Searches for stochastic gravitational wave background in ... · Outline 1 Gravitational waves 2 Interferometric detectors and GW search methods 3 Searches for stochastic GW background

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


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.


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


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.


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).


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.



Interferometric GW detector



Sensitivity of LIGO detectors

Data is acquired in batches, called science runs.

Below is a sensitivity plot of LIGO detectors during their fifth sciencerun.



Sensitivity of LIGO detector

Data is acquired in patches, called science runs.

Below is a sensitivity plot of LIGO detectors during their fifth sciencerun.



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))




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))




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))




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))


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



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






Cosmic strings


Exotic physics









Cosmic strings


Exotic physics









Cosmic strings


Exotic physics






Cosmological stochastic GW background



Cosmological and astrophysical stochastic GW background



Search method

Once source; matched filtering



Search method

Many sources; cross-correlation



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



...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.


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.




















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.

































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


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.



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.



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

















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.



BICEP-2 results






BICEP-2 results






BICEP-2 results






Results from other measurements



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



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



Results from other measurements



Future Prospects


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


Conclusions

Thank you!


Conclusions

Extra slides


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.


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.


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


[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


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


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Searches for stochastic gravitational wave background in ... · Outline 1 Gravitational waves 2 Interferometric detectors and GW search methods 3 Searches for stochastic GW background