Test of scalar-tensor gravity theory from observations of gravitational

LIGO-G1100039
Test of scalar-tensor gravity theory from
observations of gravitational wave bursts
with advanced detector network
Kazuhiro Hayama
National Astronomical Observatory of Japan
Max Planck Institute for Gravitational Physics
(Albert Einstein Institute Hannover)
1
2011年1月29日土曜日
Search for scalar gravitational waves
Testing relativistic gravity theory is important for fundamental physics
and cosmology e.g. dark matter, dark energy, accelerating the Universe.
One of plausible gravity theories is scalar-tensor theory. Significant
difference from the general relativity is the existence of a scalar field
which is connected with the gravity field with coupling parameters, and
a resulting scalar gravitational wave. Brans-Dicke theory is famous
scalar-tensor theory which has a coupling parameter ωBD.
Tensor GW search might miss some type of sources, e.g. highly spherical
core collapse if scalar-tensor theory is correct. In this sense, search for
SGW is complementary to current GW search.
This talk will focus on search for SGW from Galactic spherical core
collapses in Brans-Dicke theory.
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2011年1月29日土曜日
Antenna pattern for scalar mode
Antenna pattern function as a function of
sky position (θ,Φ) is written as
1
F+ (Ω̂) =
(1 + cos2 θ) cos 2φ
2
F× (Ω̂) = cos θ sin 2φ
F◦ (Ω̂) = − sin2 θ cos 2φ.
M.Tobar etal(1999), M. Maggiore etal(2000), K.Nakao etal(2001)
Polarization of tensor, scalar gravitational wave
Tensor GW
h+
hx
GW
Fo(ϑ,φ)
Scalar GW
ho
Spin0
C.Will, Living Review (2006)
2011年1月29日土曜日
3
Antenna pattern sky-map of scalar mode
H1
HLV
90 N
Fav(fo,H1)
90 N
latitude
45 N
latitude
Latitude
45 N
0
0
45 S
45 S
90 S
180 W
90 S
180 W135 W 90 W 45 W 0
45 E 90 E 135 E 180 E
longitude
135 W
0.05
0.1
0.2
0.3
0.15
0
longitude
0.2
45 E
0.25
90 E
0.3
135 E
0.35
180 E
0.4
HLVA
HLVAJ
90 N
45 N
latitude
45 N
latitude
0.1
45 W
0.4
Longitude
90 N
90 W
0
45 S
0
45 S
90 S
180 W
0.05
2011年1月29日土曜日
135 W
0.1
90 W
0.15
45 W
0.2
0
longitude
0.25
45 E
0.3
90 E
0.35
135 E
0.4
90 S
180 W
180 E
4
135 W
0.1
90 W
0.15
45 W
0.2
0
longitude
0.25
45 E
90 E
0.3
135 E
0.35
180 E
Coherent network analysis
Coherent network analysis can extract scalar gravitational
wave with more than 3 world-wide detectors. This approach
combines data taking account of the sky position (ϑ,φ), arrival
time difference τ(ϑ,φ) coherently, and calculates all polarization
components at a certain direction of the sky which is most
likely.
Mathematical expression of the coherent network analysis
Expression
can be taken

  as  
of d-detectors


F1+
x1
 ..   ..
 . = .
Fd+
xd
F1×
..
.
Fd×
F1◦
h+
..   h  + 

×
. 
h◦
Fd◦
n1
.. 
. 
nd
The reconstruction of a gravitational wave is an inverse problem.
Maximum likelihood method to solve the inverse problem:
L[h] :=� x − F h �2
Changing sky position (ϑ,φ), time difference τ(ϑ,φ).
The mathematical formula of the reconstructed scalar
gravitational wave is
1
h◦ =
(((F+ × F× ) · (F× × F◦ )) · F+
det(M )
− ((F+ × F× ) · (F+ × F◦ )) · F×
+ ((F+ × F× ) · (F+ × F× )) · F◦ ) · x
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2011年1月29日土曜日
Likelihood residual sky-map
Scalar pipeline
Full featured coherent network analysis pipeline(Data
conditioning, detection stat., Veto analysis)
One can apply the pipeline to H1,L1,V1,A1,LCGT
Analysis result is output by a Web-based event display.
amplitude spectrum density [Hzï1/2]
Data set (H1,L1,V1,A1,LCGT)
Data conditioning
H1
ï21
10
ï22
10
ï23
10
2
10
3
10
frequency [Hz]
Residual sky-map
Coherent network analysis
Likelihood stat
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2011年1月29日土曜日
Demonstration of pol. reconstruction
Reconstruction of h+, hx, ho
As to injection signal, to see ho clearly, I used
spike-like burst as ho.
Although the grid of lat-lon map is coarse
(4°x4°) in the simulation, ho is reconstructed
clearly.
h+, hx : SG235Q9
ho : Not injected
h+, hx : SG235Q9
ho : Spike-like burst
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2011年1月29日土曜日
Reconstructed scalar GW
Astrophysical model used is a spherically symmetric core collapse
with 10Mo at the distance of 10kpc from the earth.(M.Sibata,1994)
ï21
x 10
strain
HLV
5
0
ï5
HLVA
strain
0
ï21
x 10
4
50
100
since GPS=873750608.4893[s]
150
[ms]
200
50
100
since GPS=873750608.4893[s]
8
150
[ms]
200
ï2
4
strain
200
0
ï21
x 10
2
0
ï2
ï4
0
2011年1月29日土曜日
150
[ms]
2
ï4
0
HLVAJ
50
100
since GPS=873750608.4893[s]
ROC curve for adv. networks
Simulated GWs is from spherical core collapse at 10kpc. Sky
directions are uniformly distributed.
0
10
detection probability
~x5
ï1
~x3
10
ï2
10
HLVAJ
HLVA
HLV
ï3
10 ï4
10
2011年1月29日土曜日
ï3
10
ï2
ï1
10
10
9
false alarm
rate
0
10
Waveform reconstructions for ωBDs
We performed simulations to reconstruct scalar gravitational waves with ωBD =
40000,80000,120000,160000.
This simulation uses the design sensitivity of advLIGO for LIGO, VIRGO, and LCGT.
Astrophysical model used is the same as the previous simulation.
ωBD=160000
ωBD=120000
ωBD=80000
ωBD=40000
h+
hx
ho
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2011年1月29日土曜日
ROC curve for ωBD
1
!BD
10-2
current constraint
by Cassini
10-2
2011年1月29日土曜日
11
1
Summary
We discuss search for scalar GW from Galactic spherical core
collapse in Brans-Dicke theory with various adv det.
network.
Although depending sky location and models, it is possible to
put stronger constraint on ωBD.
LCGT and LIGO-Australia play an important role for search
for scalar gravitational waves
We need numerical simulations of scalar GW in S-T theory.
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2011年1月29日土曜日
Wavrform comparison
Red plot is injected ho signal and blue plot is the reconstructed ho.
The difference at the low frequency region comes from the data conditioning step.
Detector noise at low frequency is very high, such region is cut at the step.
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2011年1月29日土曜日