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- Compact Binary Coalescence Search in the LIGO

Scientific Collaboration

Colliding Black Holes, National Center for

Supercomputing Applications

Outline

- The signal we are trying to detect
- How far we can detect
- How many sources we can detect
- establishing an upper limit on the sources
- How to suppress noise
- The analysis pipeline
- detection confidence
- parameter estimation
- software

Compact Binary Coalescence

- LIGO, GEO, Virgo and TAMA search for GW signals

from the last few minutes of coalescence of a

compact binary system with component masses

between 1 and 100 solar masses, within a few

100 Mpc of the Earth. - Inspiral ?? Merger ? Ringdown

The inspiral signal in the detector

Inspiral signal in t-f

- time-frequency spectrogram

q-scan

Signal parameters

- For non-spinning binaries, we have 7 parameters

that affect the amplitude of the signal but not

its general form (extrinsic parameters) - source sky location (ra, dec) or, in detector

frame, (?,??) - source physical distance r (sometimes written d)
- orientation of orbital plane inclination angle ?

and polarization ? - orbital phase at coalescence ?0, and time of

coalescence tc - And two parameters that do affect the form of the

signal (the evolution of its amplitude and phase

intrinsic parameters) - (m1, m2),
- or chirp mass Mc Mtot ?(2/5) and symmetric mass

ratio ? m1 m2 / mtot2 - or total mass Mtot m1 m2 and reduced mass ?

Mtot

Signal parameters

- For spinning binaries, add three more parameters

each for the spin vector of each component

relative to the orbital plane of the binary

(total 15 parameters). - Late in the inspiral, the orbits have

circularized due to radiation back-reaction, but

early on, orbits are in general elliptical add

initial ellipticity ??, and two angles for the

orientation of the semi-major axis. - Current LIGO searches use non-spinning templates

even in a 2-D intrinsic parameter space, we have

tens of thousands of templates. - Much effort is now going in to searches using

spinning templates, but tricks are required to

make the problem computationally manageable. - BCV and BCV-spin detection template families
- Physical template family developed by Pan et el

Signal templates in frequency space, in

Stationary Phase Approximation (SPA)

Normalization

Effective distance

Evolution of Binary System

- This is just the inspiral phase, well predicted

by post-Newtonian PT, expanding in x (v/c)2

- What about the merger and ringdown? Lots of GWs!
- In the last few years, breakthroughs in numerical

relativity are giving us quantitative results

on these phases!

Evolution of amplitude and frequency through

merger and ringdown

comparison of analytic and numerical coalescing

binary waveforms nonspinning case

arXiv0704.1964v2 (2007), Pan, Buonanno, et al

Energy radiated through IMR

Inspiral, merger and ring-down of equal-mass

black-hole binaries Buonanno, Cook, Pretorius,

arXivgr-qc/0610122v2 2007

Inspiral-Merger-Ringdown

- NR waveforms covering the full parameter space

are still under development, and trust in their

veracity is still pending - Generation of NR waveforms for a given set of

parameters is slow, and generating families of

templates covering the intrinsic parameter space

would take too long - Much work is in progress to match NR waveforms

with analytical models (PN, EOB, ringdowns) to

enable hybrid IMR waveforms for template banks

and testing of detection pipelines - Meanwhile, the LSC has chosen to search for

inspiral, merger, and ringdown phases in separate

search pipelines - Inspiral and ringdown searches use matched

filtering with template banks - merger phase is the burst search
- Bringing them together in IMR coincident

trigger analyses is only now under development,

and not yet in place. - today, focus on inspiral search analysis.

Science Runs

A Measure of Progress

Milky Way

Andromeda

Virgo Cluster

NN Binary Inspiral Range

4/02 E8 5 kpc

10/02 S1 100 kpc

4/03 S2 0.9Mpc

1103 S3 3 Mpc

Design 18 Mpc

Best Performance to Date .

