LIGO-G060549-00-D

Stochastic Group Summary and Plans

Vuk Mandic

LSC Meeting

MIT, 11/05/06

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Stochastic Background of Gravitational Waves

Energy density:

Characterized by log-frequency spectrum:

Related to the strain power spectrum:

Strain scale:

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Detection Strategy Cross-correlation estimator

Theoretical variance

Optimal Filter

Overlap Reduction Function

For template:

Choose N such that:

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Analysis Details Data divided into segments:

» Yi and i calculated for each interval i.

» Weighed average performed. Sliding Point Estimate:

» Avoid bias in point estimate» Allows stationarity (Δσ) cut

|σi±1 – σi| / σi < Data manipulation:

» Down-sample to 1024 Hz» High-pass filter (~40 Hz cutoff)

50% overlapping Hann windows:» Overlap in order to recover the SNR

loss due to windowing.

ii

iii Y

Y2

2

opt

i

i22

opt

i-1 i i+1 i+2

Yi

i

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S4 H1L1 Isotropic

Combined H1L1 + H2L1:

» Ω0 σΩ = (-0.8 4.3) × 10-5

» 90% UL: 6.5 × 10-5

» H0 = 72 km/s/Mpc

» 51-150 Hz (includes 99% of inverse variance)

Paper submitted to ApJ.

» Resubmit with minor revisions.

» 1st S4 paper

» 1st ApJ paper

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S4 H1L1 Radiometer Design optimal filters for point-like sources

on the sky:» Avoid overlap reduction at high

frequencies. S4 H1L1 result nearly completed (S.

Ballmer):» Review Committee approved

preliminary results to be presented at the Texas Symposium in December 2006.

» Goal for the paper: final draft to be circulated to the LSC by the end of 2006.

» Paper geared toward PRD. Successfully injected and recovered 5

point-sources at SNR=10.» Isotropic search could not detect these

sources!

S. Ballmer

Flat spectrum in Ω

Simulated Sources

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S4: ALLEGRO-LLO

Cross-correlating ALLEGRO and LLO:» Strain sensitivity similar around 915 Hz.» Overlap reduction very small.

90% upper limit: Ω0 < 1.02» Strain < 1.5 × 10-23

» ~100× better than the previous limit at these frequencies.

Review committee approved preliminary results to be presented at GWDAW XI. » Paper is still under review, should be

available to the LSC by the end of the year.

» Paper geared toward CQG. At the moment, there are no plans to repeat

this experiment during S5.

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S4 H1H2 FSR Strain sensitivity of interferometers at free-

spectral-range (FSR) frequency is similar to low-frequency region.

Cross-correlate H1 and H2 at (Rochester group):» 37.5 kHz: H1 sensitivity similar to DC,

H2 ~130× worse than DC.» 75 kHz: H1, H2 sensitivities similar to

DC.» Acquire at 262 kHz, heterodyne to FSR

frequencies, use 200 Hz around FSR. Results are nearly finalized:

» Internal review to start in 2-3 weeks.» First draft of the paper should be

available soon. Remaining issues:

» Calibration to be reviewed.» Estimate of the time-jitter in the fast

channels.

S4 LHO-LLO

S4 ALLEGRO-LLO

1 FSR

2 FSR

Very Preliminary Results

A. Melissinos

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S5 H1L1 Isotropic First pass at H1L1:

» Time-shift: defining cuts blindly.» Analyzed up to Apr 3, 2006.

» σΩ = 1.67 × 10-5 (H0 = 72 km/s/Mpc)

» Coherence much cleaner than S4.

Online H1L1 analysis» Also done with time-shift.» Calibration and DQ cuts not

optimal.» As of Oct 11 2006:

– σΩ = 4.75 × 10-6

» BBN integral bound: 1.5 × 10-5

Coh = CSD2 / PSD1 / PSD2

Frequency (Hz)

σ

Days into the run

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S5 H1H2 Isotropic

Attempts to estimate and suppress instrumental and environmental correlations» PEM coherence method» Time-shift method

Independent and complementary methods.

Promising in terms of identification of “bad” frequency bands, but it is not clear yet how successful these approaches will be.

Hope to achieve sensitivity within a factor of 2-3 of the best possible.» Analysis of 11/05 – 04/06 data may

give σΩ ~ 2-3 × 10-6

» S5 H1H2 potential: few × 10-7

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S5 H1L1 Radiometer R. Ward is taking the lead in this

analysis. Repeat the H1L1 radiometer analysis,

but also deconvolve the antenna pattern and estimate errors on the deconvolved map.

Deconvolution of the antenna pattern (S. Mitra, Ph. D. Thesis):» Solved problem.» Also developed a method for

calculating the covariance matrix of the deconvolved map.

Goal: Have first results by the March LSC meeting.

S. Mitra

Effect of Deconvolution

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Potential LIGO-only S5 papers

S5 H1H2 isotropic, 40-220 Hz

» Potentially including results up to ~ 1 kHz. S5 H1L1 radiometer

» Including deconvolution and errors on deconvolved map.

» Including S5 LHO-LLO isotropic result. S5 H1H2 FSR

» Relatively straightforward repetition of the S4 FSR analysis.

» Better control of the time-jitter.

» Efforts toward understanding the noise budget at the FSR.

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LSC-VIRGO

Motivation» Multiple comparable all-sky stochastic searches above 200 Hz

» Possible improvements over the H1L1 search in the “zeros” of the overlap reduction function.

» Better resolution for anisotropic stochastic searches

Bi-weekly telecons» Comparing different (LSC and VIRGO) codes on simulated data.

» Recovering software injections with different codes.

