CBC gravitational wave data analysisthe way it is done by the and

Frédérique MARION

GW Detectors

Compact binary coa lescences

2

CBCDetection & Science

Multi-messenger as tronomy

Waveforms

Source popula tion

Analys is techniques

Search s tra tegies

3

Outline

What, why, how? » A reminder of what we are looking for

– Sources– Waveforms

» The bas ic search technique– Matched filte ring

How, in rea l life» Exploring the parameter space» Dealing with background

– Multi-de tector ana lys is– Background es timation– Vetoes– Detection s ta tis tics

Tying it a ll toge ther» A typica l search pipe line» A brie f review of LIGO-Virgo CBC searches

4

Chapter 1What, why, how?

Evolution of ground-based GW detectors

5

1s t genera tion inte rfe rometric de tectors» Initia l LIGO, Virgo, GEO600

Enhanced LIGO, Virgo+

2nd genera tion de tectors Advanced LIGO, Advanced Virgo,

GEO-HF, LCGT

3rd genera tion de tectors Eins te in Telescope , US counterpart to ET

Unlike ly de tection

Science da ta taking Firs t ra te upper limits Se t up ne twork observa tion

Improved sens itivity

Like ly de tection

Routine observa tion GW as tronomy

Lay ground for multi-messenger as tronomy

Thorough observa tion of Universe with GW

6

The ta rge t sources

Fina l evolution s tage of compact binary sys tems» Sys tems like PSR1913+16 reaching coa lescence of the two s ta rs

Sys tem may involve» Neutron s ta rs (NS)» Black holes (BH)

– For ground based de tectors , s te lla r mass black holes– Advanced de tectors : up to inte rmedia te mass black holes– Super-mass ive BH: lower frequency, space based de tectors , pulsa r timing

Orbit decays by radiating energy as Gravitational Waves

Chirp ends at frequency inversely proportional to total mass

Strain versus time: chirp

What makes CBC promising sources? We know “a lot” about the sources

» Such sys tems do exis t– Although ra tes a re uncerta in and low…

» The emitted waveform is known with some accuracy

Genera l Rela tivity» Tes t theory in s trong fie ld» Tes t/cons tra in a lte rna tive gravity theories

Astrophys ics» Measure merger ra tes

– As a function of parameters» Inform source dis tribution» Study effect of matte r in BNS/NSBH waveform» Short, hard GRBs

– Confirm or rule out merger progenitor

Cosmology» CBC inspira ls as s tandard s irens

– Independent measurement of Hubble cons tant7

Many of these require combining information from gravita tiona l wave , e lectromagnetic and/or particle observa tions Multi-messenger as tronomy

[Ref.1]

Source population: rates Uncerta in, even for mos t confident predictions BNS

» Extrapola tions from observed Galactic binary pulsars– Small sample , few parameters

» From popula tion-synthes is models– Observa tiona l and theore tica l cons tra ints on parameters

NS-BH and BBH» From popula tion-synthes is models

– Many open ques tions for BBH» Extrapola tion from extra -Galactic X-ray binaries

– IC10 X-1 and NGC300 X-1– Formed by a 20-30 black hole and a mass ive Wolf-Raye t s ta r – Should evolve into a binary black hole with Mchirp~15 M

Still an open point whether BNS or BBH domina te

8GW ra te upper limits and measurements like ly to be key

input to further cons tra in parameters

Expected number of detected events

9

Source popula tion: expected event ra tes (I)

Astrophys ica l ra teNumber of observable ga laxies

Search dura tion

Per ga laxy orper unit volume

Volume probed Depends on de tector sens itivity

» Horizon dis tance : dis tance a t which an optimally loca ted and oriented source would produce an s ignal to noise ra tio of 8

» Relies on the ability of the ana lys is to extract s igna l from noise a t tha t threshold

[Ref. 2]

Source population: expected event rates (II)

10

Rea lis tic ra tes do ge t subs tantia l for advanced de tectors

[Ref. 3]

Source population: parameters

MassesWhat is the component mass dis tribution in BBH sys tems ? Especia lly, how large ?

– ~ 20 M in sys tems from isola ted binary evolution– ~ 30 M in sys tems from dynamica l formation in dense s te lla r environments

Intermedia te mass black holes ?

Spin Small for neutron s ta rs Not well cons tra ined for black holes , can be high

Dis tribution Mergers may occur away from hos t ga laxies in case of high kicks

11

Inspiral» The rea lm of pos t-Newtonian expans ions» Accura te ana lytica l computa tions , under

assumption of adiaba tic evolution of quas i-circular orbit

» Valid up to innermost s table circular orbit

»

Plunge/Merger » The rea lm of numerica l re la tivity» Dura tion << 1 s

Ringdown» The rea lm of black hole perturba tion theory» Relaxation of perturbed fina l black hole» Dura tion << 1 s 12

Phases of the evolution

Inspiral (I) PN approximants a re found under various ava ta rs

» Choice of parameter used in PN expans ion / method used to solve diffe rentia l equations different families of waveforms

» Time domain or frequency domain– Frequency domain uses the s ta tionary phase approximation

13

Known up to order PN2.5 for the amplitude and order PN3.5 for the phase» Current searches use restricted waveforms

