Ricerca di onde gravitazionali

1. Ricerca di onde gravitazionali • Generalita’ • Sorgenti di onde gravitazionali • Rivelatori di o.g. (overview) • Rivelatori (un po’ piu’ in dettaglio) • Tecniche di rivelazione e tecnologie • Uno sguardo al futuro: nuovi rivelatori.... M.Bassan 12 Feb 2004

2. 1 Generalities Gravitational Waves (g.w.) in General Relativity Features of a g.w.

3. Gravity is a manifestation of spacetime curvature induced by mass-energy 10 non linear equations in the unknown g  ds2=gmndxmdxn

4. 1915 Theory of G.R. • 1916 Einstein predicts gravitational waves (g.w.) • 1960 Weber operates the first detector • 1970 Construction of cryogenic detectors begins • 1984 Taylor and Hulse find the first indirect evidence of g.w. (Nobel Prize 1993) • 2003 First operation of large interferometer • 2004 year of discovery ??? • 2012 Lisa launch foreseen

5. Weak field approximation The Einstein equation in vacuum becomes Having solutions Spacetime perturbations, propagating in vacuum like waves, at the speed of light : gravitational waves

6. Gravitational waves are strain in space propagating with the speed of light • Main features • 2 transversal polarization states • Associated with massless, spin 2 particles • (gravitons) • Emitted by time-varying quadrupole mass moment • no dipole radiation can exist (no negative mass)

7. GRAVITATIONAL WAVE DETECTION • General Relativity Gravitational Waves are ripples of space-time propagating with the speed of the light metric tensor metric of flat space Perturbation introduced by GW with (10-18÷ 10-20) • Equation of geodesic deviation shows how two geodesic lines, described by two test bodies, deviate one respect to the other one by effect of gravitational field.

8. A GW propagating along x axes in TT gauge produces a tiny relative acceleration of the particles, proportional to their distance, in a plane perpendicular to the gravitational wave direction: y y z z

9. Effect on test body …….  In any realistic wave is so weak that the oscillatory changes i are so small compared to the original distance i. => GW

10. PROPAGATION AND POLARIZATION OF G-WAVES The gravitational wave produce a time dependent strain h of space. The gravitational wave detectors will measure this strain directly. Deformation of a ring of test particles due to a gravitational wave propagating in the direction normal to the plane of the ring. + polarization  polarization

11. PROPAGATION AND POLARIZATION OF G-WAVES The quadrupole force field of plus and cross polarization of a gravitational wave.

12. No laboratory equivalent of Hertz experiments for production of GWs • Luminosity due to a mass M and size R oscillating at frequency w~ v/R: M=1000 tons, steel rotor, f = 4 Hz L = 10-30 W Einstein: “ .. a pratically vanishing value…” Collapse to neutron star 1.4 Mo L = 1052 W h ~ W1/2d-1; source in the Galaxy h ~ 10-18, in VIRGO clusterh ~ 10-21 Fairbank: “...a challenge for contemporary experimental physics..”

13. GWs are detectable in principle • The equation for geodetic deviation is the basis for all experimental attempts to • detect GWs: • GWs change (dl) the distance (l) between freely-moving particles in empty • space. • They change the proper time taken by light to pass to and fro fixed points in • space In a system of particles linked by non gravitational (ex.: elastic) forces, GWs perform work and deposit energy in the system

14. Gravitational radiation is a tool for astronomical observations • GWs can reveal features of their sources that cannot be learnt by electromagnetic, cosmic rays or neutrino studies (Kip Thorne) • GWs are emitted by coherent acceleration of large portion of matter • GWs cannot be shielded and arrive to the detector in pristine condition

15. SUPERNOVAE. • If the collapse core is non-symmetrical, the event can give off considerable radiation in a millisecond timescale. • Information • Inner detailed dynamics of supernova • See NS and BH being formed • Nuclear physics at high density • SPINNING NEUTRON STARS. Pulsars are rapidly spinning neutron stars. If they have an irregular shape, they give off a signal at constant frequency (prec./Dpl.) • Information • Neutron star locations near the Earth • Neutron star Physics • Pulsar evolution • COALESCING BINARIES. • Two compact objects (NS or BH) • spiraling together from a binary orbit • give a chirp signal, whose shape • identifies the masses and thedistance • Information • Masses of the objects • BH identification • Distance to the system • Hubble constant • Test of strong‑field general relativity • STOCHASTIC BACKGROUND. • Random background, relic of the early • universe and depending on unknown • particle physics. It will look like noise • in any one detector, but two detectors • will be correlated. • Information • Confirmation of Big Bang, and inflation • Unique probe to the Planck epoch • Existence of cosmic strings

