Rivelatori di onde gravitazionali ricerca iniziata da J. Weber in America e in Italia da Edoardo Amaldi negli anni sessanta

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1 Rivelatori di onde gravitazionali ricerca iniziata da J. Weber in America e in Italia da Edoardo Amaldi negli anni sessanta Antenne risonanti: EXPLORER (CERN) in funzione dal 1990 NAUTILUS (Frascati) AURIGA (Legnaro ) n ~ 1 khz ALLEGRO (Lousiana) per es. EXPLORER e' un cilindro di una lega di alluminio lungo 3 metri, 60 cm di diametro, peso 2300 kg, opera a 2 K

2 In funzione dal 1990 EXPLORER ( CERN )

3 MiniGRAIL Gravitational Radiation Antenna In Leiden Kamerlingh Onnes Laboratory, Leiden University, The Netherlands MiniGRAIL cryogenic run 5 Last update: August Webmaster The MiniGRAIL is a cryogenic 65 cm diameter spherical gravitational wave antenna made of CuAl(6%) alloy with a mass of 1150 Kg, a resonance frequency of 3250 Hz and a bandwidth around 230 Hz, possibly higher. The quantumlimited strain sensitivity dl/l would be ~4x The antenna will operate at a temperature of 20 mk. Two other similar detectors will also be built, one in Rome and one in São Paulo (already financed), which will strongly increase the chances of detection by looking at coincidences. The sources we are aiming at are for instance, non-axisymmetric instabilities in rotating single and binary neutron stars, small blackhole or neutron-star mergers etc.

4 Rivelatori interferometrici L onda gravitazionale cambia la distanza propria tra gli specchi: i due raggi laser fanno un cammino ottico diverso rispetto a quando l onda e assente, quindi arrivano al fotodetector con una differenza di fase Misurando la variazione delle frange di interferenza possiamo rivelare l onda gravitazionale

5 Perche' i bracci dell'interferometro devono essere cosi' lunghi? Equazione della deviazione geodetica Se l'onda e' perpendicolare al braccio, questo varia di l = ½ h l Le fluttuazioni nel numero di fotoni laser che vengono usati simula una variazione della lunghezza del braccio pari l = Ö ( h c l n / p P ) l lunghezza d'onda della luce di potenza P n banda di frequenza del segnale δx j = δ x 0j +1/2 η ij h TT ik δ x 0 k Quindi il limite per la misura e' h > 2 l /l = 2 Ö ( h c l n / p P l 2 )

6 limite per la misura e' h > 2 l /l = 2 Ö ( h c l n / p P l 2 ) l lunghezza d'onda della luce di potenza P n banda di frequenza del segnale Se P = 1000 W, l =0.6 µ m n ~ 1000 Hz per misurare un h > I bracci dell interferometro dovrebbero essere l= 15 km!!!

7 Interferometri terrestri: VIRGO (Pisa) (3 km) LIGO (Hanford (WA)- Livingston (CA)) GEO600 (Hannover) (600 m) TAMA300 (Giappone) (300 m) (3,4 km) 10 Hz < n < 1-2 khz recycling: trucco per aumentare il cammino ottico

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9 Gravitational wave interferometric detectors: first generation GEO600 (British-German) Hannover, Germany LIGO- I (USA) Hanford, WA LIGO-II (USA) Livingston, LA TAMA300 (Japan) Virgo interferometer (Cascina, Italy)

10 advanced LIGO, Virgo) Design sensitivity curves for the Advanced LIGO, Advanced Virgo and LCGT secondgeneration detectors. The Kamioka Gravitational Wave Detector (KAGRA), is a planned Japanese detector to be sited underground in the Kamioka mine. (expected to be operating in ~2018) A further detector is expected in India future ET-B ET-D Third-generation detectors: Einstein Gravitational-Wave Telescope (ET) Strain (Hz -1/2 ) design study funded by the European Framework Programme FP Frequency (Hz)

