i (t) - apctp

Foundation of gravitational wave data
analysis III, IV
Kazuhiro Hayama
Osaka City University
13年8月9日金曜日
Content
Feature of observed data
Search for gravitational wave bursts
Single detector case
Multiple detector phase
Multimessenger observation
13年8月9日金曜日
Expected gravitational wave sources
Continuous
Stochastic
Transient
Waveform parameterization
Waveform highly uncertain
Supernovae
Gamma-ray bursts
Pulsar glitches
Soft Gamma Repeater
13年8月9日金曜日
GW bursts
−22
3
x 10
amplitude
2
1
0
Kotake et al.
−1
0
0.2
0.4
time[s]
0.6
0.8
−20
4
x 10
amplitude
3
2
1
0
−1
Takiwaki et al.
−2
0
0.02
0.04
0.06
time[s]
0.08
0.1
−21
4
x 10
2
amplitude
0
−2
−4
Kuroda et al.
−6
−8
0
13年8月9日金曜日
0.01
0.02
0.03
time[s]
0.04
0.05
0.06
GW bursts
Pulsar glitches
∆Ω/Ω~10-6
τ~50-500[ms]
Starquake from LMXBs etc
Crust collapse due to accretion onto a neutron star,
Coincidence emission of a X-ray and a GW
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GW bursts
Gamma-ray bursts
NSNS binaries
Hypernovae
Soft Gamma Repeater
Flares from magnetars
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Search for
gravitational wave bursts
Feature of observed data
Search method for GW bursts
13年8月9日金曜日
Search for gravitational wave bursts
Unlike search for inspiraling signals, the burst search
cannot use template.
Every burst-like signal showing up has to be regarded
as a candidate of true GW signal at first.
We have to watch observation data very carefully,
how well the data condition is, what kind of statistical
property the data has, ...
13年8月9日金曜日
Interferometric Gravitational Wave Detector
Abramovici et al. Science (1992)
13年8月9日金曜日
Detector and Noise
v = G(Γ(x + xn + xe ) + en )
Object
Sensor
Pre-amplifier
Amplifier
&Filter
Γ
x
Sensor Noise
xn
External Noise xe
Electric Noise
en
Experimental Apparatus
Mio, 2013
v is observed data. Strain h is calibrated from v.
13年8月9日金曜日
Calibration
−1
h = H Verr + AVfb
Interferometer
h
Verr
H
−
D
A
F
Vfb
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Feedback
Detector and Noise
Input-equivalent noise
xequ = xn + en / Γ
Important “xequ is small”
Noise that limits the detector sensitivity is
the ones near the sensors
The fundamental noise : Noise that the sensors have
cannot be removed. The detector is designed so that the
sensitivity of the detector is limited by the fundamental
noise of the sensor
13年8月9日金曜日
Fundamental detector noise
Seismic Noise
test mass
(mirror)
Residual gas
scattering
Beam
splitter
LASER
Wavelength &
amplitude
fluctuations
photodiode
Radiation
pressure
"Shot" noise
Quantum Noise
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Rana
Detector noise
There are various kinds of noise
Stationary noise
The statistical property is well known. Mathematically
called stochastic process.
Non-Stationary noise
Unexpected noise transients, Non-reproducible noise.
Very difficult for treat. This kind of noise affects the
burst search in particular.
13年8月9日金曜日
How do you see feature of noise ?
Two signals have same variance, but apparently their frequency
are much different.
13年8月9日金曜日
Spectral Analysis
Variance is mean squared value of a signal, which lose
frequency information.
x(t) = Asin(ω t + φ )
Variance = A / 2
2
Spectral analysis is a powerful tool for seeing the
frequency structure.
Power spectrum density will be introduced here.
13年8月9日金曜日
Power Spectral Density
(Two-sided )Power spectral density S(ω) is defined as
| XT (ω ) |
2
S(ω ) = lim
2π T
T →∞
The Variance σ2 is written as
σ = x(t)
2
2
1
= lim
T →∞ T
∫
T /2
− T /2
x(t)2 dt
dω
= lim ∫ | XT (ω ) |
T →∞ − T /2
2π T
T /2
=
∫
∞
−∞
2
S(ω )dω
The PSD decomposes a signal power
into power at frequency components.
