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Gravitational Waves Generating Phenomena and Detection

Gravitational Waves Generating Phenomena and Detection. Marino Maiorino. Table of Contents. Basics of Gravitational Waves (GW) GW’s propagation GW’s generation Low Frequency Astrophysical Phenomena High Frequency Astrophysical Phenomena Basics of Gravitational Waves Detection

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Gravitational Waves Generating Phenomena and Detection

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  1. Gravitational WavesGenerating Phenomena and Detection Marino Maiorino

  2. Table of Contents • Basics of Gravitational Waves (GW) • GW’s propagation • GW’s generation • Low Frequency Astrophysical Phenomena • High Frequency Astrophysical Phenomena • Basics of Gravitational Waves Detection • Resonating Bar Detectorss • Long Base Interferometers • VIRGO-EGO • Data Processing • Space-Based Interferometers (LISA)

  3. Basics of Gravitational Waves (GW) • Special Relativity: time is the 4th dimension • Through Minkowski formalism (metric tensor)

  4. Basics of Gravitational Waves (GW) • General Relativity: space-time structure linked to matter presence through the gravitational field • Gravity is not a force, it is rather a bending of space-time: straight lines are defined by the trajectories of free-falling objects

  5. Basics of Gravitational Waves (GW) • In General Relativity space-time is flat no more: another metric tensor must be used. In the weak-field hypothesis, this can be written as: • With a special, transverse and null-trace gauge, one obtains… which is the wave equation for a perturbation of the metric tensor which propagates with speed c!

  6. GW’s Propagation • As in electrodynamics, let us study GW’s propagation in the approx. of a multipole series of a delayed potential (hyp.: source dim. << wavelength): • Monopole term: dm/dt = 0 for an isolated system • Dipole term: constant because of momentum conservation of an isolated system • Gravitational “magnetic” momentum: no contribution because of angular momentum conservation of an isolated system

  7. GW’s Propagation • First non-null term of the series is the quadrupole term: • United with the transverse and null-trace gauge, this lets us see a GW as made up of two independent polarizations:

  8. GW’s Propagation

  9. GW’s Generation • Let’s derive the irradiated power from the quadrupole term: • This corresponds to an estimation of space-time distortion: (R = distance from source; second derivative of quadrupole computed at time t – R/c) • You get strong GW’s close to a source with inconstant variations in quadrupole momentum!

  10. GW’s Generation • Let’s try to generate GW’s in a lab: two masses, 1 ton each, 2 m apart, 1 kHz rotation: • hlab = 2.6·10-33 m 1/R!

  11. GW’s Generation • Let’s study it better for a two-stars system: • Whence you get:

  12. GW’s Generation • In one picture:

  13. Low Frequency Astrophysical Phenomena • Coalescing binaries: • Two stars revolve one around the other and get closer as they dissipate gravitational power. • In these conditions, you get big values of h (~10-16) at too low frequencies (1 pHz)! • When the two stars unite, on the other hand, you get h ~ 10-21 between 10 and 1000 Hz up to 40 Mpc! Note: our galaxy diameter is 50 kpc only.

  14. High Frequency Astrophysical Phenomena • Supernovae (SN) • Star explosion  HUGE mass acceleration. From pulsars population we deduce that rotating SN’s are common  HUGE quadrupole momentum variation. h ~ 10-23 @ 500 Hz @ 15 Mpc • Pulsar (I) • Supernova remnant spinning like the hell. A solar mass of 10 km rotating (sometimes) in ms! h ~ 10-26 @ 100 Hz @ 10 kpc. Small, but integrable in time as it is periodic.