‒ Amplitude kept at Newtonian order– Good enough for detection, at least for initial detectors– May cost some accuracy in parameter estimation, especially for high mass systems

» Spin effects appear from order PN1.5 (spin-orbit) and PN2 (spin-spin)– Expected to be negligible for NS, may be significant for BH– Spins not aligned with orbital momentum cause orbital plane to precess, leading to

more complex waveforms

[Ref. 4]

[Ref. 5]

Inspiral (II)

14

From A.Buonanno

High order te rms matte r more for

higher mass sys tems

Number of useful cycles takes de tector sens itivity

into account

Inspiral (III)

15

Design sensitivity of initial Virgo

Inspiral Signal from a 1.4/1.4 M system m1 / m2 fISCO

1.4 /1.4 M 1600 Hz

12.5/12.5 M 180 Hz

Low mass sys tems» Inspira l ends out of the

de tector bandwidth» What happens a fte r inspira l

can safe ly be ignored

High mass sys tems» Inspira l ends within the de tector bandwidth» Merger and ringdown carry s ignificant s ignal to noise ra tio and

mus t be taken into account

Plunge/Merger

Boring for BBH» But a grea t success of numerica l re la tivity!» Smooth trans ition from inspira l to ringdown

Rich waveform for BNS and NS-BH» Not essentia l for de tection» Observa tion with advanced de tectors (poss ibly

in narrow-band configura tion) may a llow to cons tra in NS equation of s ta te

16

Small compactness(stiff EOS)

Large compactness(soft EOS)

Moderatecompactness/stiffnessBNS (from J.Read)

NS-BH (from K.Kiuchi)

Ringdown

Perturbed black hole re laxes to fina l equilibrium s ta te by emitting gravita tiona l waves» Superpos ition of quas inormal modes , dominated

by fundamenta l mode, l = m = 2, n = 0» Frequency and quality factor depend on mass

and spin of fina l black hole

17

» Amplitude depends on ,and fraction of fina l black hole mass radia ted as GW

» scales with

symmetric mass ra tiofor equal mass sys tems

Significance of inspira l, merger, ringdown signa ls for LIGO/Virgo, depending on sys tem mass

We need analytical waveforms» Computa tional cos t of numerica l s imula tions to genera te long and accura te

waveforms over full parameter space is prohibitive» Truly analytica l or obta ined solving ordinary diffe rentia l equations

Inspira l-Merger-Ringdown (I)

18

From A.Buonanno

Inspiral-Merger-Ringdown (II) Effective one body approach

» Uses PN theory and NR computa tions» Plunge is smooth continuation of adiaba tic inspira l» Very short trans ition from merger to ringdown» Model parameters tuned to NR s imula tions of non-

spinning binaries with mass ra tios 1:1 – 4:1

Phenomenologica l IMR waveforms» Hybrid waveforms obta ined matching PN and NR

waveforms» Approximated with ana lytica l, phenomenologica l

waveforms in frequency domain

19

[Ref. 6]

[Ref. 7]

20

The s igna l (I)Signal sensed by de tector is a combination of two polariza tions

21

The s igna l (II)

» h(t) is a linear combination of harmonics of the orbita l phase– k runs over harmonics , m/2 is PN order in amplitude

» Res tricted waveforms: a ll te rms with k ≠ 2 are neglected– other harmonics of the orbita l frequency a re ignored

[Ref.21]

ϕ(t)

22

The s igna l (III)

(dis tance of an optimally loca ted and oriented source tha t would produce the same s ignal s trength)

At Newtonian order:

The res tricted waveform a t the de tector can be written:

20Hz

1.4/1.4 M

Inspiral signal length

23

Time-frequency spectrogram

Simulated inspiralsignal injected in

detector noise

f0m1 / m2

10 Hz 30 Hz 50 Hz

1.4 /1.4 M 984s 52.5s 13.5s

3.0 /3.0 M 277s 14.8s 3.8s

10.0 /10.0 M 37.2s 2.0s 0.5s

19.0/1.0 M 196s 10.5s 2.7s

Higher mass sys tems give shorte r s igna ls

Length increases if de tector bandwidth s ta rts a t lower frequency

At a given tota l mass , asymmetric sys tems

give longer s igna ls than equa l mass sys tems

24

Matched filte ring (I)

» Cons truct a filte red s ignal

» S can also be written in the frequency domain

» If the detector output is noise + some signal

» The expectation value of the signal S is

calibrated detector output filter chosen to optimize the signal to noise ratio (SNR)

25

Matched filte ring (II)» The noise is defined as :

where is the one-s ided noise power spectrum of the de tector:

» We can define an inner product

and rewrite

» What is the optimal filte r Q maximizinguse property

26

Matched filte ring (III)

» We choose

» Signal S for arrival time offset t0 is given by

S can be easily obtained for all arrival times t0 by means of an FFT» The optimal signal to noise ratio is:

Fourier transform of S

S distribution for noiseS distribution for signal with α = 5

Now tha t we know the optimal filte r, we can redefine the inner product inthe more usua l way:

Matched filtering & likelihood (I)

27

Res idua l (da ta – s igna l) is dis tributed as noise

Data is dis tributed as noise

Like lihood ra tio

The noise model defines the likelihood function

Matched filtering & likelihood (II) Why is the noise dis tribution expressed in te rms of the

sca la r product defined earlie r?» Single da ta point, Gauss ian noise» Uncorre la ted noise da ta points

