The Multi-IFO Hough Search using LIGO S4 Data Badri Krishnan (For - - PowerPoint PPT Presentation

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The Multi-IFO Hough Search using LIGO S4 Data

Badri Krishnan (For the LIGO Scientific Collaboration)

Max Planck Institut für Gravitationsphysik Albert Einstein Institut, Germany

11th Gravitational Wave Data Analysis Workshop Potsdam, December 2006

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Outline

1

Overview of CW Signals

2

The Hough Algorithm

3

Summary of S2 Results

4

The S4 Hough Search

5

Outlook

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Overview

Rapidly rotating and non-axisymmetric isolated Neutron stars are the most promising sources for long-lived periodic gravitational wave signals. Possible mechanisms for GW emission: Deformation of the crust due to elastic stresses or magnetic fields Unstable fluid oscillation modes (the r-modes) Free precession of the whole star

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The Waveform

In the rest frame of the star, the signal is a slowly varying sinusoid with a quadrupole pattern: h+(t) = A+ cos Φ(t) h×(t) = A× sin Φ(t) A+ = h0 1 + cos2 ι 2 A× = h0 cos ι h0 = 16π2G c4 Iǫf 2

r

d ι: pulsar orientation w.r.t line of sight ǫ: equatorial ellipticity fr: rotation frequency d: distance to star

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The Waveform

The received signal is amplitude modulated due to the detector antenna pattern h(t) = F+(t; α, δ, ψ)h+(t) + F×(t; α, δ, ψ)h×(t) (1) and the frequency is also Doppler modulated f(t) − ˆ f(t) = ˆ f(t)v(t) · n c . (2) The Doppler modulation allows us to locate the pulsar in the sky but it is also responsible for the computational cost – each sky location has to be demodulated separately.

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Semicoherent Searches

Fully coherent searches are computationally expensive – analysis of, say, 1 year of data is not possible with these methods alone Semi-coherent methods are computationally efficient but less sensitive for a given observation time These methods combine short segments of Fourier transformed data (SFTs)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Semicoherent Searches

Three methods are used currently within the LSC

Stackslide sums normalized SFT power ρ =

N

• i=1

|˜ x(i)

k |2

Power-Flux sums weighted SFT power ρ =

N

• i=1

wi|˜ x(i)

k |2

Hough sums weighted binary counts n =

N

• i=1

win(i)

k

where n(i)

k =

• 1

if |˜ x(i)

k |2 ≥ ρ0

if |˜ x(i)

k |2 < ρ0

.

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Semicoherent Searches

The three methods have different advantages

Powerflux is the most sensitive Hough is more robust and computationally efficient Stackslide is the simplest and also does quite well on sensitivity and cost

The weights are (optimally) proportional to the SNR of a signal in the different SFTs. For Hough, the weights are: wi ∝ F 2

+(ti) + F 2 ×(ti)

S(i)

n (f)

Weights normalized so that n ∈ [0, N]:

N

• i=1

wi = N

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Sensitivity

Hough weights suggested by Palomba et al (GWDAW 9) Improvement in sensitivity due to weights is important when non-stationarities in SNR are large For a given false dismissal rate β, weakest signal that can cross a threshold corresponding to a false alarm rate α is h0 = 3.38S1/2 || w||

• w ·

X 1/2 S(eff)

n

Tsft where Xi = S(eff)

n

F 2

+(ti) + F 2 ×(ti)

S(i)

n (f)

and S = erfc−1(2α) + erfc−1(2β)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The S2 Search

All sky search, 200-400 Hz, 11 spindowns including 0 with δ˙ f = 1.1 × 10−10Hz/s. No weights used: n = ni. L1, H1 and H2 analyzed separately using 1800s SFTs No signal detected Population based frequentist upper limit set by Monte-Carlo signal injections using loudest event in 1Hz bands Known spectral lines consistently avoided while finding loudest events and also during signal injections

• Phys. Rev. D 72, 102004 (2005)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The S2 Hough Upper-Limits

200 250 300 350 400 10

−23

10

−22

10

−21

Frequency (Hz) 95% confidence upper limits for h0 L1 H1 H2

Best UL: 4.43 × 10−23 (L1 at 200Hz)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Parameter Space for the S4 Search

Weights allow us to use SFTs from all three IFOs together Sensitivity increases by ∼ 10% due to weights 899 SFTs from L1, 1004 from H1, and 1063 from H2 Frequency band is 50-1000 Hz All sky search Sky is broken up into 92 patches each ∼ 0.4 rad wide 10 spindown parameters analysed with resolution δ˙ f = (TobsTsft)−1 ≈ 2.2 × 10−10 Hz All-sky upper limits set in 0.25 Hz bands based on loudest event

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Skypatch size

Size of skypatch is limited because weights are not valid for entire sky Size of each skypatch depends on angular variation of F+,× Sky broken up into 92 patches, each ∼ 0.4rad × 0.4rad. For this choise of skypatch size, mismatch between sky-position where weights are calculated and where signal is injected can lead to loss of ∼ 5% in SNR

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Contribution of the Different IFOs

Look at the quantity fractional noise weight contribution of each IFO, for example

• H1 wi
• H1 wi +

L1 wi + H2 wi

200 400 600 800 1000 0.2 0.4 0.6 0.8 1 Frequency (Hz) Relative Weights Relative contributions from the three IFOs L1 H2 H1

It is worthwhile to in- clude H2 in multi-IFO search, especially at high frequencies. H1 always contributes most.

