravity by moon of the of the motion perturbation the »unified. Kepler and Copernicus Galileo, of Work Three (centripetal force) disparate phenomena Solved most known problems of astronomy and terrestrial physics are Gravitational fields static (or slowly changing), the force Œ Œ Œ 8 2 r / 2 m 1 Gm = a 1 m space that the “test mass” occupies, occupies, “test mass” the that space = F time: Einstein’s

AJW, Caltech, LIGO Project LIGO AJW, Caltech, General Relativity (1916) Warped space- theory of gravity theory

geometric LIGO-G000162-00-R for gravity (as opposed to all other forces), motion (acceleration) depends only on location, not mass gravitational acceleration depends only on the geometry of the of the geometry the on only depends acceleration gravitational A Imagine space as a stretched rubber sheet. sheet. rubber stretched a as space Imagine a deformation. will cause surface the mass on A willthe sheet that mass.toward roll onto mass dropped Another are they because not masses, larger toward travel masses smaller that theorized Einstein the largerthe object. not any properties of the test mass itself mass test the of properties any not ½ Œ Œ Œ Œ is that space through travel smaller objects the because but force, a mysterious by "attracted" by warped ½ Œ 9 “Einstein Cross”

gravitational lensing central glow formed by nearby nearby by central glow formed images are used to detect a ‘dark a ‘dark detect to used are images The bending of light rays matter’ body as the central object matter’ body galaxy. Such gravitationalgalaxy. lensing Quasar image appears around the appears Quasar image with pass. each Mercury’s orbit experimental tests shifts slightly withshifts slightly each orbit twice Newton’s theory (or "perihelion") shifts forward perihelion shifts forward

AJW, Caltech, LIGO Project LIGO AJW, Caltech, such that its closest point to the Sun point closest its such that Mercury's elliptical path around the Sun Mercury's Einstein’s Theory of Gravitation cluster LIGO-G000162-00-R bending of light

of massive objects eclipse Sir of 1919 by Arthur Eddington, when the Sun was First observed during the solar First observed

As it passes in the vicinity silhouetted against the Hyades star 10 QFD theory QCD QED GR…? ) ) 0 ) G g γ , Z - , W + W Gluons ( Photon ( Graviton( Carried by (massive) (massless) (massless) (massless) “flavor” charge Color Electric charge Charge Mass Quarks, leptons Acts on Quarks Charged particles All particles

AJW, Caltech, LIGO Project LIGO AJW, Caltech, -2 -13 -40 Strength 10 10 10 10 Strength of gravitational force LIGO-G000162-00-R Gravitational force is very weak! Gravitational force is very it dominates universe) stars, galaxies, scales (planets, But at large Interaction Strong nuclear Electromagnetic Weak nuclear Gravitational 11 ) weak-field But we can search for ( weBut can search of their waves as a signal gravitational dynamics and presence Strong-field GR and AJW, Caltech, LIGO Project LIGO AJW, Caltech, effect effect tiny non-linear The universe in the earlyin moments of The universe holes the horizon of black Near/in LIGO-G000162-00-R the big bang the big ½ ½ Most tests of GR focus on small deviations small GR focus on Most tests of is a curvature Space-time gets GR This is where holes black any close to We aren’t very interesting! • • • • from Newtonian dynamics dynamics from Newtonian approximation) weak-field (post-Newtonian with light (fortunately!), see them and can’t everywhere except: everywhere 12

Einstein’s Theory carried information by gravitational radiation at the speed of light

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Spacetime curvature Dynamics of changing Newton’s Theory LIGO-G000162-00-R

“instantaneous action at a distance” 13

T π

= 8

G matter and energy ⇔ 2 r / AJW, Caltech, LIGO Project LIGO AJW, Caltech, 2 m 1 Einstein’s field equation: General Relativity (1916) Gm = a 1 spacetime curvature m = spacetime warps in response to the presence of matter, energy, motion motion of matter is determined by spacetime curvature for gravity (as opposed to all other forces), motion (acceleration) depends only on location, not mass 16 coupled non-linear differential equations; analytical solutions in only the simplest of cases (spherical symmetry, static, etc) F Œ Œ Œ Œ LIGO-G000162-00-R        0 0 0 1 14 0 0 0 1

g 0 0 0 1 1 0 0 0 −        =

µν 2 η

dt

2

c ν h<< 1 h<< −

dx 2

µ

µν

+dz dx

2

µν +h

µν +dy 2 =g η

2 =

ds is a function only of the space-time metric = dx µν Project LIGO AJW, Caltech,