Current all three detectors are at design

sensitivity from 60 Hz up!

h 2?10-23 /rtHz ?x 8 ?10-20 m/rtHz

Inspiral horizon distance

- Much of the accumulated SNR is in the last few

cycles, so the horizon distance depends on where

we (our templates) take the inspiral phase to end

(ie, at what component separation r or velocity

v/c (GM/c2r)(1/2) - Innermost stable circular orbit r 6M
- Equivalent-one-body (EOB) light-ring orbit r

2.8M(circular orbit of photons in the

Schwarzschild metric) - Where you think the perturbation expansion in v/c

breaks down - Geometric units Rsun GMsun/c2 1477 m Tsun

GMsun/c3 4.9 µs - GW Frequency at r bM fGW 2 forb

(GMr3)(1/2)/?? (Kepler)

c3/(?GMb(3/2))

Signal templates in frequency space, in

Stationary Phase Approximation (SPA)

Normalization

Effective distance

Inspiral Horizon Distance

- Distance to optimally located and oriented

1.4,1.4 solar mass BNS, at SNR 8using

templates that end at ISCO

S3 Science Run Oct 31, 2003 - Jan 9, 2004

Inspiral Horizon Distance

- Distance to optimally oriented 1.4,1.4 solar mass

BNS at SNR 8

S4 Science Run Feb 22, 2005 - March 23, 2005

Inspiral Horizon Distance

- Distance to optimally oriented 1.4,1.4 solar mass

BNS at SNR 8

First Year S5 Science Run Nov 4, 2005 - Nov 14,

2006

Inspiral horizon distance

- SNR depends strongly on the ending frequency

(relative to the noise curve bucket, which in

turn depends strongly on the mass of the system

Horizon Distance vs. Mass S5

Binary Neutron Stars

Inspiral duration

- In-band duration of inspiral, in seconds and in

cycles, also depends strongly on mass t

(5MTsun/256??) (?MTsun flow)-8/3

Higher-order effects!

Inspiral duration

- Initial LIGO (flow 40 Hz) BNS 15 s BBH

100Msun a few msec, lt 3 cycles burst! - Advanced LIGO (flow 15 Hz) BNS 300 s or

more, requiring new filtering techniques

MultiBandTemplateApprox MBTA)

Higher-order effects!

Matched Filtering

- Assume the signal we are searching for is known,

up to unknown arrival time, constant phase and

amplitude - Construct matched filter statistic for this signal

Matched Filtering

- Choose templates to be normalized to strain at 1

Mpc - Cutoff flow is determined by detector noise

curve, fmax by template - Effective distance to signal is given by

Triggers threshold on peaks in the matched

filter output time series

Mismatch

- What if the template is incorrect?
- Loss in signal to noise ratio is given by the

mismatch

Mismatch and Event Rate

- Any mismatch between signal and template reduces

the distance to which we can detect inspiral

signals - Loss in signal-to-noise ratio is loss in detector

range - Loss in event rate (Loss in range)3
- We must be careful that the mismatch between the

signal and our templates does not unacceptably

reduce our rate

Mismatch for Low Mass Signals

Inspiral Template Banks

- To search for signals in the mass region of

interest, we must construct a template bank - Lay down grid of templates so that loss in SNR

between signal in space and nearest template is

no greater than 3

Overview of S1 - S4 Searches

40.0

BBH Search S2 - S4 Detection Templates

Ringdowns S4

3.0

BNS S1-S4 PN

NS/BH S3 Spin is important Detection Templates

1.0

1.0 3.0

40.0 100.0 150.0

Overview of S5 Searches

40.0

Ringdowns

Burst

EOB

3.0

PN Templates

1.0

1.0 3.0

40.0 100.0 150.0

Astrophysical source distribution

- Our primary goal is to detect GWs from compact

binary coalescences and study the properties of

individual systems. - Once we observe many such systems, we wish to

constrain the astrophysical source distribution. - Until we make detections, we wish to bound the

CBC rate in the universe. - To do this, we need a model of the astrophysical

source distribution spatial distribution and

mass distribution.

