A Radiometer for a Stochastic Background of Gravitational ... · July 13, 2007 Robert Ward, Caltech...
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Transcript of A Radiometer for a Stochastic Background of Gravitational ... · July 13, 2007 Robert Ward, Caltech...
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 1
A Radiometer for a Stochastic Background of Gravitational Radiation
Robert Wardfor the
LIGO Scientific Collaboration
Amaldi 7Sydney, Australia
July 2007
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 2
GW Radiometer Motivation
Stochastic GW Background due to Astrophysical Sources?Not isotropic if dominated by nearby sources
Do a Targeted Stochastic Search with LIGO
Source position information fromSignal time delay between different sites (sidereal time dependent)
Sidereal variation of the single detector acceptance
Time-Shift and Cross-Correlate!
Effectively a Radiometer for Gravitational Waves
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 3
The Radiometer
( ) ( ) ( )''')(~
21 ttQtstsdtdtYsiderealt −=Ω Ω∫ ∫
Detailed description in gr-qc/0510096),(
4)(2
ΩΩ≈Ω
siderealsidereal tt QQTσ
∆t
W
( ) ( )( ) ( )fPfP
ffHfQ sidereal
sidereal
tt
21
)( ΩΩ ∝
γ
H(f) is the source spectrum
3000km
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 4
Data Analysis Flow
Compute Cross Correlation spectrum & InvFFT(=CC time series)
Compute optimal filter Qiand theoretical variance σi
2
Estimate PSD (data from i-1, i+1 intervals)
Hann window, FFT
Detector 1 60 sec data segments
Inject simulated signal into data
Hann window, FFT
Detector 2 60 sec data segments
i = 1 2 3 …t
60sec
Downsample, HP filter,Calibrate, Mask Freq: 60 Hz,
120 Hz, …; Pulsars, …
Downsample, HP filter, Calibrate, Mask Freq: 60 Hz,
120 Hz, …; Pulsars, …
Estimate PSD (data from i-1, i+1 intervals)
Read out CC time series for each pixel (time shifted and scaled)
Optimally combine data from all segments for each pixel
Apply Blinding Here
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 5
LIGO’s Fourth Science Run (S4)
( )3147%90 /10010)2.112.0( fHzHzH −−×−=
astro-ph/0703234submitted to PRD
(corresponds to scale-invariantprimordial perturbation spectrum)
3
3100)( ⎟⎟
⎠
⎞⎜⎜⎝
⎛∝= f
HzfH β
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 6
Upper Limit map H(f)=const (b=0)
148%90 10)1.685.0( −−×−= HzH
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 7
Narrowband RadiometerSco-X1 (nearest LMXB), S4
Consistent with no signal
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 8
But the maps are convolved
'ΩΩ∝ YY
Point spread function
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 9
Point Spread Function
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 10
Convolution:Inject a diffuse source map
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 11
Deconvolution: Invert the covariance matrix
to get a maximum likelihood map
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 12
Or use a Spherical Harmonic Basis:Maximum Likelihood Estimation
Advantage of a smaller (tens instead of thousands), block diagonal, covariance matrix→lower computational cost.
Being actively pursued by the stochastic analysis group.
Rotational Symmetrycovariance =0 for m≠m’
different l’s at the same m are correlatedSymmetry broken due to diurnal sensitivity variations
Covariance matrix
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 13
Blinded Data from S5time shift the detector streams by more than the light
travel time between detectors→no true gw signal remains
SNR
With only the first 4 months of S5, upper limit sensitivity bound can reach (for H(f) = const (b=0)):
149%90 10)9.982.0( −−×−= HzH
already 10x better than S4 result
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 14
Finding for another detection metric:autocorrelation at each declination
For all i,j separated by DRANOT a standard 2-point correlation function
Can’t because of variability of point spread function with sky position
X(∆RA) at each declination (integral is over RA)Yi’s are point estimates of GW strainwi’s are statistical weights of each point on the sky (1st
attempt: use reciprocal of theoretical sigma)Overall normalization is X(0)
∑=∆ji
jjii wYYwRAX,
)(
i
iiw
σσ
=
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 15
Autocorrelation at each declination
90º
-90º
First 4 months of S5,blinded
H(f) = const
Working on a “detectionmetric”—what quantifies absence/presence of signal?
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 16
Average the autocorrelations at each declination, over all declinations
In the absence of signal, this can tell us about the resolving power of the instrument; consistentwith other estimates.
°⇒ 11500
3000
Hz
kmDλ
diffraction limited gw astronomy
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 17
Theoretical Sigma Maps from 2006 (S5)
Nov-Feb March
Because the IFOs still work better at night, the region of best sensitivity moves across the sky as the earth goes around the sun
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 18
The Near Future
Projected sensitivity increase and longer run time means we should surpass BBN bound during S5
Narrowband searches from more directions (Virgo cluster, galactic plane)
Continue development of maximum likelihood analysis, in both point-source (pixel) basis and spherical harmonic basis.
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 19
some questions for reviewers
I’ve included still-blind results from the first 4 months of S5, which reveal sensitivity and data quality. If I redo these results with more data (longer averaging for better sensitivity), can I replace them in the slides?
Can I add a blinded narrow-band result (repeat of Sco-X1 search) to show sensitivity increase?
should I add some more general introduction/motivation at the beginning?
advice on what to cut first if this is too long
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 20
The End
July 13, 2007 Robert Ward, Caltech LIGO-G070406-00-Z 21
Sigma Ratio DQ cut
0 0.5 .8 1 1.2 1.5 2 2.5 3 100
101
102
103
104
105
sigma ratio
num
ber o
f seg
men
ts
i = 1 2 3 …t
60sec
Don’t include any 60 second segments whose PSD gives a 20% larger sigma than neighboring PSD’s to reduce effects of nonstationarity.
This rejects 1.80% of the data1st 4 months of S5