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Gravitational Waves Gravitational Waves Physics, Technology, Astronomy and Opportunities Unnikrishnan. C. S. Tata Institute of Fundamental Research Mumbai [email protected] www.tifr.res.in/~filab IIT-K, 2014 Gravitational Waves The Structure of Physics: Matter, Fields, Space and Time a= Fm/ and Principle of relativity Laws of Motion Physical Understanding Laws of Fundamental Forces F= − GMm/ r2 Conservation Laws (Constraints) Conservation of momentum. Energy etc… Four Fundamental Interactions and several fundamental particles Gravity, Electromagnetism, Weak interactions and sub-nuclear strong interactions. Electromagnetism Weak Interaction Gravity Strong Interaction IIT-K, 2014 Gravitational Waves Magnetic Field Electric Field Charges and Currents are fundamental, fields are ‘theoretical’. Current Magnetic field Electromagnetic waves need electric AND magnetic field for generation and propagation. ∂∂BE − =∇×E, µε =∇×B... Maxwell ∂∂tt00 Unobservables in Physics Fields, Wavefunction, Space and Time… IIT-K, 2014 Gravitational Waves GRAVITY, ITS FIELDS and THEIR WAVES IIT-K, 2014 Gravitational Waves F= − GMm/ r2 22 ag =−=− GMm// r m GM r a= Fm/ Independent of the mass of the falling body F= kQq/ r2 2 kQ q aem = kQq/ r m = 2 a= Fm/ rm Gravity seems to be a special interaction Inertia turns out to be identical to the gravitational charge – Equivalence Principle (physics of gravity identical to physics in accelerated frames) IIT-K, 2014 Gravitational Waves Universality of Free-Fall −−δ a δ a<1012 ms / 2 →< 10 13 a IIT-K, 2014 Gravitational Waves So, gravitational field ‘g’ and acceleration ’-a=g’ seem equivalent This is called the Equivalence Principle This is the same as saying that in g free-fall, there is no gravitational field But it does not mean that in free-fall there is no gravity! IIT-K, 2014 Gravitational Waves So, tidal deviations cannot be eliminated by free-fall (description in the General Theory of Relativity) IIT-K, 2014 Gravitational Waves Torsion balance: Harmonic potential Ultra-sensitive IIT-K, 2014 Gravitational Waves 0.3 mm 0.3 mg g≈×5 10−82 cm / s 1 mm Flux−∝ density1/ R2 0.01 gm (For 3D space) What if space is higher dimensional at some tiny scales (micrometers or less) ? Inverse-square law for ‘g’ will change! IIT-K, 2014 Gravitational Waves TIFR Gravitation Laboratory Gauribidanur, Karnataka IIT-K, 2014 Gravitational Waves ‘g’ of Sun ~0.6 cm/s2 δ a( earth−< moon) 10−14 cm / s 2 IIT-K, 2014 Gravitational Waves Dark matter IIT-K, 2014 Gravitational Waves 3% of total estimated matter: So 97% is invisible, and NOT made of ANY known particle So, we are not sure of gravity’s behaviour at very small scales and at very large scales. IIT-K, 2014 Gravitational Waves Magnetic Field Electric Field Current Magnetic field Electromagnetic waves need electric AND magnetic field for generation and propagation. ∂∂BE − =∇×E, µε =∇×B... Maxwell ∂∂tt00 IIT-K, 2014 Gravitational Waves What is an electromagnetic wave? Q IIT-K, 2014 Gravitational Waves IIT-K, 2014 Gravitational Waves Gamma rays and galaxies IIT-K, 2014 Gravitational Waves Spectral view – multi-wavelength Radio IR H-α UV X-ray IIT-K, 2014 Gravitational Waves Spectral view – multi-wavelength Crab Nebula IIT-K, 2014 Gravitational Waves Multi-wavelength galaxy