Gravitational-Wave Physics Gravitational-Wave Detectors Gravitational-Wave Astronomy Gravitational-Wave Astronomy 1060-711: Astronomical Observational Techniques and Instrumentation Guest Lecturer: Prof. John T. Whelan 2013 May 1 Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Gravitational-Wave Detectors Gravitational-Wave Astronomy References Creighton & Anderson, Gravitational-Wave Physics and Astronomy (Wiley, 2011). ISBN 978-3-527-40886-3 Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford, 2007). ISBN 978-0-198-57074-5 Saulson, Fundamentals of Interferometric Gravitational Wave Detectors (World Scientific, 1994). ISBN 978-9-810-21820-1 Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Gravitational-Wave Detectors Gravitational-Wave Astronomy Outline Gravitational-Wave Physics 1 Physical Motivation Mathematical Description Generation of Gravitational Waves Gravitational-Wave Detectors 2 Overview Details of Ground-Based Interferometers Prospects for Space-Based Interferometers Gravitational-Wave Astronomy 3 Gravitational Wave Sources Gravitational Wave Data Analysis Selected Results from First-Generation GW Detectors Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Outline Gravitational-Wave Physics 1 Physical Motivation Mathematical Description Generation of Gravitational Waves Gravitational-Wave Detectors 2 Overview Details of Ground-Based Interferometers Prospects for Space-Based Interferometers Gravitational-Wave Astronomy 3 Gravitational Wave Sources Gravitational Wave Data Analysis Selected Results from First-Generation GW Detectors Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Action at a Distance Newtonian gravity: mass generates gravitational field Lines of force point towards object Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Issues with Causality Move object; Newton says: lines point to new location Relativity says: can’t communicate faster than light to avoid paradoxes You could send me supraluminal messages via grav field Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravitational Speed Limit If I’m 10 light years away, I can’t know you moved the object 6 years ago Far away, gravitational field lines have to point to old location of the object Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravitational Shock Wave Sudden motion (acceleration) of object generates gravitational shock wave expanding at speed of light Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Ripples in the Gravitational Field Move object back & forth − → gravitational wave Same argument applies to electricity: can derive magnetism as relativistic effect accelerating charges generate electromagnetic waves propagating @ speed of light Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravitational Wave from Orbiting Mass? Move around in a circle Still get grav wave pattern, but looks a bit funny Time to move beyond simple pseudo-Newtonian picture Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravity + Causality = Gravitational Waves In Newtonian gravity, force dep on distance btwn objects If massive object suddenly moved, grav field at a distance would change instantaneously In relativity, no signal can travel faster than light − → time-dep grav fields must propagate like light waves Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravity as Geometry Minkowski Spacetime: ds 2 = − c 2 ( dt ) 2 + ( dx ) 2 + ( dy ) 2 + ( dz ) 2 tr − c 2 dt 0 0 0 dt dx dx 0 1 0 0 = η µν dx µ dx ν = dy dy 0 0 1 0 dz 0 0 0 1 dz General Spacetime: tr dx 0 dx 0 g 00 g 01 g 02 g 03 dx 1 dx 1 g 10 g 11 g 12 g 13 ds 2 = = g µν dx µ dx ν dx 2 dx 2 g 20 g 21 g 22 g 23 dx 3 dx 3 g 30 g 31 g 32 g 33 Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravitational Wave as Metric Perturbation For GW propagation & detection, work to 1st order in h µν ≡ difference btwn actual metric g µν & flat metric η µν : g µν = η µν + h µν ( h µν “small” in weak-field regime, e.g. for GW detection) Convenient choice of gauge is transverse-traceless: η νλ ∂ h µν η µν h µν = δ ij h ij = 0 h 0 µ = h µ 0 = 0 ∂ x λ = 0 In this gauge: Test particles w/constant coörds are freely falling Vacuum Einstein eqns = ⇒ wave equation for { h ij } : � � ∂ 2 − 1 ∂ t 2 + ∇ 2 h ij = 0 c 2 Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Gravitational Wave Polarization States Far from source, GW looks like plane wave prop along � k TT conditions mean, in convenient basis, 0 h + h × 0 { k i } ≡ k = 0 { h ij } ≡ h = h × − h + 0 1 0 0 0 � � � � t − x 3 t − x 3 where h + and h × are components c c in “plus” and “cross” polarization states More generally � � � � � � k · � k · � r r ↔ ↔ ↔ = h + t − + + h × t − h e e × c c Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves The Polarization Basis wave propagating along � k ; ↔ + , × from ⊥ unit vectors � ℓ & � construct e m : ↔ ↔ + = � ℓ ⊗ � × = � m ⊗ � ℓ − � m ⊗ � ℓ ⊗ � m + � e m e ℓ Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Effects of Gravitational Wave Fluctuating geom changes distances btwn particles in free-fall: Plus ( + ) Polarization Cross ( × ) Polarization Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
Gravitational-Wave Physics Physical Motivation Gravitational-Wave Detectors Mathematical Description Gravitational-Wave Astronomy Generation of Gravitational Waves Multipole Expansion for Gravitational Radiation “Electric Dipole”? � � No, “dipole moment” r dm ∝ ctr of mass COM can’t oscillate (also no negative “charge” in GR) “Magnetic Dipole”? No, “mag moment” � � 1 r × � v dm ∝ spin, another conserved quantity 2 “Electric Quadrupole”? Yes! In TT gauge, h ij ( t ) = 2 G c 4 d P TT � ij ¨ k k ℓ − I k ℓ ( t − d / c ) in terms of mass quadrupole moment � � � r 2 − I ij = r i r j − δ ij dm 3 Astronomical Observational Techniques and Instrumentation Gravitational-Wave Astronomy
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