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Most Significant Events in 0.25 Hz bands – Preliminary

200 400 600 800 1000 50 100 Frequency (Hz) Multi−IFO 200 400 600 800 1000 50 100 Frequency (Hz) H1 200 400 600 800 1000 20 40 60 Frequency (Hz) L1 Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Following up the outliers

Set a significance threshold of 7 in multi-IFO results For every candidate, look for coincident events in L1 and H1 with threshold 6.6 Exclude 60Hz harmonics and violin modes 7 events survive these criteria Further follow-ups of these 7 candidates shows them not to be of astrophysical origin Aim to perform a coherent F-statistic follow-up in future searches

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Following up the outliers

Hough significance Band (Hz) Multi-IFO H1 L1 Comment 1 78.602-78.631 12.466 12.023 10.953

• Inst. Lines

2 108.850-108.875 29.006 23.528 16.090

• Inj. Pulsar3

3 130.402-130.407 7.146 6.637 6.989 ? 4 193.92-193.96 27.911 17.327 20.890

• Inj. Pulsar8

5 575.15-575.23 13.584 9.620 10.097

• Inj. Pulsar2

6 721.45-721.50 8.560 6.821 13.647 L1 Inst. Lines 7 988.80-988.95 7.873 8.322 7.475

• Inst. Lines

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Following up the outliers

Parameters of the outlier at 130.4 Hz Detector s f0 (Hz) df/dt (Hz/s) α (rad) δ (rad) Multi-IFO 7.146 130.4028 −1.745 × 10−9 0.8798

• 1.2385

H1 6.622 130.4039 −1.334 × 10−9 2.1889 0.7797 H1 6.637 130.4050 −1.334 × 10−9 2.0556 0.6115 L1 6.989 130.4067 −1.963 × 10−9 1.1690

• 1.0104

Candidate does not pass coincidence test in sky-location

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Preliminary Upper Limits

Hough ULs are predicted by h95% = 11.0S1/2

• S(eff)

n

Tsft where S(eff)

n

=   

N

• i=0

1

• S(i)

n

2   

−1/2

and S = erfc−1(2α) + erfc−1(2β)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Preliminary Hough S4 Upper Limits

200 400 600 800 1000 10

−24

10

−23

10

−22

10

−21

10

−20

10

−19

Frequency (Hz) Hough 95 % UL L1 H1 Multi

Best upper-limit on h0: 4.3 × 10−24 (140.25 Hz-140.50 Hz)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Preliminary Hough S4 Upper Limits

100 200 300 400 500 600 700 800 900 1000 10

−24

10

−22

10

−20

Frequency (Hz) Hough Multi−IFO 95% UL measured predicted 100 200 300 400 500 600 700 800 900 1000 10

−24

10

−22

Frequency (Hz) Hough H1 95% UL measured predicted 100 200 300 400 500 600 700 800 900 1000 10

−24

10

−22

Frequency (Hz) Hough L1 95% UL measured predicted

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Improvements Due to the Weights – Preliminary

800 820 840 860 880 900 1.8 2 2.2 2.4 2.6 x 10

−23 frequency Hough coarse 95 % UL

with weights with no weights

Average improvement by using weights in this band is 9.25% for multi-IFO case (but only ∼ 6% for single IFO)

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Hardware Injections – Preliminary

575.12575.14575.16575.18 575.2 5 10 15 20 Frequency (Hz) Significance Pulsar 2 Multi H1 L1 108.82108.84108.86108.88 108.9 10 20 30 40 Frequency (Hz) Significance Pulsar 3 193.9 193.95 194 10 20 30 40 Frequency (Hz) Significance Pulsar 8 763.8 763.82763.84763.86763.88 2 4 6 8 10 Frequency (Hz) Significance Pulsar 9 Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Hardware Injections – Preliminary

Right Ascension Declination Pulsar 2, Freq =575.1633 Hz s =0 Hz/s 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 −0.1 −0.05 0.05 0.1 0.15 0.2 0.25 −2 2 4 6 8 10 12 14 Right Ascension Declination Pulsar 3, Freq =108.8572 Hz s =0 Hz/s 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 −0.75 −0.7 −0.65 −0.6 −0.55 −0.5 −0.45 −0.4 5 10 15 20 25 30 35 Right Ascension Declination Pulsar 8, Freq =193.9411 Hz s =−8.3968e−09 Hz/s 5.95 6 6.05 6.1 6.15 6.2 6.25 6.3 −0.75 −0.7 −0.65 −0.6 −0.55 −0.5 −0.45 −0.4 5 10 15 20 25 30 35 Right Ascension Declination Pulsar 9, Freq =763.8472 Hz s =0 Hz/s 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 −2 2 4 6 8

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

Where we are going

Wide parameter space searches: We aim to carry out a multi-IFO Hierarchical search consisting of Hough on F-statistic segments to optimize sensitivity We aim to implement this for the S5 search

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z

Overview of CW Signals The Hough Algorithm Summary of S2 Results The S4 Hough Search Outlook

The "Big Picture"

10-26 10-25 10-24 10-23 10-22 10-21 10 100 1000 h0 GW Frequency [Hz] LIGO-I Virgo A d v L I G O Crab B1937+21[S1] J0537-69 B1951+32 ScoX1 ScoX1[S2] Vela F s t a t [ S 2 ] Hough[S2] Blandford-LSC E@H[S3] S e m i C

• h

[ S 4 ] E@Hopt[S5] Spindown UL Targeted[S2] Targeted [S4]

Badri Krishnan(For the LIGO Scientific Collaboration) LIGO-G060651-00-Z