» Corre la ted noise

» Noise corre la tion matrix» For s ta tionary noise , depends only on» Autocorre la tion» Continuous vers ion

» is the Fourier transform of» In the frequency domain

28

Least squares fitting of model to data

Uncorrelated noise

29

Chapter 2How, in real life

30

Matched filte ring in practice (I)

The FFT a llows to extract S for a ll poss ible a rriva l times» Easy to maximize SNR over t0

⊗ /

Signal To Noise Ratio

threshold

Calibrated detector output Template Noise Power Spectrum

[Ref.10]

31

Matched filte ring in practice (II)

The phase of the chirp s igna l is unknown

» The SNR has to be maximized over a ll poss ible va lues of Φ

cos ine and s ine phases of the waveform

32

Matched filte ring is optimal

If the noise is Gauss ian, the matched filte ring provides the optimal s ta tis tic» Selecting events by se tting a threshold on the SNR ρ > ρ*

guarantees the lowes t fa lse a la rm probability for a given de tection probability

ρ* ρ*

Detection probability for s ignal with SNR ρS

False a la rm probability

Matched filtering requires waveform knowledge Waveform depends on parameters

» As many as 17 parameters for generic waveform» 15 if circular orbit assumed (no eccentricity)» 9 if components assumed non-spinning

Parameters for non-spinning sys tem on circula r orbit» Component masses » Sky loca tion of source » Dis tance to source » Orienta tion of binary sys tem

– inclina tion , pola riza tion , coa lescence phase» Coalescence time

In the s imples t case , we need to explore the 2-dimens iona l mass space

Waveforms parameter space

33

Intrins ic parametersDrive sys tem dynamics

Extrins ic parametersCan be maximized

over ana lytica lly

34

Scanning the parameter space (I)

Scanning the parameter space (II)

35

Map of match a round point in

parameter space

Define minimal match

acceptable SNR loss isomatch contour

36

Scanning the parameter space (III)

» From the match, define a metric on the parameter space

» In the regime 1-M << 1 the match can be approximated by

» Ins tead of the masses m1, m2, it is more convenient to use as parameters :

» For matches above ~95%, isomatchcontours a re e llipses

» In the τ0, τ1 space , the metric components gij a re cons tant a t 1PN order, and have small varia tions a t higher order.

[Ref.8]

37

Scanning the parameter space (III)» Each isomatch contour defines a region of the parameter space which overlaps

with the templa te in the center with a match be tte r than some va lue M» The templa te in the center can be used to search for s ignals in tha t region of the

parameter space , a t the price of a controlled loss of SNR (< 1 – M )» Templa tes should be placed over the parameter space in order to

– Achieve coverage of space (no holes )– Preserve computa tiona l e fficiency: keep number of templa tes as low as poss ibleTake into account varia tions of e llipse s ize and orienta tion across the parameter space

[Ref.9]Example of coverage

Template bank example

38

CBC Low Mass search, Mtot∈ [2 ; 35M]Coming back to m1, m2 variables

2PN 1.4/1.4M

17.5/17.5M

τ0 ≈ 14s (~1100 cycles)

τ0 ≈ 0.17 s (~14 cycles)

High mass templa tes a re short and conta in few cycles

It is eas ie r to match diffe rent templa tes in the high mass region

flow = 50 Hz

» Reques t 0.97 minimum match» Low Mass region is more

dense ly popula ted than high mass region

– Rela ted to dura tion and number of cycles of the templa tes

Template banks in practice (I)

39

Examples of template bank size (a week in S6/VSR2)Low Mass [2; 35 M] High Mass [25; 100 M]

7 days 7 days» Template bank size varies between 1,000 and 12,000 templates depending on

type of search and detector

Template banks in practice (II)

40

Examples of template bank size (a week in S6/VSR2)Low Mass [2; 35 M]

7 days

» Template bank size varies between 1,000 and 12,000 templates depending on type of search and detector

» Differences between detectors different shapes of noise power spectrum

Template banks in practice (III)

» Template bank size varies between 1,000 and 12,000 templates depending on type of search and detector

» Differences between detectors different shapes of noise power spectrum» Fluctuations in time non-stationary detector noise

41

Examples of template bank size (a week in S6/VSR2)Low Mass [2; 35 M]

7 days

Estimate power spectrum from the median of fifteen 256s data segments

Why is spin a difficult problem?

Waveforms» Inspira l s igna l from PN-theory ava ilable for spinning components» Reliable inspira l-merger-ringdown waveforms for spinning components

not ava ilable over full parameter space– Needed as spin expected mos tly for black holes high mass sys tems

Scanning the parameter space with templa te banks becomes more complex with additiona l dimens ions

Taking additiona l parameters explicitly into account is not a lways the bes t s tra tegy» Non-spinning templa tes have some ability to capture spinning s ignals» Extra degrees of freedom increase background

– Detection e fficiency may increase , but fa lse a la rm ra te as well» Need to identify regions of parameter space where searching explicitly

for spinning sources is warranted

42

43

Background is not Gauss ian!

