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.

3

horizon sta3c limit ergosphere SpaceEme described by the Kerr metric.

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.

4

At the source Locally

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

• Remarkably good approximaEon for the strain

from a black hole merger (actually ~10-21).

5

h ~ 105 m /1025 m = 10-20

Laser Interferometer Gravita3onal-wave Observatory

6

freely falling mirrors

f > 10 Hz

LIGO

7

4 km arms Uluru (for scale) Control StaEon

The LIGO Hanford Observatory

LIGO

8

4 km arms Uluru (for scale) Control StaEon

The LIGO Hanford Observatory

Worldwide network: Now with three advanced detectors!

9

LIGO India LHO LLO GEO Virgo KAGRA

Advanced LIGO noise budget

10

Adhikari, Rev. Mod. Phys. 86 (2014)

O1/O2 sensi3vity

GW150914

11

PhysRevLee.116.061102

Inspiral, merger, ringdown

12

strong field, high velocity PhysRevLee.116.061102

13

T

“the second Monday event” “Boxing Day” GW150914 GW170104

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

• Use black hole spin to esEmate the fracEon of

mergers in the field versus in globular clusters.

15

field: preferenEally aligned spins dynamic: isotropic

• rientaEon

Colm Talbot

PhysRevD.96.023012

Spin changes the waveform morphology.

• Spin parameterised by (the cosine of the)

black hole Elt angles z=cos(θ).

• Aligned spins (z1≈z2≈1) spend relaEvely longer

in band while anE-aligned spins (z1≈z2≈-1) spend relaEvely less Eme in band.

16

z1 z2

PhysRevD.96.023012

ˆ a1 ˆ a2

EsEmaEng Elts in fineen dimensions

• Black hole Elts are esEmated using Bayesian

inference along with 13 other astrophysical parameters, e.g., m1, m2, …

• Hard to calculate.
• LIGO uElises large clusters and employs

techniques like reduced order modelling (ROM) to compute posteriors.

17

p( ! θ | h) = L(h | ! θ )p( ! θ ) L(h | ! θ )p(θ)d ! θ

∫

PhysRevD.96.023012

prior posterior likelihood

Example PE with simulated data

• In this example, the LIGO MulENest sampler

guesses values of z1 = cos(θ1) for a simulated black merger unEl we derive a reliable posterior distribuEon for z1.

18

z1 = cos(θ1) z1 = cos(θ1) iteraEon posterior for z1 true value true value PhysRevD.96.023012 posterior samples

Hierarchical modelling

• Define “hyper-parameters” that describe

populaEon properEes with condiEonal priors.

19

p(z1|ξ,σ1) typical spin misalignment fracEon of BBH merging dynamically PhysRevD.96.023012

Posteriors for populaEon hyper- parameters

• We derive posteriors on populaEon hyper-

parameters (σ1, σ2, ξ) using (z1, z2) posterior samples from LIGO parameter esEmaEon.

20

condi3onal prior sum over posteriors samples product over N detec3ons posterior

PhysRevD.96.023012

Posteriors for populaEon hyper- parameters

• We derive posteriors on populaEon hyper-

parameters (σ1, σ2, ξ) using (z1, z2) posterior samples from LIGO parameter esEmaEon.

21

condi3onal prior sum over posteriors samples product over N detec3ons posterior

PhysRevD.96.023012

p(zα1, zα 2 | 0)

ini3al prior

Results with simulated data

• LIGO measurements can be used to determine

the populaEon properEes of BBH aner tens of events like GW150914.

22

PhysRevD.96.023012

σ1 σ2 ξ

dark, medium, light = 1σ, 2σ, 3σ confidence dashed line: true value See also:

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.

23

PhysRevLeU.117.061102

Lasky 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

• peraEng at design sensiEvity…

24

PhysRevLeU.117.061102

Merger memory

25

band-passed signal memory only full signal

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
• scillatory 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

• scillatory signal unchanged.

27

h22(ψ, φc) = h22(ψ+π/2, φc +π/2) hmem(ψ, φc) = -hmem(ψ+π/2, φc +π/2)

22 degeneracy:

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.

29

PhysRevLeU.117.061102 (like GW150914)

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.

30

arxiv/1706.05152

Lasky 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 tcut?

31

perturba3ve descrip3on numerical rela3vity

tcut

arxiv/1706.05152

Bias

• Otherwise, biased confidence intervals:
• The variable tcut should depend on loudness.

32

tcut = 6.5 ms bias

not-so-loud medium loud very loud true

arxiv/1706.05152

Choosing tcut with GR+ formalism

• SoluEon: choose tcut so that the t>tcut

numerical relaEvity waveform is indisEnguishable from an exponenEally damped sine.

• Detector-dependent

33

residuals perturba3ve numerical rela3vity matched filter SNR tcut

arxiv/1706.05152

NR waveform: G. Lovelace et al., CQG 33 244002 (2016)

Scaling

• Surprising finding: confidence intervals do not

shrink monotonically with loudness.

34

arxiv/1706.05152

NR waveform: G. Lovelace et al., CQG 33 244002 (2016)

NR vs PT

35

by-eye deviaEons from perturbaEon theory

22 33

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

39

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