Gravitational wave physics with LISA and pulsar timing arrays - - PowerPoint PPT Presentation

SLIDE 1

Gravitational wave physics with LISA and pulsar timing arrays

Jonathan Gair, Albert-Einstein-Institute, Potsdam, Germany Kavli RISE Summer School on Gravitational Waves, September 26th 2019

SLIDE 2

Talk Outline

❖

The Laser Interferometer Space Antenna (LISA)

❖

Pulsar-timing detection of gravitational waves

❖

Sources for LISA and pulsar timing arrays (PTAs)

❖

Tests of gravitational physics with LISA observations

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Cosmography with LISA observations

❖

Fundamental physics with PTA observations

SLIDE 3

The Laser Interferometer Space Antenna

❖

Long history. Original design (1998)

• Gravitational wave detector
• perating in millihertz band.
• Three satellites, 5 million km

apart, in heliocentric, Earth- trailing orbit. 6 laser links.

• Joint NASA/ESA project.
• Technology demonstrator

mission, LISA Pathfinder,

• approved. Launched 2015.

❖

NASA dropped out in 2011. New ESA-only mission eventually selected for L3 (2034).

SLIDE 4

LISA Status

❖

LISA now reinvigorated and timetable accelerated

• LISA Pathfinder spectacularly

demonstrated the technology.

• Detection of GW150914+ renewed

interest in gravitational waves.

• mission now in phase A, adoption

in 2022-2024;

• mission launch: 2034.

❖

Mid-decadal review expressed strong support for NASA re-involvement, at probe-class level (~$400m).

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Design: 2.5Gm arms, 6-link geometry.

SLIDE 5

Pulsar timing

❖

Pulsars are rapidly rotating Neutron

• Stars. Observations indicate great

homogeneity in pulse profile, and little variation in frequency.

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Pulsars are very accurate clocks.

Plots from I H Stairs (2003)

SLIDE 6

Pulsar timing arrays

❖

GW passing between source and

• bserver induces periodic change in

pulse time of arrival.

❖

Use a network (array) of pulsars to increase signal to noise.

SLIDE 7

Pulsar timing arrays

❖

There are three major pulsar timing efforts

• EPTA - the European Pulsar Timing
• Array. Data collected from six

telescopes in UK, Netherlands, France, Germany and Italy.

SLIDE 8

Pulsar timing arrays

❖

There are three major pulsar timing efforts

• EPTA - the European Pulsar Timing
• Array. Data collected from six

telescopes in UK, Netherlands, France, Germany and Italy.

• NANOGrav - US/Canada PTA.

Data collected using Arecibo and the Green Bank Telescope.

SLIDE 9

Pulsar timing arrays

❖

There are three major pulsar timing efforts

• EPTA - the European Pulsar Timing
• Array. Data collected from six

telescopes in UK, Netherlands, France, Germany and Italy.

• NANOGrav - US/Canada PTA.

Data collected using Arecibo and the Green Bank Telescope.

• PPTA - the Parkes Pulsar Timing
• Array. Australian collaboration.

❖

The three PTAs combine data as the International Pulsar Timing Array (IPTA).

SLIDE 10

Detector sensitivities

http://gwplotter.com

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Gravitational wave sources for LISA

SLIDE 12

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Expected to occur following mergers of the host galaxies. LISA can observe gravitational waves from these with very high signal-to-noise ratio.

LISA sources: massive black hole mergers

SLIDE 13

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Expected to occur following mergers of the host galaxies. LISA can observe gravitational waves from these with very high signal-to-noise ratio.

LISA sources: massive black hole mergers

SLIDE 14

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Expected to occur following mergers of the host galaxies. LISA can observe gravitational waves from these with very high signal-to-noise ratio.

❖

Expected event rate depends on assumptions about black hole population (Klein+, 2016)

• Light pop-III seed model: baseline configuration expected to see ~350

events.

• Heavy seed model, no delay in binary formation: ~550 events.
• Heavy seed model, with delays: ~50 events.

❖

Baseline configuration would see 150/300/4 events at z > 7 under the different models.

LISA sources: massive black hole mergers

SLIDE 15

LISA sources: extreme-mass-ratio inspirals

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The inspiral of a compact object into a massive black hole in the centre of a galaxy.

❖

Form as a result of scattering in dense galacto-centric stellar clusters.

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Orbits are expected to be both eccentric and inclined - rich waveform structure.

SLIDE 16

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There are large astrophysical uncertainties, but expect to see between a few tens and a few hundreds of events.

LISA sources: extreme-mass-ratio inspirals

Mass MBH Cusp M–σ CO EMRI rate [yr1] Model function spin erosion relation Np mass [M] Total Detected (AKK) Detected (AKS) M1 Barausse12 a98 yes Gultekin09 10 10 1600 294 189 M2 Barausse12 a98 yes KormendyHo13 10 10 1400 220 146 M3 Barausse12 a98 yes GrahamScott13 10 10 2770 809 440 M4 Barausse12 a98 yes Gultekin09 10 30 520 (620) 260 221 M5 Gair10 a98 no Gultekin09 10 10 140 47 15 M6 Barausse12 a98 no Gultekin09 10 10 2080 479 261 M7 Barausse12 a98 yes Gultekin09 10 15800 2712 1765 M8 Barausse12 a98 yes Gultekin09 100 10 180 35 24 M9 Barausse12 aflat yes Gultekin09 10 10 1530 217 177 M10 Barausse12 a0 yes Gultekin09 10 10 1520 188 188 M11 Gair10 a0 no Gultekin09 100 10 13 1 1 M12 Barausse12 a98 no Gultekin09 10 20000 4219 2279

SLIDE 17

Stellar-origin black hole binaries

❖

GW150914 would have been

• bservable by LISA ~5 years

before being observed by LIGO, with S/N~10 in a 5yr

• bservation. (Sesana 2016)

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LISA provides sky location to ~0.few square degrees and time of coalescence to ~few s.

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Number of events could be high (several hundred) but there are significant uncertainties.