13年8月9日金曜日
Power Spectral Density
It is useful to define one-sided PSD as a function of
frequency:
σ =
2
∫
∞
−∞
S(ω )dω =
∫
∞
0
G( f )df ,
G( f ) = 4π S(2π f )
What is the unit of the PSD ?
σ =
2
V2
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∫
∞
0
G( f )df
V2/Hz
Hz
Feature of observation data
Frequency dependent data
Narrow frequency band feature
Non-Stationarity
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Frequency dependent noise spectrum
ic
Seism
r
e
s
Th
e
rm
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La
al
t
o
sh
Narrowband Feature in Spectrum
Violin modes in LIGO
2010NIMPA.624..223A
Barish 1999
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V. Boschi D. thesis
Thermal noise spectrum
Solving EoM of harmonic oscillator driven by random force,
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Non-Stationarity
Changing the sensitivity in short time scale
Different statistical properties of different frequency
bands
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Non-Stationarity
There are many burst-like noise coming from the
detector, environment around.
It is hard to distinguish between noise and true GWs
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Spectrogram
A series of PSDs of short time segments.
Good tool for seeing signals in the time-frequency map.
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Data Conditioning
The GW data is not ready for search for very weak,
unknown transients.
We need data conditioning
Whitening
Removing artifacts ( Line removal )
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Whitening : Linear Prediction Error Filter
Linear Prediction Part:
Assume x[n] can be expressed as a linear combination
of previous M samples
M

x[n]
= ∑ c[m]x[n − m]
m=1
Prediction Error:

e[n] = x[n] − x[n]
Determining c[m]:
Determine c[m] so that the mean square of the
prediction error is minimum
N
1
2
2
σ e = ∑ e[n]
N n=1
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Linear Prediction Error Filter
The necessary condition is
∂σ
= 0, 1 ≤ k ≤ M
∂c[k]
2
e
This equation results in Yule-Walker equation
M
∑ r[m − k]c[m] = r[k],
1≤k ≤ M
m=1
N /2
1
r[k] = lim
x[n]x[n − k]
∑
N→∞ N
n=− N /2
r[k] is autocorrelation coefficients. In practice, N is finite,
N
1
r[k] =
x[n]x[n − k]
∑
N n=k+1
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Example of the Linear Prediction Error Filter
5
x 10
20
band pass filterd at 64Hz 2000Hz
0
5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.1
0.12
after conditioning
0.5
0
0.5
0
13年8月9日金曜日
0.02
0.04
0.06
0.08
Line removal (MBLT)
x
ei
: time series to be line removed
(k )
: estimate in stage k of a line at frequency fi
(k )
To obtain ei , first subtract ei
is obtained by x (k )
i
xi
(k )
= x − ei
(k −1)
and the modified time series
ei
(k )
i-th line
(k −1)
M lines
fi
Frequency
13年8月9日金曜日
Line removal
(k )
Heterodyne xi at the carrier frequency fi
X = L({xn * cos(2π fi n)})
Y = − L({xn * sin(2π fi n)})
Apply a running median to both quadratures
Xn = median({X j }), j = n − m,..n,..n + m
(k )
The line estimate ei
is obtained by modulating a
carrier at fi with two quadrature
en
13年8月9日金曜日
(k )
= Re((Xn + iYn )exp(2π fi n))
Example of line removal
Before
13年8月9日金曜日
After
Detection statistics
Observation data h can be written as summation of a gravitational
wave(if it contains) s and detector noise n
h= s+n
+
−
s = F+ s + F− s
Our goal is to decide a gravitational wave s exist or not from the
observed data h. The decision is performed using the statistical
hypothesis testing. Standard method is Neyman–Pearson’s
likelihood ratio test
p[h | s] ： Probability to obtain h when s exists.
p[h | 0] ： Probability to obtain h when s exists.
