# Presentation: 848516

## Analysis of the first LIGO dataResults from S1

- Presented by Nergis MavalvalaOn behalf of the LIGO Scientific Collaboration
- GW Sources Workshop, MD April 2003

- LIGOLaboratory

- LIGOScientificCollaboration

- U.S. National Science Foundation

- U.K.GermanyJapan Russia
- India
- Spain
- Australia

- The Laser Interferometer Gravitational-wave Observatory

## Global network of inerferometers

- AIGO

**LIGO**

**LIGO**

**LISA**

**VIRGO**

**TAMA**

**GEO**

** ****Detection confidence**
** ****Source polarization**
** ****Sky location**

## LIGO

**LA**

**WA**

- 4 km(L1)

- 2 km (H2)

- 4 km (H1)

## Science Running Plan

**Interferometer performance**
- Intersperse commissioning and data taking consistent with obtaining one year of integrated data at *h = 10**-21* by end of 2006
**Astrophysical searches**
- Two “upper limit” runs S1 and S2 (at unprecedented early sensitivity) are  interleaved with commissioning
**S1****	****Aug-Sep 2002****	****   duration:  2 weeks**
**S2****	****Feb-Apr 2003****	****   duration:  8 weeks**
- First search run (S3) planned for late 2003 (duration: 6 months)
**Finish detector integration & design updates... **
- Engineering "shakedown" runs interspersed as needed
**Advanced LIGO**

## S1 Run Summary

**August 23 – September 9, 2002: 408 hrs (17 days).**
- _H1__ (4km): duty cycle 57.6% ; Total Locked time: 235 hrs _
- _H2__ (2km): duty cycle 73.1% ; Total Locked time: 298 hrs _
- _L1__ (4km): duty cycle 41.7% ; Total Locked time: 170 hrs _
**Double coincidences: **
- _L1__ && __H1__ : duty cycle 28.4%; Total coincident time: 116 hrs _
- _L1__ && __H2__ : duty cycle 32.1%; Total coincident time: 131 hrs _
- _H1__ && __H2__ : duty cycle 46.1%; Total coincident time: 188 hrs _

** ****Triple Coincidence****: **_L1__, __H1__, _**and **_H2__ : duty cycle 23.4% ; total 95.7 hours_

## Strain Sensitivities During S1

- 3*10-21 Hz -1/2@ *f* ~300 Hz

- H2 & H1

- L1

**Notes:**
Substantially
Equals level of best strain sensitivity of TAMA (data taking 7, during S1), but at lower frequency

## Analysis working groups

- Inspiral
- Coalescing compact binaries
- Periodic
- Periodic continuous waves
- Burst
- Triggered
- Untriggered
- Stochastic
- Primordial Big Bang background
- Continuum of sources

**Notes:**
Coalescing compact binaries  chirp sources
NS-NS  far away; long periods; final inspiral gives GW chirp
NS-BH  tidal disruption of NS by BH; merger  GRB triggers
Inspiral  accurate predition with PPN proportional to (v/c)^11
Merger  nonlinear dynamics of highly curved spacetime
Ringdown  ringdown of modes of coalesced object

Periodic sources
Spinning NS  axisymmetry unknown
Galactic pulsars in SN remnant gases   non-axisymmetry unknown
LMXBs  mass accretion from companion
  Is accretion spin-up balanced by GW spin-down?
Issues  axisymmetric distortion from radiation reaction force

Supernovae
Collapse  Dynamics not understood. If instability makes star into tumblong bar, then GWs
Core convection  detect via correlations with neutrinos

## Data Analysis Approach

- Interferometric **GW data **(0.2 MB/sec)
- Continuous time series (16 kS/sec) of anti-symmetric port measures the strain of a gravitational wave
- Additional **auxiliary** channels (9 MB/sec)
- Report on instrument servo systems and  physical environment
- Instrument **calibration** at the 10% level
- Response tracking  continuous fixed sinusoids
- Transfer function mapping  complete sweep sine calibration
- Analysis** **emphasis
- Establish** methodology**, no sources expected
- End-to-end **check and validation** via software and hardware **injections** mimicking passage of a gravitational wave

## Search for GW Bursts

**Sources:** known and unknown phenomena emitting short transients of gravitational radiation with unknown waveform (supernovae, black hole mergers)
**Analysis goals:**  broad frequency band search to
- Establish a **bound on their rate** at the instruments
- Interpret  bound in terms of a source and population model on a **rate vs. strength** exclusion plot
**Search methods:**
**Time domain**** **algorithm (“SLOPE”)  identifies rapid increase in amplitude of a filtered time series (threshold on ‘slope’)
**Time-Frequency domain**** **algorithm (“TFCLUSTERS”)  identifies regions in the time-frequency plane with excess power (threshold on pixel power and cluster size)

## Upper Limit on Rate of Bursts

- End result of analysis pipeline  number of triple coincidence events
- Time-shift experiments  establish number of background events
- Feldman-Cousins  set 90% confidence upper limits on rate of foreground events
- TFCLUSTERS  < 1.4 events/day
- SLOPE  < 5.2 events/day
- Determine detection efficiency of the end-to-end analysis pipeline via signal injection of various morphologies
- Assuming a population of sources uniformly distributed on a sphere around detectors, establish upper limit on rate of bursts as a function of their strength