An example on quietVirgo data (WSR7)

» Bas ic da ta qua lity cuts a lready applied

Coincidences » Reduce fa lse a la rm ra te by

requiring coincident triggers in severa l de tectors

» Allows to es timate the non-Gauss ian background from the da ta themselves

Ins trumenta l ve toes » Check for anomalies in de tector

behavior, s ta tis tica lly associa ted with excess triggers

Signa l based ve toes» Check trigger inte rna l

cons is tency with expected CBC s ignal

An example on LIGO da ta

Specia l case of ta rge ted searches» e .g. GRB» Es timate background “off source”

44

Coincidences

Require coincident triggers in 2 or more de tectors» Check parameter cons is tency within a llowed « windows »

» Smaller coincidence windows ⇒ la rger reduction of FAR– Window s ize depends on the resolution with which each de tector is

able to de te rmine those parameters– mus t a llow for time of flight be tween de tectors

LIGO Hanford – LIGO Livings ton: 10 msVirgo – LIGO: 30 ms

Timing precis ion: typica lly a few ms

Chirp mass very well de te rmined

η le ss precise ly de te rmined

45

Coincidences (II)

Fixed coincidence windows are not optimal

Parameters a re corre la tedErrors on parameters vary

across the parameter space

[Ref.12]

46

Coincidences (III)

Use e llipsoids to define coincidences» Builds in corre la tion and accuracy varia tion» One tunable sca le parameter

Achieves background reduction of a factor 10

[Ref.13]

Background estimation (I)

47

A zero-lag trigger (true coincidence)

t

tDetector 2

Detector 1

Background estimation (II)

48

Detector 2

Detector 1 t

t

A time-slide trigger (accidental coincidence)

∆T

Background estimated by shifting detector data in time

∆T much la rger than GW trave l time and ana lys is method autocorre la tion time severa l seconds typica lly

Background estimation (III) Background dis tribution obta ined by counting number

of coincident triggers found in each s lide experiment» 100 time s lide experiments performed routine ly» Works well for dis tant s ites , not so well for co-loca ted de tectors

because of corre la ted background

Compare dis tribution of ze ro-lag triggers to background es timated with time s lides

49

Histogram of coincident triggers versus combined SNR

Background distribution (time-slides)

Zero-lag triggers

Region where outlier triggers would appear

Background estimation limitations (I)

Number of ava ilable time s lides» Depends on tota l ana lyzed time and s lide s tep

Different time s lides a re not comple te ly independent» They a ll reuse the same da ta» OK if mos t s ignificant events a re due to random coincidences of

re la tive ly quie t (common) events in each de tector» Not OK if mos t s ignificant events a re due to uncommon (loud) event

in de tector 1, coincident with very common events in de tector 2

Background non-s ta tionarity» Averaging over time s lides tends to wash out the s tructure

50

Somewhat a rbitra ry(fraction of) run ≡ s tre tch of da ta reasonably homogeneous in sens itivity and glitchiness

For a given FAR, sigma smallest if and s imila r

Background es timation limita tions (II)

False a la rm ra te es timated with R time s lides for 2 de tectors

Uncerta inty on FAR

As increases , sa tura tes

51

Expected te rm if time s lides independent

Uncerta inty on s ingle de tector trigger ra te es timation propagates to

[Ref. 19]

Background estimation limitations (III) FAR es timated for a (blind) hardware injection during S6/VSR3 runs

» Was cons idered as a potentia l de tection until un-blinded» Much work went into es timating FAR beyond upper limit given by 100 time s lides

» Presence of s igna l biases FAR es timate» Didn’t prevent from reaching FAR of (1 / 7000 years) – with trials factor» Might be more of an issue when numerous signals are present in the data

– But then we won’t care so much about requiring very low FARs 52

From 100 time s lidesFrom millions of time

s lides , including s ignal

Injection

From millions of time s lides , excluding s ignal

53

Signal based ve toes : χ2 tes t (I)

Basic idea : look a t how the SNR is dis tributed across the de tector bandwidth and check whether this is cons is tent with what is expected from a true s igna l

54

Signal based ve toes : χ2 tes t (II)

» The matched filte r integra l can be written as a sum over dis tinct frequency bands

[Ref.15]

» The frequency interva ls a re chosen so tha t for a true s ignal the SNR is uniformly shared among the frequency bands

» The filte red SNR can be written as

» A discriminating s ta tis tics is built

» If the noise is s ta tionary and Gauss ian, the χ2 has a χ2-dis tribution with p-1 degrees of freedom both for noise and for true s ignals

» Excess noise is expected to produce χ2 va lues which are outlie rs with respect to the Gauss ian noise /s ignal dis tribution

55

Signal based ve toes : χ2 tes t (III)

χ2 dis tribution for true s igna ls in practice» Large SNR events tend to show larger χ2 va lues

than expected from the na ive dis tribution» An effect of us ing templa te banks» The s light mismatch be tween the s ignal and the

templa te is enough to evidence diffe rences be tween the expected SNR frequency dis tribution and the measured one ⇒ high χ2

» The cut used to e liminate background must a llow some quadra tic dependence of the χ2 on the SNR

» Apply threshold on variable

Tuning» Adjus t p, δ and threshold not to re ject true s ignals» Cut mus t be loose enough to be robus t with

respect to miss ing fea tures in the templa tes– Spin– Ringdown

[Ref.16]