IIT-K, 2014 Gravitational Waves Gravity and Electromagnetism Both have ‘electric’ and ‘magnetic’ parts Charges and currents. Mass is the ‘charge’ of gravity and Spin is its ‘gravito-magnetic moment’ One important different between the two is that while electric and magnetic fields have no electric charge, gravitational field has gravitational charge! With m=E/c2, all forms of energy is equivalent to mass, and hence generate gravity. Therefore, all fields including the gravitational field, which carry energy, also generate gravitational fields. This is one reason why the theory of gravity (The General Theory of Relativity) is complicated to work with. IIT-K, 2014 Gravitational Waves Gravity and electromagnetism Charges (static): Coulomb force – electric fields Electromagnetic Currents (motion): Ampere’s force – magnetic fields Waves What about relativistic gravity? We know static gravitational charge (mass/energy) generates g-field. Does moving and rotating masses generate a gravito-magnetic field?! If so, then there is a possibility of gravitational waves… IIT-K, 2014 Gravitational Waves Gravito-magnetism A natural consequence of relativistic gravity, and yet, was not detected experimentally till recently. GJ GIΩ GM µ M B == →Ω = 0 g 23 23 2 B 3 cr cr cr r IIT-K, 2014 Gravitational Waves The real gravitational field near the earth GM − ω ≈ Ω≈5 × 1014 rad / s cr2 Gravity Probe – B (Stanford U.) IIT-K, 2014 Gravitational Waves Physics of Gravitational Waves What is an electromagnetic wave? Q So, can we expect gravitational waves from oscillating (accelerated) masses? IIT-K, 2014 Gravitational Waves Radiation E vt at aR t =≈= and E = qR/ 2 E 2 r t Er ct c c Er q aRsinθθ qr sin Et = 22= 2 ct R c Rc ct d sinθ vt qr=→= d E t Rc2 Since area=R2, number of flux lines/area 1/R2 So, radial Electric field (flux/area) ~ 1/R2 What about the Transverse Electric field (radiation)? Since, circumference of a great circle on the sphere increases only as R, transverse radiation field decrease as 1/R. IIT-K, 2014 Gravitational Waves 0 Phase diff. GM r sinθ E = ×⋅kr gt Rc2 GM rsinθω r cos θ = × Rc2 c GMr 23ω = sinθθ cos 0 cR3 IIT-K, 2014 Gravitational Waves The force-field of gravitational waves + + IIT-K, 2014 Gravitational Waves The relation between spin of the field and polarization of the force field IIT-K, 2014 Gravitational Waves What is the physical effect of a passing gravitational wave? Quadrupole Radiation formula ∆L G Mr22ω G Mv2 Strain h =≈≈ L c4 R cR 22 c IIT-K, 2014 Gravitational Waves Are we confident that Gravitational Waves exist, apart from the belief in the correctness of the theory? Jl. Franklin Inst. 1937 IIT-K, 2014 Gravitational Waves Binary Pulsar 1913+16 (Hulse-Taylor) dE32 G =G ≈ 2ω 64 EG 5 Mr 231 dt c ω≈GM/ a →≈ νρ2π G 8 tc ≈×3 10 yrs IIT-K, 2014 Gravitational Waves Orbital decay and speeding up of the binary pulsar: dE32 G E =G ≈ Mr2ω 64 G dt c5 IIT-K, 2014 Gravitational Waves Signal Strength at Earth for neutron star spiral in milky way: Distance: 10 kpc ~ 1020 meters 2 G Mv − Strain h ≈≈10 64Mv 2 cR4 Gm vc≈=0.1 (3 × 107 m/s) for neutron stars at r≈100 km 2r ∆l − With M~1030 kg, v~3x107 m/s, Strain h = ≈ 10 19 l If the event happens in another galaxy, 100 Mpc ( 1024 m away), Strain h ≈ 10−23 This small strain requires the measurement of <10-20 meters in a