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Searches for stochastic gravitational wave background inLIGO data
Shivaraj Kandhasamy
University of Mississippi
September 23, 2014
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 1
Outline
1 Gravitational waves
2 Interferometric detectors and GW search methods
3 Searches for stochastic GW backgroundSources and search methodResults using non-colocated detectorsAnalysis using colocated detectorsOther stochastic analyses
4 Conclusions
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 2
Gravitational waves
Gravity and General relativity
In Newton’s theory (1686), gravity is an instantaneous force actingbetween two massive objects.
Space and time are just observers; everything happens in this absoluteunchangeable spacetime.
Einstein’s special theory of relativity (1905),
Time and space are relative;Speed of light is the maximum possible speed at which information canbe transferred.
In 1916, Einstein proposed a new theory of gravity, called generalrelativity (GR).
Gravity is the curvature of spacetime. Gravitational force is response ofthe objects to the curvature of spacetime.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 3
Gravitational waves
Einstein field equations
In GR, Einstein field equations relate mass-energy and curvature ofspacetime around it.
Gµν = Rµν −1
2gµνR =
8πG
c4Tµν
where Gµν , called the Einstein tensor, describes the curvature andTµν , called stress-energy tensor, represents mass-energy content.
The metric tensor gµν defines ‘distances’ in spacetime; for flatspacetime (i.e., no curvature), gµν is equal to the Minkowski metricηµν = diag(-1,1,1,1).
For spacetime that is close to flat, gµν = ηµν + hµν , where |hµν | 1;Linearized GR.
For Tµν = 0, in Linearized GR, Einstein field equations become,(52 − 1
c2∂2
∂t2
)hµν = 0
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 4
Gravitational waves
Gravitational waves (propagation)
The spacetime perturbations hµν in the previous equation are calledas gravitational waves (GWs).
In transverse traceless (TT) gauge, GWs propagating along z-axis canbe described by two components h+ and h×.
Since GWs interact very weakly with matter, they can travel fardistances without diminishing in amplitudes.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 5
Gravitational waves
Gravitational waves (production)
Accelerating charges → Electromagnetic wavesAccelerating mass distributions with quadrupole (or higher) moment→ Gravitational wavesStrength of GWs, strain
h (= ∆L/L) ∼ G
c4Q
rFor a NS-NS binary, separated by 100 km, at distance of 15 Mpch ∼ 10−21
Indirect evidence from Hulse-Taylor pulsar (PSR 1913+16).
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 6
Interferometric detectors and GW search methods
GW detectors
Since GWs produce differential change in lengths perpendicular totheir direction of propagation, interferometers are well suited for GWdetection.
LIGO (Laser Interferometer Gravitational-waves Observatory) hasbuilt three multi-kilometer interferometers (Hanford - 4 km and 2 km,Livingston - 4 km) with sensitivity of h ∼ 3× 10−23/
√Hz at 100 Hz.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 7
Interferometric detectors and GW search methods
Interferometric GW detector
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 8
Interferometric detectors and GW search methods
Sensitivity of LIGO detectors
Data is acquired in batches, called science runs.
Below is a sensitivity plot of LIGO detectors during their fifth sciencerun.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 9
Interferometric detectors and GW search methods
Sensitivity of LIGO detector
Data is acquired in patches, called science runs.
