Gravitational Wave Astronomy

Home , GW170104, GW170817

Riccardo Sturani

International Institute of Physics - UFRN - Natal (Brazil)

Dark Universe ICTP-SAIFR, Oct 25th, 2019

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 1 / 29 GW basics in 1 slide

Gauged ﬁxed metric perturbations hµν after discarding h0µ components, which are not radiative transverse waves →

h+ h× 0 hij = h× h+ 0  −  0 0 0  2 pol. state like any mass-less particle

h×

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 2 / 29 LIGO and Virgo: very precise rulers

Robert Hurt (Caltech)

Light intensity ∝ light travel diﬀerence in perpendicular arms Eﬀective optical path increased by factor N ∼ 500 via Fabry-Perot cavities Phase shift ∆φ ∼ 10−8 can be measured ∼ 2πN∆L/λ → ∆L ∼ 10−15/N m Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 3 / 29 Almost omnidirectional detectors

Detectors measure hdet : linear combination F+h+ + F×h× L H

-101 F+

F×

h+,× depend on source pattern functions F+,× depend on orientation source/detector

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 4 / 29 Almost omnidirectional detectors

Detectors measure hdet : linear combination F+h+ + F×h× L V

-101 F+

F×

h+,× depend on source pattern functions F+,× depend on orientation source/detector

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 4 / 29 2 2 Pattern functions: F+ + F × p

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 5 / 29 The LIGO and Virgo observatories

• Observation run O1 Sept ’15 - Jan ’16 ∼ 130 days, with 49.6 days of actual data, PRX (2016) 4, 041014, 2 detectors,3BBH • O2 Dec. ’16 – Jul’17 2 det’s + Aug ’17 3 det’s 3(+4) BBH +1BNS in double(triple) coinc. • O3a:3 detectors, Apr 2nd - Oct 1st 2019 • O3b: Nov 1st – 6 months In ∼ end of 2019 Japanese KAGRA and ∼ 2025 Indian INDIGO will join the collaboration Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 6 / 29 Wave generation: localized sources

Einstein formula relates hij to the source quadrupole moment Qij Z 1 Q = d 3xρ x x − δ x 2 , v 2 ' G M/r , η ≡ m m /M2 ij i j 3 ij N 1 2 2G d 2Q 2G ηMv 2 h ∼ g(θ ) N ij ' N cos(2φ(t)) ij LN D dt2 D

r −3/2 M 1/2 M −1 f = 2kHz < fMax ' 12kHz 30Km 3M 3M f 1/3 M 1/3 1 v = 0.3 < √ 1kHz M 6

Geometric factor g(θLN ) takes account of transversality projection (angular momentum L of the binary, observation direction N)

1 + cos2(θ ) Mv 2 h ∼ LN η cos φ(t /M, η, S 2/m4,...) + 2 D s i i Mv 2 h ∼ cos(θ ) η sin φ(t /M, η, . . .) × LN D s

Amplitudes of 2 polarizations modulated by θLN (h % for θLN &0), never both vanishing unlike dipolar motion for the electromagnetic case

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 7 / 29 Wave generation: localized sources

r −3/2 M 1/2 M −1 f = 2kHz < fMax ' 12kHz 30Km 3M 3M f 1/3 M 1/3 1 v = 0.3 < √ 1kHz M 6

Geometric factor g(θLN ) takes account of transversality projection (angular momentum L of the binary, observation direction N)

1 + cos2(θ ) M(1 + z)v 2 h ∼ LN η cos φ(t /(M(1 + z)), η, S 2/m4,...) + 2 D(1 + z) O i i M(1 + z)v 2 h ∼ cos(θ ) η sin φ(t /(M(1 + z)), η, . . .) × LN D(1 + z) O

Amplitudes of 2 polarizations modulated by θLN (h % for θLN &0), never both vanishing unlike dipolar motion for the electromagnetic case Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 7 / 29 Wave generation: localized sources

Einstein formula relates hij to the source quadrupole moment Qij Z 1 Q = d 3xρ x x − δ x 2 , v 2 ' G M/r , η ≡ m m /M2 ij i j 3 ij N 1 2 2G d 2Q 2G ηMv 2 h ∼ g(θ ) N ij ' N cos(2φ(t)) ij LN D dt2 D r −3/2 M 1/2 M −1 f = 2kHz < fMax ' 12kHz 30Km 3M 3M f 1/3 M 1/3 1 v = 0.3 < √ 1kHz M 6 Geometric factor g(θLN ) takes account of transversality projection (angular momentum L of the binary, observation direction N) 2 2 1 + cos (θLN ) Mv 2 4 h+ ∼ η cos φ(tO /M, η, Si /mi ,...) 2 dL Mv 2 h× ∼ cos(θLN ) η sin φ(tO /M, η, . . .) dL