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Implications: Cosmic Strings X. Siemens, V. Mandic, and J. Creighton,

astro-ph/0610920» Modified the work of Damour & Vilenkin

to include more accurate Universe model and to allow different cosmic string models

» Explore accessibility of cosmic string models to different experiments.

Conclusions:» Already exclude some models, with

great future potential.» Already more sensitive than BBN for a

few models.» Experiments are complementary.» Burst and stochastic LIGO searches:

overlap partly, partly complementary.» 1/p dependence. S4

S5

H1L

1

S5 H1H2

AdvLIGO

LISA

Pulsars

S5Burst

BB

N

CM

B

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Implications: Cosmic Strings X. Siemens, V. Mandic, and J. Creighton,

astro-ph/0610920» Modified the work of Damour & Vilenkin

to include more accurate Universe model and to allow different cosmic string models

» Explore accessibility of cosmic string models to different experiments.

Conclusions:» Already exclude some models, with

great future potential.» Already more sensitive than BBN for a

few models.» Experiments are complementary.» Burst and stochastic LIGO searches:

overlap partly, partly complementary.» 1/p dependence. S5 H

1L1

S5 H1H2

AdvLIGO

LISA

Pulsars

S5Burst B

BN

CM

B

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Implications: Cosmic Strings X. Siemens, V. Mandic, and J. Creighton,

astro-ph/0610920» Modified the work of Damour & Vilenkin

to include more accurate Universe model and to allow different cosmic string models

» Explore accessibility of cosmic string models to different experiments.

Conclusions:» Already exclude some models, with

great future potential.» Already more sensitive than BBN for a

few models.» Experiments are complementary.» Burst and stochastic LIGO searches:

overlap partly, partly complementary.» 1/p dependence.

S5 H1H2

AdvLIGO

LISA

Pulsars

S5Burst

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Implications: Cosmic Strings

In some models, loops are large at formation and long lived

» Models preferred by some. Again, exclude parts of the parameter

space. But, pulsar limit is more constraining

in this case. AdvLIGO and LISA will eventually

surpass the pulsar bound.

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Conclusions

S4 isotropic paper to be published in ApJ soon. S4 radiometer and ALLEGRO-LLO results approved for conference

presentations.» Papers largely reviewed, should be submitted to journals by the March

LSC meeting. S4 FSR results almost finalized

» Review should start in 2-3 weeks S5 H1L1 online analysis already surpassed the BBN integral bound. Potential LIGO-only S5 papers:

» H1H2 isotropic» H1L1 Radiometer, with deconvolution of antenna pattern» S5 H1H2 FSR

Efforts toward LIGO-VIRGO joint stochastic analysis have started Already excluding some theoretical models.

» Intend to continue such studies.

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Reach as a Function of Spectral Slope

- S3 H1L1: Bayesian 90% UL.

- S4 H1L1+H2L1: Bayesian 90% UL.

- Expected S5: design strain sensitivity and 1 year exposure.

- For H1L1, sensitivity depends on frequency band.

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S4 Injections

Software injections:

» Signal added to data in software.

» Successfully recovered down to Ω~5×10-5.

» Theoretical error agrees with the standard error over 10 trials.

Hardware injections:

» Physically moving the mirrors.

» Successfully recovered (within errors).

SoftwareInjections

HardwareInjections

HardwareInjection

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Interferometer Sensitivity

Sensitivity steadily improved over time.

Reached design sensitivity.

Started 1-year long run in November 2005.

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Summary of Analyses

“conversion”: Bad data segments defined in 60-sec analysis, then converted to 192-sec analysis

H1L1

H2L1

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Landscape

Cosmic Strings models and Pre-Big-Bang models:

- can easily escape other experimentalbounds

- accessible to LIGO.

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Cosmic Strings: Model Cosmic strings are:

» Topological defects formed in the early Universe.

» Fundamental strings (in string theory). Cosmic string cusps, with large Lorentz

boosts, can create large GW signals. Integrating over all directions and redshift yields a stochastic background.

Calculation done by Damour & Vilenkin, PRD71, 063510 (2005)

» Uncertainties exist.» Some of them can be resolved by

improving the calculation (ongoing work with X. Siemens et al).

Three parameters:» String tension: 10-12 < G < 10-6

» Reconnection probability: 10-3 < p < 1» Efficiency of damping perturbations with

GW radiation: 10-13 < < 10-2

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Cosmic Strings: Results

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Cosmic Strings: Results

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Cosmic Strings: Results

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Cosmic Strings: Results

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Pre-Big-Bang: Model

Amplification of vacuum fluctuations:» Universe transitions between different

regimes.» Super-horizon modes of vacuum

fluctuations are amplified. Inflation: Inflationary phase RD MD Pre-Big-Bang Models:

» Dilaton-dominated phase» Stringy phase» Radiation, followed by matter phase.

Three parameters: < 1.5 » fs – unconstrained» f1 – high-frequency cutoff

~f3

~f3-2

fs

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Pre-Big-Bang: Results

Scan f1 - plane for fs=30 Hz. For each model, calculate ΩGW(f) and

check if it is within reach of current or future expected LIGO results.

Beginning to probe the allowed parameter space.

Currently sensitive only to large values of f1.

Sensitive only to spectra close to flat at high-frequency.

But, not yet as sensitive as the BBN bound:

S3

S4

S5 H1L1

S5 H1H2

AdvLIGO H1H2

BBN

Mandic & Buonanno, PRD73, 063008, (2006).

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Pre-Big-Bang: Results

Can also define:

» zs = f1/fs is the total redshift in the stringy phase.

» gs/g1 = (fs/f1), where 2 = |2 - 3|

– gs (g1) are string couplings at the beginning (end) of the stringy phase

Probe fundamental, string-related parameters, in the framework of PBB models.

Assumed f1 = 4.3 × 1011 Hz (relatively large).