Antenne risonanti:EXPLORER (CERN) infunzione dal1990NAUTILUS (Frascati)AURIGA (Legnaro ) n ~1 kHzALLEGRO (Lousiana)peres.EXPLORERe'uncilindro diuna lega dialluminiolungo 3metri,60cmdidiametro,peso2300kg,operaa2K

Rivelatori di onde gravitazionaliricerca iniziata da J. Weber in America e in Italia da EdoardoAmaldi negli anni sessanta

EXPLORER(CERN)

Infunzionedal1990

MiniGRAILGravitational Radiation Antenna In Leiden

Kamerlingh Onnes Laboratory, Leiden University, The Netherlands MiniGRAIL cryogenic run 5

Last update: August 18 - 2003Webmaster

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 quantum-limited strain sensitivity dL/L would be ~4x10-21. 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 black-hole or neutron-star mergers etc.

Rivelatori interferometriciL’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 variazionedelle frange di interferenzapossiamo rivelare l’onda

gravitazionale

Equazione della deviazione geodetica

Sel'onda e'perpendicolare albraccio,questo varia di∆ l=½hlLe fluttuazioni nel numero di fotoni laser che vengono usatisimula 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 difrequenza delsegnale

Quindi il limite perlamisura e'

h>2∆ l/l=2Ö ( h c l ∆ n /p P l2 )

Perche'ibraccidell'interferometrodevonoesserecosi'lunghi?

𝛿xj=𝛿 x0j +1/2𝜂ij hTTik 𝛿 x0k

limiteperlamisurae'

h>2∆ l/l=2Ö ( h c l ∆ n /p P l2 )l lunghezza d'onda della luce di potenza P∆ n banda di frequenza del segnale

SeP =1000W,l =0.6µ m∆ n ~1000Hz

permisurareun h>10-20

Ibraccidell’interferometrodovrebbero essere l=15km!!!

10Hz<n <1-2kHz

Interferometri terrestri:VIRGO (Pisa)(3km)LIGO (Hanford(WA)- Livingston(CA)) (3,4km)GEO600 (Hannover)(600m)TAMA300 (Giappone)(300m)

recycling:‘trucco’peraumentareilcamminoottico

Gravitationalwaveinterferometric detectors:firstgeneration

Virgointerferometer(Cascina,Italy)

GEO600(British-German)Hannover,Germany

LIGO- I(USA)Hanford,WA

TAMA300(Japan)LIGO-II(USA)Livingston,LA

100 101 102 103 104

Frequency (Hz)

10-25

10-24

10-23

10-22

10-21

Stra

in (H

z-1/2

)

ET-BET-D

advancedLIGO,Virgo)

futureThird-generationdetectors:EinsteinGravitational-WaveTelescope(ET)

designstudyfundedbytheEuropeanFrameworkProgramme FP7

DesignsensitivitycurvesfortheAdvancedLIGO,AdvancedVirgoandLCGTsecond-generationdetectors.

TheKamioka Gravitational Wave Detector(KAGRA), isaplannedJapanesedetectortobesitedundergroundintheKamioka mine.(expectedtobeoperatingin~2018)AfurtherdetectorisexpectedinIndia

Advanceddetectors

Initialdetectors

afactor10insensitivitywillallowustoseesorcesinaspacevolume1000timeslarger

eLISA: 3 spacecraft in orbita eliocetrica. Formano un triangolo equilateroinclinato di 60° rispetto all’eclittica

equilateral triangle L=106 km : sensitiviy range ~10-4 Hz < ν < 1 Hz

LISA path finder e’ stato lanciato con successo a febbraio 2015 pertestare la tecnologiadi eLISA.

Se tutto va bene, eLISAvolera’ nel 2034

NELFUTURO:peresplorarelebassefrequenzebisognaandarenellospazio

Compact Binary systems in the last phases of coalescence

lISCO0 � 6GMtot/c2, �ISCO

GW =c3

⇥G⇥

63

1Mtot

Expected waveform before the ISCO(Innermost Stable Circular Orbit)

lISCO0 ⇠ 6GM

c2M = m1 +m2

⌫GW =2!K

2⇡=

sGM

l30=

1

⇡

rGM

c6

63G3M3

lafrequenzadelsegnaleemessoall’ultimaorbitacircolareinstabilee’ inversamenteproporzionaleallamassatotaledelsistema