Amplitudes of 2 polarizations modulated by θLN (h % for θLN &0), never both vanishing unlike dipolar motion for the electromagnetic case h sensitive to red-shifted masses M → M(1 + z) ≡ M

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 7 / 29 Binary systems and compact detected so far

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 8 / 29 https://www.gw-openscience.org/catalog/

Binary black hole events in O1 and O2 1.00 1.0

0.75 0.8 0.50

0.25 See however Princeton’s group 0.6 o f r f t s e

0.00 a p results 0.4 0.25

0.50 arXiv:1904.07214 LVC-reported 0.2 0.75 This work Zackay et al. (2019) 1.00 0.0 20 40 60 80 100 source Mtot (M )

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 9 / 29 Sky localization of GW binary systems detected so far

60° GW170104 60° 60° 60°

GW170608 GW170823 GW151012 GW170729 GW151226 30° 30° 30° 30°

0° 0° GW170818 0h 21h 18h 15h 12h 9h GW170104 6h 3h 0h 0h 21h 18h 15h 12h 9h 6h 3h 0h

GW170104

GW170809 -30° -30° -30° -30°

GW170729 GW170817 GW151012 GW170823 GW150914 -60° GW170814 -60° -60° GW151226 -60°

Sky localization regions shrinks when Virgo in: 3rd detector matters!

LIGO/Virgo 1811.12907

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 10 / 29 Astro sources emitting transient GWs/EM/ν radiation

2 Coalescing binary systems of compact objects: η ≡ m1m2/M 5/3 2/3 −2 M fmax ∆EGW ∼ 4 × 10 M η 3M 1 kHz

A good proxy of the fmax is the Innermost Stable Circular Orbit frequency 1 1 M −1 fISCO = √ ' 2kHz 6 6 M M For NS-NS/BH ejected material supposed to produce short (< 2 sec) GRBs Eγ ∼keV-MeV, ejected sub-relativistic material may produce radio signals TeV-PeV ν @ γ emission ν: baryon loaded jets may emit νs: PeV-EeV ν @ optical afterglow NS-NS/BH → energetic outflows at different timescale/wavelength Rapid neutron capture in the sub-relativistic ejecta can produce a kilonova or macronova, with optical and near-infrared signal (hours - weeks) Eventually radio blast from sub-relativistic outflow (months to years)

LIGO/Virgo + EM partners ApJ Let. 2016

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 11 / 29 Association with 20 short GRB during O1 (before GW170817)

100

10−1

cumulative distribution BNS exclusion NS-BH exclusion BNS extrapolation NS-BH extrapolation EM observation 10−2 10−2 10−1 100 redshift

GW searched in a [-5,+1) sec window with GRB GW constraints far from EM exclusion distance, but extrapolation to design Advanced LIGO sensitivity (2 years of data) will lead to detection/non-trivial constraints LIGO/Virgo Astrophys.J. 841 (2017) no.2, 89 Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 12 / 29 GW170817

GW trigger on Aug 17th, 2017, ended at 12h 41’ 04.4” UTC, first in in LIGO Hanford, then confirmed as a triple coincidence → localized in an area of ∼ 28 deg2 GRB trigger from Fermi-GBM 1.7” after first optical image 10.87 hr afterwards by One-Meter Two Hemisphere team with Swope telescope at Las Campanas Observatory in Chile X obtained by the X-Ray Telescope on Swift after 14.9 h (NuSTAR 16.8 h) radio (∼ 3, 6 GHz) by VLA 16 days after GW event LIGO/Virgo & Partner Astronomy groups, Astrophys.J. 848 (2017) no.2, L12

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 13 / 29 An example of the optical image

Transient Optical Robotic Observatory of the South

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 14 / 29 GW170817 and ν detectors

Potential νs down-going for Antares and IceCube, grazing for Auger

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 15 / 29 GW170817 and ν detectors

Potential νs down-going for Antares and IceCube, grazing for Auger Source location at optical detection

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 15 / 29 ANTARES and ICECube look for ν

GW170817 Neutrino limits (fluence per flavor: x + x) 103 ±500 sec time-window ANTARES 2

] 10 2 Auger

m 1

c 10 IceCube V e 0 G 10 [

0 Kimura et al. IceCube and ANTARES looked for F 4 2 10 1 EE moderate E µ ν sec 8 at 500 , observation for 2 2 − 10 Kimura et al. 0 Kimura et al. weeks EE optimistic 4 0 prompt 10 3 no detection 103 2 Auger

