A"er GW150914: gravita3onal- wave astronomy in the era of - PowerPoint PPT Presentation

A"er GW150914: gravita3onal- wave astronomy in the era of rou3ne detec3on Eric Thrane (Monash University) University of Melbourne Colloquium August 30, 2017

Outline • GravitaEonal waves and LIGO • Binary black holes observed to date • Astrophysics with binary black holes 1. ObservaEonally-driven analysis of binary black hole formaEon channels 2. Measurements of gravitaEonal-wave memory 3. Tests of the no-hair theorem 2

Black holes • Predicted by general relaEvity. • One of the simplest objects in the Universe. • The no-hair theorem states black holes are characterised by just their mass and spin. horizon SpaceEme sta3c limit described by the Kerr metric. 3 ergosphere

GravitaEonal waves • Changes in (quadrupole moment of) the stress- energy tensor create ripples in spacetime, e.g., from merging black holes. • These ripples travel at the speed of light, carrying energy and angular momentum. At the source Locally 4

Dimensional analysis • Schwarzschild radius for a ~30 M ¤ black hole: 90 km. • If two black holes merge 1.3 Gly away, the raEos of length scales is h ~ 10 5 m /10 25 m = 10 -20 • Remarkably good approximaEon for the strain from a black hole merger (actually ~10 -21 ). 5

Laser Interferometer Gravita3onal-wave Observatory freely falling mirrors f > 10 Hz 6

LIGO The LIGO Hanford Observatory Uluru (for scale) 4 km arms Control StaEon 7

LIGO The LIGO Hanford Observatory Uluru (for scale) 4 km arms Control StaEon 8

Worldwide network: Now with three advanced detectors! GEO LHO Virgo KAGRA LLO LIGO India 9

Advanced LIGO noise budget O1/O2 sensi3vity 10 Adhikari, Rev. Mod. Phys. 86 (2014)

GW150914 11 PhysRevLee.116.061102

Inspiral, merger, ringdown strong field, high velocity 12 PhysRevLee.116.061102

T GW170104 GW150914 “the second Monday event” “Boxing Day” 13 credit: hep://www.ligo.org/

The era of rouEne detecEon • LIGO has announced the detecEon of 3.5 binary black holes. • At design sensiEvity, the strain sensiEvity will improve by a factor of ~3 compared to previously published results → a few detecEons every week. • What are the pressing astrophysical quesEons we can answer with GW astronomy? 14

How do these binary black holes form? (QuesEon 1) • Two leading hypotheses: – Field model – Dynamic model Colm Talbot • Use black hole spin to esEmate the fracEon of mergers in the field versus in globular clusters. field: preferenEally dynamic: isotropic aligned spins orientaEon 15 PhysRevD.96.023012

Spin changes the waveform morphology. • Spin parameterised by (the cosine of the) black hole Elt angles z=cos( θ ). ˆ a 2 z 2 ˆ a 1 z 1 • Aligned spins (z 1 ≈z 2 ≈1) spend relaEvely longer in band while anE-aligned spins (z 1 ≈z 2 ≈-1) spend relaEvely less Eme in band. 16 PhysRevD.96.023012

EsEmaEng Elts in fineen dimensions • Black hole Elts are esEmated using Bayesian inference along with 13 other astrophysical parameters, e.g., m 1 , m 2 , … ! ! ! L ( h | θ ) p ( θ ) ! ! p ( θ | h ) = posterior prior ∫ L ( h | θ ) p ( θ ) d θ likelihood • Hard to calculate. • LIGO uElises large clusters and employs techniques like reduced order modelling (ROM) to compute posteriors. 17 PhysRevD.96.023012

Example PE with simulated data • In this example, the LIGO MulENest sampler guesses values of z 1 = cos( θ 1 ) for a simulated black merger unEl we derive a reliable posterior distribuEon for z 1 . true value true value posterior for z 1 z 1 = cos( θ 1 ) posterior samples z 1 = cos( θ 1 ) iteraEon 18 PhysRevD.96.023012

Hierarchical modelling • Define “hyper-parameters” that describe populaEon properEes with condiEonal priors. p(z 1 | ξ , σ 1 ) typical spin misalignment fracEon of BBH merging dynamically 19 PhysRevD.96.023012

Posteriors for populaEon hyper- parameters • We derive posteriors on populaEon hyper- parameters ( σ 1 , σ 2 , ξ ) using (z 1 , z 2 ) posterior samples from LIGO parameter esEmaEon. condi3onal prior posterior product over N detec3ons sum over posteriors samples 20 PhysRevD.96.023012

Posteriors for populaEon hyper- parameters • We derive posteriors on populaEon hyper- parameters ( σ 1 , σ 2 , ξ ) using (z 1 , z 2 ) posterior samples from LIGO parameter esEmaEon. condi3onal prior posterior p ( z α 1 , z α 2 | 0) ini3al prior product over N detec3ons sum over posteriors samples 21 PhysRevD.96.023012