## Rate vs. Strength Plots for a Burst Model

## Burst Search Results and the Future

- Search and raw results sensitive to a wide variety of waveform morphologies and broad frequency features** **(provided signal has significant strain amplitude in LIGO frequency band)
- Strain upper limit assumes a burst model of 1 ms Gaussian pulses  **1.4** events/day
- Rate increases as the detection efficiency decreases
- 50% efficiency point is at **h ~ 3 x 10****-17**
- In the near future
- Use multiple-interferometer information on amplitude of putative signal and correlation statistic of their raw time-series.
- Improve time-resolution of event  trigger generators.
- Externally triggered (by GRB’s, neutrinos) search for bursts

## Search for Inspirals

**Sources**
- Orbital-decaying neutron star binaries
- Black hole binaries
- MACHOs
**S1 analysis goals**
- determine an upper limit on the rate of binary neutron star inspirals in the universe
- Search for black hole binaries and MACHOs  will be pursued in the future
**Search method **
- waveforms calculable
- use optimal** **matched filtering ****** **correlate detector’s output with template waveform

## Sensitivity to Inspirals in S1

- 1-3M neutron star search
- Second-order post-Newtonian template waveforms for **non-spinning** binaries
- Discrete set of 2110 templates designed for at most 3% loss in SNR
**Range **of detectability of a 1.4 M -1.4 M inspiral (optimally oriented, SNR = 8)
**L1:** 110 kpc < D < 210 kpc
**H1:**  40 kpc < D < 75 kpc
**H2:**  38 kpc < D < 70 kpc
- Sensitive to inspirals in
- Milky Way, LMC & SMC

## Results of the Inspiral Search

- Upper limit on binary neutron star coalescence rate
- Use all triggers from Hanford and Livingston: 214 hours
- Use **maximum signal-to-noise ratio** statistic to establish the rate limit
- Monte Carlo simulated injections  **efficiency**  =  0.51
- 90% confidence limit rate ** **
- Express the rate as a rate per **Milky-Way Equivalent Galaxies** (MWEG)

- R < 2.3 / (0.51 x 214 hr) = 164 /yr/(MWEG)

- Previous observational limits
- TAMA (Japan)   R < 30,000 / yr / MWEG
- Caltech 40m      R <  4,000 / yr / MWEG
- Theoretical prediction
- R < 2 x 10-5 / yr / MWEG

- Background distr. & population events

## Search for Stochastic Radiation

**Sources**
- Early universe
- Many weak unresolved sources emitting GWs independently  a random type of radiation described by its spectrum (isotropic, unpolarized, stationary and Gaussian)
**Analysis goals**
- Constrain contribution of stochastic GW radiation energy, ********GW**** **to the total energy required to close the universe, ********critical**

## Methods for the Stochastic Search

- Optimally filtered** **cross-correlation of detector pairs
- L1-H1, L1-H2 and H1-H2
- Detector** separation** and **orientation** reduces correlations at high frequencies (*GW* _>_ 2 x baseline)  overlap reduction function
- H1-H2 best suited
- L1-H1(H2) significant <50Hz
- Achievable sensitivities  to  by detector pairs in S1

- T~200000 sec and (f~100 Hz) ~ 0.1  1/400

## Results of Stochastic Search

- Non-negligible LHO 4km-2km (H1-H2) cross-correlation
- currently being investigated
- Previous best upper limits measured
- Garching-Glasgow interferometers(1994)
- EXPLORER-NAUTILUS (cryogenic bars)(199, 2000)

**61.0 hrs**

**62.3 hrs**

**T****obs**

**still in progress**

******GW ****(40Hz - 314 Hz) < 72.4**

**90% CL Upper Limit**

**LHO 2km-LLO 4km**

**LHO 4km-LLO 4km**

**Interferometer Pair**

## Search for Continuous Waves (CW)

**Search for Continuous Waves (CW)**

**Sources**  **known rotating neutron stars**
- Gravitational waves due to small shape distortions (non-axisymmetry  ellipticity)
- Precession (damping likely)
- Excited modes of oscillation (r-mode growth saturation)
**Analysis goals**Given the position, frequency and spin-down parameter of a known pulsar establish **an** **upper limit on the characteristic amplitude** of its continuous wave emission
**Achievable sensitivities**Amplitude detectableat detector

- strain PSD

- observation time

- 1% false alarm & 10% false dismissal

## Detectable amplitudes with a 1% false alarm rate and 10% false dismissal rate 
For S1 (colored curves)
At design sensitivities (black curves)
Upper limits on <ho> from spin-down measurements of known radio pulsars (filled )
Limits of detectability for rotating NS with equatorial ellipticity 
=I/Izz 10-3 , 10-4 , 10-5 @ 8.5 kpc