11 Advanced detectors a factor 10 in sensitivity will allow us to see sorces in a space volume 1000 times larger Initial detectors

12 NEL FUTURO: per esplorare le basse frequenze bisogna andare nello spazio elisa: 3 spacecraft in orbita eliocetrica. Formano un triangolo equilatero inclinato di 60 rispetto all eclittica equilateral triangle L=10 6 km : sensitiviy range ~10-4 Hz < ν < 1 Hz LISA path finder e stato lanciato con successo a febbraio 2015 per testare la tecnologia di elisa. Se tutto va bene, elisa volera nel 2034

13 Compact Binary systems in the last phases of coalescence Expected waveform before the ISCO (Innermost Stable Circular Orbit) l ISCO 0 6GM c 2 M = m 1 + m 2 GW = 2! K 2 = s GM l 3 0 = 1 r GM c6 6 3 G 3 M 3 l ISCO 0 6GM tot /c 2, ISCO GW = c3 G M tot la frequenza del segnale emesso all ultima orbita circolare instabile e inversamente proporzionale alla massa totale del sistema

14 Interferometri terrestri elisa [ ] Hz consideriamo tre sistemi binari a) m1=m2= 1.4 M b) m1=m2= 10 M c) m1=m2= 10 6 M lisco 0 6GM c 2 LIGO-Virgo [10 Hz- 1-2 khz] in futuro, nello spazio calcoliamo la distanza orbitale tra i due corpi quando raggiungono l ISCO e la frequenza di emissione ISCO GW = 1 s GM (l ISCO 0 ) 3 a) l ISCO 0 = 24.8 km GW = Hz b) l ISCO 0 = km GW = Hz c) l ISCO 0 = , 3 km GW = Hz a) e b) possono essere rivelati da LIGO/Virgo, c) da elisa

15 calcoliamo ora il tempo che un dato segnale sta nella banda del rivelatore " GW (t) = in GW t3/8 coal [t coal t] 3/8 t = t coal 1 in 8/3 # GW GW (t) ponendo in =minima rivelabile max = ISCO )(m 1 = m 2 =1.4 M ) [ Hz] [ khz] t = s t = 16.7 m b) (m 1 = m 2 = 10 M ) [ Hz] [ khz] t =0.93 s t = s se la banda e piu larga a basse frequenze il segnale viene catturato per un tempo maggiore

16 VIRGO: distanza di orizzonte per coalescenza di NS-NS d ~ 3 Mpc : Segnale emesso durante la fase di spiraleggiamento (prima del merging) Maggiore e la massa, minore e il range di frequenza del segnale di inspiralling nella banda del rivelatore interferometri di prima generazione il segnale graficato in ordinata e la trasformata di Fourier del chirp, moltiplicata per la radice quadrata della frequenza: strain-amplitude

17 m 1 = m 2 = 10 2 M t = years m 1 = m 2 = 10 6 M [ Hz] t =0, 12 years = 43 d 18 h 43 m 24 s

18 blu band: systems with total mass between 50 and 100 solar masses 18

19 VIRGO: distanza di orizzonte per coalescenza di NS-NS d ~ 3 Mpc : Segnale emesso durante la fase di spiraleggiamento (prim del merging) Maggiore e la massa, minore e il range di frequenza del segnale di inspiralling nella banda del rivelatore interferometri di prima generazione COSA SUCCEDE QUANDO I DUE CORPI RAGGIUNGONO L ISCO?