p[h | s]
Λ[h] ≡
p[h | 0]
13年8月9日金曜日
Detection statistics
Assume the detector noise n is distributed with white Gaussian,
p[n] is
⎡ n⋅n⎤
p[n] = C exp ⎢ −
⎥
2
⎣
⎦
In case of p[h|s] and p[h|0], n can be expressed as
n= h−s
n=h
The likelihood ratio is
p[h | s]
1
⎡
⎤
= exp ⎢ (s ⋅ h) − (s ⋅ s) ⎥
p[h | 0]
2
⎣
⎦
13年8月9日金曜日
Search method
p[h | s]
1
⎡
⎤
= exp ⎢ (s ⋅ h) − (s ⋅ s) ⎥
p[h | 0]
2
⎣
⎦
We search s of which the likelihood ratio is beyond a given threshold going through all
over parameter space.
In case of CBC, the waveform is well parameterized (s(p1,p2,...)) the parameters can be
limited ~10. In such case, matched filter method is the optimal。
In case of a supernova, the waveform cannot be parameterized in practice, we have to go
other way. Flanagan&Hughes(1998) proposed a novel method in their research on a GW
from a BH-BH merger.
They found a GW from a BH-BH merger could be
expressed in a small region of the time-frequency space
Frequency
and proposed excess power method :
to find time-frequency regions
of which power excesses other regions.
Time
13年8月9日金曜日
Detection of gravitational wave bursts
Single detector case
Detector network case
13年8月9日金曜日
Single detector case
Assuming a GWB is localized in a limited timefrequency space.
Excess power method is applied to fine time-frequency
tiles.
Also this search is necessary for evaluation of the data
quality of a detector.
13年8月9日金曜日
Excess Power Method
Assume a gravitational wave signal concentrates into timefrequency region T={ts,δt,fs,δf} The Fourier components in the
Nt −1
region are
−2 π i(t −t ) f
K =
H
∑e
j =0
j
s
k
h(t j )
1 k
t j = ts + jΔt, Nt = δ t / Δt, fk =
Δt Nt
2

k2 H
K
h = h + h⊥
E ≡ h ⋅ h = 4 ∑
2
k =k1 σ
δ f = f2 − f1 , f1 = k1 / δ t, f2 = k2 / δ t
If data is noise only, E is distributed with
χ2 with degree of T=2δtδf.
Excess power tiles will be detected by
χ2 test.
13年8月9日金曜日
T(δt,δf)
s
h||
χ2 test
For the Gaussian distributed noise x(t),
the Fourier components X(f) is also Gaussian
distributed. Therefore the power |X(f)|2 is
χ2 distributed.
In order to decide the power in T(δt,δf)
comes from just noise or a GW statistically,
we test whether the power follows
the χ2 distribution. This test is called χ2 test.
N
χ =∑
2
i=1
( Ei − En )
2
Ando
En
We test whether the probability
χ2 is found in the χ2-distribution
with N degrees (called p-value)
is beyond a given threshold.
If the p-value is under the given threshold,
we reject that T(δt,δf) is noise only.
13年8月9日金曜日
χ
χ2
Excess Power Method
Project time series data onto the timefrequency space by Fourier space.
Calculate the excess power changing
the time-frequency window
Find TF tiles of which power is
beyond a given threshold.
Group the tiles coming from a same
event
The reconstruction of the event is
finished.
13年8月9日金曜日
Excess power for single data
Since we have multiple detectors, the
single detector search may not be
effective.
But the idea should be useful as
Tools for Detector characterization
Tools to extract physical information
from detected GWs
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Neutrino Heating Mechanism
Clear relation between the explosion mechanism and the
gravitational waveform
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MagnetoHydroDynamic mechanism
Kotake
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Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
Frequency
Threshold
sort by E
Select Emax
Time
Overlapped with more
stronger pixels?
no
Select next pixel
13年8月9日金曜日
yes
Remove the pixel
Clustering method
One of other methods is to combine spectrograms
considering multiple detector data.
13年8月9日金曜日
Detector network case
Data analysis with a multiple-detector network is
important for the burst searches
→ The false alarm rate is dramatically improved.
Two types of data analysis methods.