56

Signal based ve toes : χ2(t)

Look a t χ2(t): “r2 ve to”» Use as discriminating variable the time

spent by χ2(t) above some threshold in some time window prior to the measured coa lescence time

[Ref.16]

Other signal based vetoes

Bank χ2

» Check cons is tency of observed SNR across diffe rent templa tes in bank» Glitches typica lly cause high SNR in many templa tes» Signals give a well-prescribed dis tribution of SNR across templa te bank

57

Autocorre la tion χ2

» Check cons is tency of SNR time series aga ins t characteris tic shape expected for s ignals

Coherent tes ts» Coherent ana lys is a llows checking cons is tency of s ignal across de tectors» Coincidence tes t on a lready enforces some coherence» Null s tream with no GW contribution can further tes t coherence

[Ref. 20]

58

Ins trumenta l ve toes (I)

Signa l based ve toes a re powerful but» They are usua lly computa tionally expens ive» They do not provide any feedback on the de tector

Identify anomalies in the de tector behavior/environment s ta tis tica lly coincident with CBC triggers» Idea lly, unders tand origin of bad behavior and fix it» Help clean up the background by e liminating the corresponding triggers» Data quality flags and ve toes

Instrumental vetoes (II)

59

What a re the crite ria for a good ins trumenta l ve to ?» Efficiency (ε): e liminate fa lse triggers , especia lly triggers with high SNR

– ε = fraction of triggers which a re flagged High e fficiency is good!

» Use percentage (UP): they should be associa ted often enough with triggers– UP = fraction of DQ segments used to flag a t leas t one triggerHigh use percentage is good!

» Dead time (d): they should not e liminate a la rge fraction of da ta– d = fraction of science time which is flagged Low dead time is good!

» Safety: they should not e liminate true s ignals !– Checked with hardware injections Safe ty is crucia l!

Instrumental veto categories (I)

Vetoes a re ca tegorized according to severity, s ta tis tica l corre la tion and dead time» Category 1

– Data not suitable for be ing ana lyzed– e .g.: de tector not a t opera ting point; miss ing da ta…

60

Thermal Compensation System failure in V1

[REF 21]

Instrumental veto categories (II)

Vetoes a re ca tegorized according to severity, s ta tis tica l corre la tion and dead time» Category 1

– Data not suitable for be ing ana lyzed– e .g.: de tector not a t opera ting point; miss ing da ta…

» Category 2– Well unders tood ins trumenta l problems– Strong s ta tis tica l corre la tion– Usually low dead time , high e fficiency– e .g.: overflow in sens ing and control sys tem

61

Category 2 veto example

62

Overflow of sensing and control system in H2:

Time-frequency representation of two overflows as seen in the GW channel Single detector triggers

from CBC search

Time window marked by the original DQ flag

Veto window tuned for CBC search

[Ref. 18]

Instrumental veto categories (III)

Vetoes a re ca tegorized according to severity, s ta tis tica l corre la tion and dead time» Category 1

– Data not suitable for be ing ana lyzed– e .g.: de tector not a t opera ting point; miss ing da ta…

» Category 2– Well unders tood ins trumenta l problems– Strong s ta tis tica l corre la tion– Usually low dead time , high e fficiency– e .g.: overflow in sens ing and control sys tem

» Category 3– Suspected ins trumenta l problems– Pos itive s ta tis tica l corre la tion, but not well unders tood– Dead time can be la rge– Includes ad-hoc ve toes based on auxilia ry channe ls– e .g.: high se ismic activity, s trong wind

63

Category 3 veto example

64

Seismic glitches in V1: Two seismic glitches of the same amplitude will

not have the same impact on the GW channel

GW channel

Seismometer

Seismometer

GW channel

[REF 21]

Instrumental veto categories (IV)

Vetoes a re ca tegorized according to severity, s ta tis tica l corre la tion and dead time» Category 1

– Data not suitable for be ing ana lyzed– e .g.: de tector not a t opera ting point; miss ing da ta…

» Category 2– Well unders tood ins trumenta l problems– Strong s ta tis tica l corre la tion– Usually low dead time , high e fficiency– e .g.: overflow in sens ing and control sys tem

» Category 3– Suspected ins trumenta l problems– Pos itive s ta tis tica l corre la tion, but not well unders tood– Dead time can be la rge– Includes ad-hoc ve toes based on auxilia ry channe ls– e .g.: high se ismic activity, s trong wind

» Category 4– Poorly unders tood, weak but pos itive corre la tion– May ve to whole noisy epochs 65

Instrumental veto categories (V) Vetoes a re ca tegorized according to severity, s ta tis tica l

corre la tion and dead time» Category 1

– Data not suitable for be ing ana lyzed– e .g.: de tector not a t opera ting point; miss ing da ta…

» Category 2– Well unders tood ins trumenta l problems– Strong s ta tis tica l corre la tion– Usually low dead time , high e fficiency– e .g.: overflow in sens ing and control sys tem

» Category 3– Suspected ins trumenta l problems– Pos itive s ta tis tica l corre la tion, but not well unders tood– Dead time can be la rge– Includes ad-hoc ve toes based on auxilia ry channe ls– e .g.: high se ismic activity, s trong wind