16. Gravitational radiation is a tool for fundamental physics • Possible fundamental observations: • Detect GWs • WHAT WE KNOW • PSR 1913+16 (Hulse & Taylor: strong indirect evidence • WHAT WE WANT • Confirmation • Polarization • WHAT WE KNOW • Scalar component constrained by PSR 1913+16 to 1% of the tensor part • WHAT WE WANT • Test the six polarization states predicted by metric theories of gravity - test of GR

17. Speed of GWs (needs two detectors) • WHAT WE KNOW • Mass of graviton < 10-20 eV, from both PSR 1913+16 and validity of Newtonian gravity in solar system • WHAT WE WANT • If both GW and EM waves come from the same source, we may compare their speeds from the time delay (1/2 hour from Virgo Cluster for a graviton of mass 10-20 eV) • Early Cosmology - Planck-scale physics • After the Big Bang, photons decoupled after 13000 years, neutrinos after 1s, GWs after 10-43 s (Planck epoch). • Detecting a stochastic background of GWs is one of the most fundamental observation possible. Detectors can measure fraction of the closure energy density Wgw=r/rc • WHAT WE THINK • Models from standard inflaction, string cosmology, topological defects • WHAT WE WANT • Measure the energy density, spectrum and isotropy of the background

18. The search for gravitational waves

19. Comparison with electomagnetic waves: Horizontal polarization Vertical polarization Plus polarization Cross polarization

20. Einstein’s General Theory of Relativity (1915) Gravitation can propagate as waves in space-time. Actually what propagates is a ripple of space time ! Space-time is stiff  waves have little amplitude, even if they carry large energy density

21. L L+L Hoe wordt de tijdruimte vervormd door een gravitatie golf ? Quadrupole field lines

22. Detectors of Gravitational Waves Resonant Cylinder Laser interferometer Resonant Ball laser

23. Sources of Gravitational WavesSupernova Explosion Supernova 1987A

24. collapse Inspiraling phase ring down Sources of Gravitational Waves

25. Sources of Gravitational Waves Instabilities in Neutron Stars

26. Gravitational wave detectors • Two different “families”: • Massive elastic solids (cylinders or spheres) • Michelson interferometers • Both types are based on the mechanical coupling between the g.w. and a test mass • In both types the e.m. field is used as a motion transducer • A space interferometer (LISA) is planned to cover the very low frequency band

28. Possible sources at f > 2 kHz • Neutron stars in binary orbits: mergers, disruptions with black holes. • Formation of neutron stars: ringdown after initial burst. • Neutron star vibrations, wide spectrum up to 10 kHz. Can be excited by formation, merger or glitches. • Stochastic background of primordial origin. • Speculative possibilities: • Black holes below 3 M • Compact objects in dark matter • Thermal spectrum at microwave frequencies, but only if inflation did not happen!

29. Oscillation frequencies of neutron stars • Figure from Kokkotas and Andersson, gr-qc/0109054, shows modes of non rotating stars • Modes could be excited by violent events or by more modest glitches • Glitches occur often in young pulsars, making Crab a good target • Glitch energy < 10-10 Mc2

30. Sources of Gravitational WavesPulsars f=10-100 Hz • Very strong magnetic field • (109 Tesla) • + • Fast rotation • = • acceleration of rotation • emission of radio, light waves and gravitational waves

31. The Binary Pulsar PSR 1913+16(Hulse and Taylor’s pulsar) • Radio pulse every T=59 ms : a pulsar rotating 17 times/s • T varies slightly with time: T(t) with a period of 7.75 hrs • => Binary orbit (Doppler effect) • From the study of T(t) derive: • Mass of the two stars (1.4 Mo), • inclination of orbit, eccentricity, • orbital speed (75-300 km/s), • semiaxis (3 Gm).

32. The Binary Pulsar PSR 1913+16 (2) • Tight orbit => strong gravity => General Relativistic effects: • periastron advance (4.2o /yr) • Loss of energy for emission of gravitational waves , orbit shrinks (3.1 mm/orbit). Collapse in 300 Myrs !!!