SLIDE 18

Stellar-origin black hole binaries

❖

GW150914 would have been

• bservable by LISA ~5 years

before being observed by LIGO, with S/N~10 in a 5yr

• bservation. (Sesana 2016)

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LISA provides sky location to ~0.few square degrees and time of coalescence to ~few s.

❖

Number of events could be high (several hundred) but there are significant uncertainties.

Mass distribution R/(Gpc3yr1) PyCBC GstLAL Combined Event based GW150914 3.2+8.3

2.7

3.6+9.1

3.0

3.4+8.6

2.8

LVT151012 9.2+30.3

8.5

9.2+31.4

8.5

9.4+30.4

8.7

GW151226 35+92

29

37+94

31

37+92

31

All 53+100

40

56+105

42

55+99

41

Astrophysical Flat in log mass 31+43

21

30+43

21

30+43

21

Power Law (2.35) 100+136

69

95+138

67

99+138

70

SLIDE 19

Other sources for LISA

❖

Compact binaries in the Milky Way

• Binaries of stellar remnants (white dwarfs or neutron stars) with orbital

periods of ~1 hour.

• Known (verification) and unknown sources.
• Signals almost monochromatic.

SLIDE 20

Other sources for LISA

❖

Compact binaries in the Milky Way

• Binaries of stellar remnants (white dwarfs or neutron stars) with orbital

periods of ~1 hour.

• Known (verification) and unknown sources.
• Signals almost monochromatic.

10−20 10−19 10−18 10−17 10−16 Linear PSD of strain h (1/ √ Hz)

HM Cnc V407 Vul ES Cet SDSS J0651 AM CVn HP Lib CR Boo V803 Cen

• 3.5

3

• 2.5
• 2

log (f /Hz)

eLISA resolvable binaries: 100 loudest (red points) 1000 loudest (grey points) Amaro-Seoane et al. (2013)

SLIDE 21

Other sources for LISA

❖

Compact binaries in the Milky Way

• Binaries of stellar remnants (white dwarfs or neutron stars) with orbital

periods of ~1 hour.

• Known (verification) and unknown sources.
• Signals almost monochromatic.
• LISA expected to detect ~15000 binaries with S/N > 7.
• LISA should determine 2D/3D location for 4500/1250 sources, measure

df/dt for 3000 and d2f/dt2 for ~3.

❖

Cosmological sources

• Processes occurring at the TeV scale in the early Universe could generate

a mHz stochastic gravitational wave background.

• Cosmic string networks could produce both individual burst events and

a stochastic background.

SLIDE 22

Other sources for LISA

❖

Compact binaries in the Milky Way

• Binaries of stellar remnants (white dwarfs or neutron stars) with orbital

periods of ~1 hour.

• Known (verification) and unknown sources.
• Signals almost monochromatic.
• LISA expected to detect ~15000 binaries with S/N > 7.
• LISA should determine 2D/3D location for 4500/1250 sources, measure

df/dt for 3000 and d2f/dt2 for ~3.

❖

Cosmological sources

• Processes occurring at the TeV scale in the early Universe could generate

a mHz stochastic gravitational wave background.

• Cosmic string networks could produce both individual burst events and

a stochastic background.

10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL 10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL 10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL 10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL

Caprini et al. (2016)

SLIDE 23

Gravitational wave sources for pulsar timing arrays

SLIDE 24

Sources for pulsar timing arrays

❖

Primary source for pulsar timing: pre-merger supermassive black hole binaries. Signal almost monochromatic.

❖

Expect to observe stochastic

• background. An stationary,

isotropic, uncorrelated background produces a characteristic correlation signature

hsa(t)⇤sb(t0)i = ΓabC(|t t0|)

SLIDE 25

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No detection yet, but recent limits are starting to become astrophysically interesting.

Current PTA limits

NANOGrav 11-year results [Aggarwal et

• al. (2019)]

10−8 10−7 Frequency [Hz] 10−14 10−13 10−12 10−11 GW strain upper limit

5-yr data set 9-yr data set 11-yr data set

SLIDE 26

❖

No detection yet, but recent limits are starting to become astrophysically interesting.

Current PTA limits

NANOGrav 9-year results [Arzoumanian et al. (2015)]

10−9 10−8 10−7 Frequency [Hz] 10−15 10−14 10−13 10−12 Characteristic Strain [hc( f)] f 3/2

McWilliams et al. (2014) Ravi et al. (2014) Sesana et al. (2013)

SLIDE 27

Current PTA limits

• Astrophysical processes can diminish signal at low frequencies.

Environmental Coupling

• Stellar hardening
• Gas-driven inspiral
• Eccentricity

Galaxy Population Uncertainties

• Merger timescale
• SMBH - host relations
• Pair fraction
• Redshift evolution

Diminished GW Signal

• BSMBH stalling
• GW absorption

Characteristic strain, hc

1E-17 1E-16 1E-15 1E-14 1E-13 1E-12

Gravitational Wave Frequency, f (Hz)

1E-10 1E-09 1E-08 1E-07 1E-06

hc

f

SLIDE 28

PTA: time to detection

❖

Based on current theoretical understanding and observational results, expect detection in 5 to 10 years.

❖

Assumes existing pulsars continue to be observed and new pulsars are added.

❖

Hints will come earlier.

5 10 PPTA4 20 40 60 80 100 NANOGrav+ 20 40 60 80 100 EPTA+ 20 40 60 80 100 IPTA+ 5 10 15 20 T [yrs] 20 40 60 80 100 TPTA

Expected detection probability [%]

Taylor et al. (2016)

SLIDE 29

Tests of gravitational physics with LISA Observations

SLIDE 30

Fundamental physics with LISA

❖

Gravitational wave observations probe a regime of strong-field, non-linear and dynamical gravity that is inaccessible to other probes.

❖

All GW sources and detectors can be used to constrain fundamental physics.

❖

Space-based detectors are particularly good because

• High SNR events: SNR of hundreds for MBH mergers.
• Long duration signals: months to years in band; hundreds of thousands
• f cycles for typical EMRIs.
• Clean systems: main sources are black hole binaries.
• Rich dynamics: eccentricity and orbital inclination likely for EMRIs.

❖

Can test GW propagation, polarisation, energy loss, generic or specific deviations in alternative theories, constrain dark matter candidates etc.