Below is a sensitivity plot of LIGO detectors during their fifth sciencerun.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 10
Interferometric detectors and GW search methods
Signal and search methods
Compact Binary Coalescence (CBC)
Short and modeledGW inspiral signals from coalescingbinary (NS-NS, NS-BH, BH-BH)Waveform is known; uses matchedfiltering methodUpper limits on the rates of suchevents,R90%,BNS = 8.7× 10−3yr−1L−110 (Phys.Rev. D 82, 102001 (2010))
Continuous wave (CW)
Long and modeledGWs from known pulsarsPeriodic signal with twice the frequency of pulsarUpper limits on the eccentricity ε of the pulsars (ApJ. 713, 671 (2010))
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 11
Interferometric detectors and GW search methods
Signal and search methods
Compact Binary Coalescence (CBC)
Short and modeledGW inspiral signals from coalescingbinary (NS-NS, NS-BH, BH-BH)Waveform is known; uses matchedfiltering methodUpper limits on the rates of suchevents,R90%,BNS = 8.7× 10−3yr−1L−110 (Phys.Rev. D 82, 102001 (2010))
Continuous wave (CW)
Long and modeledGWs from known pulsarsPeriodic signal with twice the frequency of pulsarUpper limits on the eccentricity ε of the pulsars (ApJ. 713, 671 (2010))
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 11
Interferometric detectors and GW search methods
Signal and search methods
Burst searches
Short and unmodeledGW bursts associated with external triggers such gamma-ray bursts(targeted search) and also all-sky searchUses both modeled and unmodeled searchUpper limits on strength of GWs, lower limits on distance to GRBs(ApJ. 715, 1438 (2010))
Stochastic GW search
Long and unmodeledstochastic GW background (astrophysical and cosmological origin)Uses cross correlation methodUpper limit on the energy density of SGWB in LIGO band (Nature 460,990 (2009))
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 12
Interferometric detectors and GW search methods
Signal and search methods
Burst searches
Short and unmodeledGW bursts associated with external triggers such gamma-ray bursts(targeted search) and also all-sky searchUses both modeled and unmodeled searchUpper limits on strength of GWs, lower limits on distance to GRBs(ApJ. 715, 1438 (2010))
Stochastic GW search
Long and unmodeledstochastic GW background (astrophysical and cosmological origin)Uses cross correlation methodUpper limit on the energy density of SGWB in LIGO band (Nature 460,990 (2009))
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 12
Searches for stochastic GW background Sources and search method
Stochastic GW background
Stochastic GW background arises from incoherent superposition ofmany unresolved sources.
Energy density in GWs is
ρGW =c2
32πG〈habhab〉
The stochastic GW spectrum is characterized by
ΩGW (f ) =1
ρc
∂ρGW (f )
∂lnf
ΩGW (f ) is related to strain power spectrum S(f ) by
S(f ) =3H2
0
10π2ΩGW (f )
f 3
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 13
Searches for stochastic GW background Sources and search method
Sources of stochastic GW background
Cosmological originInflationary scenarios
e60-fold expansion in very short time.Amplification of zero-point fluctuations of spacetime perturbations.Different types inflation; Different amplitude spectra for GWs.
Cosmic strings
Topological defects formed during phase transitions in the earlyuniverse.Could also be fundamental strings of string theory.
Exotic physics
Bubble collisionsDifferent (unexpected) equation of state
Astrophysical origin
Compact binary coalescence (BNS, BBH)MagnetarsInstabilities in compact objects
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 14
Searches for stochastic GW background Sources and search method
Sources of stochastic GW background
Cosmological originInflationary scenarios
e60-fold expansion in very short time.Amplification of zero-point fluctuations of spacetime perturbations.Different types inflation; Different amplitude spectra for GWs.
Cosmic strings
Topological defects formed during phase transitions in the earlyuniverse.Could also be fundamental strings of string theory.
Exotic physics
Bubble collisionsDifferent (unexpected) equation of state
Astrophysical origin
Compact binary coalescence (BNS, BBH)MagnetarsInstabilities in compact objects
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 14
Searches for stochastic GW background Sources and search method
Sources of stochastic GW background
Cosmological originInflationary scenarios
e60-fold expansion in very short time.Amplification of zero-point fluctuations of spacetime perturbations.Different types inflation; Different amplitude spectra for GWs.
Cosmic strings
Topological defects formed during phase transitions in the earlyuniverse.Could also be fundamental strings of string theory.
Exotic physics
Bubble collisionsDifferent (unexpected) equation of state
Astrophysical origin
Compact binary coalescence (BNS, BBH)MagnetarsInstabilities in compact objects
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 14
Searches for stochastic GW background Sources and search method
Sources of stochastic GW background
Cosmological originInflationary scenarios
e60-fold expansion in very short time.Amplification of zero-point fluctuations of spacetime perturbations.Different types inflation; Different amplitude spectra for GWs.
Cosmic strings
Topological defects formed during phase transitions in the earlyuniverse.Could also be fundamental strings of string theory.