» Category 4– Poorly unders tood, weak but pos itive corre la tion– May ve to whole noisy epochs

66

Data not ana lyzed

Look for poss ible de tections

Look for poss ible de tections and compute ra te upper limits

Used only for follow-ups

Typical performance of instrumental vetoes

67

Example: VSR2 – Low latency CBC searchSNR distribution after applying vetoes (single detector)

triggers SNR >7After CAT1

After CAT1+2After CAT1+2+3

After CAT1+2+3+KW vetoesN

umbe

r of

trig

gers

These numbers a re provided as examples . They are subject to la rge varia tions be tween diffe rent runs or

diffe rent de tectors

[Ref. 17]

Detection statistics

Rank triggers according to the ir s ignificance» Rank s ignals higher than background

Matched filte r SNR ρ is the idea l de tection s ta tis tic in Gauss ian, s ta tionary noise

» But noise is ne ither Gauss ian nor s ta tionary

Replace ρ by a be tte r s ta tis tic» Get as close to idea l case as poss ible

68

Fold parameter into ranking statistic» Down-weight triggers with high va lue

For coincident search over severa l de tectors , use combined e ffective SNR

Detection s ta tis tic: e ffective SNR

69

Acknowledging differences in background Coincidence types

» For 3 de tectors for ins tance , triggers can occur as double or triple coincidences» Triple coincidences have less background than doubles

Differences across parameter space» Not a ll regions of the mass space bring the same background

70

Low Mass triggers High Mass

triggers

Fewer high mass templates in template bank, but they are short and tend to pick up glitches with higher (effective) SNR

Divide triggers into different mass bins

[Ref. 23]

Combined effective SNR

Detection statistic: false alarm rate

Gather triggers in ca tegories (coincidence type / mass bin)» For ins tance if da ta ava ilable from 3 de tectors , triples + 3 types of doubles

– H1L1V1, H1L1, H1V1, L1V1» For ins tance (low mass search), low, medium and high chirp mass bins

Rank each trigger according to its fa lse a la rm ra te in its own ca tegory

Take tria ls factor into account to compute combined FAR

Any inte rmedia te s ta tis tic ranking triggers loudness /s ignificance can be mapped into a FAR

71

Number of background triggers louder than trigger in time s lide i

Amount of analyzed time in time slide i

Detection statistic: IFAR and beyond

Inverse of combined FAR used as de tection s ta tis tics» (c)FAR in units of yr-1, IFAR in units of yr» Guarantees tha t a ll ca tegories bring the same background

72

Example: Result of the S5 1yr Low Mass Search for analyzed triple time

Zerolag triggersBackgroundTheoretical errors (“1σ”)Background trials

Categories not all equally sensitive to GW signals (e.g. if detectors have different sensitivities)Weight IFAR with probability to observe signal with higher IFAR Likelihood statistic

Region of interest for detection

Detection checklist (I)

What a re the inte res ting candida tes for de tection ?» Triggers surviving the coincidence tes t and a ll ve to cuts » Triggers s tanding above background (low fa lse a la rm ra te ) Detection candida tes a re submitted to a de tection checklis t for review

Goals of the candida te follow-up review» Perform sanity checks of the ana lys is results » Reject candida tes tha t do not match minimal quality crite ria

Checks mos tly qua lita tive» A place for tes ting new ideas /techniques tha t a re not mature enough to be

part of the main ana lys is pipe line» Require human expertise and tra ining

What candida te follow-ups cannot do» Increase s ignificance of a de tection candida te» Ranking s ta tis tic remains the key crite rion to identify poss ible de tections

73

Detection checklist (II)

74

Check for the presence of Data Quality flags or KW based VetoesStatus of the interferometersCheck for environmental or instrumental causesCheck Electronic Log Book and Glitch Reports

Examine candidate appearance (time-freq, SNR & χ² time series)Trigger SNR distribution in analyzed chunk

Consistency of candidate parametersTrigger coherence

Segmentation stabilityCalibration stability

Try to identify the cause of the trigger

Check for non s ta tionarities in the da ta , characte rize the background loca lly

Compare triggers be tween de tectors

Tes t the robus tness of the de tection

Requires a lot of information about search triggers, GW channel, auxiliary channels…

See Chunglee Kim’s lectures on

parameter es timation

75

Setting upper limits on CBC ra te» Use loudes t event s ta tis tic in a Bayes ian approach» Probability tha t a ll s igna l events have SNR below some va lue ρ:

» Neglecting the background, pos terior probability dis tribution for µ:

[Ref.22]

» Background can be taken into account to ge t be tte r upper limit

» Results from previous searches can be incorpora ted as priors

» Account for uncerta inties on de tector ca libra tion, waveforms…

The role of injections Simula ted GW s igna ls can be added to de tector da ta in

diffe rent ways , with various goa ls Hardware injections

» Phys ica lly injected in the de tector by acting on the inte rferometer mirrors– Can be done coherently across de tectors

» Tes t ana lys is end-to-end, from detector ca libra tion to search pipe line» Tes t safe ty of ins trumenta l ve toes» Invas ive , so number limited

Blind hardware injections» Secre tly injected by a small team of people» Tes t de tection process

Software injections» Added offline to de tector ca libra ted da ta , thousands can be performed» Used to tune search pipe lines – s ignal / background separa tion» Used to compute de tection efficiencies as a function of dis tance