10

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ε=M/r

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ξ

1/2=(M/r 3) 1/2 [km

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Double Binary Pulsar Lunar Laser Ranging LIGO BH-BH Merger Sun's Surface Earth's Surface LISA IMBH-IMBH Merger Perihelion Precession of Mercury LIGO NS-NS Merger IMRIs IMBH-SCO LAGEOS LISA SMBH-SMBH Merger EMRIs SMBH-SCO Pulsar Timing Arrays

Field Strength

Curvature Strength Strong Field Tests Weak Field Tests

Figure from N Yunes adapted from D Psaltis

• Liv. Rev. Rel.

(2008)

Current Tests Gravitational Wave Tests

SLIDE 31

Fundamental physics with LISA

❖

Gravitational wave observations probe a regime of strong-field, non-linear and dynamical gravity that is inaccessible to other probes.

❖

All GW sources and detectors can be used to constrain fundamental physics.

❖

Space-based detectors are particularly good because

• High SNR events: SNR of hundreds for MBH mergers.
• Long duration signals: months to years in band; hundreds of thousands
• f cycles for typical EMRIs.
• Clean systems: main sources are black hole binaries.
• Rich dynamics: eccentricity and orbital inclination likely for EMRIs.

❖

Can test GW propagation, polarisation, energy loss, generic or specific deviations in alternative theories, constrain dark matter candidates etc.

SLIDE 32

Probing the nature and structure of BHs

❖

GW emission from EMRIs encodes a map of the space-time structure outside the central massive black hole.

SLIDE 33

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GW emission from EMRIs encodes a map of the space-time structure outside the central massive black hole. Can characterize a vacuum, axisymmetric spacetime in GR by its multipole moments. For Kerr BHs, these satisfy the ‘no-hair’ theorem:

❖

Deviations from no-hair property can be indicative of violations of the Strong Equivalence Principle (implying violation of WEP or Local Lorentz Invariance or Local Positional Invariance). What are the observable consequences?

❖

Multipole moments are encoded in gravitational wave observables - precession frequencies & number of cycles spent near a given frequency (Ryan 95).

❖

Multipole moments enter at different orders in

Probing the nature and structure of BHs

Ml + iSl = M(ia)l

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∆N(f) = f 2 df/dt = f 2 dE/df dE/dt

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MΩ

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Ωp Ω = 3(MΩ)

2 3 − 4 S1

M 2 (MΩ) + ✓9 2 − 3 2 M2 M 3 ◆ (MΩ)

4 3 + · · ·

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SLIDE 34

Probing BH structure: the central object

❖

Need infinite number of multipoles to describe Kerr. Instead, consider “bumpy” black holes with small departures from Kerr.

• Many studies, e.g., Collins & Hughes (2004), Glampedakis & Babak (2005),

Barack & Cutler (2007), JG, Li & Mandel (2008), Sopuerta & Yunes (2009), Canizares, JG & Sopuerta (2012).

• Can simultaneously measure M, a to ~0.01% and excess quadrupole to ~0.1%.

Barack & Cutler (2007)

SLIDE 35

Probing BH structure: the central object

❖

Need infinite number of multipoles to describe Kerr. Instead, consider “bumpy” black holes with small departures from Kerr.

• Many studies, e.g., Collins & Hughes (2004), Glampedakis & Babak (2005),

Barack & Cutler (2007), JG, Li & Mandel (2008), Sopuerta & Yunes (2009), Canizares, JG & Sopuerta (2012).

• Can simultaneously measure M, a to ~0.01% and excess quadrupole to ~0.1%.

❖

Other information is also encoded in emitted GWs

• Tidal coupling: Energy is lost ‘into the horizon’ through tidal heating. Infer

strength of tidal interaction (Li & Lovelace 07).

• Presence of matter: gas, accretion disc, second SMBH or exotic matter can leave

measurable imprint on signal. Can’t be confused with no-hair violation.

• Horizon: presence/absence of a horizon indicated by cut-off/continuation of

emission at plunge, e.g., persistent emission for an inspiral into a Boson-Star.

SLIDE 36

Probing BH structure: the central object

❖

Need infinite number of multipoles to describe Kerr. Instead, consider “bumpy” black holes with small departures from Kerr.

• Many studies, e.g., Collins & Hughes (2004), Glampedakis & Babak (2005),

Barack & Cutler (2007), JG, Li & Mandel (2008), Sopuerta & Yunes (2009), Canizares, JG & Sopuerta (2012).

• Can simultaneously measure M, a to ~0.01% and excess quadrupole to ~0.1%.

❖

Other information is also encoded in emitted GWs

• Tidal coupling: Energy is lost ‘into the horizon’ through tidal heating. Infer

strength of tidal interaction (Li & Lovelace 07).

• Presence of matter: gas, accretion disc, second SMBH or exotic matter can leave

measurable imprint on signal. Can’t be confused with no-hair violation.

• Horizon: presence/absence of a horizon indicated by cut-off/continuation of

emission at plunge, e.g., persistent emission for an inspiral into a Boson-Star.

Kesden, Gair & Kamionkowski (2004)

SLIDE 37

Signatures of Deviations - Horizons

❖

Other signatures of deviations from the black hole hypothesis include “echoes” from the vicinity of the horizon.

ClePhO BH

50 100 150

• 0.5

0.0 0.5 1.0

time [ms ] GW strain

τecho ∼2 rg/c |log ϵ|

100 150 200 250

• 0.10
• 0.05

0.00 0.05 0.10

prompt ringdown

Cardoso & Pani (2017) Maselli et al. (2017)

▲ ▲ ▲ ▲ ▲ ▲

• ◼

◼ ◼ ◼ ◼ ◼

△ △ △ △ △ △ ▲

107M⊙

• 5×106M⊙

◼ 106M⊙

0.7 0.8 0.9 102 103 10

χ1=χ2

σγ/γ[%]

γ = 1

SLIDE 38

Signatures of Deviations - Horizons

❖

Horizonless objects are generically unstable and would generate a stochastic background of gravitational waves.