Exotic physics
Bubble collisionsDifferent (unexpected) equation of state
Astrophysical origin
Compact binary coalescence (BNS, BBH)MagnetarsInstabilities in compact objects
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 14
Searches for stochastic GW background Sources and search method
Cosmological stochastic GW background
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 15
Searches for stochastic GW background Sources and search method
Cosmological and astrophysical stochastic GW background
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 16
Searches for stochastic GW background Sources and search method
Search method
Once source; matched filtering
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 17
Searches for stochastic GW background Sources and search method
Search method
Many sources; cross-correlation
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 18
Searches for stochastic GW background Sources and search method
Search method
Use of cross-correlation techniques
Cross-correlation estimator (of strainpower spectrum)
Y = T
∫ ∞−∞
df s1∗(f )s2(f )Q(f )
Theoretical variance
σ2Y ≈T
2
∫ ∞0
df P1(f )P2(f )|Q(f )|2
Optimal filter
Q(f ) =1
N
γ(f )Ω(f )
f 3P1(f )P2(f )
overlap reduction function γ(f )
0 100 200 300
−1
−0.5
0
0.5
1
Freq (Hz)
γ(f)
H1−H2H1−L1
Ω(f ) = Ωα fα
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 19
Searches for stochastic GW background Sources and search method
...Search method
Data is divided into smaller segments,Yi and σi are calculated for each segment iWeighted average performed to get final numbers
Yopt =
∑i σ−2i Yi∑
i σ−2i
, σ−2opt =∑i
σ−2i
Apply various cuts before combining the segments,Notching 60 Hz harmonics and other problematic frequencies
Stationarity cut; segments with|σi,nai−σi |
σi> 20% are removed.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 20
Searches for stochastic GW background Results using non-colocated detectors
Results using non-colocated detectors
Analyses using LIGO (S5 and S6)and Virgo (VSR1, VSR2 and VSR3)
S5 data (2005 to 2007) : 95 %UL ΩGW < 6.9× 10−6 for a flatspectrum.For the first time, LIGO sensitivitysurpassed the indirect boundsfrom BBN and CMB in the LIGOfrequency band.S6 and VSR2-3 data (2009 to2010) : 38 % better UL than S5result.
Advanced LIGO will be able tomake interesting constraints onsome of these models.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 21
Searches for stochastic GW background Results using non-colocated detectors
Results using non-colocated detectors
Analyses using LIGO (S5 and S6)and Virgo (VSR1, VSR2 and VSR3)
S5 data (2005 to 2007) : 95 %UL ΩGW < 6.9× 10−6 for a flatspectrum.For the first time, LIGO sensitivitysurpassed the indirect boundsfrom BBN and CMB in the LIGOfrequency band.S6 and VSR2-3 data (2009 to2010) : 38 % better UL than S5result.
Advanced LIGO will be able tomake interesting constraints onsome of these models.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 21
Searches for stochastic GW background Results using non-colocated detectors
Results using non-colocated detectors
Analyses using LIGO (S5 and S6)and Virgo (VSR1, VSR2 and VSR3)
S5 data (2005 to 2007) : 95 %UL ΩGW < 6.9× 10−6 for a flatspectrum.For the first time, LIGO sensitivitysurpassed the indirect boundsfrom BBN and CMB in the LIGOfrequency band.S6 and VSR2-3 data (2009 to2010) : 38 % better UL than S5result.
Advanced LIGO will be able tomake interesting constraints onsome of these models.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 21
Searches for stochastic GW background Results using non-colocated detectors
Results using non-colocated detectors
Analyses using LIGO (S5 and S6)and Virgo (VSR1, VSR2 and VSR3)
S5 data (2005 to 2007) : 95 %UL ΩGW < 6.9× 10−6 for a flatspectrum.For the first time, LIGO sensitivitysurpassed the indirect boundsfrom BBN and CMB in the LIGOfrequency band.S6 and VSR2-3 data (2009 to2010) : 38 % better UL than S5result.
Advanced LIGO will be able tomake interesting constraints onsome of these models.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 21
Searches for stochastic GW background Analysis using colocated detectors
Analysis using colocated detectors
A similar analysis was done using colocated H1H2 detectors.
Pros: Overlap reduction function is maximum; hence better sensitivitythan the other two pairs.Cons: Suffer from environmental and instrumental correlations.
We used time-shift methods (with shifts > coherence time) toidentify some of the narrowband correlations on longer time scales .
Apart from strain data, each observatory also records data fromvarious Physical Environment Monitoring (PEM) channels.
Seismometers, Microphones, RF receivers, Magnetometers
Since most of the narrowband correlations are caused by externalsources, they can be identified by using PEM data.
To some extent, they can also be used to estimate broadbandcorrelations due to environment.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 22
Searches for stochastic GW background Analysis using colocated detectors
Analysis using colocated detectors
A similar analysis was done using colocated H1H2 detectors.