17 ] 10 > 2 Pierre Auger for 10 eV, grazing ANTARES

m 1

18 c 10

good for τ production at 10 eV V e 0 IceCube G 10 Fang & [

Metzger

F 30 days 2 10 1 E Fang & 10 2 Metzger 14 day time-window 3 days 10 3 102 103 104 105 106 107 108 109 1010 1011 E/GeV LIGO/Virgo, ANTARES, ICECUBE and Pierre Auger, Astrophys.J. 850 ’17 2, L35

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 16 / 29 3 10−

4 10− 1 − 5 yr 10− 3 −

Mpc 10−

7 10−

8 10−

Rate Estimates 9 10−

10 10− BNS NSBH BBH Astrophysical predictions, upper limit from S5/6/O1 and observation from O1/O2 LIGO/Virgo CQG (’10) 27 173001, PRX (’16), APJ (2016), PRL 119 (’17)

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 17 / 29 Fundamental physics of Neutron stars

−5 Tidal deformability Λ R Qab/ (∂a∂bUtidal ) depends on Equation of ' State

MS1 2000 Less Compact MS1b

1500 More Compact 2

Determinaton of Λ1,2 Λ 1000 H4 (assuming same EoS for 1,2) 500 MPA1 SLy APR4 WFF1 0 0 250 500 750 1000 1250 Λ1 Shading Common EoS for 2 bodies and constrain for mmax > 1.97M Lines 50%, 90% countours, No mimimum mmax , independent EoSs

LIGO/Virgo collaboration, arXiv:1805.11581

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 18 / 29 Fundamental physics of Neutron stars II

+p dp P k p Parametrizing EoS with Γ ≡ , Γ(x) = exp γk x , x ≡ log p d k p0

γ0 ∈ [0.2, 2], γ1 ∈ [1.6, 1.7], γ2 ∈ [0.6, 0.6]γ3 ∈ [0.02, 0.02], Γ(p) ∈ [0.6, 4.5] L. Lindblom PRD 82, 103011 (2010) Constraints on Mass vs- radius and p vs. rho

3.0 1037

2.5 BH limit 36 Buchdahl limit 10 ] ) 2.0 2 1035 cm / (M

m 1.5 34

[dyn 10 p

1.0 1033

H4 SLy

WFF1 APR4 MPA1 nuc nuc nuc ρ ρ ρ 0.5 1032 2 6 8 10 12 14 0 1 1014 1015 R (km) ρ [g/cm3] lighter, heavier 90% prior, posterior

LIGO/Virgo collaboration, arXiv:1805.11581

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 19 / 29 Cosmology

From GWs only: luminosity distance +8 dL ∼ 40 Mpc, viewing angle 0.4 −14 GW170817 o Planck17 θLN > 125 SHoES18 0.5 120 Fixing dL from info from EM location 0.6

+ Hubble relation dLH0 = z 130 ) g s e

o 0.7 d ( c 1 Hubble constant from 140 SuperNovae (SHoES) 0.8 o o 148 < θLN < 166 150 0.9

160

Riess et al. ApJ 826, 56 ’16 170 1.0 180 50 60 70 80 90 100 110 120 1 1 2 from Planck H0 (km s Mpc ) o 157 < θLN < 177 Planck A&A, 594, A13 ’16 LIGO/Virgo Nature 551 ’17 7678, 85 GW almost coincident with EM 0 −15 00 =⇒ ∆vGW /c ∼ 10 a 0 2 2 h + 2 h + c ∇ h+,× = 0 LIGO/Virgo, Fermi Gamma-Ray Burst +× a +,× s Monitor, INTEGRAL Ap.J. 848 (2017) 2, L13

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 20 / 29 Determining H0 without EM counterpart

Hubble law: z = H0dL DL can be measured, z degenerate with M, however if the source in the sky has been localised (α, δ) GW sources are in the galaxy catalogue with known red-shift ~ ~ P(z, DL ci ) = d dθ dα dδ P(DL , θ, α, δ ci )π(z, α, δ) | M M | | Z

Schutz, Nature (1986) 323 310 W. Del Pozzo, Phys.Rev.D86 (2012) 043011

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 21 / 29 Galaxy catalogs and H0

0.06 Joint BBH+GW170817 Counterpart Joint BBH 0.05 GW170817 Counterpart Prior (Uniform) Planck SH0ES 0.04 sky localization from DES-Y1 s Mpc)