Coincidence analysis
Coherent network analysis
13年8月9日金曜日
Coincidence analysis
In the coincidence analysis, we first analyze each detector data
separately, and generate event lists. The gravitational wave signal is
recorded in each detector with slightly different arrival times. The
arrival time depends on where the gravitational wave comes from.
The coincidence analysis will test whether the listed triggered events
in each event list are within a given coincidence window or not.
The time window is w、the peak times of triggered events in the i-th
and j-th detector are ti, tj, the durations are Δti, Δtj, the condition ti、tj
have to be satisfied is
1
| ti − t j | ≤ w + (Δti + Δt j )
2
Typically w is decided as maximum light-travel-time between
detectors.
13年8月9日金曜日
Waveform consistency test
There are lots of coincident noise transients in each detector. In
order to veto these events, we need use more information. One
method is to test waveform consistency.
Pearson product-moment correlation coefficient is defined as
N
R=
∑ (x
i
− x )( yi − y)
i=1
N
∑ (x
i=1
i
− x)
N
2
∑ ( y − y)
2
i
i=1
http://adsabs.harvard.edu/abs/2004CQGra..21S1695C
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Coherent network analysis
⎡ x1 (t)
⎢
⎢ 
⎢ xd (t)
⎣
⎤ ⎡ F1+ (θ , φ ) F1× (θ , φ )
⎥ ⎢


⎥=⎢
⎥ ⎢ F1d (θ , φ ) Fd × (θ , φ )
⎦ ⎣
data
= detector response x
Response
Reconstruction
⎤
⎡ n1 (t)
⎥ ⎡ h+ (t) ⎤ ⎢
⎥+⎢ 
⎥⎢
⎥ ⎢⎣ h× (t) ⎥⎦ ⎢ nd (t)
⎦
⎣
⎤
⎥
⎥
⎥
⎦
gravitational wave + noise
ξi (t) = Fi+ (θ , φ )h+ (t) + Fi× (θ , φ )h× (t)
h = (AT A)−1 AT x
Extraction of a gravitational wave is performed by solving the inverse
problem.
Finding most likely signals by changing sky position (θ,ϕ).
13年8月9日金曜日
Coherent network analysis
⎡ x1 (t)
⎢
⎢ 
⎢ xd (t)
⎣
x
⎤
⎥
⎥=
⎥
⎦
⎡ F1+ (θ , φ ) F1× (θ , φ )
⎢


⎢
⎢ F1d (θ , φ ) Fd × (θ , φ )
⎣
A
⎤
⎡ n1 (t)
⎥ ⎡ h+ (t) ⎤ ⎢
⎥+⎢ 
⎥⎢
⎥ ⎢⎣ h× (t) ⎥⎦ ⎢ nd (t)
⎦
⎣
h
⎤
⎥
⎥
⎥
⎦
ξi (t) = Fi+ (θ , φ )h+ (t) + Fi× (θ , φ )h× (t)
−1
h = (A A) A x
T
T
Solving the inverse problem using the maximum likelihood method.
Calculating likelihood statistic at all over the sky position.
The GW candidates are the signals of which L is beyond a given
threshold set by the background noise study.
L = max(− x − Ah )
2
where
x
2
d
= ∑ ∫ xi (t)T xi (t) dt
i=1
data(x) − estimated signal(ξ )
13年8月9日金曜日
2
T
0
h = (AT A)−1 AT x
Likelihood Sky-map
In case of noise only data, the typical pattern of the likelihood sky map
shows up.
The pattern of the noise only skymap change with which detector
network you use.
−20
1
x 10
If a gravitational wave contains, then the pattern changes
0.5
0
H1-H2-L1
−0.5
Noise
θ
−1
0
θ
ϕ
13年8月9日金曜日
Noise+Signal
ϕ
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Likelihood Sky-Map around a GW burst
13年8月9日金曜日
Ill-Poseness of Inverse Problem
At some sky positions, one of eigenvalues of the antenna
pattern A becomes very small. This lead the inverse
problem to ill-posed one.
The variance is amplified.