20 Detected chirps 2 0

21 The inspiralling part of the signal is computed by a post-newtonian expansion of the equations of motion in GR, assuming two point masses in circular orbit during the inspiralling the orbit shrinks due to GW emission: the orbital frequency increases νgw = 2 νorb the frequency increases h0 νgw 2/3 the amplitude increases CHIRP! 2 1

22 September 15th, 2015: first Gravitational Waves detection

23 PRL 119, (2017) P H Y S I C A L R E V I E W L E T T E R S week ending 20 OCTOBER s (calculated starting from 24 Hz) in the detectors sensitive band, the inspiral signal ended at 12 41:04.4 UTC. In addition, a γ-ray burst was observed 1.7 s after the coalescence time [39 45]. The combination of data from the LIGO and Virgo detectors allowed a precise sky position localization to an area of 28 deg 2. This measurement enabled an electromagnetic follow-up campaign that identified a counterpart near the galaxy NGC 4993, consistent with the localization and distance inferred from gravitational-wave data [46 50]. From the gravitational-wave signal, the best measured combination of the masses is the chirp mass [51] M ¼ þ M. From the union of 90% credible intervals obtained using different waveform models (see Sec. IV for details), the total mass of the system is between 2.73 and 3.29 M. The individual masses are in the broad range of 0.86 to 2.26 M, due to correlations between their uncertainties. This suggests a BNS as the source of the gravitational-wave signal, as the total masses of known BNS systems are between 2.57 and 2.88 M with components between 1.17 and 1.6 M [52]. Neutron stars in general have precisely measured masses as large as M [53], whereas stellar-mass black holes found in binaries in our galaxy have masses substantially greater than the components of GW [54 56]. Gravitational-wave observations alone are able to measure the masses of the two objects and set a lower limit on their compactness, but the results presented here do not exclude objects more compact than neutron stars such as quark stars, black holes, or more exotic objects [57 61]. The detection of GRB A and subsequent electromagnetic emission demonstrates the presence of matter. Moreover, although a neutron star black hole system is not ruled out, the consistency of the mass estimates with the dynamically measured masses of known neutron stars in binaries, and their inconsistency with the masses of known black holes in galactic binary systems, suggests the source FIG. 1. Time-frequency representations [65] of data containing the gravitational-wave event GW170817, observed by the LIGO- Hanford (top), LIGO-Livingston (middle), and Virgo (bottom) detectors. Times are shown relative to August 17, :04 UTC. The amplitude scale in each detector is normalized to that detector s noise amplitude spectral density. In the LIGO data, independently observable noise sources and a glitch that occurred in the LIGO-Livingston detector have been subtracted, as described in the text. This noise mitigation is the same as that GW Coalescenza di due stelle di neutroni

24 September 15th, 2015: first Gravitational Waves detection 2 4

25 LVT Third detection :GW SNR= 13 radiated EGW = 2 M c 2 None of the signals detected so far have an electromagnetic counterpart 2 5

26 2 6

27 How did the LIGO-Virgo collaboration reach the conclusion that the observed gravitational signal is due to the coalescence of two black holes? 2 7

28 Information from the wave phase Chirp mass 2 8

29 In the detector frame the wave amplitude is where 2 9

30 GW has been localized in a sky area of 230 deg deg 2 FOR GW deg 2 FOR LVT

31 DETECTORS WHICH WILL OPERATE IN THE NEXT DECADE When all detectors will be operating it will be possible to localize the source position within 4-5 deg 2 31

32 32

33 GW M=m1+m2 Too large to be two neutron stars 33

34 During the inspiralling the wave frequency is related to the orbital distance by For GW the total mass is 63.7 M over 0.2 s the wave frequency increases from 35 to 150 Hz, from which we infer that, just before merging, the distance bewteen the two masses was The two objects must be extremely compact! Are they Black Holes? 34

35 coalescing black holes 2) signal emitted during the merging: to be found by solving numerically Einstein s equations in the non linear regime Ringdown: part of the signal emitted by the final black hole, which oscillates in its proper modes: the Quasi-Normal-Modes (QNM) 1) 3) To identify the source we need: 1) improve the description of the inspiralling part of the signal near merging 2) compute the signal emitted during the merging and match it with the inspiralling part 3) compute the ringing tail and match it with the merging part of the signal 35

36 1) Modelling the inspiral: Post-Newtonian expansion beyond the quadrupole approximation Systems with (relatively) weak gravitational fields & low velocities: dynamics of GR expressed as Newton s laws + corrections, using quantities and concepts of Newtonian physics! if is a solution of Einstein s eqs. then the tensor satisfies the equations is an effective energy-momentum pseudo-tensor WARNING: we expand the solutions as is not a perturbation! Expansion parameter: and find the expansion coefficients iteratively several mathematical subtleties: different expansions in near zone and wave zone to be matched, regularization procedures (some approaches use techniques similar to field theory), etc.