1 (GW170814) − 0.03 GWENS (GW170818) (km ) 0 GLADE (GW150914, GW151226,

H 0.02 ( p GW170608) 0.01

0.00 20 40 60 80 100 120 140 1 1 H0 (km s− Mpc− )

LIGO/Virgo, arXiv:1908.06060

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 22 / 29 Upper bounds on sub-solar mass compact binaries coalescence rate

−3 −1 Mass/M Rate(Gpc yr ) Horizon(Mpc) 1 < 106 100 0.2 < 2 104 30 × 5/6 3/5 SNR Mc , Mc η M ∝ ≡ LIGO/Virgo arXiv:1808.04771, 1904.08976

Fraction f of MACHOs in binary 10% ΩMacho = ∼ −3× ⇒ 10 ΩMacho in coalescing bina- ∼ −1 ries coalescing within H0

T. Nakamura et al. in Astrophys.J.L. 487 (1997) L139-L142

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 23 / 29 Ongoing O3: towards measuring merger distribution

At https://gracedb.ligo.org/superevents/public/O3 Summary of candidate detections from O3a: 33 candidate events, 7 of which possibly involving at least a NS

Expected merger distribution from Star Formation Rate ( ) or − SFR+Poissian distributed delay ( ) −−

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 24 / 29 Ongoing O3: towards measuring merger distribution

At https://gracedb.ligo.org/superevents/public/O3 Summary of candidate detections from O3a: 33 candidate events, 7 of which possibly involving at least a NS

Expected merger distribution from Star Formation Rate ( ) or − SFR+Poissian distributed delay ( ) −−

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 24 / 29 Fundamental GR: inspiral analytic model

˙ Inspiral h = A cos(φ(t)) A φ˙ A Virial relation:

1/3 m1m2 v (GN MπfGW ) η = 2 ≡ (m1 + m2) 1 E(v)= ηMv 2 1 + #(η)v 2 + #(η)v 4 + ... −2 dE 32 P(v) = v 10 1 + #(η)v 2 + #(η)v 3 + ... ≡ − dt 5GN E(v)(P(v)) known up to 3(3.5)PN

1 1 T v(T ) ω(v)dE/dv φ(T ) = ω(t)dt = dv 2π 2π − P(v) Z Z dv 1 +#( η)v 2 + ... +#( η)v 6 + ... ∼ v 6 Z

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 25 / 29 Fundamental GR: inspiral analytic model ˙ Inspiral h = A cos(φ(t)) A φ˙ A Virial relation:

1/3 m1m2 v (GN MπfGW ) η = 2 ≡ (m1 + m2) 1 E(v)= ηMv 2 1 + #(η)v 2 + #(η)v 4 + ... −2 dE 32 P(v) = v 10 1 + #(η)v 2 + #(η)v 3 + ... ≡ − dt 5GN E(v)(P(v)) known up to 3(3.5)PN

1 1 T v(T ) ω(v)dE/dv φ(T ) = ω(t)dt = dv 2π 2π − P(v) Z Z dv 1 +#( η)v 2 + ... +#( η)v 6 + ... ∼ v 6 Z PN Coeﬃcients (tidal v 10) ∼ Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 25 / 29 Parameter estimation from φ(t)

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 26 / 29 Testing the PN series with O1/2

101

100 | i ˆ ϕ δ | 1 10− GW150914 GW151226 GW170104 2 10− GW170608 GW170814 Combined Combined (SEOBNRv4) 3 10− ) ) (l (l 1 PN 0 PN .5 PN 1 PN .5 PN 2 PN 3 PN .5 PN 0 1 .5 PN 3 PN 3 − 2

Precision in measuring the PN coeﬃcients ∼ 100%: one cannot both measure the astro parameters and test GR with same detection! Unique probe of high PN-orders LIGO/Virgo arXiv:1903.04467

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 27 / 29 Precision gravity

Future 3rd generetaion detectors (Einstein Telescope, Cosmic Explore) / space telescope LISA will detect BBH binary signals with SNR 10 − 102, with few golden events with SNR ∼ 103. Templates few % accurate OK for characterising a source with SNR O(10) (typical for LIGO/Virgo) for SNR ∼ 103 residual after extracting that source will have SNR ∼ O(10) 1 baising parameter estimation 2 contaminating the extraction of additional sources.

−7/6 5/6 h(f ) f Mc ∝ −5/3 −8/3 −8/3 ∆ti→m Mc (f fm ) ∝ i −

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 28 / 29 Conclusions (Actually just the beginning!)