– Volume (or cumula tive luminos ity) probed, for ra te upper limits 76

77

Chapter 3Tying it all together

CBC coincident search pipeline (I)

78

One data set per interferometer

CBC coincident search pipeline (II)

79

The waveform depends on the system parameters

⇒ Scan the mass space with template banks

Example for « Low Mass » search(2-35 Msun)

CBC coincident search pipeline (III)

80

Match filter:

⇒ keep triggers above some SNR threshold

Signal To Noise Ratio

threshold

CBC coincident search pipeline (IV)

81

Require coincidence between two or more detectors

• Time and mass parameters

• Allows reducing the false alarm rate

• Allows estimating the background by applying time shifts to the data

CBC coincident search pipeline (V)

82

Identify rare and weak events in detector noise that is non-Gaussian and not stationary:

⇒Need to apply vetoes

• Signal based vetoes

Check consistency between measured and expected signals (e.g. χ² test)

• Instrumental vetoes

Eliminate poor data quality times due to artifacts in detector or environment

CBC coincident search pipeline (VI)

83

Surviving coincident triggers

• Surviving coincident triggers are ranked according the a detection statistic

• Triggers that stand above the background are submitted to a detection checklist

Search strategies

84

All sky blind searches» Scan as much as the parameter space as poss ible

– Low mass , high mass , ringdown

Externa lly triggered searches» BNS or NSBH mergers like ly progenitors or short,

hard GRBs– Specific search a round times of short GRBs

» Other poss ibilities can be explored in the future– High energy neutrinos– Time de lays with GW key input parameter

Searches triggering e lectromagnetic follow-up» Low la tency required

LIGO-Virgo S5/VSR1 low mass searches (I)

Long observa tion periods a t des ign sens itivities

Sources with tota l mass be tween 2 – 35 M and minimum component mass of 1 M

» Search can be based on inspira l part of s igna l

» 2PN SPA templa tes used

85

BNS BBH NSBH

8.7 x 10-3 L10-1 yr-1

2.2 x 10-3 L10-1 yr-1

4.4 x 10-4 L10-1 yr-16 x 10-4 L10

-1 yr-1

6 x 10-5 L10-1 yr-1

2 x 10-5 L10-1 yr-1

6 x 10-5 L10-1 yr-1

2 x 10-6 L10-1 yr-1

2 x 10-7 L10-1 yr-1

LIGO-Virgo S5/VSR1 low mass searches (II)

Search parameters» 3D coincidence tes t » χ2 and r2 cons is tency tes ts» Detection s ta tis tics

– IFAR based on combined e ffective SNR for LIGO only searches– Like lihood for LIGO-Virgo search

86

[Ref. 24]

LIGO-Virgo S6/VSR2-3 low mass search

Improvements over S5-VSR1 searches» New data , from more sens itive de tectors

» Search for tota l mass be tween 2 – 25 M

– 25 – 35 M bette r covered by high mass search» 3.5 PN SPA templa tes used» Detection s ta tis tic: IFAR based on combined “new SNR”

– “new SNR” improves over e ffective SNR– Avoid “over-ranking” events with very low χ2

No GW candida te found, improved upper limits will follow87

S6/VSR2 S6/VSR3

LIGO S5 high mass search

Sources with tota l mass be tween 25 – 100 M and minimum component mass of 1 M

» Inspira l, merger and ringdown matter

IMR waveforms used» EOBNR waveforms used as templa tes» EOBNR and Phenomenologica l IMR

waveforms used as injections for e fficiency computa tions

Pipe line s imila r to low mass search» Coincidence tes t, cons is tency tes ts ,

de tection s ta tis tics» Different tuning

88[Ref. 25]

LIGO S4 ringdown search

S4: one month of da ta , be low des ign sens itivity Frequency band 50 Hz – 2 kHz

» Mass range 11 – 440 M for black hole with oscilla ting in fundamenta l mode

Ringdown search» Templa te bank covering space»

» Multi-de tector coincidences in» Amplitude cons is tency tes t for co-loca ted de tectors H1 and H2» Detection s ta tis tic: combination of individual de tector SNRs

Set ra te upper limit for frequency band 70 – 140 Hz» Mass range 85 – 390 M (sens itivity to 85 Mpc)»

89

[Ref. 26]

Multiple messengers

90

Electromagnetic counterparts to compact mergers Require matte r, so not a lways expected: none for BBH Beamed emiss ions : γ, X-ray, optica l, radio

– Afte rglows expected to be less beamed than GRB Isotropic emiss ion

– Faint trans ient powered by radioactive decay

Neutrinos Low energy ν and high energy ν

detectable in the loca l Universe

Benefits from multi-messenger as tronomy Increase confidence in GW detection Improve sens itivity of GW detectors Get as trophys ica l context Pinpoint source loca tion Break parameter degeneracy

but worth checking!

more like ly to de tect

GRB triggered searches

91

Search da ta a round times of GRBs observed by γ - Xray sa te llite based ins truments» Search in [-5 s , +1 s ] window around GRB

time

Simila r to an a ll sky, low mass search, with some diffe rences» Lower background

– Direction of potentia l source known Time de lays be tween de tectors known Tighte r coincidence poss ible– Smalle r amounts of da ta searched