Results with simulated data • LIGO measurements can be used to determine the populaEon properEes of BBH aner tens of events like GW150914. σ 1 σ 2 ξ dark, medium, light = 1 σ , 2 σ , 3 σ confidence dashed line: true value 22 See also: PhysRevD.96.023012

Can LIGO detect memory? (QuesEon 2) • The Christodoulou effect • A permanent relaEve distorEon of spaceEme • Associated with anisotropic gravitaEonal-wave emission. • A fundamental, nonlinear general relaEvisEc effect that has never been observed: – DetecEng memory will be like detecEng frame dragging, Eme dilaEon, etc. Lasky + 23 PhysRevLeU.117.061102 Levin Blackman, Chen

The challenge • Memory is a small correcEon to the oscillatory part of the waveform. • The memory from an event like GW150194 will be small: SNR=0.4 with two detectors operaEng at design sensiEvity… 24 PhysRevLeU.117.061102

Merger memory full signal band-passed signal memory only 25 PhysRevLeU.117.061102

SoluEon • The soluEon is to coherently combine data from many detecEons. • Imagine stacking a large number of weak step funcEons. Eventually, the signal will emerge from the noise. • ComplicaEon: how do we know the sign of the memory? + + + 26 PhysRevLeU.117.061102

No informaEon in the 22 mode • The leading order (lm=22) part of the oscillatory waveform does not give us any informaEon about the sign of the memory. • The geometric operaEon that flips the sign of the memory leaves the lm=22 part of the oscillatory signal unchanged. 22 degeneracy: h 22 (ψ, φ c ) = h 22 (ψ+π/2, φ c +π/2) h mem (ψ, φ c ) = -h mem (ψ+π/2, φ c +π/2) 27 PhysRevLeU.117.061102

The lm=33 mode encodes the sign of the memory. 28 PhysRevLeU.117.061102

Ensemble memory • LIGO may be able to detect memory from an ensemble of binary black holes. (like GW150914) 29 PhysRevLeU.117.061102

Can LIGO test the no-hair theorem? (QuesEon 3) • Linear perturbaEon theory: black holes ring down according to exponenEally damped sines. • Different spheroidal modes: lm=22, 33, … • The frequency and damping Eme of each mode is determined enErely by the mass and spin of the black hole. Lasky 30 arxiv/1706.05152 Levin

When does a merger waveform become linear? • Clearly, the linear approximaEon breaks down at early Emes. • How long should we wait aner merger to test the no-hair theorem: what value of t cut ? t cut perturba3ve descrip3on numerical rela3vity 31 arxiv/1706.05152

Bias • Otherwise, biased confidence intervals: medium loud very loud bias true not-so-loud t cut = 6.5 ms • The variable t cut should depend on loudness. 32 arxiv/1706.05152

Choosing t cut with GR+ formalism • SoluEon: choose t cut so that the t>t cut numerical relaEvity waveform is indisEnguishable from an exponenEally damped sine. perturba3ve numerical rela3vity residuals t cut matched filter SNR • Detector-dependent 33 NR waveform: G. Lovelace et al., CQG 33 244002 (2016) arxiv/1706.05152

Scaling • Surprising finding: confidence intervals do not shrink monotonically with loudness. 34 NR waveform: G. Lovelace et al., CQG 33 244002 (2016) arxiv/1706.05152

NR vs PT by-eye deviaEons from perturbaEon theory 22 33 35 arxiv/1706.05152

Possible explanaEons • Mode-mixing from uncorrected centre-of- mass moEon: OK. • Mismatch from spin-weighted spherical versus spheroidal harmonics: OK. • Memory and late-Eme tails. – Seem too small and the Eme scales don’t match. • Back-reacEon from ringdown: our model did not improve the fit. • Other numerical relaEvity artefact: possible. 36 arxiv/1706.05152

ImplicaEons • We introduce a formalism to rigorously test the no-hair theorem in the domain in which it applies. • By demanding that the remnant black hole seeles into a perturbaEve state, we are unable to measure ringdown parameters beyond some fixed precision. • ConEnued invesEgaEon required. 37 arxiv/1706.05152

Conclusions • Before long, gravitaEonal-wave detecEon will be rouEne, and this will enable new and exciEng science. – Where do binary black holes form? • We’ll find out aner tens of events like GW150914. – Can LIGO measure memory? • Probably. – Can LIGO test the no-hair theorem? • Probably, but there may be some subtleEes. 38

Gravity Xingjiang Zhu Colm Talbot Rory Smith Sylvia Biscoveanu Boris Goncharov Kendall Ackley Grant Meadors Paul Lasky, Yuri Levin, Chris Whiele, Duncan Galloway, LeEzia Sammut, Eric Thrane 39