Astrophysical source distribution

- Population synthesis provides limited guidance
- models of stellar formation and evolution, and

the formation and evolution of compact binaries,

contain many uncertainties. - The only real observational constraints on these

models come from the handful of relativistic

pulsar binary systems (BNS) observed in our

galaxy. - There are essentially no observational

constraints on systems containing 10 or 100 solar

mass black holes yet these are some of the most

promising sources for LIGO! - The astrophysical distribution of CB mass beyond

BNS is hardly constrained at all we choose to

measure the rate as a function of CB total mass.

Binary Neutron Star Inspiral Rate Estimates

- Base on observed systems, or on population

synthesis Monte Carlo - Kalogera et al., 2004 ApJ 601, L179
- Statistical analysis of the 3 known systems with

short merger times - Simulate population of these 3 types
- Account for survey selection effects

For reference population model (Bayesian

95 confidence) Milky Way rate 180477144 per

Myr LIGO design 0.0150.275 per year Advanced

LIGO 801500 per year Binary black holes,

BH-NS No known systems must Monte Carlo

Source Distribution Beyond the MW

- Pop.synth. and general astrophysical wisdom says

compact binary systems exist in galaxies.

Specifically, young galaxies with lots of star

formation (spirals) less so for older galaxies

like ellipticals. - Logic (as far as I understand it) CBCs

represent (one path for) the death of stars in a

steady-state situation, it should be proportional

to the stellar birth rate. - Star-birth involves young, massive, hot stars,

emitting blue light. Hence, the CBC rate is, in

this simplest model, proportional to blue-light

luminosity (Phinney, 1991).

Astrophysical source distribution

- This cant be strictly true the time scale for

coalescence can be of the same order as the age

of the universe. Some component of the CBC rate

must be proportional to the total number of stars

(mass), not the stellar birth rate. Older

galaxies (eg, ellipticals) must contribute. - Nonetheless, we stick with the simplest model

CBC rate is proportional to blue-light

luminosity. - Our only astrophysical constraints on CBC rate

are from BNS progenitors in the Milky Way, so we

can estimate the rate per Milky Way Equivalent

Galaxy (MWEG).

Astrophysical source distribution

- Problem we dont know the blue-light luminosity

of the MW very well! It is directly measurable

for our sun (Lsun-BL) and for other galaxies,

only estimated for MW (MWEG 1.5 2.0 ?? 1010

Lsun-BL with a best estimate of 1.7 ?? 1010

Lsun-BL 1.7 L10). - In LIGO S2, we were mainly sensitive to the MW,

so normalizing the astrophysical rate to MWEG was

appropriate. - By S3 we are touching M31 and beyond. But

although the MW is overdense with sources, the

empty space between the MW and M31, and between

out local cluster and the Virgo cluster, is

underdense. - Fortunately, its not distances that matter so

much as effective distance sources that are not

optimally located (detector zenith) or oriented

(face-on) have a correspondingly larger effective

distance that is always larger than the physical

distance. This smooths out the fluctuations in

source density.

Astrophysical source distribution

- By S4 and S5, our source population is dominated

by galaxies beyond the MW, so we have switched to

normalizing the CBC rate to L10 1/1.7 MWEG. - Beyond about 20 Mpc, the source density is

more-or-less uniform at ?? 0.01 L10 per Mpc3 ,

and number of sources grows like horizon distance

cubed. - The LSC now quote rate upper limits in units of

1 / L10 / yr . - Some of the most significant systematic errors

associated with the search upper limits are due

to uncertainties in the astrophysical source

distribution! Nearby source distances and

luminosities. - By S5, we will be well into the uniform regime

where we only need to know ?? 0.01 L10 / Mpc3

with, say, 10 error.

