Gravitational waves

Lecture about gravitational waves targeted at undergraduate students and first year grad students in physics and astronomy. Prepared and taught by Prof. Rodrigo Nemmen at IAG USP.

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

https://blackholegroup.org

Transcript

1. Rodrigo Nemmen IAG USP Gravitational Waves blackholegroup.org @nemmen
2. 1916 1918 https://einsteinpapers.press.princeton.edu
3. Electrodynamics accelerated charges produce electromagnetic radiation Gravitation accelerated masses produce gravitational radiation 1 μ 0 E × B c c hμν electromagnetic wave gravitational wave
4. The Elegant Universe. Crédito: Nova Accelerated masses produce wave of disturbance in spacetime curvature Gravitational waves
5. LIGO’s was first direct detection of GWs But before LIGO we already knew GWs existed!
7. PSR 1913+16: A binary system of pulsars (Hulse & Taylor pulsar) precisely determined orbital parameters r = 5 kpc M1 = M2 = 1.4 Msun
8. GWs emitted by binary system Accelerated masses emit GWs System loses energy Distance between two bodies shrinks
9. GWs GWs emitted by binary system Accelerated masses emit GWs System loses energy Distance between two bodies shrinks NS NS NS NS Distance Period
10. Hulse & Taylor pulsars r = 5Kpc, M1 ≈ M2 ≈ 1.4M⊙ , T = 7h45min fGW = 7 × 10−5 Hz GR prediction h ∼ 10−23 · T = − 2.4 × 10−12 sec/sec Orbital shrinkage due to GW radiation τ = 3.5 × 108yr timescale for coalescence
11. First evidence of existence of GWs Weisberg & Taylor (2005) GR prediction observations Monumental discovery in 1974 by Hulse & Taylor
13. Linearized gravitational waves Far away from the source, r ≫ M, gμν ≈ ημν Gravitational wave (GW) will be weak (space empty of matter) Einstein equation can be linearized and solved giving simpler solutions
14. Weak gravitational field gμν = ημν + hμν Minkowski metric Perturbation hμν = Aμν eikα xα Solution: plane wave traveling with c wave vector GW amplitude Einstein equation Rμν = 0 Ricci curvature (in vacuum) Reduces to wave equation ( ∂2 ∂t2 − ∇2 ) hμν = □ hμν = 0 Linearized gravitational waves
15. hμν = Aμν eikα xα Plane wave wave vector GW amplitude Properties of linear GWs Transverse waves Aμν kμ = 0 kμ kμ = 0 Null wave vector: GWs move like light-rays homework
16. Polarization of GWs Aμν = h+ Aμν + + h× Aμν × Wave moving in the z-direction = 0 0 0 0 0 h+ h× 0 0 h× −h+ 0 0 0 0 0 two polarizations Aμν + = 0 0 0 0 0 1 0 0 0 0 −1 0 0 0 0 0 Aμν × = 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 Polarization components
17. GW polarization x y
18. Effect of GWs on test particles x y z L0 ds2 = gμν dxμdxν ⇒ L = ∫ gμν dxμdxν = ∫ g11 dx = L0 [1 + 1 2 h11 (t,0)] ∴ ΔL L0 = 1 2 h11 (t,0) strain produced by GW Particles oscillate after GW passes ⟂ k homework
19. Example 1: periodic wave ΔL L0 = 1 2 h(t,0) h(t − z) = a sin[ω(t − z) + ϕ] x y z L0 GW propagating in z-direction ΔL L0 = a 2 sin[ωt + ϕ]
20. https://www.youtube.com/watch?v=aVFf8UcX1A8 x y z ⊙
21. Example 2: wave packet ΔL L0 = 1 2 h(t,0) h(t − z) = a exp [ − (t − z)2 σ2 ] x y z L0 GW propagating in z-direction ΔL L0 = a 2 exp [ − (t − z)2 σ2 ]
22. Example 3: Change in distance between two masses due to GW x y z L0 ΔL L0 = h 2 ΔL = hL0 2 = 10−21 × 2 km = 2 × 10−18 m ~ 1 proton radii L0 = 4 km h = 10−21
23. https://www.youtube.com/watch?v=RzZgFKoIfQI Michelson- Morley interferometer
24. https://www.youtube.com/watch?v=RzZgFKoIfQI
25. LIGO Observatory at Livingston, Louisiana 4 km
26. black hole neutron star neutron star neutron star GW sources High mass concentrations + Extreme accelerations star supermassive black hole GWs
28. Strain = h(t) ≡ Δx L Δx = 10−21 × 4 km = 4 × 10−18 m a v v a = 3 proton radii Numerically solve Einstein’s field equation Rμν − 1 2 gμν R = 8πG c4 Tμν spacetime curvature = constant× matter-energy
30. Abbott+2015, PRL
31. Importance of GW detection “I liken this to the first time we pointed a telescope at the sky, […] people realized there was something to see out there, but didn’t foresee the huge, incredible range of possibilities that exist in the universe.” Janna Levin
32. Importance of GW detection 100-yr wait for this: new astronomy Direct, unabsorbed information about dynamics/ mass of relativistic sources
 Black holes really do exist!
33. https://www.nobelprize.org/prizes/physics/2017/weiss/lecture/
34. A moment long-awaited…
35. Birth of multimessenger astronomy: GWs and EM radiation from same source
37. Rezzolla+2011
38. Rezzolla+2011
39. Diaz+2017 10 hours after GW signal: A strange optical glow appears
40. A “kilonova” is born lighter elements (lanthanide-poor) heavier elements (lanthanide-rich) (UV) (NIR) cf. also Cowperthwaite+2017 place where neutron stars merged
42. Importance of GW170817 Birth of multimessenger astronomy: photons + gravitons Short gamma-ray bursts are due to neutron star collisions Neutron star collisions seem to produce most of the gold in the universe (lanthanides)