detector of size 1 km! (almost million times smaller than the atomic nucleus). Is it a mad venture trying to make a ‘detector’? IIT-K, 2014 Gravitational Waves h ≈ 10−17 IIT-K, 2014 Gravitational Waves A modern cryogenic resonant mechanical detector IIT-K, 2014 Gravitational Waves When these waves reach earth, what can they do to free masses? Michelson Interferometer 2 −11 30 G Mv 6.7⋅ 10 ×⋅ 3 10 2− 19 Strain h≈→22 2 0.05< 10mm / ! cR c (3×× 108) 10 20 Much less than the size of the nucleus. This is the primary device for gravitational wave detection IIT-K, 2014 Gravitational Waves Signal Thermal noise, 1/R, G/c2, Seismic Noise, Random source… << Quantum Noise Tidal Noise, All instrument Noise, Any Noise one can think of… Signal Lower Limits of all 1/R, G/c2, these noises allowed Random source… > or ~ by Physics and today’s technology… IIT-K, 2014 Gravitational Waves I / I Signal in the interferometer ∆l The general problem of ‘fringe splitting’ (centroid, locking…) Mean number of photons @ intensity I= N, N= Ph/ ν N∆φ Change in the number of photons, ∆≈N π Noise =NN ≈∆ min With 1 W of optical power, N=1019 /s , π∆Nmin π −9 ∆≈φmin = ≈10 N N IIT-K, 2014 Gravitational Waves There is another equivalent way to talk about photon shot noise that explicitly brings out the basic feature of quantum mechanics involved. The energy-time uncertainty relation ∆∆≥Et ∆∆=Etω() ∆ N ∆ φω / ≈ 11 →∆N ∆φφ ≥1 →∆ ≈ = ∆N N IIT-K, 2014 Gravitational Waves Detection of gravitational waves requires the measurement of movements 10-17 to 10-20 meters in a detector of size 1 km. With 1 W of optical power, N=1019 /s , and 10 ms (100 Hz), π −−8 14 ∆φmin ≈ ≈10 →∆Lm =∆φλmin × ≈10 N STABLE Laser − 1) Increase Laser Power 10 kW→∆ L ≈10 16 m 2) Increase Length up to 4 km: Not much gain, though very important (1/R). 3) Fold optical path − nm=10 → 10 17 Reaching there, but not comfortable yet! IIT-K, 2014 Gravitational Waves Optimal length of the Interferometer arm: 8 λνggc / 3× 10m /100 Hz L ≈≈ ≈ =750km ! opt 44 4 This is the optimal distance the light should travel for maximal signal. In other words light should be in the interferometer for an optimal duration of about 750 km/c seconds or a quarter of the GW period of 10 ms or so. This is achieved by multiple bounces with average time equal to about quarter of the GW period such that 4 km x nB = 750 km. So, the number of bounces is about 200. IIT-K, 2014 Gravitational Waves Detection of gravitational waves requires the measurement of movements 10-17 to 10-19 meters in a detector of size several km. Improvements: 1) Folding Fabry-Perot Cavity Finesse ~ n : 300 + 10kW , 4 km→ 10−−16 m →× 3 1019 m with F ≈300 Intra-cavity power > 1 MW ! Radiation Pressure Noise and Thermal Lensing are problems IIT-K, 2014 Gravitational Waves Large Interferometer VIRGO at Pisa, Italy ( 3 km) IIT-K, 2014 Gravitational Waves LIGO-HO IIT-K, 2014 Gravitational Waves ∆L G Mr 22ω = ≈ 231 Strain h 4 ω≈GM/ a →≈ νρG Lc R 2π IIT-K, 2014 Gravitational Waves But, every bit counts… because waves strength is 1/R If sensitivity is increased by factor X, then the distance reach increases by X, and the number of astrophysical sources increases as X3! So, a factor of 10 in sensitivity means a factor of 1000 in number of possible detections.
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