Interferometriterrestri LIGO-Virgo [10 Hz- 1-2 kHz]

eLISA [10-4-10-1] Hz infuturo,nellospazio

consideriamotresistemibinaria)m1=m2=1.4M¤

b) m1=m2=10 M¤

c) m1=m2=106 M¤

calcoliamoladistanzaorbitaletraiduecorpiquandoraggiungonol’ISCOelafrequenzadiemissione

⌫ISCOGW =

1

⇡

sGM

(lISCO0 )3lISCO

0 ⇠ 6GM

c2

a) l0ISCO = 24.8 km ⌫GW = 1570.4 Hz

b) l0ISCO = 177.2 km ⌫GW = 219.8 Hz

c) l0ISCO = 17.720.415, 3 km ⌫GW = 2.2 · 10�3 Hz

a)eb)possonoessererivelatidaLIGO/Virgo,c)daeLISA

⌫GW

(t) =⌫inGW

t3/8coal

[tcoal

� t]3/8t = t

coal

"1�

✓⌫inGW

⌫GW

(t)

◆8/3#

calcoliamoorailtempocheundatosegnalestanellabandadelrivelatore

ponendo ⌫max = ⌫ISCO⌫in = minima ⌫ rivelabile

a) (m1 = m2 = 1.4 M�) [40� 1570.4 Hz] [10� 1570.4 kHz]

�t = 24.86 s �t = 16.7 m

b) (m1 = m2 = 10 M�) [40� 219.8 Hz] [10 � 219.8 kHz] �t = 0.93 s �t = 37.82 s

selabandae’piu’largaabassefrequenzeilsegnalevienecatturatoperuntempomaggiore

VIRGO: distanza di orizzonte per coalescenza di NS-NS d ~ 3 Mpc :Segnale emesso durante la fase di spiraleggiamento (prima del merging)

14

Maggioree’lamassa,minore e’il rangedifrequenza delsegnalediinspiralling nellabanda delrivelatore

interferometri di prima

generazione

ilsegnalegraficato inordinatae’ latrasformatadiFourierdelchirp,moltiplicataperlaradicequadratadellafrequenza:strain-amplitude

m1 = m2 = 102M�

�t = 556.885 years

m1 = m2 = 106M� [10�4 � 2.2 · 10�3 Hz]

�t = 0, 12 years = 43 d 18 h 43 m 24 s

18

bluband:systemswithtotalmassbetween50and100solarmasses

VIRGO: distanza di orizzonte per coalescenza di NS-NS d ~ 3 Mpc :Segnale emesso durante la fase di spiraleggiamento (prim del merging)

14

Maggioree’lamassa,minore e’il rangedifrequenza delsegnalediinspiralling nellabanda delrivelatore

interferometri di prima

generazione

COSASUCCEDEQUANDOIDUECORPIRAGGIUNGONOL’ISCO?

20

Detected chirps

CHIRP!

theorbitalfrequencyincreases 𝜈GW =2𝜈orbthefrequencyincreases

h0∝𝜈GW2/3

theamplitudeincreases

21

during the inspiralling the orbit shrinks due to GW emission:

Theinspirallingpartofthesignaliscomputedbyapost-NewtonianexpansionoftheequationsofmotioninGR, assumingtwopointmassesincircularorbit

September15th,2015:firstGravitationalWavesdetection

∼100 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 thecoalescence time [39–45]. The combination of data fromthe LIGO and Virgo detectors allowed a precise skyposition localization to an area of 28 deg2. This measure-ment enabled an electromagnetic follow-up campaign thatidentified a counterpart near the galaxy NGC 4993, con-sistent with the localization and distance inferred fromgravitational-wave data [46–50].From the gravitational-wave signal, the best measured

combination of the masses is the chirp mass [51]M ¼ 1.188þ0.004

−0.002M⊙. From the union of 90% credibleintervals obtained using different waveform models (seeSec. IV for details), the total mass of the system is between2.73 and 3.29 M⊙. The individual masses are in the broadrange of 0.86 to 2.26 M⊙, due to correlations between theiruncertainties. This suggests a BNS as the source of thegravitational-wave signal, as the total masses of knownBNS systems are between 2.57 and 2.88 M⊙ with compo-nents between 1.17 and ∼1.6 M⊙ [52]. Neutron stars ingeneral have precisely measured masses as large as 2.01#0.04 M⊙ [53], whereas stellar-mass black holes found inbinaries in our galaxy have masses substantially greaterthan the components of GW170817 [54–56].Gravitational-wave observations alone are able to mea-

sure the masses of the two objects and set a lower limit ontheir compactness, but the results presented here do notexclude objects more compact than neutron stars such asquark stars, black holes, or more exotic objects [57–61].The detection of GRB 170817A and subsequent electro-magnetic emission demonstrates the presence of matter.Moreover, although a neutron star–black hole system is notruled out, the consistency of the mass estimates with thedynamically measured masses of known neutron stars inbinaries, and their inconsistency with the masses of knownblack holes in galactic binary systems, suggests the sourcewas composed of two neutron stars.