After the beginning of GW astronomy, we have witnessed the start of multi-messenger astronomy

New era for Cosmology: H0 from GWs! (and EM) New input for fundamental physics: test of gravity in the strong ﬁeld at short scale, radiative gravity sector tested at large distances and soon precision gravity is going to be needed

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 29 / 29 Spare slides

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 30 / 29 How binary systems progenitors formed? I A binary system of massive stars (Mbinary < 100Modot ) can go through a common envelope phase that shrinks considerably the orbit and align the spins collapse to compact → objects BNS requires complex evolution from massive binaries + mass transfer and 2 core-collapse SN explosions through which the binary system survives Asymmetries in collapse imparts natal kick to the (galactic pulsar proper motion)

Izzard et al. Proc. IAU 2012 LIGO/Virgo Ap.J. 850 (2017) L40 vs.

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 31 / 29 For BBH another mechanism is possible

Globular Cluster: medium with high density of black holes/stars, when 3 black holes meet one is ejected and the binary shrinks

LIGO/VirgoAstrophys.J. 818 (2016) no.2, L22

Remnants of the ﬁrst stars, produced at z 6 can give only a small ∼ contribution to the total rate

T. Hartwig et al. Mon.Not.Roy.Astron.Soc. 460 (2016) L74

−2 Primordial black-holes? viable if 10 . MBH /M . 1 (constraints from evaporation, microlensing and CMB) but could grow later to 20-100 M by merger If present in globular cluster may also explain their cosmological abundance as dark matter

Sasaki M. et al. PRL 2016, Bird S. et al. PRL 2016, Clesse S. and Garc´ıa-BellidoPhys. Dark Univ. 2017

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 32 / 29 Metzer & Berger Astrophys.J. 746 (2012) 48

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 33 / 29 NS merger short γRB kilonova → →

Jet models for the ejecta (spherical fireball model) ↓ o o BNS merger emitted γ rays, expected opening angles θj ' 3 − 10 : early time θj ∼ 1/γ (jet collimated and relativistic), prompt emission from energy dissipation inside relativistic jet: X rays ∼ energy output and geometry Shock wave from sGRB jet hitting surrounding medium, θj < 1/γlate ↓ broadband synchrotron afterglow, with radio source ∼ months and UV, optical & IR emission from sub-relativistic ejecta νs expected only from near GRB (or in late emission by flares and plateaus) Alexander et al., Astrophys. J. 848 (2017) no.2, L21 NS merger frees neutron-rich radioactive species, decaying in kilonova in ∼ days Observation: Faint gamma ray emission: 1046 erg (isotropic), raising Xray flux 2.4 - 5.4 day, continued up to 15 days (Chandra), delayed afterglow ↓ o short GRB viewed off-axis θobs & 20 Berger E, 2014, ARA&A, 52, 43 Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 34 / 29 GW170817

BNS horizon (Mpc) was 218 for LL, 107 for LH, 58 for V

LIGO/Virgo Phys.Rev.Lett. 119 (2017) 161101

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 35 / 29 Detected waves (best ﬁt)

GW150914

LVT151012

GW151226

GW170104

GW170608

GW170814

GW170817

0 6 12 18 24 30 36 42 48 54 60 time observable (seconds)

LIGO/University of Oregon/Ben Farr

Smaller objects can get closer = reach higher frequency before merger ⇒

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 36 / 29 Parameter estimation for GW170817

Low spin prior High spin prior

1.40 1.4 TaylorF2 TaylorF2 PhenomDNRT PhenomDNRT 1.35 PhenomPNRT 1.3 PhenomPNRT SEOBNRT SEOBNRT 1.30 1.2 ) )

m 1.25 1.1 M 1,2 M ( ( 2 1.20 2 1.0 m m

1.15 0.9

1.10 0.8

1.05 0.7 1.4 1.5 1.6 1.7 1.8 1.4 1.6 1.8 2.0 2.2 2.4 m1 (M ) m1 (M )

Spin χeﬀ = (m1S1z + m2S2z )/M - mass ratio q, distance - inclination

χ < 0.89 χ < 0.05

1.0 55

50 0.9 45 0.8 40

0.7 35 q (Mpc)

0.6 L 30 D 25 0.5 20 0.4 15 volumetric prior EM distance prior 0.3 10 0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 100◦ 120◦ 140◦ 160◦ 180◦ − χeﬀ θJN

LIGO/Virgo PRL 119, 161101 (2017), arXiv:1805.11579 Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 37 / 29 Templates need to be 2 orders of magnitude more accurate for use in LISA than in Advanced LIGO/Virgo.