Catalog of nearby galaxies

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Loudest event statistic

- This is a novel, but rather natural method for

establishing a Bayesian confidence interval or

upper limit on the rate for a process

characterized by events with a loudness (eg,

coincident inspiral triggers characterized by a

combined SNR). - Loudness measures how signal-like an event is

loud events are more likely to be signal than

noise (background). It is also referred to as a

detection statistic ?. - It can be more complicated than an SNR for

example, it could contain information about how

signal-like the signal is, eg, from a chisq

test.

Loudest event statistic

- Traditionally, one sets a fixed threshold on

event loudness ? louder events are called

signal (although they may be contaminated by

background) and less loud events are ignored as

background. - One then assumes a certain parent (source)

distribution, and uses Monte Carlo simulation to

estimate the probability that an event drawn from

that distribution would be louder than the

threshold (the search efficiency). - The confidence interval or upper limit on the

rate is then established by combining the number

of events observed above threshold, the estimated

background, and the efficiency for detecting an

event from the assumed source distribution. Eg,

Rate (Nobs Nbcknd)/(efficiency time). - In absence of detection (and background), with no

events observed, Rate lt -ln(1-CL)/(efficiency

time) 2.3/(efftime) _at_ 90 CL.

Loudest event statistic

- For Initial LIGO, this traditional procedure is

dangerous - The expected detection rate is below our current

sensitivity (we expect to see less than one event

in S5). - Our background rate is difficult to determine,

because our detectors are novel and not very well

understood, and glitchier than we would like. - The stakes are high! We dont want to declare a

detection just because weve accidentally

underestimated our background. - The traditional procedure has already bitten us

The LIGO burst search established a fixed

threshold where we believed that the false alarm

rate was ltlt 1 per observation time. Then we

observed an event above that threshold in S2! It

was caused by acoustic pickup from a low-flying

airplane. - Moral setting a priori fixed thresholds can be

dangerous!

Loudest event statistic

- Better approach set a threshold just above the

loudest observed event. - Then, by definition, there will be no signal

events to sweat over! - Set a (conservative) upper limit on the rate,

based on the efficiency for detecting events from

the source distribution with loudness above that

threshold. - If we have true signal below our threshold, the

true rate should be below the resulting upper

limit (with a specified statistical confidence)

the upper limit is conservative. - We can still detect! Examine each of the loudest

events in the search (all below the loudest event

threshold), and use a variety of tests (the

detection checklist) to establish detection

confidence.

S4 PBH

S4 BBH

S4 BNS

Loudest event

Loudest event statistic

- We wish to measure the rate R of events/yr/L10
- Predicted number of events expected above a given

detection statistic threshold (eg, that of the

loudest observed event) Np RTCL(? ) - We can compute an estimate of the cumulative

luminosity CL (in units of L10) to which we are

sensitive. Crudely, CL ??L10 (4??/3) D(?

)3where ? is our SNR (or detection statistic)

thresholdand D is the (average over sky location

and orientation) distance below which we can

detect a signal with detection statistic ? lt ? . - This will depend on the signal parameters

(mainly, chirp mass). - More precisely, we perform a convolution integral

over our source density model (as a function of

physical distance) and our detection efficiency

vs distance (as measured using simulated signal

injections, run through the full detection

pipeline).

Loudest event statistic

- Detection efficiency is a gentle function of

physical distance but its a sharper function of

effective distance. More efficient to use that. - But effective distance depends on the detector

its different at LHO and LLO. Need to do the

convolution in 2D for LIGO-only analysis.

Loudest event statistic

- Predicted number of events expected above a given

detection statistic threshold (eg, that of the

loudest observed event) Np RTCL(?m ) - Probability of observing no events above x (in

absence of background) is P(?m) exp(-Np) - If we estimate that the background has a

probability Pb(?m) of having (at least) one event

above x, thenP(?m) Pb(?m) exp(-Np(?m)) - Applying a Bayesian analysis with uniform prior

on R, we can turn this into a probability

distribution for R, and set an upper limit (at

xome confidence level) on R, R

Loudest event statistic

- Here, in the presence of background, ? measures

the lilelihood that the loudest event is real, as

opposed to background - Limiting casesloudest event is unlikely to be

bgloudest event is most likely bg - ? is pretty small for the S4 searches.