90 N
θ
latitude
45 N
0
45 S
90 S
180 W135 W90 W 45 W 0 45 E 90 E 135 E180 E
longitude
ϕ
13年8月9日金曜日
Injected signal:
sineGaussian235HzQ9
Condition Number
Ill-poseness are characterized by condition number.
Cond(A) over the skymap of H1-H2-L1-V1
log10 scale
Feature:
Cond(A)
, then,
error of the solution
Strength of Ill-poseness
strongly depends on the sky location
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Tikhonov regularization
Tikhonov regularization: technique to address this Ill-pose problem
Impose regulator on the maximum likelihood
Regulator should be a function of the sky location
Consider eigenvector of M=ATA:
We can assume
0 (detectors are co-aligned)
Condition number
Regulator so that condition number ~ 1
13年8月9日金曜日
Cond(A) over the skymap
Effect of regulator
After adding regulator
90 N
90 N
45 N
45 N
0
latitude
latitude
Before adding regulator
0
45 S
45 S
90 S
180 W135 W90 W 45 W 0 45 E 90 E 135 E180 E
longitude
90 S
180 W135 W90 W 45 W 0 45 E 90 E 135 E180 E
longitude
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Error of the regularized ML approach
The error consists of two components: Bias and Variance
Bias
Variance
Total error
Bias
g
g
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0
Bias
1
Bias
+
Variance
Variance
Variance
corresponds to Gursel&Tinto
formula
corresponds to constraint coherent
approach by Klimenko
Position reconstruction of a burst
10
LHV is >10°, but adding KAGRA~1°
Important for multi-messenger obs.
1
Klimenko et al.(2011)
13年8月9日金曜日
Error region
H1L1V1 network Likelihood skymap burst signal containing
Median Error Region
The region where likelihood is
larger than at true position and
the true position is included with
50% probability
The root of the total error area is
called median error region
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Triggered events
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S5+S6 result
LVC, 2012
13年8月9日金曜日
But everything is under assumption of Gaussian....
Yes, it is.
Should we go to non-Gaussian world and construct
new tools? PSD, likelihood, data conditioning, ...
At present, nobody knows.
13年8月9日金曜日
Noise modeling(inspiral case)
Roever(2011)
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Noise modeling(burst case)
0
10
Student
Student
detection efficiency
−1
10
Gauss
Student
−2
10
Gauss
Student
Gauss
Gauss
Student
Gauss
Hayama, Roever
−3
10 −4
10
−3
10
−2
10
false alarm probability
76
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−1
10
0
10
Multimessenger observation
13年8月9日金曜日
Difficulty of the detection and confirmation
A lot of GW-like noise transients
→ Cannot veto even taking coincidence
The accuracy of position reconstruction is
not enough
→ Difficult to identify what is the source.
It is very important to identify the source of
the gravitational wave in collaboration with
multi-ray, multi-band astronomical telescopes
13年8月9日金曜日
Multi-Messenger observation
http://www.gw.hep.osaka-cu.ac.jp/gwastro/overview.html
13年8月9日金曜日
Multimessenger Observation
Mainly two ways
GW → EMs Follow-up
EMs→ GW Follow-up
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EM triggers → GW observation
GW event alert → Follow-up by EM telescopes
EM event alert → Follow-up by deep analysis of GW archived data
Position, time, source type
13年8月9日金曜日
Triggered GW searches
γ ray、X ray event triggered GW searches
Sources：GRB、SGR、pulsar glitches
Can use information event time, sky location
Confident detection
Astronomy from multiple inormation
GRB triggered search
Off-source
On-source
GRB
13年8月9日金曜日
Off-source
SGR1806-20 hyper flare
SGR hyperflare showed on Dec. 27th, 2004
Distance：6-15kpc, E~1046erg, lasting ~6 min
LIGO Hanford(4km) in science mode
13年8月9日金曜日
GW search associated with GRB
137 GRB found during
S5(2005-2007)
binary merger search
ApJ 715 1435(2010)
at 150Hz with
0.01M⦿c2=1.8x1052erg
Upper limit equivalent
distance
unmodeled search
ApJ 715 1438(2010)
13年8月9日金曜日
S6 GRB searches
S6(July 2009-October 2010)
LIGO Hanford-LIGO Livingston-Virgo network
404 GRBs observed by GCN (Gamma-ray burst
coordinates network)
Unmodeled bursts with Egw=10e-2
Mpc
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B150Hz
17
B300Hz
7
Merger
NSNS
16
NSBH
28
GRB070201, GRB051103
Short GRBs
GRB070201 : sky location overlapped with
M31 (770kpc)
GRB051103 : sky location overlapped with
M81 (3.6Mpc)
no GW found
Binary coalescence in M31 were excluded at >
99% CL
Binary coalescence in M81 were excluded at >
98% CL
Maybe
Neutron star quake in M31, M81
Coalescence in galaxy behind M31, M81...