**Detectable amplitudes** with a 1% false alarm rate and 10% false dismissal rate
- For S1 (colored curves)
- At design sensitivities (black curves)
- Upper limits on *<h**o**>**** ***from spin-down measurements of known radio pulsars (filled )
**Limits** of detectability for rotating NS with equatorial ellipticity
*********=************I/I******zz********** *****10****-3**** , 10****-4**** , 10****-5***** ******@ *****8.5 kpc**

***<h******o******>= 11.4 [S******h******(f******o******)/T]******1/2***

**Expectations for Continuous Waves**

**S1: NO DETECTION**
**EXPECTED**

**Notes:**
This slide shows that with the S1 sensitivity and observation time we cannot set astrophysically interesting ULs – this is why I highlit “methods” in the title. This is what the S1 analysis is about:methods. In fact we have exercised the analysis pipeline, established methods for setting UL that we will use when we get to a more interesting sensitivity region and are anyway setting upper limits that, using  GW data, have not been set before. 

## Algorithms for CW Search

- Central parameters in detection algorithms
** ****Frequency** **modulation** of signal due to
- Earth’s motion relative to the Solar System barycenter
- Intrinsic frequency changes
** ****Amplitude** **modulation** due to
- The detector’s antenna pattern
- Search for **known pulsars** dramatically reduces the parameter space
-  computationally feasible
- Two search methods used
** ****Frequency-domain** based (Frequentist)
** ****Time-domain** based (Bayesian)

**Notes:**
I think that here a comment on the time-domain analysis along the lines of where the technique comes from and how it compares to what’s done in radio astronomy should, if not appear explicitly in the slides, at least be known to the person presenting. Graham/Stuart/Rejean would you mind summarizing your email exchange on the subject ? Thanks.

## Results of CW Search

- PSR J1939+2134  ** **no evidence of continuous wave emission
- Summary of 95% upper limits** **on h

_**IFO**__**	**__**    Frequentist FDS       Bayesian TDS**_
**GEO**	    (1.940.12)x10-21       (2.1 0.1)x10-21
**LLO** 	    (2.830.31)x10-22       (1.4 0.1)x10-22
**LHO-2K**     (4.710.50)x10-22       (2.2 0.2)x10-22
**LHO-4K**	    (6.420.72)x10-22       (2.7 0.3)x10-22
**Joint**	  	-                       (1.0 0.1)x10-22

- ho<1.0x10-22 constrains ellipticity < 7.5x10-5  (M = 1.4M    r = 10 km    R = 3.6 kpc)** **
- Previous results for PSR J1939+2134
**h****o**** < 10****-20**  (Glasgow, Hough et al., 1983)
**h****o**** < 3.1(1.5) x 10****-17**  (Caltech, Hereld, 1983)

**Notes:**
This slide shows preliminary results obtained with S1 data.

## Summary of upper limits for S1 

** ****Upper limits as presented at AAAS meeting Feb 2003**
**Stochastic backgrounds   **
**Upper limit ********0**** < 72.4****(H1- H2 pair)**
**Neutron star binary inspiral****     **
**Range of detectability < 200 kpc****(1.4 – 1.4 M****SUN**** NS binary with SNR = 8)**
**Coalescence Rate for Milky Way equivalent galaxy < 164/yr 90% CL**
**Periodic sources ****PSR J1939+2134 at 1283 Hz****   **
**GW radiation *****h < 2 10******-22*****  90% CL ****(expect *****h***** ~ 10****-27**** if pulsar spindown entirely due GW emission*****)***
**Burst sources**
**Upper limit*****  h < 5 10******-17*****  90% CL**
**S2 is ~10x more sensitive and ~4x longer **

**Limit from Big Bang ****Nucleosynthesis < 10****-4**

**Standard Inflation ****Prediction < 10****-15**

- S1

- 6 Jan

- Strain Sensitivity coming into S2

## Displacement Sensitivity(Science Run 1, Sept. 2002)

## LIGO has started taking data
First science run (S1) last summer
Collaboration has carried out first analysis looking for
Bursts
Compact binary coalescences
Stochastic background
Periodic sources
Second science run (S2) ended last week
Sensitivity is ~10x better than S1
Duration is ~ 4x longer
Bursts  4x lower rate limit  & 10x lower strain limit
Inspirals  reach > 1 Mpc -- includes M31 (Andromeda)
Stochastic background  limits on GW < 10-2
Periodic sources  limits on hmax ~ few x 10-23  ~ few x 10-6 @ 3.6 kpc

**First science run** (S1) last summer
- Collaboration has carried out first analysis** **looking for
- Bursts
- Compact binary coalescences
- Stochastic background
- Periodic sources
**Second science run** (S2) ended last week
- Sensitivity is ~10x better than S1
- Duration is ~ 4x longer
- Bursts  4x lower rate limit  & 10x lower strain limit
- Inspirals  reach > 1 Mpc -- includes M31 (Andromeda)
- Stochastic background  limits on GW < 10-2
- Periodic sources  limits on hmax ~ few x 10-23  ~ few x 10-6 @ 3.6 kpc

**LIGO Science Has Started**