Loudest event statistic

- This procedure can be repeated for different

parameters on which it can strongly depend, eg,

upper limits vs total mass

LIGO S4 upper limits on compact binary

coalescence (gr-qc0704.3368, submitted to PRD)

Loudest event statistic

- Because this is a Bayesian analysis, resulting in

a a-postiori probability distribution on the

parameter we wish to measure (true rate), the

result can be used to - combine P(R ) from different measurements (eg,

from different independent analyses, searches,

detectors) into an improved probability

distribution, to better bound or bracket the true

rate - The result from, eg, S4 can be used as a prior

for the S5 analysis,

Picking up where we left off last time

- Upper limits on CBC rate systematic errors
- Calibration uncertainties
- Coincident triggers. eThinca
- Background time slides
- Glitchs and non-gaussian noise
- Detector characterization, DQ flags
- Chisq veto, effective SNR
- Heirarchical pipeline
- Coherent SNR
- Template bank veto
- Detection confidence, qscans
- Parameter accuracy and estimation
- Software tools, LIGO Data Grid
- Future work

Sources of Systematic Uncertainty

- On e
- Distances to galaxies
- Accuracy of template waveforms
- Effect of cuts on real vs. simulated signals
- Calibration
- Finite statistics of simulation
- On CL
- Number of sources in galaxies other than the

Milky Way - Use blue light luminosity
- Metallicity corrections
- Blue light luminosity of the Milky Way
- Most of our uncertainties are due to the

astrophysical source distribution, not under our

control! - Strong correlation between errors on distances to

nearby galaxies and absolute luminosity of those

galaxies. - This will get less significant as our sensitivity

becomes mnore dominated by the average source

density ?? 0.01 L10 / Mpc3 with, say, 10

error - Theoretical errors (real waveforms vs templates,

real waveforms vs injected simulated signals)

will improve as theory improves (NR, AR) - Experimental errors (calibration, simulation

statistics) will improve with more work and

computer time. - Much work will go into improving calibration

errors to better than the current 10

CalibrationDARM control loop

Open loop gainmodel vs measurement

Resulting DARMERR response function

Time dependence

- Mostly due to time-varying optical power in the

arms, thereby varying the gain from strain to

output to photodiode - Use digital suspended optic controllers to place

sinusoidal signal on end test mass mirrors, with

known frequency and amplitude in strain.

Three lines one below UGF, one near it, one

well above. 54.7, 396.7, and 1151.5Hz Monitor

and record height of these lines every minute ?

??(t)

Calibration Uncertainties -- L1 during S4

Summary Numbers 5 Amplitude5o Phase

Coincidence

- In the presence of Gaussian detector noise, the

SNR from matched filtering is the optimal method

for distinguishing signal from background due to

noise. - Coincidence of triggers from multiple instruments

can greatly suppress the loudest noise events,

since it is very unlikely that the (rare) loudest

noise triggers will be coincident in time and

Mchirp - This allows us to turn our threshold down much

lower, greatly increasing detection rate Rate

(Dhorizon)3 (1/?)3 - The Gaussian noise SNR spectrum falls very

steeply with SNR. Coincidence allows us to reduce

our threshold (in, eg, 1 year of running) from 8

to 6, while keeping the probability of false

detection below 1.

Coincidence

- BUT, coincidence means that multiple detectors

must be online if the duty cycle for each

detector to be in Science Mode is 80, the

probability that 3 are in Science Mode is (0.8)3

50! We lose lifetime. - Also, our detectors do not all have the same

sensitivity, and they are not co-aligned. They

each see slightly different signals. This

complicates coincidence. - The LIGO S1-S5 inspiral searches used

triple-coincident triggers (negligible

background) as well as double-coincident triggers

(in both triple-time and double-time) - We thus have 7 kinds of triggers!
- triples in H1H2L1 coincident time
- H1H2, H1L1, and H2L1 doubles in H1H2L1 coincident

time - doubles in H1H2 time, H1L1 time, and H2L1 time

International network

- detection confidence
- locate the sources
- verify light speed propagation
- decompose the polarization of gravitational

waves - Open up a new field of astrophysics!