Lower threshold poss ible– More sens itive search

» Background es timated from off-source data

Trust model prediction for prompt γ emission

» S5/VSR1 GRB searches used likelihood statistic

LIGO-Virgo S5/VSR1GRB triggered sea rches (I)

92

» Not a merger in M31

22 short GRBs with enough da ta from a t leas t 2 de tectors

No de tection candida te Dis tance lower limits derived

The inte res ting case of GRB 070201

[Ref. 27]

LIGO-Virgo S5/VSR1GRB triggered sea rches (II)

93

Look a t a ll GRBs as a whole False a la rm probability

dis tribution for on-source da ta cons is tent with off-source da ta

Null stream consistency» Null SNR» Should be small for s ignals

– χ2 dis tributed with (2N-4) d.o.f.» Can be la rge for incoherent noise trans ients

LIGO-Virgo S6/VSR2-3 GRB triggered sea rches

Move to coherent ana lys is pipe line

94

known in case of GRB trigger

» Computa tionally a ffordable because direction of potentia l source is known

» N-detector coincident SNR has 2N noise degrees of freedom

– N de tectors x 2 phases» Coherent SNR has 4 noise

degrees of freedom– 2 pola riza tions x 2 phases– Equiva lent for non-degenera te 2-

de tector ne twork, superior for >2-de tector ne twork [Ref. 28]

LIGO-Virgo S6/VSR3 low la tency search

Uses MBTA pipe line» Multi-band templa te ana lys is , low la tency

oriented pipe line» Typica l la tency for trigger genera tion 2-3

minutes

Rapid sky-loca liza tion and online da ta qua lity check» Typica l la tency for a le rts (with human

cross -check) 30-40 minutes

Only triple -coincident candida tes with low FAR are sent for follow-up

» FAR es timated loca lly from s ingle de tector trigger ra tes (no time s lides )

95

96

MBTA (I)

The computing cos t of a matched filte r search based on a templa te bank is due to» The number of templa tes ⇐ detector bandwidth» The s ize of the FFT involved in the matched filte ring opera tion

– Templa te dura tion ⇐ domina ted by the low frequency evolution– Sampling frequency ⇐ imposed by the high frequency content of the s igna l

The ana lys is can be split in a few bands (two or three)

samplingduration

[Ref.11]

97

Build one bank of real templates per frequency band» Less templa tes in each bank» Short templa tes in high frequency band» Data can be downsampled for the low

frequency bands filte ring⇒ Less and shorte r FFTs

Filte r da ta with each templa te bank» Complex filte red s ignal (phase and

quadra ture) for each templa te

M1

M2

M2

M2

M2

M1

M1

M1

MBTA (II)

98

MBTA (III)

Build a bank of virtual templates on the full frequency band» To each virtua l templa te associa te a rea l

templa te in each frequency band

Add coherently the filte red s igna ls» Interpola te low frequency band results» Apply time de lays and phase offse ts

be tween frequency bands– Take s igna l evolution into account

» Conditiona l combination– If SNR exceeds some threshold in a t leas t

one of the bands– Built-in hie ra rchy

Fina l threshold is applied on combined s igna l

REAL

REAL

REAL

VIRTUAL

Sky localization for low latency search

Online sky loca liza tion uses» Timing information from 3 de tectors

– Time s ingle de tector s igna ls a t re fe rence frequency where SNR is la rges t to improve accuracy

» Amplitude information– Helps breaking symmetry w.r.t.

de tector plane» Galaxy ca ta log information

Accuracy remains modes t» Tens of square degrees typica l

99

100

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B.Owen et a l., Phys . Rev. D 60 (1999)[9] D.Buskulic e t a l., Class . Quant. Grav. 22 (2005)[10] B. Allen e t a l., a rXiv:gr-qc/0509116[11] F.Marion e t a l., Moriond Proceedings (2003)[12] K.G.Arun e t a l., Phys . Rev. D 71 (2005)[13] C.Robinson e t a l., GWDAW 11 (2006)[14] T.Cokelaer e t a l., LSC, GWDAW 11 (2006)[15] B.Allen, Phys . Rev. D 71 (2005)

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LSC, Tuning matched filte r searches for compact binary sys tems (2007)[17] F.Robine t e t a l., Class . Quant. Grav. 27, 194012 (2010)[18] J . S lutsky e t a l., a rXiv:1004.0998[19] M.Was e t a l., Class . Quant. Grav. 27, 194014 (2010)[20] C. Hanna , PhD. Disserta tion, Louis iana S ta te Univers ity (2008)[21] C.Van Den Broeck e t a l., gr-qc/0610126v2 (2007)[22] P .Brady e t a l., Class . Quantum Grav. 21 (2004)[23] D. Keppel, LIGO-T080347 (2010)[24] LSC, Phys . Rev. D 79 , 122001 (2009)

LSC, Phys. Rev. D 80 , 047101 (2009)LVC, Phys. Rev. D 82 , 102001 (2010)

[25] LVC, Phys. Rev. D83, 122005 (2011)[26] LSC, Phys. Rev. D80 (2009)[27] LVC, Astrophys. J. 715, 1453 (2010)[28] I.Harry et al., Phys. Rev. D 83, 084002 (2011)