2 G g ds

ds Space-time geometry metric is flat space Minkowski metric, is space-time metric is metric perturbation

(generalization of Pythagorean theorem to space-time): η Einstein field tensor which describes local geometry Space-time interval g h for weak gravitational fields, components of LIGO-G000162-00-R Œ Œ Œ Œ Œ 15 h

h

k| 0

f = c|

= π

µν h     2 2 t ∂ ∂ 2 1 c ), where 2 ), Einstein’s field equations can be

− x

• 2

k ∇ << 1

AJW, Caltech, LIGO Project LIGO AJW, Caltech,     ft- h π Metric perturbation

h(2 linearized In the “transverse traceless” (TT) gauge, they become a wave eqn for In the weak-field limit ( (no matter sources): The metric perturbation is interpreted as a gravitational wave amplitude, travelling at the speed of light: Gravitational wave metric perturbations stretch and squeeze the space they pass through (strain amplitude) LIGO-G000162-00-R Œ Œ Œ Œ 16 , others (60’s) others ,

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Reality of gravitational waves of laser beam between the masses the between of laser beam

ikx » GW stretches and squeezes space between two test masses » GW accelerates test masses in fixed space Alternate perspectives: Alternate Due to non-linearity and other complexities of GR, the energy energy the GR, of complexities other and non-linearity Due to is ill-defined GW carried by a real! are even GWs whether debated it was long by Bondi arguments Finally, convincing advance phase measuring by effect sense we can Either way, e an equal wavelength laser the Doesn’t stretch/squeeze GW effect? the cancel to amount, effect masses from falling” testis on “freely different NO! Effect this difference! measure interferometers on light beams; LIGO-G000162-00-R Œ Œ Œ Œ Œ Œ Œ 17 black holes, dark matter holes, dark black with matter with matter

AJW, Caltech, LIGO Project LIGO AJW, Caltech, field theory astrophysical sources Gravitational Waves from Einstein's Theory of General Relativity of Theory Einstein's astrophysical objects astrophysical strong weak –weak to detect! hard very

extremely weakly extremely Рobjects massive very motion of quadrupolar coherent Рmasses test two between distance measured changes Рattenuation with no universe the cross can Interacts Radiated by "dark" mass distributions: distributions: by "dark" mass Radiated Radiated by Predicted by by Predicted of the Test Warps space as it passes by (changes the metric) the (changes by as it passes space Warps Extremely LIGO-G000162-00-R ΠΠΠΠΠΠΠ! 18 TOO WEAK 2 orb f Terrestrial sources Terrestrial 2 r 4 c GMR 2

π 4 electromagnetic radiation gravitational radiation Sources of GWs ≈ AJW, Caltech, LIGO Project LIGO AJW, Caltech, h ⇒ ⇒ ⇒

µν & & I r 4 G c 2 = second derivative =

µν µν & & is a small number! I h moving at 15% of speed of light: kinetic energy) G Need huge mass, relativistic Amplitude of the gravitational wave (dimensional analysis): Accelerating mass Accelerating charge For a binary neutron star pair, 10m light-years away, solar masses of mass quadrupole moment (non-spherical part of velocities, nearby. Œ Œ Œ Œ Œ Œ Œ LIGO-G000162-00-R 19

AJW, Caltech, LIGO Project LIGO AJW, Caltech, ⇒ ⇒ ⇒ ) ⊗ Nature of Gravitational Radiation two polarizations no dipole radiation no monopole radiation no monopole ) and cross ( ) and ⊕ •quadrupole 2) wave (spin •conservation of energy of energy •conservation •conservation of momentum of momentum •conservation LIGO-G000162-00-R plus ( General predicts Relativity : • transverse space-time distortions, of light freelypropagating at speed • Conservation laws: 20 GW Hz and down 3 Space-time itself Space-time 10 measure amplitude measure poor spatial resolution spatial poor very small interaction; no shielding no interaction; small very wavelength ~large compared to sources - sources to compared ~large wavelength detectors have large solid angle acceptance angle solid large have detectors coherent motions of huge masses (or energy) (or masses huge of motions coherent