GEO

Virgo

LIGO

TAMA

AIGO

Trigger Coincidence

- We require triggers to be coincident in time ?t,

? mchirp, ? ?(or equivalently, ?t, ??0, ??3) - These parameters are all correlated, so we define

correlation ellipsoids in 3D ?parameter space,

and require overlap of the ellipsoids - ethinca ellipsoidal thoughtful inspiral

coincidence analysis

Estimating background

- If noise in multiple detectors are uncorrelated

in time, we can estimate the rate of coincident

triggers due to accidental coincidence of noise,

via time-slides (anti-coincidence). - These cant be GWs!
- The trigger data streams from two detectors are

slid by multiples of some fixed time, chosen to

be longer than the correlations between triggers

(due to template durations) and shorter than the

noise non-stationarity of the detectors. - For our S5 searches, we slide by 5, 10, 250

seconds.

Time-slides for H1H2

- But co-located detectors can have correlated

noise triggers! The two detectors at LHO H1

(4km) and H2 (2km), below. - In principle, loud noise triggers are due to

displacement noise, not strain noise, and the

strain will be different between H1 and H2

require h(t) amplitude (or equivalently, trigger

effective distance) consistency.

- Still, lots of correlated noise triggers get

through. - This problem is much more serious for the

stochastic search!!

Glitches

- But the big problem is that the LIGO detectors do

not exhibit only Gaussian, stationary noise. - There are loud glitches, due to seismic bumps,

acoustic noise, servo instabilities, power line

glitches, - These can be loud, can ring up templates, and

can dominate our searches and loudest events!

Detector Characterization

- DMT tools analyze data from hundreds of

interferometric and environmental channels in

near real-time for detector monitoring and

characterization purposes - Minute trends, Band-limited noise, Line

monitoring, Glitch identification and cataloguing - Correlation studies between glitches in the

gravitational wave channel and auxiliary channels - Detector characterization work reflects on data

quality and veto flags which are crucial to all

burst and inspiral analyses - Coincidence analysis and event classification has

provided evidence of events resulting from

extreme power line glitches reflected all across

the H1-H2 instruments

Data quality flags

- The Detector characterization group and Glitch

subgroup are charged with studying the data

quality and establishing DQ flags. - Flag extended time periods when a detector is

misbehaving. - Cat1 exclude these time periods from the search

(deadtime). - Cat2, Cat3 analyze the data, but study the

effect of the veto on the fake rate and

efficiency. - Cat3 vetoes tend to be less certain, and they

veto larger time periods - Set upper limits after requiring Cat3 veto.
- Detection candidates vetoed by Cat4 are to be

treated with suspicion. - Cat5 vetoes triggers that are coincident with

glitch triggers in auxiliary channels. CBC group

doesnt use these burst group does.

DQ flags for S5

SNR isnt the only tool required, in the

presence of non-Gaussian noise

Signal Based Vetoes

- A large transient (glitch) in the data can cause

the matched filter to have a large SNR output

- We use signal based vetoes to check that the

matched filter output is consistent with a signal - If we have enough cycles, one of the strongest

vetoes is the ?2 veto

The ?2 veto

- An effective method for distinguishing

(well-modeled broad-band) inspiral signals from

non-Gaussian noise glitch backgrounds. - It performs a time-frequency decomposition,

breaking up the template in time/frequency, to

test whether the matched-?lter output has the

expected SNR accumulation in all the frequency

bands. - Noise glitches tend to excite the matched ?lter

at the high frequency or the low frequency, but

seldom produce the same spectrum as an inspiral.

