INTERPRETATION of IGEC RESULTS

Lucio Baggio, Giovanni Andrea Prodi

University of Trento and INFN Italy

or unfolding gw source parametersstarting point:• IGEC 1997-2000 results (P.Astone et al., PRD 68 (2003) 022001)

with reference to:• LIGO S1 burst gw results (B.Abbott et al., gr-qc/0312056)

COMPARISON at a GLANCEIGEC 1997-2000

• systematic search over many amplitude thresholds:

many data selectionsmany data points

• bound of maximum false dismissal probability of detection:

conservative efficiency is estimated for -like waveform

results are upper limits on rate of detected burst gws above threshold:

rate vs search thresholdcumulative

Lacking the “unfolding” to gw source parameters (“uninterpreted” results)

LIGO S1 • playground data to tune the search:

one data selectionone data point

• montecarlo for some specific source models:

efficiency is measured vs gw amplitude for sample waveforms

results are upper limits on rate of incoming burst gws:

rate vs true amplitudes

Source model:sample waveforms incoming at fixed amplitude + directional corrections…

UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION

• signal template = -like gw from the Galactic Center direction

Poissonrate of

detectedgw

[year –1]

search threshold

dashed region excluded with probability 90%

overcoverage

212 10 0 02~ / .S Hz M converted in burst gw at GalacticCeH nter

signal amplitude HS= FT[hS ] at 2 900 Hz

UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (2)

• no coincidences found, limited by the observation time

Poissonrate of

detectedgw

[year –1]

search threshold

dashed region excluded with probability 90%

overcoverage

• limited by accidental coincidences• observation time cuts off: sensitivity cut

1.8 yr -1

UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (3)

• analysis includes all the measured signal amplitudes search threshold result is cumulative for HM Ht

Poissonrate of

detectedgw

[year –1]

search threshold

• systematic search vs threshold Ht many trials (20 /decade)almost independent results

Poissonrate of

incominggw

[year –1]true

amplitude HS

Case of gw flux of constant amplitude: -like signal from GC

Poissonrate of

detected gw

[year –1]

search threshold

correct each result for the detection efficiency as a

function of gw amplitude HS

convert in terms of parameters of the source

model

at HS 2 Ht

efficiency = 1

enough above the threshold

at HS Ht

efficiency 0.25 due to 2-fold observations at threshold

Poissonrate of

incominggw

[year –1]

true amplitudeHS

Case of gw flux of constant amplitude: -like signal from GC (2)

• complete conservative efficiency estimation for the single data point

• … on all data points

• convert from HS= FT[hS ] at 2 900 Hz to template amplitude parameter

e.g. for a sine-gaussian(850 Hz;Q=9) hrss= 10 Hz 0.5 HS

Remarks

• IGEC time coincidence search provides a systematic search as a function of common thresholda directional search strategy

is able to deal with• detectors with different sensitivities (level & bandwidths)

search with templatessearch resctricted on the common sensitivity bandwidth

• detectors with different antenna patterns and locationsif gw polarization is modeled or simply linear

• IGEC method is able to assess the false detection probability

Of course, relevant improvements are possible:- provide measurements of detection efficiency

Monte Carlo injection of selected templates- feed a further stage of coherent analysis - effective control of false detections of surveys

1

10

100

1,000

1E-21 1E-20 1E-19

0.60

0.80

0.90

0.95

search threshold(Hz -1 )

rate(year –1)

HOW to UNFOLD IGEC RESULTSin terms of GW FLUX at the EARTH

• Compare with IGEC results to set confidence intervals on gw flux parameters

1

10

100

1,000

1E-21 1E-20 1E-19

0.60

0.80

0.90

0.95

search threshold (Hz -1 )

rate(year –1)

• Estimate the distribution of measured coincidences HM Ht (cont.line)

Ht

• Take a model for the distribution of events impinging on the detector HS Ht (dashed line)

coverage

Poissonrate of

detectedgw

[year –1]

search threshold

Case of gw flux of constant amplitude: -like signal from GC (3)

• the resulting interpreted upper limit

• convert from HS= FT[hS ] at 2 900 Hz to template amplitude parameter

e.g. for a sine-gaussian(850 Hz;Q=9) hrss= 10 Hz 0.5 HS

Poissonrate of

detectedgw

[year –1]

hrss

Case of gw flux of constant amplitude: comparison to LIGO

• the resulting interpreted upper limit

• convert from HS= FT[hS ] at 2 900 Hz to template amplitude parameter

e.g. for a sine-gaussian(850 Hz;Q=9) hrss= 10 Hz 0.5 HS

Case of gw flux of constant amplitude: comparison with LIGO results

Poissonrate of

detectedgw

[year –1]

search threshold

• IGEC sets an almost independent result per each tried threshold Ht

• correct each result for the detection efficiency as a function of gw amplitude HS:

at HS 2 Ht efficiency = 1 enough above the threshold

e.g. at HS Ht efficiency 0.25 due to 2-fold observations at threshold

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amplitude directional sensitivity