Barausse et al. (2018) t0/tH~1010 t0/tH~1011 t0/tH~1012

10-5 10-4 0.001 0.010 0.100 10-13 10-11 10-9 10-7

f (Hz)

ΩGW

LISA

SLIDE 39

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

SLIDE 40

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

4 5 6 7 8 9 10 11 12 !0.2 !0.15 !0.1 !0.05 0.05 0.1 0.15 !/" d!/d#

SLIDE 41

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

0.8 1 1.2 1.4 1.6 1.8 2 !3 !2 !1 1 2 3 4 !/" d!/d#

SLIDE 42

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

❖

How to identify this in practice is not obvious.

• Might detect this via a time-frequency analysis, or if waveform SNR stops

accumulating prematurely.

• Could even see intermittent ‘bursts’ of regular periodic radiation as orbit passes into

and out of ergodic regime.

SLIDE 43

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

❖

How to identify this in practice is not obvious.

• Might detect this via a time-frequency analysis, or if waveform SNR stops

accumulating prematurely.

• Could even see intermittent ‘bursts’ of regular periodic radiation as orbit passes into

and out of ergodic regime.

SLIDE 44

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

❖

How to identify this in practice is not obvious.

• Might detect this via a time-frequency analysis, or if waveform SNR stops

accumulating prematurely.

• Could even see intermittent ‘bursts’ of regular periodic radiation as orbit passes into

and out of ergodic regime.

SLIDE 45

Deviations in the strong field

❖

Strong field deviations can be more extreme. Kerr is special in having orbits with a complete set of integrals. This need not hold for other systems.

❖

Explore orbital properties using a Poincare map.

• Many orbits show closed curves, indicating that they have an effective third integral.
• Some orbits show space-filling maps, indicating ergodic behaviour - a ‘smoking gun’

for a non-Kerr spacetime.

❖

How to identify this in practice is not obvious.

• Might detect this via a time-frequency analysis, or if waveform SNR stops

accumulating prematurely.

• Could even see intermittent ‘bursts’ of regular periodic radiation as orbit passes into

and out of ergodic regime.

❖

Unlikely to be astrophysically relevant, as fine-tuning is needed.

SLIDE 46

Signatures of Deviations - Resonances

❖

When an integrable system is perturbed, resonant points become smeared out into resonant chains of islands (Poincare-Birkhoff theorem). Such deviation may therefore show up as a persistent resonance in the observed GWs.

Apostolatos et al. (2009)

SLIDE 47

❖

No-hair theorem violations as also encoded in frequency and damping time

• f quasi-normal modes, excited after massive black hole mergers. Need to
• bserve 2 or more modes.

Probing the nature and structure of BHs

Berti, Cardoso & Will (2006)

SLIDE 48

❖

No-hair theorem violations as also encoded in frequency and damping time

• f quasi-normal modes, excited after massive black hole mergers. Need to
• bserve 2 or more modes.

Probing the nature and structure of BHs

N 1 A 1 N 1 A 2 N 1 A 5 N 2 A 1 N 2 A 2 N 2 A 5 100 101 102 103 events/year

ρ > 8 ρ > ρGLRT Q3nod 4L Q3d 4L PopIII 4L Q3nod 6L Q3d 6L PopIII 6L Q3nod 4L Q3d 4L PopIII 4L Q3nod 6L Q3d 6L PopIII 6L

Berti et al. (2016)

SLIDE 49

Tests of gravitational physics

❖

Inspiral phasing: in order to offer sensitivity to un-modelled deviations from GR, consider generic deviations to inspiral phase.

❖

Modify pN phase coefficients (Arun et al.) ˜ h(f) = Af − 7

6 exp

h iΨ(f) + iπ 4 i Ψ(f) = 2πftc + Φc + X

k∈Z

h ψk + ψlog

k

log f i f (k−5)/3

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SLIDE 50

Tests of gravitational physics

❖

Inspiral phasing: in order to offer sensitivity to un-modelled deviations from GR, consider generic deviations to inspiral phase.

❖

Modify pN phase coefficients (Arun et al.) ˜ h(f) = Af − 7

6 exp

h iΨ(f) + iπ 4 i Ψ(f) = 2πftc + Φc + X

k∈Z

h ψk + ψlog

k

log f i f (k−5)/3

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0.5 1 1.5 2 10

6(m1/MO)

. 0.5 1 1.5 2 10

6(m2/MO)

.

4 3 6 7 6l 5l

Arun et al. 2006

SLIDE 51

Tests of gravitational physics

❖

Inspiral phasing: in order to offer sensitivity to un-modelled deviations from GR, consider generic deviations to inspiral phase.

❖

Modify pN phase coefficients (Arun et al.)

❖

LISA could measure ˜ h(f) = Af − 7

6 exp

h iΨ(f) + iπ 4 i Ψ(f) = 2πftc + Φc + X

k∈Z

h ψk + ψlog

k

log f i f (k−5)/3

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∆ψ0 ∼ 0.1%, ∆ψ2, ∆ψ3 ∼ 10%

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SLIDE 52

Tests of gravitational physics

❖

Parameterised post-Einsteinian formalism (Yunes & Pretorius 2009) uses ˜ hppE(f) = ˜ hGR(f) × (1 + α(πMf)a) exp ⇥ iβ(πMf)b⇤

<latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit>

SLIDE 53

Tests of gravitational physics

❖

Parameterised post-Einsteinian formalism (Yunes & Pretorius 2009) uses ˜ hppE(f) = ˜ hGR(f) × (1 + α(πMf)a) exp ⇥ iβ(πMf)b⇤

<latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit>

Chamberlain & Yunes (2017)

SLIDE 54

Tests of gravitational physics

❖

Parameterised post-Einsteinian formalism (Yunes & Pretorius 2009) uses

❖

Many specific alternative theories can be directly mapped to the ppE parameterisation, allowing results to be interpreted physically. ˜ hppE(f) = ˜ hGR(f) × (1 + α(πMf)a) exp ⇥ iβ(πMf)b⇤

<latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">ACYXicdZHRa9RAEMY3sWp72hrY18WD+GKcCRFbAWFQin6IlTx2sJtekz2Jpelm2TZnUiPkH+yb70xX/EvesJ2urAwsdvmFnv82MVo7i+EcQPlh7+Ojx+kbvydPNrWfR8+1TVzdW4kjWurbnGTjUqsIRKdJ4bixCmWk8y6PFv2z72idqtvNDeYljCrVK4kEeT6EqQ0lNsi+6iFbkxhx3g3z3wx38euCck9LdIPkNRegTQEDYRvhQTNP3f57gV4C14ZoTGnsRIZ0j1LJqyaFZROon48TN69jfcP+H2RDONl9dmqTibRtZjWsimxIqnBuXESG0pbsKSkxq4nGocG5CXMcOxlBX7TtF0m1PFXnkx5Xlt/KuJL+udEC6Vz8zLzhKocHd7C/iv3rih/CBtVWUawkreXpQ3mlPNF3HzqbIoSc+9AGmV35XLAixI8p/S8yH8fin/vzjdGyY+mS9v+ofvV3Gsx32kg1YwvbZIfvETtiISXYTrAWbwVbwM9wIo3D71hoGq5kX7K8Kd34BDmK1yQ=</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">ACYXicdZHRa9RAEMY3sWp72hrY18WD+GKcCRFbAWFQin6IlTx2sJtekz2Jpelm2TZnUiPkH+yb70xX/EvesJ2urAwsdvmFnv82MVo7i+EcQPlh7+Ojx+kbvydPNrWfR8+1TVzdW4kjWurbnGTjUqsIRKdJ4bixCmWk8y6PFv2z72idqtvNDeYljCrVK4kEeT6EqQ0lNsi+6iFbkxhx3g3z3wx38euCck9LdIPkNRegTQEDYRvhQTNP3f57gV4C14ZoTGnsRIZ0j1LJqyaFZROon48TN69jfcP+H2RDONl9dmqTibRtZjWsimxIqnBuXESG0pbsKSkxq4nGocG5CXMcOxlBX7TtF0m1PFXnkx5Xlt/KuJL+udEC6Vz8zLzhKocHd7C/iv3rih/CBtVWUawkreXpQ3mlPNF3HzqbIoSc+9AGmV35XLAixI8p/S8yH8fin/vzjdGyY+mS9v+ofvV3Gsx32kg1YwvbZIfvETtiISXYTrAWbwVbwM9wIo3D71hoGq5kX7K8Kd34BDmK1yQ=</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit><latexit sha1_base64="kNdmkZ6xmkyj/i+c56p5Xnurg=">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</latexit>

GR Deviation PN Parameter Best Space Const. Best Ground Const. Current Const. Best Space Sys. Best Ground Sys. Dipole Radiation

• 1
• 4.9 × 10−12

1.9 × 10−10 4.4 × 10−5 EMRI NSNS ˙ EDip 7.8 × 10−8 3.2 × 10−8 1.8 × 10−3 EMRI/GW150914 NSNS Large Extra-Dimension

• 4
• 2.2 × 10−22

6.4 × 10−20 9.1 × 10−11 EMRI NSNS ` [µm] 3.0 × 102 7.5 × 104 10 − 103 [28–32] EMRI/GW150914 BHBH Time-Varying G

• 4
• 2.2 × 10−22

6.4 × 10−20 9.1 × 10−11 EMRI NSNS ˙ G [1/yr] 6.8 × 10−8 1.1 × 10−3 10−12 − 10−13 [33–37] EMRI NSNS Einstein-Æther Theory

• 4.0 × 10−8

6.7 × 10−5 3.4 × 10−3 EMRI `BHNS (c+, c−) (10−3, 3 × 10−4) (10−2, 4 × 10−3) (0.03, 0.003) [38, 39] EMRI NSNS Khronometric Gravity

• 4.0 × 10−8

6.7 × 10−5 3.4 × 10−3 EMRI `BHNS (KG, KG) (10−4, 10−2)/2 (10−2, 10−1)/5 (10−2, 10−1)/2 [38, 39] EMRI GW150914 Graviton Mass +1

• 4.3 × 10−5

1.0 × 10−3 8.9 × 10−2 EMRI/IMBH `BHBH mg [eV ] 9.0 × 10−28 9.9 × 10−25 10−29 − 10−18 [40–44] SMBH/IMRI GW150914

SLIDE 55

Tests of gravitational physics

Large extra dimensions Varying Newton’s constant b = -13/3

= dm dt 25 851968 ✓3 − 26⌘ + 34⌘2 ⌘2/5(1 − 2⌘) ◆

˙ ma = −2.8 × 107 ✓M Ma ◆2✓ ` 10µm ◆2 M yr1

10-2 100 102 104 106 108 1010 1012 1014 1016 1018 a L I G O V

• y

. A + C E E T

• D

N 2 A 1 N 2 A 2 N 2 A 5 L I S A Ground-based Space-based Current Bounds

Constraint on ` [µm]

lBHBH BHBH GW150914 EMRI IMRI IMBH SMBH

= 25 65526 ˙ Gz G Mz

10-14 10-12 10-10 10-8 10-6 10-4 10-2 100 102 104 106 aLIGO Voy. A+ CE ET-D N2A1 N2A2 N2A5 LISA Ground-based Space-based

Constraint on ˙ G/G [1/yr]

NSNS lBHNS lBHBH BHBH GW150914 EMRI IMRI IMBH SMBH

SLIDE 56

Tests of gravitational physics

Einstein-Aether gravity

β = − 3 128 ✓ 1 − c14 2 ◆ (AEA,1 + SAEA,2 + S2AEA,3)

• Khronometric gravity

β = − 3 128 ✓ 1 − αKG 2 ◆ (AKG,1 + SAKG,2 + S2AKG,3)

• b = -5/3

SLIDE 57

❖

Energy loss: inspiral rate could differ from quadrupole formula prediction due to, e.g., dipole radiation in scalar-tensor gravity.

Dipole radiation

SLIDE 58

❖

Energy loss: inspiral rate could differ from quadrupole formula prediction due to, e.g., dipole radiation in scalar-tensor gravity.