1/2 G M5/6 Z f −4/3 df SNR ∝ N c D Sn(f ) f (G M )5/6 1/2 = N c S −1/2(f¯) f −4/3 − f −4/3 D n i f  −2/3 5/6 fi (GN Mc ) −1/2  r = Sn (fi ) ∆f D 7/3  fi

1/2 1/2 −1 5/6 −1 Sn Hz η 1/2 M f −2/3 D ' 200 −24 10 0.25 10M 150Hz 500Mpc 1/2 1/2 −1 5/6 −1 Sn Hz η 1/2 M f −7/6 D ' 40 −21 −4 10 0.25 70M 10 Hz 100Mpc ∆f 1/2 × 10−5Hz

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 38 / 29 Long duration signals

Remember that: dt 5 = (πG Mf )−5/3 f −2 df 96πη N M −5/3 f −8/3 t = 10yrs 70M 10−2Hz 5/3 2 96π 5/3 2 −3 η M f ∆f (πGN Mc f ) f ∆t 10 Hz −2 ' 5 ' 0.25 70M 10 Hz M −1 M −1 fISCO 1.5kHz fmax 20kHz ' 3M ' 3M 5/8 3/8 1.21M 1sec fgw 134Hz ' M τ c 5/3 8/3 1.21M 100Hz τ 2.2sec ' M f c gw Need for longer duration templates, as for the third-generation ground based detectors, since the signals are present in the data stream for months Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 39 / 29 D 1 F 1 − h i ∼ − 2SNR2 Upper bounds on sub-solar mass compact binaries coalescence rate

−3 −1 Mass/M Rate(Gpc yr ) Horizon(Mpc) 1 < 106 100 0.2 < 2 104 30 × 5/6 3/5 SNR Mc , Mc η M ∝ ≡ LIGO/Virgo arXiv:1808.04771

Fraction f of MACHOs in binary 10% ΩMacho = ∼ −3× ⇒ 10 ΩMacho in coalescing bina- ∼ −1 ries coalescing within H0

T. Nakamura et al. in Astrophys.J. 487 (1997) L139-L142 Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 40 / 29 2 2/3 2/3 Formula for the N of cycles x v (Mωs ) = (πMfGW ) ≡ ≡ v dE/dv 0(v 0) 2ηG M 1 1 N = 2 ω(v 0) dv 0 = N 1 + #v 2 + ... v −5 F (v) η2G M v 6 ∝ η Zv0 N Z M f 1/3 M f −5/3 v = 0.12 GW = v −5 = 4.7 104 GW 5 104 10M 10Hz ⇒ × 10M 10Hz ×

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 41 / 29 The EFT point of view on the 2-body problem

Diﬀerent scales in EFT (borrowing ideas from NRQCD):

Very short distance . rs = GN M negligible up to 5PN (eﬀacement principle) Short distance: potential gravitons Hµν, kµ (v/r, 1/r) 2 ∼ with r rs /v ∼ Long distance: GW’s GW kµ (v/r, v/r) GWs h ∼ µν coupled to point particles with moments M. Beneke and V. A. Smirnov, NPB ’98; I. Stewart and W. Manohar, PRD ’07; W. Goldberger and I. Rothstein, PRD ’06

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 42 / 29 Eﬀective Generic v-dependent potential terms Instantaneous couplings between world-line particles

p i j 2 GN h00/2 + vi h0i + v v hij /2 + GN h00 ...

Z 1 G m 1 G 2 m G m S = m dt d 3x v 2 + N 2 + v 4 + N 2 N 1 + v 2 + v v + 1 ↔ 2 eﬀ 1 2 1 2r 8 1 2r 2 2r 1 1r 2r

3PN: Jaranowski, Schäfer,Damour; Blanchet, Faye; Itoh Futamase; Foffa & RS 4PN: Jaranowski, Schäfer,Damour; Blanchet et al, RS Foffa; RS Foffa, Mastrolia, Sturm

EFT for compact binary systems

Fundamental Fundamental gravitational ﬁelds Fundamental coupling to particle world line Z exp [iSeﬀ (xa, hGW )] = DH(x) exp [iSEH (H + hGW ) + iSpp(H + hGW )]

Z Spp = −m dτ Z 1 4 h 2 2 2 2 i SEH = d x (∂h) + h(∂h) + h (∂h) ... 32πGN

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 43 / 29 Eﬀective Generic v-dependent potential terms Instantaneous couplings between world-line particles

p i j 2 GN h00/2 + vi h0i + v v hij /2 + GN h00 ...