AJW, Caltech, LIGO Project LIGO AJW, Caltech, E&M Hz and up images 6 10 Contrast EM and GW information space as medium for for field as medium space • mostlyexclusive information, mutually different Very •E&M observations on predict GW sources based to Difficult wavelength small compared to sources - absorbed, scattered, dispersed by matter dispersed scattered, absorbed, measure amplitude (radio) or intensity (light) intensity or (radio) amplitude measure detectors have small solid angle acceptance angle solid small have detectors LIGO-G000162-00-R incoherent superpositionsincoherent molecules atoms, of 21

AJW, Caltech, LIGO Project LIGO AJW, Caltech, What will we see? LIGO-G000162-00-R 22 Astrophysical

AJW, Caltech, LIGO Project LIGO AJW, Caltech, neutron star) Sources of Gravitational Waves (rotating, beaming (rotating, beaming supernova collapse Non-axi-symmetric Non-axi-symmetric Non-axi-symmetric pulsar pulsar Non-axi-symmetric (neutron stars, black holes) Coalescing compact binaries binaries Coalescing compact LIGO-G000162-00-R 23 uncertain

very !

AJW, Caltech, LIGO Project LIGO AJW, Caltech,

certain Waveforms of Gravitational Waves » Surprises are »pairs binary Neutron star (NS/NS) » Black hole (BH/BH) binaries; NS/BH binaries » with ellipticity Pulsars »instabilities) with up, (neutron stars spinning "Wagoner" stars » Supernova bursts » Background from primordial cosmological event (Big Bang) » Rates, signal sizes, waveforms for all the above are “Chirps” (reasonably known waveforms) known (reasonably “Chirps” Periodic (well defined waveforms) waveforms) (unknown Impulsive noise) from indistinguishable (random, Stochastic Unknown??? Œ Œ Œ Œ Œ LIGO-G000162-00-R 24

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Compact binary mergers Compact binary GWs from coalescing binaries LIGO-G000162-00-R 25 “Chirp Signal”

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Compact Binary Inspirals LIGO-G000162-00-R 26 LIGO II (2007- ) LIGO I (2002-2005) Advanced LIGO Thorne diagrams

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Astrophysical sources: LIGO-G000162-00-R 27

AJW, Caltech, LIGO Project LIGO AJW, Caltech, How far out can we see? ) ! 3 LIGO-G000162-00-R Improve sensitivity to Improve of sources goes Number Improve sensitivity by a Improve sensitivity factor of 2x, and… ⇒ distance by 10x (h ~ 1/r) ⇒ up 1000x (1/r 28 LIGO II LIGO I Virgo cluster AJW, Caltech, LIGO Project LIGO AJW, Caltech, How many sources can we see? LIGO-G000162-00-R ) ! 3 Improve Improve of Number Improve sensitivity Improve by a factor of 2x ⇒ sensitivity to distance by 2x (h ~ 1/r) ⇒ sources goes up 8x (1/r i 29 determine

AJW, Caltech, LIGO Project LIGO AJW, Caltech, distance from the earth r the earth from distance bodies two of the masses e and orbital inclination orbital eccentricity • • • Chirp signal from Binary Inspiral LIGO-G000162-00-R 30 • 17 / sec Neutron Binary System Binary Neutron • ~ 8 hr PSR 1913 + 16 -- Timing of pulsars

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Hulse-Taylor binary pulsar LIGO-G000162-00-R 31

AJW, Caltech, LIGO Project LIGO AJW, Caltech, shortening of of period shortening ⇒ GWs from Hulse-Taylor binary LIGO-G000162-00-R negligible loss from friction, material flow friction, material negligible loss from universe!) age of (<< Œ Œ emission of gravitational waves by compact binary system compactwaves binary by gravitational emission of Apparently, loss is due to GWs! to due is loss Apparently, Only 7 kpc 7 Only away Nobel Prize, 1993 period speeds up 14 sec from 1975-94 orbital energy loss measured to ~50 msec accuracy deviation grows quadratically with time Merger in about 300M years beautiful agreementwith GR prediction Compact system: Œ Œ Œ Œ Œ Œ Œ Œ Œ Œ 32 Collision of two blackholes computer simulations