Dipole radiation

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 aLIGO Voy. A+ CE ET-D N2A1 N2A2 N2A5 LISA Ground-based Space-based A0620-00 LMXB

Constraint on δ ˙ EDip

NSNS lBHNS lBHBH BHBH GW150914 EMRI IMRI IMBH SMBH

Dipole radiation, b = -7/3

β = − 3 224δ ˙ EDipη2/5

SLIDE 59

❖

Energy loss: inspiral rate could differ from quadrupole formula prediction due to, e.g., dipole radiation in scalar-tensor gravity.

❖

Can translate into bound on Brans-Dicke theory. Best bounds from NS+MBH

• r SOBH inspirals.

ωBD > 2 × 104 ✓ S 0.3 ◆ ✓ 100 ∆ΦD ◆ ✓ T 1yr ◆ 7

8 ✓104M

M• ◆ 3

4

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Dipole radiation

SLIDE 60

Modified propagation speed

❖

Propagation: in GR GWs travel at the speed of light. Constrain “graviton mass” using GW observations.

❖

Can parameterise the modified dispersion relation in different ways, e.g.,

❖

Or the form popular in a cosmological setting

❖

Constraints come from observation of EM counterparts to GW observations and (lack of) dispersion in GW chirps. Current LIGO constraints from GW170817 and GW150914 are quite similar.

ω2 + iHω (3 + αM) = (1 + αT ) kiki

ω2 = kiki + m2

g

~2 + A(kiki)α ,

SLIDE 61

Massive graviton, b = -1

β = π2 D0 Mz λ2

10-28 10-27 10-26 10-25 10-24 10-23 10-22 a L I G O V

• y

. A + C E E T

• D

N 2 A 1 N 2 A 2 N 2 A 5 L I S A Ground-based Space-based Current Bound

Constraint on mg [eV]

NSNS lBHNS lBHBH BHBH GW150914 EMRI IMRI IMBH SMBH

Modified propagation speed

SLIDE 62

❖

Can also combine data from multiple events to strengthen the constraints. Bounds of the order are possible. λg = h/mg > few × 1016km

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100 200 300 400 10

16

10

17

λg

100 200 300 400

LISA New LISA C2 New LISA C5

10

16

10

17

λg SE LE One Michelson Two Michelsons

Berti, JG & Sesana (2011)

Modified propagation speed

SLIDE 63

Tests of gravitational physics

❖

Polarisation: in GR there are only two GW polarisation states - plus and cross, but four additional states are possible in metric theories.

y x y x x z y z y x y z (a) (b) (c) (d) (e) (f)

SLIDE 64

Tests of gravitational physics

❖

Polarisation: in GR there are only two GW polarisation states - plus and cross, but four additional states are possible in metric theories.

• At frequencies greater than one over the light travel time, LISA is ten

times more sensitive to scalar-longitudinal and vector modes than scalar- transverse and tensor modes.

SLIDE 65

Tests of gravitational physics

❖

Polarisation: in GR there are only two GW polarisation states - plus and cross, but four additional states are possible in metric theories.

• At frequencies greater than one over the light travel time, LISA is ten

times more sensitive to scalar-longitudinal and vector modes than scalar- transverse and tensor modes.

10

−4

10

−3

10

−2

10

−1

10 10

−24

10

−23

10

−22

10

−21

f(Hz) X Sensitivity Scalar T Tensor Vector Scalar L (a)

Tinto, da Silva Alves (2010)

SLIDE 66

Brito et al. (2017a)

Dark matter candidates: bosons

❖

Ultra-light boson fields are subject to super-radiant instability, leading to formation of boson condensates outside black

• holes. These produce GW backgrounds when they dissipate.
• ----
• µ ∼ ω < mΩH

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Brito et al. (2017b)

EM LIGO LISA, popIII LISA, Q3 LISA, Q3nod

10-1 100 101 102 103 104 105 106 107 108 109 0. 0.2 0.4 0.6 0.8 1. 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 BH mass [M ⊙] BH spin f/Hz

10-11eV 10-12eV 10-13eV 10-14eV 10-15eV 10-16eV 10-17eV 10-18eV 10-19eV

SLIDE 67

Dark matter candidates: bosons

❖

Can also see lead resonant depletion of boson clouds during binary inspirals, e.g., EMRIs.

Brito et al. (2019)

2.×10-6 5.×10-6 1.×10-5 2.×10-5 10-6 10-5 10-4 0.001 0.010 0.100 1 2.×10-5 5.×10-5 1.×10-4 2.×10-4 10-6 10-5 10-4 10-3 10-2 10-1 100

SLIDE 68

Dark matter candidates: primordial BHs

❖

Primordial BHs formed directly in the early Universe will generate

• GWs. Direct detection of these black holes possible as SOBHs. LISA

measurements of eccentricity crucial for identifying primordial origin.

Cholis et al. (2016)

Mvir=1012(M /h) Mvir=109(M /h) Mvir=106(M /h)

PDF of eccenticity at rp=22·RSch Orbit, e22, for PBH binaries

m1=m2=30·M

⊙ ⊙ ⊙ ⊙ 0.0 0.2 0.4 0.6 0.8 1.0 10-5 10-4 0.001 0.010 0.100 1 e22 PDF(e22)PBH

Kovetz et al. (2017)

SLIDE 69

Dark matter candidates: primordial BHs

❖

LISA will probe a previously poorly constrained mass range by (non?)-

• bservation of a stochastic GW background.

Bartolo et al. (2018)

10-18 10-15 10-12 10-9 10-6 10-3 100 103 10-5 10-4 10-3 10-2 10-1 100 1015 1018 1021 1024 1027 1030 1033 1036

γ EG bkg

WD

HSC

HSC (extrap.) Kepler

EROS U F D C M B

10-5 10-4 10-3 10-2 10-1 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7

LISA

SLIDE 70

Cosmography with LISA Observations

SLIDE 71

Science: cosmography

❖

Dimensionless gravitational wave strain scales as

❖

Phase evolution determines intrinsic parameters precisely. Amplitude then gives distance accurately (Schutz 1986).

❖

Need another way to break the mass/redshift degeneracy - electromagnetic counterpart.