Z 1 G m 1 G 2 m G m S = m dt d 3x v 2 + N 2 + v 4 + N 2 N 1 + v 2 + v v + 1 ↔ 2 eﬀ 1 2 1 2r 8 1 2r 2 2r 1 1r 2r

3PN: Jaranowski, Schäfer,Damour; Blanchet, Faye; Itoh Futamase; Foffa & RS 4PN: Jaranowski, Schäfer,Damour; Blanchet et al, RS Foffa; RS Foffa, Mastrolia, Sturm

EFT for compact binary systems

Fundamental Fundamental gravitational ﬁelds Fundamental coupling to particle world line Z exp [iSeﬀ (xa, hGW )] = DH(x) exp [iSEH (H + hGW ) + iSpp(H + hGW )]

Z 3 i j 2 Spp = −m dt d x δ(~x − ~xa(t)) h00/2 + vi h0i + v v hij /2 + h00 ... Z 1 4 h 2 2 2 2 2 i SEH = d x (∂i h) − (∂t h) + h(∂h) + h (∂h) ... 32πGN

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 43 / 29 Eﬀective Generic v-dependent potential terms Instantaneous couplings between world-line particles

Z 1 G m 1 G 2 m G m S = m dt d 3x v 2 + N 2 + v 4 + N 2 N 1 + v 2 + v v + 1 ↔ 2 eﬀ 1 2 1 2r 8 1 2r 2 2r 1 1r 2r

3PN: Jaranowski, Schäfer,Damour; Blanchet, Faye; Itoh Futamase; Foffa & RS 4PN: Jaranowski, Schäfer,Damour; Blanchet et al, RS Foffa; RS Foffa, Mastrolia, Sturm

EFT for compact binary systems

Fundamental Fundamental gravitational ﬁelds Fundamental coupling to particle world line Z exp [iSeﬀ (xa, hGW )] = DH(x) exp [iSEH (H + hGW ) + iSpp(H + hGW )]

Z 3 p i j 2 Spp = −m dt d x δ(~x − ~xa(t)) GN h00/2 + vi h0i + v v hij /2 + GN h00 ... Z 1 4 h 2 2 p 2 2 2 i S = d x (∂ h) − (∂ h) + G h(∂h) + G h (∂h) ... EH 2 i t N N

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 43 / 29 EFT for compact binary systems

Fundamental Effective Fundamental gravitational Generic v-dependent potential fields terms Fundamental coupling to Instantaneous couplings between particle world line world-line particles Z exp [iSeff (xa, hGW )] = DH(x) exp [iSEH (H + hGW ) + iSpp(H + hGW )]

Z 3 p i j 2 Spp = −m dt d x δ(~x − ~xa(t)) GN h00/2 + vi h0i + v v hij /2 + GN h00 ... Z 1 4 h 2 2 p 2 2 2 i S = d x (∂ h) − (∂ h) + G h(∂h) + G h (∂h) ... EH 2 i t N N Z 1 G m 1 G 2 m G m S = m dt d 3x v 2 + N 2 + v 4 + N 2 N 1 + v 2 + v v + 1 ↔ 2 eﬀ 1 2 1 2r 8 1 2r 2 2r 1 1r 2r

3PN: Jaranowski, Schäfer,Damour; Blanchet, Faye; Itoh Futamase; Foffa & RS 4PN: Jaranowski, Schäfer,Damour; Blanchet et al, RS Foffa; RS Foffa, Mastrolia, Sturm

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 43 / 29 How to compute eﬀective potential?

Iteratively solve Einstein equations for point particles (J(x) ∼ δ3(x − x¯)): Z Z 0 3 3 0 0 0 − dtV1−2(t, r) ∼ dt dt d x d x J(x)G(x − x )J(x ) µ Z d 4k eik (x1(t1)−x2(t2))µ = 32πG m m dt dt0 N 1 2 (2π)4 k2 − ω2 Z 0 0 m1m2 ' GN dt dt δ(t − t ) 0 |x1(t) − x2(t )| where k0 has been neglected. Considering eﬀects of v

Z e−iωt12+ikx12 Z e−iωt12+ikx12 ω2 V ∝ dωd 3k = dωd 3k 1 + + ... k2 − ω2 k2 k2 Z eikx12 ∂ ∂ Z eikx12 k · v k · v = δ(t ) d 3k 1 + t1 t2 + ... = d 3k 1 − 1 2 + ... 12 k2 k2 k2 k2

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 44 / 29 Trading knowledge over the full trajectory with knowledge of all derivatives of the trajectory at equal time time