37 if we use this approach, compute the waveform for the inspiralling going beyond the quadrupole a contains information on the mass ratio of the two coalescing bodies: combining this with the measured chirp mass, the individual masses can be resolved The quantity which is actually measured is which shows the degree of alignments of the individual spins with the orbital angular momentum (0 o =aligned, 180 o antialgned) 37

38 if we use this approach, compute the waveform for the inspiralling going beyond the quadrupole a Quadrupole induced by rotation Tidal contributions become relevant when the NS velocities are high, i.e. before merging 38

39 coalescing black holes 2) signal emitted during the merging: to be found by solving numerically Einstein s equations in the non linear regime Ringdown: part of the signal emitted by the final black hole, which oscillates in its proper modes: the Quasi-Normal-Modes (QNM) 1) 3) To identify the source we need: 1) improve the description of the inspiralling part of the signal near merging 2) compute the signal emitted during the merging and match it with the inspiralling part 3) compute the ringing tail and match it with the merging part of the signal 39

40 signal emitted during the merging: to be found by solving numerically Einstein s equations in the non linear regime These studies started in the late 1990s with the Grand Challenge project to simulate head-on binary black hole collision 40

41 Ringdown: part of the signal emitted by the final black hole, which oscillates in its proper modes: the Quasi-Normal-Modes (QNM) the ringdown is a superposition of damped sinusoids at the frequencies and with the damping times of the QNMs In General Relativity the QNM frequencies depends only on the black hole mass and the angular momentum (no hair theorem) The frequency of the lowest quasi-normal mode has been extracted from the detected ringdown of the firts event GW The black hole mass and angular momentum agree with the values found from the merging 41

42 stellar mass BH in LMXB observed in the Milky Way Orosz etal 2003 Ozel etal 2013 We now know that there is a population of binary black holes with masses 20 M and merger rates are large enough to expect more detections. 42

43 How did the heavy BHs and BH binaries form? heavy BHs as in GW and in GW ~ 30 M or larger, are most likely formed in the direct collapse of low metallicity stars (below Z 0.5 Z, where Z 1,6 % of the total mass) B.P. Abbott et al., Physical Review Letters 116 (2016), 118 (2017) but low mass loss may have been possible at higher metallicity if the progenitor stars were strongly magnetized or, part of these large mass black holes may be be primordial, i.e. generated by inflation fields fluctuations, which may produce large curvature peaks (Carr, Kuhnel, Sandstad, Phys. Rev. D ) the observed BH binaries may have been formed: by the evolution of isolated binaries by a BH and a star, or dinamically, by close encounters in three-body systems possible in dense clusters Ziosi et al MNRAS 441, 2014, Kimpson et al MNRAS 463, 2016 The formation channel depends not only on the mass ratio, but also on the BH spins: these are not measured with sufficient accuracy in the detected signals. More events and larger signal-to-noise ratios will be needed 43

44 Heavy Black hole binaries: how did they form? 1) 44

45 The coalescing compact objects were two black holes or something else? We are sure that the coalescing objects are extremely compact the mass and spin of the final BH estimated from the merging part of the signal agrees with those extracted from the ringing tail, in the frame of General Relativity However, the quality of the data is such that some room is left for alternative interpretations that do not involve black holes, but other objects that, either within classical General Relativity, or in modified theories of gravity, can be equally massive and compact, i.e. gravastars, boson stars, whormholes etc More signature to be considered: tidal heating, tidal deformability, etc Future detections with larger SNR will shed light on this important question 45