14 16 18 20 22 24 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.5 0.0 0.5 1.0

• mag. residual

from empty cosmology 0.25,0.75 0.25, 0 1, 0 0.25,0.75 0.25, 0 1, 0 redshift z Supernova Cosmology Project Knop et al. (2003) Calan/Tololo & CfA

Supernova Cosmology Project effective mB

ΩΜ , ΩΛ ΩΜ , ΩΛ

h ∼ M D ∼ (1 + z)M DL(z)

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SLIDE 72

Science: cosmography

❖

Dimensionless gravitational wave strain scales as

❖

Phase evolution determines intrinsic parameters precisely. Amplitude then gives distance accurately (Schutz 1986).

❖

Need another way to break the mass/redshift degeneracy - electromagnetic counterpart.

❖

Massive black hole mergers were seen as promising candidates, but

• counterpart mechanism is unclear.
• weak lensing dominates errors for most

sources.

• LISA distance precision is poor.

h ∼ M D ∼ (1 + z)M DL(z)

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SLIDE 73

❖

Even without a counterpart, can estimate cosmological parameters statistically from GW observations.

❖

Use LISA observations of EMRIs to measure the Hubble constant (McLeod & Hogan 08)

• Let every galaxy in the LISA error box “vote” on the Hubble constant.

Science: cosmography

SLIDE 74

❖

Even without a counterpart, can estimate cosmological parameters statistically from GW observations.

❖

Use LISA observations of EMRIs to measure the Hubble constant (McLeod & Hogan 08)

• Let every galaxy in the LISA error box “vote” on the Hubble constant.

Science: cosmography

McLeod & Hogan (2008)

SLIDE 75

❖

Even without a counterpart, can estimate cosmological parameters statistically from GW observations.

❖

Use LISA observations of EMRIs to measure the Hubble constant (McLeod & Hogan 08)

• Let every galaxy in the LISA error box “vote” on the Hubble constant.

Science: cosmography

McLeod & Hogan (2008)

SLIDE 76

❖

Even without a counterpart, can estimate cosmological parameters statistically from GW observations.

❖

Use LISA observations of EMRIs to measure the Hubble constant (McLeod & Hogan 08)

• Let every galaxy in the LISA error box “vote” on the Hubble constant.
• If ~20 EMRI events are detected at z < 0.5, classic LISA would determine

the Hubble constant to ~1%. Probably ~2% with 20 events and new baseline.

• LISA expected to observe a few tens of EMRIs per year, all at z<0.5.

❖

Same analysis for SMBH mergers suggests classic LISA (5Gm, 6-link) could improve constraints on equation of state of dark energy by a factor of ~2-8 (Babak et al. 2011). May not be possible with shorter configurations.

Science: cosmography

SLIDE 77

Future H0 measurements: LISA

0.01 0.1 1 10 0.1 1 10 100 z dL HGpcL Example of possible LISA cosmological data

MBHBs EMRIs

LCDM

Stellar mass BHBs

Tamanini (2017)

SLIDE 78

❖

Posteriors (best case)

Future H0 measurements: LISA

Figure credit: Nicola Tamanini

SLIDE 79

❖

Posteriors (typical case)

Future H0 measurements: LISA

Figure credit: Nicola Tamanini

SLIDE 80

Fundamental physics with PTA

• bservations

SLIDE 81

Gravitational wave backgrounds

❖

Primary source for PTAs is the astrophysical background of gravitational waves generated by supermassive black hole mergers.

❖

Natural to ask what (gravitational) information is encoded in such a background.

❖

GW background is a transverse- traceless tensor on the sky

❖

Analogous to polarisation of the cosmic microwave background.

hTT

ab =

✓ h+ h× h× −h+ ◆

SLIDE 82

PTA response

❖

PTAs measure redshifts in pulsars

❖

is the difference in the metric perturbation between the Earth and the pulsar and can be written

❖

There are 2 polarisation states in GR

❖

4 additional states can exist in metric theories z(t, ˆ k) ≡ ∆v(t) ν0 = 1 2 ˆ uaˆ ub 1 + ˆ k · ˆ u ∆hab(t, ˆ k)

e+

ij =

  1 −1   e×

ij =

  1 1  

eB

ij =

  1 1   eL

ij =

  1   eX

ij =

  1 1   eY

ij =

  1 1  

∆hab

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∆hab = X ∆hAeA

ab

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SLIDE 83

PTA response

❖ The redshift induced by a GW background can be written as ❖ where the response functions for individual modes are given by ❖ Writing and working in the frame of the pulsar we

find . The total response takes the form

z(t) = Z ∞

−∞

df Z

S2 d2Ωˆ k

1 2 ˆ uaˆ ub 1 + ˆ k · ˆ u hab(f, ˆ k) h 1 − e−i2⇡fL(1+ˆ

k·ˆ u)/ci

ei2⇡f(t−ˆ

k·~ x/c)

= Z ∞

−∞

df X

(lm)

X

P

RP

(lm)(f)aP (lm)(f)ei2⇡ft

RP

(lm)(f) =

Z

S2 d2Ωˆ k

1 2 ˆ uaˆ ub 1 + ˆ k · ˆ u Y P

(lm)ab(ˆ

k)e−i2⇡fˆ

k·~ x/c h

1 − e−i2⇡fL(1+ˆ

k·ˆ u)/ci

y ≡ 2πfL/c

RP

I(lm)(f) = Ylm(ˆ

uI)RP

l (yI)

RI(f) = X

lm

⇣ aB

(lm)(f)RB l (yI) + aL (lm)(f)RL l (yI)

+aVG

(lm)(f)RVG l

(yI) + aG

(lm)(f)RG l (yI)

⌘ Ylm(ˆ uI)

SLIDE 84

PTA response to tensor modes

SLIDE 85

PTA response to breathing modes

SLIDE 86

PTA response to vector modes

SLIDE 87

PTA response to scalar-longitudinal modes

SLIDE 88

PTA background mapping

❖ If we have pulsars all over the sky, can decompose “pulsar response” map

into spherical harmonic basis. Coefficients are linear combinations of different polarisations.

❖ No confusion between B and G modes due to range of l. Confusion with

VG and L possible unless have pulsars at several distances. But - can only measure Np modes, i.e., equal to number of pulsars.