2sin GC2sin GC

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time (hours)

ampl

itude

(H

z-1·1

0-21)

time (hours)

DIRECTIONAL SEARCH: sensitivity modulationam

plitu

de (

Hz-1

·10-2

1)

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Resampling statistics by time shiftsam

plitu

de (

Hz-1

·10-2

1)

We can approximately resample the stochastic process by time shift.

in the shifted data the gw sources are off, along with any correlated noise

Ergodicity holds at least up to timescales of the order of one hour.

The samples are independent as long as the shift is longer than the maximum time window for coincidence search (few seconds)

Setting confidence intervalsIGEC approach is

frequentistic in that it computes the confidence level or coverage as the probability that the confidence interval contains the true value

unified in that it prescribes how to set a confidence interval automatically leading to a gw detection claim or an upper limit

based on maximum likelyhood confidence intervals (different from Feldman & Cousins)

false dismissal is under control (but detection efficiency is only lower-bounded)

estimation of the probability of false detection (many attempts made to enhance the chances of detection)

0

2

4

6

8

10

12

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1.0 10.0 100.0

search threshold [10-21/Hz]

Ngw

many trials !all upper limits but one:

testing the null hypothesis

overall false alarm probability 33% for 0.95 coverage56% for 0.90 coverage

at least one detection in the set in case

NO GW are in the data

NULL HYPOTHESIS WELL IN AGREEMENT WITH THE

OBSERVATIONS

TESTING the NULL HYPOTHESIS

FALSE ALARM RATES

2E-21 1E-201E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

AL-AU AL-AU-NA

falsealarm rate

[yr-1]

common search threshold [Hz-1]

dramatic improvement byincreasing the detector number:

3-fold or more would allow to identify the gw candidate

meanrate ofevents[ yr -1]

mean timing[ms]

UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (3)

• analysis includes all the measured signal amplitudes search threshold result is cumulative for HM Ht

Poissonrate of

detectedgw

[year –1]

search threshold

• systematic search vs threshold Ht many trials (20 /decade)almost independent results

MULTIPLE DETECTOR ANALYSIS

efficiency of detection

fluctuations of false alarmsmaximize the chances of detection i.e. the ratio

network is needed to estimate (and reduce) the false alarms

time coincidence search among exchanged triggerstime window is set according to timing uncertainties by requiring

a conservative false dismissal

2 22

1i j i jt t k false dismissal

k

false alarms k

measure the false alarms:time shifts resampling the stochastic processes so that:

• gw sources are off (as well as any correlated noise)• statistical properties are preserved (max shift ~ 1 h)• independent samples (min shift > largest time window ~ few s)

by Tchebyscheff inequality

DIRECTIONAL SENSITIVITY

The achieved sensitivity of bar detectors limits the observation range to sources in the Milky Way. The almost parallel orientation of the detectors guarantees a good coverage of the Galactic Center

ALLEGROAURIGA -EXPLORER –NAUTILUS

NIOBE

amplitude directional sensitivity factor vs sideral time (hours)

TARGET GW SIGNALS

Fourier amplitude of burst gw

0 ( ) ( )h tH tt

arrival timeeach detector applies

an exchange threshold on measured H

Detectable signals:transients with flat Fourier amplitude at the detector frequencies (900 Hz)

threshold on burst gw

OBSERVATIONTIME 1997-2000(days)

EXCHANGED PERIODS of OBSERVATION 1997-2000

fraction of time in monthly bins

threshold on burst gw

21 16 10 Hz 21 13 6 10 Hz

21 13 10 Hz

ALLEGRO

AURIGA

NAUTILUS

EXPLORER

NIOBE

AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS

relat

ive c

ount

s

10-5

10-4

10-3

10-2

10-1

1

relat

ive c

ount

s

10-5

10-4

10-3

10-2

10-1

1

NIOBENIOBEAMP/THR1 10

NAUTILUSNAUTILUSAMP/THR1 10

AURIGAAURIGAAMP/THR1 10

ALLEGROALLEGROAMP/THR1 10

EXPLOREREXPLORERAMP/THR1 10

normalized to each detector threshold for trigger search

      typical trigger search thresholds:SNR 3 ALLEGRO, NIOBESNR 5 AURIGA, EXPLORER, NAUTILUS The amplitude range is much wider than expected: non modeled outliers dominate at high SNR