Effect of signal/template mismatch on ?2

- After subtracting out the expected contribution

to the SNR from each frequency bin, as predicted

by the template, the resulting ?2 should follow a

?2 distribution with 2(p-1) degrees of freedom. - But if the template isnt perfectly matched to

the signal, the ?2 will deviate from this, with a

non-centrality parameter that depends on the

amount of mismatch (?? lt ?max 0.03) and the

strength of the signal (SNR ?). - It can be shown that in the presence of a signal

and Gaussian noise that ?2 has a non-central

chi-squared distribution with 2(p-1) degrees of

freedom and non-central parameter ?? bounded by 2

?2?. - However, ? may possibly be slightly greater than

2? times the measured ?2 owing to the presence of

noise. - We treat ? as a tunable parameter in the LSC

searches.

The ?2 veto

- The resulting ?2 is used both as a veto and as a

means of rescaling the raw SNR into an effective

SNR that combines SNR with ?2 information,

optimally discriminating between signal and

background glitches.

p number of ?2 bins 16 for LIGO

Glitches in the Data

- Glitches can still be a problem, even with signal

based vetoes (particularly in higher mass

searches) - A lot of work in the LSC is devoted to finding,

identifying and eliminating glitches - Loud glitches reduce our range (and hence rate)

by hiding signals - Even if a template has excellent overlap with

signals, if it picks up lots of glitches we have

a problem

Effective SNR

- Effective SNR combines SNR with ??2 to produce a

noise spectrum that is much more Gaussian,

suppressing the loud tails

Calculating chisq,the hierarchical pipeline

- Unfortunately, the calculation of the chisq

signal-based veto quantity is computationally

expensive. - theres no point in computing it if the triggers

arent coincident (in time and mchirp) between 2

or more detectors. - So we had to break the inpiral pipeline into two

steps, and only compute chisq for coincident

triggers.

Coherent SNR

- The output of filtering the data with (complex

SPA) template is an SNR time-series, which is

complex the phase selects the best combination

of cosine/sine (h,hx) components of the signal. - A single-detector trigger is a peak in the

magnitude of this time series in time, and across

templates in the bank. - A coincident trigger is a set of single-detector

triggers that are coincident in time and template

parameters. - The complex SNR time series for the templates in

that coincident trigger can be combined together

coherently, by applying suitable time delays,

depending on location of the source in the sky. - One can maximize the combined coherent SNR over

sky location. - One can apply thresholds or other criteria to

favor coherent signals from multiple detectors,

over ones that dont tend to add coherently. - One need not go back to the raw data only the

SNR time series in the neighborhood of the

coincident trigger (eg, 1 s) from the multiple

detectors is necessary.

Coherent SNR

- coherent signal injection

incoherent coincident glitch

Other trigger information

- There is more information from our triggers that

can be used to distinguish signal from

backgrounds in the presence of glitches. - For example, glitches can ring up large areas of

the template bank, signals only ring up templates

within their ambiguity function. - We cluster triggers in template space before the

coincidence test. - The template bank veto is currently under

development and study. - More info is available, and can be used in

multivariate classification programs to more

effectively separate signal from background and

assign each event candidate a more meaningful

detection statistic louder events are more

signal-like.

Template bank veto

- A glitch will ring up a broad swath of templates

in the bank. - Different templates ring up over duration of

injection or glitch (fraction of a second). - For signal injections, SNR peaks at best-match

chirp mass and coalescence time. - Time evolution of SNR and motion across the

template bank is different for glitches.

Trigger bank chisq

- SNR, chirp mass over time can be combined into a

chisq designed to match signal-like behavior. - This test is still under development and not yet

employed in the LSC CBC pipeline (but soon!).

Multivariate classification

- Kari Hodge uses a package called

StatPatRecognition, and a particular algorithm

called Bagged Decision Trees to create a random

forest of decision trees, making use of a vector

of input variables. - Train the algorithm on background (time slide

triggers) and foreground (software injection

triggers) - Choose an optimization criterion (maximize S/B,

S/v(SB), many others). - Evaluate ROC using an independent sample of S, B.