(l, m) mode (0, 0) (1, −1) (1, 0) (1, 1) (2, −2) (2, −1) (2, 0) (2, 1) (2, 2) G: transverse-tensor (gradient) − − − − 0.44 0.38 0.32 0.38 0.44 G: transverse-tensor (gradient) − − − − 0.49 0.39 0.37 0.39 0.49 B: scalar-transverse (breathing) 0.16 0.53 0.46 0.53 − − − − − G: transverse-tensor (gradient) − − − − 16.2 10.5 11.4 10.5 16.2 B: scalar-transverse (breathing) 4.36 16.1 14.1 16.1 − − − − − L: scalar-longitudinal 0.71 0.96 0.84 0.96 1.21 0.78 0.86 0.78 1.21 G: transverse-tensor (gradient) − − − − 1.4e5 5.4e4 8.0e4 5.4e4 1.4e5 B: scalar-transverse (breathing) 18.4 9.4e4 6.2e4 9.4e4 − − − − − L: scalar-longitudinal 3.08 11.5 8.68 11.5 20.9 7.51 11.9 7.52 20.9 VG: vector-longitudinal (gradient) − 6.6e4 4.4e4 6.6e4 7.0e4 2.7e4 4.0e4 2.7e4 7.0e4

SLIDE 89

Implications

• Individual modes of the background represent GW emission that is

correlated between different points on the sky.

• No well-established physical mechanism to create such correlations -

discovery of a correlated background would be a profound result.

• Mild anisotropy expected in power of GW background - could be

consistent with either uncorrelated or correlated background.

hh+(f, ˆ k) h⇤

+(f 0, ˆ

k0)ik = 1 2

1

X

l=2

2l + 1 4π (Nl)2 ⇥ CGG

l

(f)G+

l2(cos θ) + CCC l

(f)G

l2(cos θ)

⇤ δ(f f 0)

SLIDE 90

PTA background measurements

• Polarization of background can distinguish correlated and

uncorrelated origin. Correlated Uncorrelated

2 4 6 8 10 12 14 16 18 20 22 2 4 6 8 10 12 14 16 18 20 22

SLIDE 91

Overlap reduction function: PTAs

• 0.4
• 0.2

0.2 0.4 0.6 0.5 1 1.5 2 2.5 3 Correlation Pulsar separation Isotropic background Expansion to lmax=2 Expansion to lmax=3 Expansion to lmax=4

Scalar longitudinal Scalar transverse Tensor transverse Vector longitudinal

❖ If we assume background is isotropic there are fewer parameters to fit.

SLIDE 92

Overlap reduction function: astrometry

π/2 π −1.0 −0.5 0.5 1.0 angular separation Θ tensorial correlation P(Θ) = Γ+

zθ

T (Θ) = Γ+,×

xθ

= Γ+,×

yφ

hellings-downs curve H(Θ) π/2 π −1.0 −0.5 0.5 1.0 angular separation Θ scalar correlation ΓS

xθ(Θ)

ΓS

yφ(Θ)

redshift correlation π/2 π −1.0 −0.5 0.5 1.0 angular separation Θ vectorial correlation Γ

X,Y

xθ

= Γ

X,Y

yφ

redshift correlation (analytic) redshift correlation (numerical) π/2 π −1.0 −0.5 0.5 1.0 redshift correlation angular separation Θ longitudinal correlation ΓL

xθ(Θ)

Lxθ(Θ) ΓL

yφ(Θ)

Lyφ(Θ)

Mihaylov, JG et al. 2018

❖ Astrometric measurements (Gaia) help break degeneracies.

SLIDE 93

Massive Gravitons

❖

Setting

❖

in the pulsar response

❖

corresponds to a change in propagation speed for the graviton. This modifies the correlation between pairs of pulsars on the sky and is therefore in principle detectable. z(t, ˆ k) ≡ ∆v(t) ν0 = 1 2 ˆ uaˆ ub 1 + ˆ k · ˆ u ∆hab(t, ˆ k)

kµ = !

• 1, (1 ✏) q

SLIDE 94

Massive Gravitons

❖

Setting

❖

in the pulsar response

❖

corresponds to a change in propagation speed for the graviton. This modifies the correlation between pairs of pulsars on the sky and is therefore in principle detectable. z(t, ˆ k) ≡ ∆v(t) ν0 = 1 2 ˆ uaˆ ub 1 + ˆ k · ˆ u ∆hab(t, ˆ k)

kµ = !

• 1, (1 ✏) q
• −1.0

−0.5 0.5 1.0 ⇡/2 ⇡ 0 −1.0 −0.5 0.5 1.0 ⇡/2 ⇡ pta-pta correlations, ✏ > 0 Γ+,×

zz (Θ, 0)

Γ+,×

zz (Θ, 0.1)

Γ+,×

zz (Θ, 0.2)

Γ+,×

zz (Θ, 0.5)

ΓS

zz(Θ, 0)

ΓS

zz(Θ, 0.1)

ΓS

zz(Θ, 0.2)

ΓS

zz(Θ, 0.5)

ΓX,Y

zz (Θ, 0)

ΓX,Y

zz (Θ, 0.1)

ΓX,Y

zz (Θ, 0.2)

ΓX,Y

zz (Θ, 0.5)

ΓL

zz(Θ, 0)

ΓL

zz(Θ, 0.1)

ΓL

zz(Θ, 0.2)

ΓL

zz(Θ, 0.5)

Mihaylov, JG et al. (2019)

SLIDE 95

Summary

❖

LISA will launch in the early 2030s and will open a new window on the gravitational wave Universe, at mHz frequencies.

❖

LISA is expected to observe GWs from massive BH mergers, extreme-mass- ratio inspirals and (perhaps) cosmological stochastic backgrounds.

❖

LISA observations have massive potential for gravitational physics, including tests of the no-hair property of BHs, tests of GW propagation and polarisation, constraining dark matter candidates and constraining a variety

• f modified theories of gravity.

❖

Pulsar timing arrays are expected to make the first observations of the nHz GW background in the next 5-10 years.

❖

PTAs can in principle detect polarisation properties of the stochastic GW background which would be indicative of new physics.