II. DATA

At the time of GW170817, the Advanced LIGO detec-tors and the Advanced Virgo detector were in observingmode. The maximum distances at which the LIGO-Livingston and LIGO-Hanford detectors could detect aBNS system (SNR ¼ 8), known as the detector horizon[32,62,63], were 218 Mpc and 107 Mpc, while for Virgothe horizon was 58 Mpc. The GEO600 detector [64] wasalso operating at the time, but its sensitivity was insufficientto contribute to the analysis of the inspiral. The configu-ration of the detectors at the time of GW170817 issummarized in [29].A time-frequency representation [65] of the data from

all three detectors around the time of the signal is shown inFig 1. The signal is clearly visible in the LIGO-Hanfordand LIGO-Livingston data. The signal is not visible

in the Virgo data due to the lower BNS horizon and thedirection of the source with respect to the detector’s antennapattern.Figure 1 illustrates the data as they were analyzed to

determine astrophysical source properties. After data col-lection, several independently measured terrestrial contribu-tions to the detector noise were subtracted from the LIGOdata usingWiener filtering [66], as described in [67–70]. Thissubtraction removed calibration lines and 60 Hz ac powermains harmonics from both LIGO data streams. The sensi-tivity of the LIGO-Hanford detector was particularlyimproved by the subtraction of laser pointing noise; severalbroad peaks in the 150–800 Hz region were effectivelyremoved, increasing the BNS horizon of that detectorby 26%.

FIG. 1. Time-frequency representations [65] of data containingthe gravitational-wave event GW170817, observed by the LIGO-Hanford (top), LIGO-Livingston (middle), and Virgo (bottom)detectors. Times are shown relative to August 17, 2017 12∶41:04UTC. The amplitude scale in each detector is normalized to thatdetector’s noise amplitude spectral density. In the LIGO data,independently observable noise sources and a glitch that occurredin the LIGO-Livingston detector have been subtracted, asdescribed in the text. This noise mitigation is the same as thatused for the results presented in Sec. IV.

PRL 119, 161101 (2017) P HY S I CA L R EV I EW LE T T ER S week ending20 OCTOBER 2017

161101-2

GW170817Coalescenzadiduestelledineutroni

24

September15th,2015:firstGravitationalWavesdetection

LVT151012

25

Noneofthesignalsdetectedsofarhaveanelectromagneticcounterpart

Thirddetection:GW170104

SNR=13

radiatedEGW=2M☉ c2

26

27

HowdidtheLIGO-Virgocollaborationreachtheconclusionthattheobservedgravitationalsignalisduetothecoalescenceoftwoblackholes?

28

“Chirpmass”

Informationfromthewavephase

29

where

Inthedetectorframethewaveamplitudeis

30

GW150914hasbeenlocalizedinaskyareaof230deg2

850deg2FORGW151226

1600deg2FORLVT151012

Whenalldetectorswillbeoperatingitwillbepossibletolocalizethesourcepositionwithin4-5deg2

31

DETECTORSWHICHWILLOPERATEINTHENEXTDECADE

32

33

M=m1+m2

Toolargetobetwoneutronstars

GW150914

34

Duringtheinspirallingthewavefrequencyisrelatedtotheorbitaldistanceby

Thetwoobjectsmustbeextremelycompact!

AretheyBlackHoles?

ForGW150914thetotalmassis≿ 63.7M☉

over0.2sthewavefrequencyincreasesfrom35to150Hz,fromwhichweinferthat,justbeforemerging,thedistancebewteenthetwomasseswas

35

coalescingblackholes signal emitted during the merging: to befound 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)

2)

3)

Toidentifythesourceweneed:

1) improvethedescriptionoftheinspirallingpartofthesignalnearmerging2) computethesignalemittedduringthemergingandmatchitwiththeinspirallingpart3) computetheringingtailandmatchitwiththemergingpartofthesignal

1)Modellingtheinspiral:Post-Newtonianexpansionbeyondthequadrupoleapproximation

Systemswith(relatively)weakgravitationalfields&lowvelocities:dynamicsofGRexpressedasNewton’slaws+corrections,usingquantitiesandconceptsofNewtonianphysics!