Detection confidence

- The end of a search pipeline is a rank-ordered

list of event candidates. - If there are none, we turn down our thresholds

until we see some (including a loudest event). - Nice to have some manageable amount of event

candidates to consider ( 10s). - the events may or may not be consistent with

estimated background - Eg, for H1H2 double coincident event candidates,

where we systematically underestimate our

background using time-slides, the remaining

foreground events are naively inconsistent with

the background - Even with our best automated tools, the

detection statistic ?eff does not give us

sufficient confidence in declaring detection. - Events must still be scanned by hand. Could they

be due to environmental or instrumental glitches? - We have a very long, elaborate, time-consuming

detection checklist. - Our best tools so far qscans, coherent SNR,

null-stream.

First page of a many-page detection checklist

for one event

qscans, null stream

(this ones a hardware injection!)

qscans, loud glitches

Once we detect

- We want to estimate the parameters of the signal

masses, sky location, orbit orientation, spins - Our non-spinning templates can do an OK job of

estimating the chirp mass, not much else. - To do metter, use more sophisticated tools

Bayesian Monte Carlo Markov Chains

Mass Accuracy

- Good accuracy in determining chirp

mass. where - Accuracy decreases significantly with higher mass

BNS 1-3 M?

BBH 3-35 M?

Mass Accuracy

- Very little ability to distinguish mass ratio.
- Width of accuracy plots similar to entire search

range.

BNS 1-3 M?

BBH 3-35 M?

Timing Accuracy

- As before, parameter accuracy better for longer

templates. - Timing accuracy determines ability to recover sky

location - Timing systematic is due to injecting TD,

recovering FD. - Overall systematic (same at all sites) does not

affect sky location.

BBH 3-35 M?

BNS 1-3 M?

Markov Chain Monte Carlo Parameter Estimation

- A candidate would be followed up with MCMC

parameter estimation routine. - Example from simulated LIGO-Virgo data with

injection.

Plot from Christian Roever, Nelson Christensen

and Renate Meyer

MCMC convergence

- The MCMC explores a large-dimensional parameter

space (for non-spinning binaries, 9 parameters

per detector). - It performs a Markov-chain random walk through

that space, minimizing the mismatch between the

data and a template with those parameters. - To avoid landing in false minima, random termal

noise is added. Turn up the temperature

(simulated annealing) to escape from local

minima. - Also run parallel chains with different initial

parameters. - Iterate until it converges robustly on a minimal

mismatch. - Explore around that minimum to establish

posterior PDFs for each parameters

Nelson Christensen, Hans Bantilan

Posterior PDFs

- We get peak (most likely) parameters, and

confidence intervals on the parameters. - Some parameters are determined better than

others!

Correlations and degeneracies

Sky localization using MCMC runs with multiple

detectors

H1H2L1

Software tools

- LSC Data Analysis Software Working Group
- code C, python, matlab, c/root
- LIGO Algorithm Library (LAL) and LALApps

(applications that use LAL, such as the inspiral

matched filter code and waveform simulations),

both written in C) - Most post-processing (coincidence, plots, )

written in python - 3rd-party scientific software FFTW, GSL, pylab,

ROOT, MV classifiers, - search/analysis pipelines are run using Condor

DAGs on the LIGO DATA Grid (linux clusters). - Plans underway to use NSF OSG.

LIGO Data Grid clusters

Future

- More signal-based vetoes and better

signal/background discrimination - Better, more automated, less biased detection

confidence procedures - Better spinning BBH searches
- Incoherent IMR
- Coherent IMR using analytical waveforms guided by

NR - Better parameter estimation, source sky location
- Tests of GR using detected waveforms
- Faster pipelines, more computing resources (OSG)
- Follow-up with EM detectors (ground- and

space-based telescopes, neutrino detectors, etc) - Open up the new and wildly exciting field of

gravitational wave astrophysics!

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