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Pulsar glitch
∆Ω/Ω~10-6
Sudden change of spin frequency
Possible GW source
Spin frequency[Hz]
103
PSR J1824-2452
102
Crab
Vela
PSR J0537-6910
101
100
10-1
10-2
10-1
100
101
Distance[kpc]
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102
GW search associated with pulsar glitches
10-15
h[f]
10-20
10-25
10-30
10-35
10-1
100
101
102
Frequency[Hz]
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103
104
Process of multimessenger obs.
GW alert --> EM followup observation
Transient alert from EM telescopes --> GW data analysis
position reconstruction
sky area for obs
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Process of MultiMessenger Observation
Winter run : FAR < 1 per day
Autumn run : FAR < 0.25 for most telescopes, < 0.1
for PTF and Swift
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Select Observation region for follow-up
Blue Luminosity
(Bigger, More stars form)
GW data
LB × Likelihood
P=
Distance
GWGC
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GWGC: Gravitational Wave Galaxy Catalog
Contains ~50,000 galaxies within
100Mpc
Four catalog compilation:
Tully Nearby Galaxy Catalog,
Neighboring Galaxies, V8k,
HyperLEDA
Uses Principal Galaxy Catalog(PCG)
identifier to improve removal of
degenerate galaxies from multiple
catalog
Main problem:
Incompleteness
D. White et al, 2011
92
13年8月9日金曜日
Coordinated search with EM telescopes
Optical
TAROT, Zadko, QUEST
ROTSE
Pi of the Sky
SkyMapper
PTF
Liverpool Telescope
X-ray Swift
13年8月9日金曜日
EM Partners
winter/autumn
autumn
Optical telescopes (sq. deg.)
o TAROT : 3.4
o Zadko : 0.17
o ROTSE : 3.5
o QUEST : 9.4
o SkyMapper : 5.7
o Pi of the Sky : 400
o PTF : 7.8
o Liverpool : 21
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Radio
o LOFAR : 30-240MHz, 25 sq. deg.
o EVLA : 5GHz, 7sq. arcmin.
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Follow up observation conducted in S6
Optical telescopes
Winter run : 8 GW alerts →4 observed by > 1 telescopes
Autumn run : 6 GW alerts →5 “
Obtained ~ 1800 images in total.
X-ray satellite : Swift
2GW alerts were sent and observed
Radio telescopes
LOFAR : 5GW alerts were sent and observed
Expanded-VLA : 2GW alerts observed but high-latency followup(3weeks, (5weeks, 8months) later.) 6cm observations
13年8月9日金曜日
Optical Follow-up Analysis
Image subtraction
Reference image
subtracted from images
Resulting image contains
transients
Thresholds used to remove
background
PTF, ROTSE, SkyMapper
and Liverpool
13年8月9日金曜日
Catalog-based search
Catalog of objects visible in
fields created (SExtractor)
Track variability across multiple
images
Threshold flux changes used to
find interesting transients
TAROT, QUEST, Zadko and Pi of
The Sky
G18666
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G19377
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G20190
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G21852
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G23004
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LOFAR
Low frequency array
LOFAR can image up to 24 5°x5° fields
simultaneously.
Low latency radio all-sky monitor
LVC awarded ~4 hours-per-week
observing-time during S6
Followed up 6 GW alerts.
Results not yet
13年8月9日金曜日
Expanded VLA
Radio source detection
Variability analysis
Identification of contaminating
transients (AGN?)