AJW, Caltech, LIGO Project LIGO AJW, Caltech, “Grand Challenge” – “Grand Challenge” Project Supercomputer Black holes: Distortion of spacetime of spacetime Distortion a blackhole by LIGO-G000162-00-R Testing General Relativity in the Strong Field Limit Testing General Relativity 33

Optical Light Curve Optical

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Supernova collapse

The Collapse LIGO-G000162-00-R 34 Within about 0.1 second, the core collapses and gravitational waves are emitted. After about 0.5 second, the interacts with collapsing envelope the outward shock. Neutrinos are emitted. Within 2 hours, the envelope of the star is explosively ejected. When the photons reach the surface of the star, it brightens by a factor of 100 million. Over a period of months, the expanding remnant emits X-rays, and light radio waves in a visible decreasing fashion. Œ Œ Œ Œ

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Gravitational waves Gravitational Supernova collapse sequence LIGO-G000162-00-R 35 Rate Œ Tycho’s Supernova, Supernova, Tycho’s - Supernava Kepler’s - Crab Supernava The in Centaurus in the SN 1604 SN1054 SN 1572 SN1006 within Virgo Cluster ~ 1 Cluster within Virgo year our galaxy our galaxy years 1/50 +other possible Milky Way Way Milky possible +other Œ studied in detail by Tycho Brahe Tycho by in detail studied Œ Œ supernovae southern sky Œ Chinese by recorded in Taurus American astronomers and Native Œ Œ Œ

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Historical Supernova (our galaxy) LIGO-G000162-00-R Kepler SNR Cygnus Cygnus Loop Remnant 36 SN explosion

Supernovae - SN1994I

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Supernova optical observations Supernova optical SN remnant

Crab Nebula 1054 AD 1054 Crab Nebula LIGO-G000162-00-R 37 ‘burst’ signal

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Supernova collapse Gravitational Waves from Rate

3/yr - cluster Virgo 1/50 yr - our galaxy LIGO-G000162-00-R Non axisymmetric collapse 38 LIGO

AJW, Caltech, LIGO Project LIGO AJW, Caltech, astrophysical sources SN1987A LIGO-G000162-00-R 39 < 10-6 ε non axisymmetric: 10-4 < science: neutron star precession; interiors instabilities “R-mode” narrow band searches best » » » » Pulsars in our galaxy Œ

AJW, Caltech, LIGO Project LIGO AJW, Caltech,

Pulsars and continuous wave sources LIGO-G000162-00-R 40

AJW, Caltech, LIGO Project LIGO AJW, Caltech, GWs from dark matter More than 95% of the Universe is non luminous matter (dark matter) Gravitational openwaves will up an entirely new window on the Universe LIGO-G000162-00-R ΠΠ41

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Stochastic Background • Standard big bang models predict an unmeasurably small strain • big bang Exotic models predict large structures that radiate GWs • cross-correlate Must separatedwidely“noise”detectors random between two • sum Incoherent of all the weak sources in the universe, added up. • Expected to be measureable at very low frequencies (LISA) Several possible (speculative) sources: (speculative) possible Several • primordial “big-bang” background • strings cosmic • noise properties are indistinguishable from Statistical • confusion limit LIGO-G000162-00-R 42

Cosmic

microwave background microwave

AJW, Caltech, LIGO Project LIGO AJW, Caltech, Gravitational waves from Big Bang LIGO-G000162-00-R 43

AJW, Caltech, LIGO Project LIGO AJW, Caltech, times after the Big Bang GWs probe the universe at earliest LIGO-G000162-00-R 44 Scales

AJW, Caltech, LIGO Project LIGO AJW, Caltech, LIGO-G000162-00-R 45 Songlines » Relativity of General tests Basic »astrophysics and astronomy of field A new Space-time of the universe is (presumably!) filled vibrations:with Einstein’s Songlines soon LIGO ‘listen’ for Einstein’s Songlines will gravitationalwith permitting waves, A new window on the universe! Œ Œ Œ

AJW, Caltech, LIGO Project LIGO AJW, Caltech,

Einstein’s LIGO-G000162-00-R