  15. High Frequency Astrophysical Phenomena • Pulsar (II) • Pulsar with fellow star. Two pulsars revolving one around the other at a 20 km distance, would generate: h ~ 10-21 @ 400 Hz @ 15 Mpc! • Black Holes (BH) • Even bigger masses. Theoretical estimations say that for a BH of 1 M (solar mass) one could have: h ~ 10-20 @ 1 kHz @ 1Mpc

  16. Basics of GW’s Detection • How to measure distortions of 1/1021? Einstein himself doubted it could have EVER be done. • Pioneering work of Joseph Weber (1960): resonating bar detectors. • Problems: small effects and plenty of noises. • SN 1987A in LMC (Large Magellan Cloud) was detectable for these devices but… …ALL of them were shut off for maintenance!

  17. Basics of GW’s Detection

  18. Resonating Bar Detectors • Let’s monitor the normal vibration modes of an aluminum cylinder (through piezoelectric sensors). • Sharp resonance (like diapason), but sensitivity confined to a narrow bandwidth (a few Hz) around the resonance frequency. • An incident GW is supposed to excite such vibration modes. • Primary drawback: sensitive to signals with frequency close to the bar mechanical ringing frequency (~1 kHz). They respond to the signal at their own frequency.

  19. Long Base Interferometers • Present strategy: monitoring the length of the arms of a Michelson interferometer of suitable length.

  20. Long Base Interferometers • An incoming GW will stretch one interferometer arm and will shrink the other one: • The typical GW distortion (10-21) could cause a change of one fringe in the interference pattern on an interferometer in infrared light (~ 1 µm wavelength) with arms of 5·1011 km! • On a 500 km instrument, the change would be of 10-9 fringes!

  21. Long Base Interferometers • Does this formula actually mean: “the longer, the better”? • A light beam will stay in the instrument for a time t = 2L/c, so that the measured length variation will be only: • Optimum length makes maximum dL. Its value is: • GW interferometers are antennas: they are tuned on search frequencies!

  22. Long Base Interferometers • Frequency limits for a GW interferometer detector: • Minimum frequency (earthbound) = 10 Hz because of the seismic noise • Minimum frequency (space bound): much lower • Maximum useful frequency = a few kHz (maximum frequency for astrophysical sources • Lengths range from 8 to 8000 km (earthbound). • Choice is made based on the sources you want to detect and the noise sources.

  23. VIRGO-EGO • Detection band is centred around 625 Hz (minimum noise contribution), which means an interferometer with arms of 120 km!

  24. VIRGO-EGO • Cascina, near Pisa, Italy • But 120 km is too much: even Earth curvature would affect the instrument! *

  25. Ein E0 t2Ein r2Eint1 E1 t2E0 r2E0t1 t2E1 VIRGO-EGO • 120 km can be also made by folding 40 times a 3 km path: Fabry-Perot cavities • Fabry-Perot cavities rely on the interference of multiple reflected beams . Erif Etr t1 r1 r2 t2 d

  26. VIRGO-EGO Fabry-Perot cavities: Reflected phase gives signal to lock the cavity! So, FPs have to be insensitive to ANY noise (even seismic)!

  27. VIRGO-EGO Superattenuator (SA): A pendulum is a mechanical low-pass filter of the second order for solicitations to its suspension point. A simple expr. for the Transfer Function of an n-stage pendulum is:

  28. VIRGO-EGO The Superattenuator (SA)

  29. Data Processing • VIRGO is an “active” instrument! • Interferometer, polarizers and photodiodes (Detector) • Electronics (Reaction Filter) • Superattenuator coils (Actuators) D F A

  30. Space-Based Interferometers • LISA (Laser Interferometric Space Antenna) • ESA-NASA, launch in 2010 • Frequencies: 0.1 mHz ÷ 0.1 Hz • Two arms make a Michelson interferometer; third arm measures another interferometric observable. • Laser light of 1 µm, 1 W. • Only a single pass in the arms. • Disturbances: forces from the Sun (fluctuations in radiation pressure, solar wind). • The proof masses are free-floating within, shielded by and not attached to the spacecraft. The spacecraft is in a feedback loop with precision thrust control to follow the proof masses (drag-free tech.) • SNR ~ 1000 or more @ z = 1

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