WARNING:isnotaperturbation!

isaneffectiveenergy-momentumpseudo-tensor

satisfiestheequations

isasolutionofEinstein’seqs. thenthetensorif

Expansionparameter:

weexpandthesolutionsas

andfindtheexpansioncoefficientsiteratively

severalmathematicalsubtleties:differentexpansionsinnearzoneandwavezonetobematched,regularizationprocedures(someapproachesusetechniquessimilartofieldtheory),etc….

37

ifweusethisapproach,computethewaveformfortheinspirallinggoingbeyondthequadrupoleapproximation,andtaketheFo

containsinformationonthemassratioofthetwocoalescingbodies:combiningthiswiththemeasuredchirpmass,theindividualmassescanberesolved

The quantity which is actually measured is

which shows the degree of alignments of the individual spins with the orbital angular momentum(0o=aligned, 180o antialgned)

38

Quadrupole induced by rotation

TidalcontributionsbecomerelevantwhentheNSvelocitiesarehigh,i.e.beforemerging

ifweusethisapproach,computethewaveformfortheinspirallinggoingbeyondthequadrupoleapproximation,andtaketheFo

39

coalescingblackholes signal emitted during the merging: to befound 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)

2)

3)

Toidentifythesourceweneed:

1) improvethedescriptionoftheinspirallingpartofthesignalnearmerging2) computethesignalemittedduringthemergingandmatchitwiththeinspirallingpart3) computetheringingtailandmatchitwiththemergingpartofthesignal

40

signalemittedduringthemerging:tobefoundbysolvingnumericallyEinstein’sequationsinthenonlinearregime

Thesestudiesstartedinthelate1990swiththe GrandChallengeproject tosimulatehead-onbinaryblackholecollision

41

Ringdown:partofthesignalemittedbythefinalblackhole,whichoscillatesinitspropermodes:theQuasi-Normal-Modes(QNM)

theringdownisasuperpositionofdampedsinusoidsatthefrequenciesandwiththedampingtimesoftheQNMs

InGeneralRelativitytheQNMfrequenciesdependsonlyontheblackholemassandtheangularmomentum(nohairtheorem)

Thefrequencyofthelowestquasi-normalmodehasbeenextractedfromthedetectedringdownofthefirtseventGW150914.Theblackholemassandangularmomentumagreewiththevaluesfoundfromthemerging

42

Oroszetal2003Ozeletal2013

stellarmassBHinLMXBobservedintheMilkyWay

Wenowknowthatthereisapopulationofbinaryblackholeswithmasses≿ 20M☉ andmergerratesarelargeenoughtoexpectmoredetections.

43

✢ “heavy”BHsasinGW150914 andinGW170104~30M☉ orlarger,aremostlikelyformedinthedirectcollapseoflowmetallicitystars(belowZ≈0.5Z☉ ,whereZ☉ ≈1,6%ofthetotalmass)

B.P.Abbottetal.,PhysicalReviewLetters116(2016),118(2017)

Howdidthe“heavy”BHsandBHbinariesform?

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

✢ theobservedBHbinariesmayhavebeenformed:— bytheevolutionofisolatedbinariesbyaBHandastar,— ordinamically,bycloseencountersinthree-bodysystemspossibleindenseclusters

ZiosietalMNRAS441,2014,KimpsonetalMNRAS463,2016

… but low mass loss may have been possible at higher metallicity if the progenitor stars were strongly magnetized

…or,partoftheselargemassblackholesmaybebeprimordial,i.e.generatedbyinflationfieldsfluctuations,whichmayproducelargecurvaturepeaks…(Carr,Kuhnel,Sandstad,Phys.Rev.D942016)

44

“Heavy”Blackholebinaries:howdidtheyform?

1)

45

Thecoalescingcompactobjectsweretwoblackholesor…somethingelse?

✭Wearesurethatthecoalescingobjectsareextremelycompact

✭ themassandspinofthefinalBHestimatedfromthemergingpartofthesignalagreeswiththoseextractedfromtheringingtail,intheframeofGeneralRelativity

✭ However,thequalityofthedataissuchthatsomeroomisleftforalternativeinterpretationsthatdonotinvolveblackholes,butotherobjectsthat,eitherwithinclassicalGeneralRelativity,orinmodifiedtheoriesofgravity,canbeequallymassiveandcompact,i.e.gravastars,bosonstars,whormholesetc

FuturedetectionswithlargerSNRwillshedlightonthisimportantquestion

Moresignaturetobeconsidered:tidalheating,tidaldeformability,etc