+v ˙ +v ¨ + ... →

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 45 / 29 Newtonian potential:

GN m1m2 Seﬀ dt L ∼ r ∼ R At 1PN:

2 2 GN m1m2 2 Seﬀ = dt 2 Lv r ∼ R

v v2

Gm1m2 GN m1 3 2 7 1 V1PN = 1 + (v ) v1v2 v1ˆrv2ˆr + − 2r − 2r 2 1 − 2 − 2 1 2 ↔

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 46 / 29 The 4PN sector

G: : 3 diagrams

G2: 21 diagrams, RS and S. Foﬀa, PRD ’12 G3: 212 diagrams G4: 317 diagrams RS and S. Foﬀa ArXiv:1902.xxxx G5: 50 diagrams, RS et al. PRD ’18

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 47 / 29 5 4PN static GN topologies

1,1 1,2 0,1 M M M

1,3 1,4 2,2 M M M

3,6 M

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 48 / 29 5 GN master integrals expressed via integration by parts reduction in terms of 7 master integrals:

1,1 1,2 0,1 M M M

1,3 1,4 2,2 M M M

3,6 M Mapping the problem into 4-loop 3-D self-enrgy diagrams RS, S. Foﬀa, P. Mastrolia, C. Sturm PRD (2017) 104009

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 49 / 29 2 body dynamics expansions (spin-less)

Post-Minkowskian expansion parameter is GN M/r, vs PN expansion µv 2 GMµ 1 1 = Mc2 + + + [...] + [...] L − 2 r c2 c4 Terms known so far N 1PN 2PN 3PN 4PN 5PN . . . 0PM1 v 2 v 4 v 6 v 8 v 10 v 12 ... 1PM1 /r v 2/r v 4/r v 6/r v 8/r v 10/r ... 2PM1 /r 2 v 2/r 2 v 4/r 2 v 6/r 2 v 8/r 2 ... 3PM1 /r 3 v 2/r 3 v 4/r 3 v 6/r 3 ... 4PM 1/r 4 v 2/r 4 v 4/r 4 ... 5PM 1/r 5 v 2/r 5 ...... 3PM recently computed (!) by Z. Bern, C. Cheung et al. arXiv:1901.04424 What’s next? Amplitude program with modern methods: generalized unitarity, gravity as a double copy of gauge theory. . . Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 50 / 29 Fundamental Gravity tests at cosmological scale

GWs travel at the speed of light, with deviations . 1015 Model of dark energy/modiﬁed gravity with a single scalar degree of freedom drastically constrained

↓ standard conformal coupling to the Ricci scalar (for Horndeski theories)

G. W. Horndeski, Int. J. of Th. Phys. (1974) 10, 6, 363384 T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, and I. Sawicki, Phys. Rev. Lett. 119, 251301 (2017) P. Creminelli & F. Vernizzi, Phys. Rev. Lett. 119, 251302 (2017) J. Sakstein & J. Jain, Phys. Rev. Lett. 119, 251303 (2017) J. M. Ezquiaga & M. Zumalacrregui, Phys. Rev. Lett. 119, 251304 (2017) L. Amendola, M. Kunz, I. D. Saltas and I. Sawicki arXiv:1711.04825

Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 51 / 29 EM/ν from binary black hole coalescences?

BHs with accretion disks may lead to relativistic outflows with TeV - PeV ν (hadrons accelerated by jets, if magnetic fields and long-lived debris from BH progenitor, or dense gaseous environment) exotic but not impossible e.g. R. Perna et al. Ap.J. 821 (2016) 1, L18, I. Bartos et al., Ap.J. 835 (2017) 2, 165 GW150914: γ, X optical, radio counterparts not found Ap.J. 826 (2016) 1, L13 ν: E O(100) GeV, time window 500 sec, coincidences backg. Limit on ν spectral fluence (10% - 90%): < 1051 1054 erg∼ − LIGO, ANTARES and ICECube Phys.Rev. D93 (2016) no.12, 122010 51 54 GW151226 (LVT151012): Eiso < 2 10 2 10 erg × − × LIGO, ANTARES, IceCube, Phys.Rev. D96 (2017) 2, 022005 GW170104: No ν detection with a 500 sec window, nor in 3 months ANTARES Eur.Phys.J. C77 (2017) 12, 911 54 51 49 For reference: EGW 150914 ∼ 10 , long(short) GRB Eiso ∼ 10 , (10 erg) Riccardo Sturani (IIP-UFRN) Gravitational Wave Astronomy DU - Oct 25th, 2019 52 / 29 EM/ν from binary black hole coalescences? Nope