6 sources in the fields of each galaxy
consistent with number of expected
serendipitous sources (Windhorst,
2003)
13年8月9日金曜日
Image region ~30’ around one galaxy
Nominal FOV of 7’
Green Bank Telescope
Radio pulses from Green Bank Telescope Drift-scan
Possible joint sources includes CBCs, pulsar glitches, cosmic strings, ... (although
most pulses are probably just terrestrial background...)
32 single pulse candidates coincident with S5/VSR1
Analysis is in progress(almost finished).
13年8月9日金曜日
Nasu radio telescope
One can observe any direction within +/- 5deg
from the zenith (Dec. +32deg ~ +42deg)
For RT19870422-like events,
Nasu reaches ~100Mpc
106
13年8月9日金曜日
http://www.astro.phys.waseda.ac.jp/index-e.html
WJN Radio transients
3min.
3min.
Flux
2Jy
2Jy
Time
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107
10
Niinuma et al. 2009
Radio afterglow ?
RT19840613
RT19870422
o flux: 0.4-0.6mJy at 140Mpc
o duration: < 7days
o event rate: 6000-150000Gpc-3yr-1
(consistent with estimated CBC
rate ref:J.Abadie et al. (2010))
o flux: 1.5-2.0mJy at 1.05Gpc
o duration: ~2months
o event rate: 80-20000Gpc-3yr-1
(consistent with estimated CBC
rate)
108
13年8月9日金曜日
Bower et al. ApJ 666 346-360 (2007)
RXTE PCA
Crust collapse due to accreting mass etc.
rho, LIGO
SNRGW
3
4
3.5
2.5
3
2
2.5
1.5
2
1.5
1
1
0.5
0.5
0
0
20
40
60
80
100
120
140
energy/noise_variance, RXTE
PowerX
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0
Swift Observatory
Three telescopes on one platform
BAT: γ rays(15-150keV), wide FOV
XRT: X rays(0.3-10keV), 0.4°x0.4°FOV
UVOT: 170nm, 0.28°x0.28°FOV
Provided a few pointing to GW candidates
via ToO program in 2009-2010
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GW-XRT pipeline
raw sky-map by GW
Sky-map provided by the burst pipeline
(O(100deg2))
GWGC: within 50Mpc (O(100deg2)→ O(1deg2))
Re-calculation of sky-map weighted by blue light
luminosities, distances,
Mi L
P∝∑
Di
i
Five tiles at one event were sent to Swift.
Joint event significance
Λ joint (η , S,Ω) = Λ GW (η )Λ EM (S)Λ cor (Ω)
GW obs
p(η | signal)
Λ GW =
p(η | noise)
13年8月9日金曜日
from 2XMMi-DR3
Inverse of P of observing an accidental P for position correlation
serendipitous Xray sources not correlated between X and GW
with GW
Summary of XRT detections
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UVOT analysis
20 reduced-threshold XRT detections were examined
in UVOT.
No XRT detection corresponds to an UV-optical
transients or a variable source.
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Summary of XRT detections
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Process of the first detection
R. Weiss (MIT)
3
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2010年9月16日
Human Check
Burst pipeline (cWB)
L1
tdog+8[m]
H1
tdog+42[m]
6
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Requested sky region for follow-up
Top$1000$pixels$reported$
• $total$area:$129$sq$deg$
• $es5mated$containment:$19%$
Telescopes$pointed$at$$
nearby$galaxies$(<50$Mpc)$$
in$this$area$
Zadko'
Swi$%
Usable'images:'
•  TAROT:&20,&+&[44&min&0&4&day]&
•  ROTSE:&102,&+&[0.5&0&29]&day&
•  Zadko:&63,&+&[1,&160]&day&
•  SkyMapper:&21,&+&8&day&
•  Swi$:&4,&+&[0.5,&105]&day&
SkyMapper
TAROT,'
ROTSE'
Zadko'
13
13年8月9日金曜日
nearby''
galaxies'
Big Dog in the sensitivity curves
SNR=15@LHO
SNR=10@LLO
13年8月9日金曜日