POISSON STATISTICS of ACCIDENTAL COINCIDENCES

Poisson fits of accidental concidences: 2 test

sample of EX-NA background

one-tail probability = 0.71

histogram of one-tail 2

probabilities for ALL two-fold observations

agreement with uniform distribution coincidence times are random

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0 6 12 18 24 30 36 42 48 54 60time (hours)

Data selection at work

Duty time is shortened at each detector in order to have efficiency at least 50%

A major false alarm reduction is achieved by excluding low amplitude events.

ampl

itude

(H

z-1·1

0-21)

time

amplitude

time

amplitude

time

amplitude

time

amplitude

A

FALSE ALARM REDUCTIONby amplitude selection of events

consequence:

selected events have consistent amplitudes

Auto- and cross-correlation of time series (clustering)

Auto-correlation of time of arrival on timescales ~100s

No cross-correlation

UPGRADE of the AURIGA resonant bar detector

Previous set-up during1997-1999 observations current set-up for the

upcoming II run

• beginning cool down phase• at operating temperature by November

Transducer

Electronics wiring support

LHe4 vesselAl2081 holder

Main Attenuator

Compression Spring

Thermal Shield Sensitive bar

AURIGA II run

new mechanical suspensions: attenuation > 360 dB at 1 kHz FEM modelled

new capacitive transducer: two-modes (1 mechanical+1 electrical) optimized mass

new amplifier: double stage SQUID 200 energy resolution

new data analysis: C++ object oriented code frame data format

AURIGA II run: upgrades

initial goal of AURIGA II: improving amplitude sensitivity by factor 10 over IGEC results

FUTURE PROSPECTS we are aiming at

DUAL detectors estimated sensitivity at SQL:

• Only very few noise resonances in bandwidth.

• Sensitive to high frequency GW in a wide bandwidth.

PRD 68 (2003) 1020XX in press

PRL 87 (2001) 031101

Science with HF GW• BH and NS mergers and ringdown• NS vibrations and instabilities • EoS of superdense matter• Exp. Physics of BH

Mo Dual 16.4 ton height 2.3 m Ø 0.94m SiC Dual 62.2 ton height 3 m Ø 2.9m

T~0.1 K , Standard Quantum Limit

New concepts - new technologies:

measure differential motion of massive cylindrical resonators

• No resonant transducers:

• Mode selective readout:

• High cross section materials

(up to 100 times larger than Al5056 used in bars)

measured quantity: X = x1+x2-x3-x4

Dual detector: the concept

Intermediate frequency range:• the outer resonator is driven above resonance, • the inner resonator is driven below resonance → phase difference of

In the differential measurement: → the signals sum up → the readout back action

noise subtracts

2 nested masses: below both resonances: the masses are driven in-phase → phase difference is null

above both resonances: the masses are driven out-of-phase → phase difference is null

Differential measurement strategy

• Average the deformation of the resonant masses over a wide area:

• Readout with quadrupolar symmetry: ‘geometrically selective readout’ that rejects the non-quadrupolar modes

reduce thermal noise contribution from high frequency resonant modes which do not carry the gravitational signal

bandwidth free from acoustic modes not sensitive to gw.

Example:

- capacitive readout -

The current is proportional to:

Dual Detector with √Shh~10-23/√Hz in 1-5 kHz range

Readout:

• Selective measurement strategy

• Quantum limited

• Wide area sensor

• Displacement sensitivity

Detector:

• Massive resonators ( > 10 tons )

• Cooling

• Suspensions

• Low loss and high cross-section materials

Feasibility issues

Silicon Carbide (SiC)

• Q/T > 2x108 K-1 - Mass = 62 tons

• R = 1.44 m - height = 3 m

Molybdenum

• Q/T>2x108 K-1 - Mass = 16 tons

• R = 0.47 m - height = 2.3 m

R&D on readouts: status

• Requirement: ~ 5x10-23 m/√Hz • Present AURIGA technology: 10-19 m/√Hz

with:optomechanical readout - based on Fabry-Perot cavities

capacitive readout - based on SQUID amplifiers

Develop non-resonant devices to amplify the differential deformation of the massive bodies.

Foreseen limits of the readout sensitivity: ~ 5x10-22 m/√Hz.Critical issues:

optomechanical – push cavity finesse to current technological limit together with Watts input laser power

capacitive – push bias electric field to the current technological limit

Idea to relax requirements on readout sensitivity: mechanical amplifiers

Requirements:

GOAL:Amplify the differential deformations of the massive bodies

over a wide frequency range.

• based on the elastic deformation of monolithic devices • well known for their applications in mechanical engineering.

* Gain of at least a factor 10.* Negligible thermal noise with respect to that of the

detector.