Pros: Overlap reduction function is maximum; hence better sensitivitythan the other two pairs.Cons: Suffer from environmental and instrumental correlations.
We used time-shift methods (with shifts > coherence time) toidentify some of the narrowband correlations on longer time scales .
Apart from strain data, each observatory also records data fromvarious Physical Environment Monitoring (PEM) channels.
Seismometers, Microphones, RF receivers, Magnetometers
Since most of the narrowband correlations are caused by externalsources, they can be identified by using PEM data.
To some extent, they can also be used to estimate broadbandcorrelations due to environment.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 22
Searches for stochastic GW background Analysis using colocated detectors
Analysis using colocated detectors
A similar analysis was done using colocated H1H2 detectors.
Pros: Overlap reduction function is maximum; hence better sensitivitythan the other two pairs.Cons: Suffer from environmental and instrumental correlations.
We used time-shift methods (with shifts > coherence time) toidentify some of the narrowband correlations on longer time scales .
Apart from strain data, each observatory also records data fromvarious Physical Environment Monitoring (PEM) channels.
Seismometers, Microphones, RF receivers, Magnetometers
Since most of the narrowband correlations are caused by externalsources, they can be identified by using PEM data.
To some extent, they can also be used to estimate broadbandcorrelations due to environment.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 22
Searches for stochastic GW background Analysis using colocated detectors
Analysis using colocated detectors
A similar analysis was done using colocated H1H2 detectors.
Pros: Overlap reduction function is maximum; hence better sensitivitythan the other two pairs.Cons: Suffer from environmental and instrumental correlations.
We used time-shift methods (with shifts > coherence time) toidentify some of the narrowband correlations on longer time scales .
Apart from strain data, each observatory also records data fromvarious Physical Environment Monitoring (PEM) channels.
Seismometers, Microphones, RF receivers, Magnetometers
Since most of the narrowband correlations are caused by externalsources, they can be identified by using PEM data.
To some extent, they can also be used to estimate broadbandcorrelations due to environment.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 22
Searches for stochastic GW background Analysis using colocated detectors
Results from H1H2 analysis
UL of 7.7× 10−4 for f 3 spectrum; 460 Hz - 1000 Hz band
∼ 180 times better than S6-VSR23 result in this band
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 23
Searches for stochastic GW background Other stochastic analyses
Spherical harmonics and radiometer
Spherical harmonics analysis decomposes SGWB measurement intovarious spherical harmonics
Sky maps of SGWB (upperlimits)Is there a particular spatial distribution?
For point sources (eg., Sco X-1, galactic center), radiometer analysisis used.
Can provide constrains on source parameters such as (average)ellipticity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 24
Searches for stochastic GW background Other stochastic analyses
Spherical harmonics and radiometer
Spherical harmonics analysis decomposes SGWB measurement intovarious spherical harmonics
Sky maps of SGWB (upperlimits)Is there a particular spatial distribution?
For point sources (eg., Sco X-1, galactic center), radiometer analysisis used.
Can provide constrains on source parameters such as (average)ellipticity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 24
Searches for stochastic GW background Other stochastic analyses
Cosmological GWs and CMB polarization
Fluctuations in CMB are expected to provide information about thestate of the universe at the time of recombination (formation ofstable atoms).
Density fluctuations
It is also expected carry imprints of events (interactions) that tookplace before and after recombination.Inflation could stretch the quantum spacetime fluctuations intomacroscopic scales.
This would affect the polarization of observed CMB photonsThe strength of this polarization (tensor-to-scalar ratio r) wouldprovide clues about when the inflation happened; larger r correspondsto earlier inflation
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 25
Searches for stochastic GW background Other stochastic analyses
Cosmological GWs and CMB polarization
Fluctuations in CMB are expected to provide information about thestate of the universe at the time of recombination (formation ofstable atoms).
Density fluctuations
It is also expected carry imprints of events (interactions) that tookplace before and after recombination.Inflation could stretch the quantum spacetime fluctuations intomacroscopic scales.
This would affect the polarization of observed CMB photonsThe strength of this polarization (tensor-to-scalar ratio r) wouldprovide clues about when the inflation happened; larger r correspondsto earlier inflation
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 25
Searches for stochastic GW background Other stochastic analyses
Cosmological GWs and CMB polarization
Fluctuations in CMB are expected to provide information about thestate of the universe at the time of recombination (formation ofstable atoms).
Density fluctuations
It is also expected carry imprints of events (interactions) that tookplace before and after recombination.Inflation could stretch the quantum spacetime fluctuations intomacroscopic scales.
This would affect the polarization of observed CMB photonsThe strength of this polarization (tensor-to-scalar ratio r) wouldprovide clues about when the inflation happened; larger r correspondsto earlier inflation
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 25
Searches for stochastic GW background Other stochastic analyses
BICEP-2 results
BICEP-2 (Background Imaging of Cosmic Extragalactic Polarization)is an experiment at south pole aims to measure CMB polarization.
Recently (in March 2014) the team announced the detection ofimprints of cosmological GWs in CMB spectra
r = 0.2; higher than upper limits from other experimentsCould be due to dust background? PLANK expected to announce theirresult (in collaboration with BICEP-2) soon; PLANK’s recent dustresults (strongly) indicate that the BICEP-2’s result might be due todust.Assuming slow-roll inflation, this correspond to Ωgw = 10−15 in LIGOsensitivity band (and all other bands); Many orders of magnitude belowaLIGO sensitivity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 26
Searches for stochastic GW background Other stochastic analyses
BICEP-2 results
BICEP-2 (Background Imaging of Cosmic Extragalactic Polarization)is an experiment at south pole aims to measure CMB polarization.
Recently (in March 2014) the team announced the detection ofimprints of cosmological GWs in CMB spectra
r = 0.2; higher than upper limits from other experimentsCould be due to dust background? PLANK expected to announce theirresult (in collaboration with BICEP-2) soon; PLANK’s recent dustresults (strongly) indicate that the BICEP-2’s result might be due todust.Assuming slow-roll inflation, this correspond to Ωgw = 10−15 in LIGOsensitivity band (and all other bands); Many orders of magnitude belowaLIGO sensitivity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 26
Searches for stochastic GW background Other stochastic analyses
BICEP-2 results
BICEP-2 (Background Imaging of Cosmic Extragalactic Polarization)is an experiment at south pole aims to measure CMB polarization.
Recently (in March 2014) the team announced the detection ofimprints of cosmological GWs in CMB spectra
r = 0.2; higher than upper limits from other experimentsCould be due to dust background? PLANK expected to announce theirresult (in collaboration with BICEP-2) soon; PLANK’s recent dustresults (strongly) indicate that the BICEP-2’s result might be due todust.Assuming slow-roll inflation, this correspond to Ωgw = 10−15 in LIGOsensitivity band (and all other bands); Many orders of magnitude belowaLIGO sensitivity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 26
Searches for stochastic GW background Other stochastic analyses
BICEP-2 results
BICEP-2 (Background Imaging of Cosmic Extragalactic Polarization)is an experiment at south pole aims to measure CMB polarization.
Recently (in March 2014) the team announced the detection ofimprints of cosmological GWs in CMB spectra
r = 0.2; higher than upper limits from other experimentsCould be due to dust background? PLANK expected to announce theirresult (in collaboration with BICEP-2) soon; PLANK’s recent dustresults (strongly) indicate that the BICEP-2’s result might be due todust.Assuming slow-roll inflation, this correspond to Ωgw = 10−15 in LIGOsensitivity band (and all other bands); Many orders of magnitude belowaLIGO sensitivity.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 26
Searches for stochastic GW background Other stochastic analyses
Results from other measurements
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 27
Searches for stochastic GW background Other stochastic analyses
Other measurements of SGWB
Pulsar Timing array
Pulsars emit very stable periodic pulses;stability can even beat atomic clocks.The timing residuals of a pulsar could tell uswhat happens inside the pulsar as well asoutside of that pulsar.A correlated timing residuals from manypulsars would indicate a common source ofinterference; could be GWs.Sensitive to low-frequency GWs; frequencyinversely proportional to observation time
Earth’s normal modesEarth’s normal modes are observed after strong earthquakes; decayafter a few daysThese normal modes can also be excited by GWs of same frequency;forced oscillation (concept of bar detector).Look for the earth’s normal modes when there are no earthquakes
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 28
Searches for stochastic GW background Other stochastic analyses
Other measurements of SGWB
Pulsar Timing array
Pulsars emit very stable periodic pulses;stability can even beat atomic clocks.The timing residuals of a pulsar could tell uswhat happens inside the pulsar as well asoutside of that pulsar.A correlated timing residuals from manypulsars would indicate a common source ofinterference; could be GWs.Sensitive to low-frequency GWs; frequencyinversely proportional to observation time
Earth’s normal modesEarth’s normal modes are observed after strong earthquakes; decayafter a few daysThese normal modes can also be excited by GWs of same frequency;forced oscillation (concept of bar detector).Look for the earth’s normal modes when there are no earthquakes
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 28
Searches for stochastic GW background Other stochastic analyses
Results from other measurements
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 29
Searches for stochastic GW background Other stochastic analyses
Future Prospects
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 30
Conclusions
Conclusions
Searches for stochastic GW background in LIGO data, so far, didn’tfind any GW signal.
We have set upperlimits and constrained parameters of certain modelsFor the first time, upper limit from using GW detectors surpassed theindirect bounds from other observations.
With the advanced LIGO sensitivity, these limits are expected toimprove by a factor of ∼ 1000
There might be some surprise signals
Other experiments are also making significant progress; race for thefirst SGWB detection
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 31
Conclusions
Thank you!
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 32
Conclusions
Extra slides
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 33
Conclusions
Constraints on cosmic string models
10−9
10−8
10−7
10−6
10−12
10−10
10−8
10−6
10−4
10−2
100
Gµ
ε
p = 10−3
S4S5PulsarBBNCMBPlanckLIGO Burst
Figure: Probing of ε− Gµ plane by various experiments, for a typical value ofp = 10−3 (p is expected to be in the range 10−4 − 1). The excluded regions(always to the right of the corresponding curves) correspond to the S4 LIGOresult, current result, BBN bound, CMB bound, and the pulsar limit. Inparticular, the bound presented in this paper excludes a new region in this plane(7× 10−9 < Gµ < 1.5× 10−7 and ε < 8× 10−11), which is not accessible to anyof the other measurements.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 34
Conclusions
Constraints on Pre-Big-Bang models
1.35 1.4 1.45 1.510
10
1011
µ
f 1 (H
z)
AdvLIGOS5S4BBNCMBPlanck
Figure: The f1 − µ plane for a representative value of fs = 30 Hz in Pre-Big-Bangmodels. Excluded regions corresponding to the S4 result and to the resultpresented here are shaded. The regions excluded by the BBN and the CMBbounds are above the corresponding curves. The expected reaches of theAdvanced LIGO and of the Planck satellite are also shown.
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 35
Conclusions
PEM method2
In general, the strain data of the detectors can be written as
X (f ) = αGG (f ) +∑i
αi (f )Zi (f ) + nX (f )
Y (f ) = βGG (f ) +∑i
βi (f )Zi (f ) + nY (f )
where X ,Y are strain data, G (f ) represents GW signal, nX ,Y areuncorrelated noise in the detectors, α and β are coupling constantsbetween PEM channel Z and detectors X ,Y respectively.
The instrumental part of complex coherence between X (f ) and Y (f )can be written as
γinst =
∑i ,j α
∗i βjPZiZj√
PXXPYY=∑i ,j
γXZiγ−1ZiZj
γZjY
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 36
[2] N V Fotopoulos, Class. Quantum. Grav. 23 S693 (2006).
Conclusions
...PEM method
Estimates of γinst requires matrix inversion of γZiZj.
In practice, these matrices can be close to singular.
Assuming one dominant channel, we get,
γinst ≈ γXZiγZiY
and we maximize this quantity over all PEM channels to get a betterestimate.
The PEM (measurable noise correlation) contribution to stochasticGW estimators can be quantified by
SNRPEM =√
2Tdf γinst
where T is duration and df is frequency bin width used.We removed frequency bins that exceeded a certain SNRPEM
thresholdweekly, monthly and for full S5 run
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 37
Conclusions
SNRPEM for two channels over S5 run
Total of 172 PEM channels used for this analysis.
PEM channel: ISCT4−ACCX
Weeks
f (H
z)
20 40 60 80 10080
90
100
110
120
130
140
150
160
SN
RP
EM
−1
−0.5
0
0.5
1PEM channel: BSC1−MIC
Weeks
f (H
z)
20 40 60 80 10080
90
100
110
120
130
140
150
160
SN
RP
EM
−1
−0.5
0
0.5
1
Shivaraj Kandhasamy Searches for stochastic gravitational wave background in LIGO dataSeptember 23, 2014 38