Search for Gravitational Waves from Inspiraling

TAMA binary inspiral event search
Hideyuki Tagoshi (Osaka Univ., Japan)
3rd TAMA symposium, ICRR, 2/6/2003
Coalescing compact binaries
Neutron stars
Black holes
Inspiral phase of coalescing compact binaries are main target because
Expected event rate of NS-NS merger: a few within 200Mpc /year
Well known waveform,
etc.
Possibility of MACHO black holes
TAMA Binary inspiral search
1. Neutron star binary search 1 M 2 M
2. TAMA-LISM coincident event search for mass
range (onestep search)
1 M 2M
3. Lower mass
4. Higher mass
 0.2M
 10M
Matched filter
• Detector outputs: s(t )  Ah(t )  n(t )
h ( t ) ： known gravitational waveform (template)
Post-Newtonian
n ( t ) ： noise.
approximation
• Outputs of matched filter:
~*
~
s ( f )h ( f )
( m1, m2 , tc ,...)  2
df
Sn ( f )
z
•
Sn ( f ) noise spectrum density
• signal to noise ratio SNR =  / 2
• Matched filtering is the process to find optimal
parameters which realize
F
max (m , m , t ,...)I
H
K
m1 ,m2 ,tc ,...
1
2
c
Matched filtering analysis
52 sec
t
Read data
  2 (S / N )
FFT of data
Apply transfer function
Conversion to stain equivalent data
 (tc , M , )
(tc
25ms)
max  (t , M(if, )  7)
tc
c
 2 (tc , M , )
Evaluate noise spectrum
S ( f ) near the data
n
Event list (only
  7 events)
 max  (t , M , )
M ,
c
TAMA events and Galactic event
 /  2  16
 2 selection will produce
loss of strong S/N events
Search Result TAMA DT6
2

Log10[Number of events]
 /  2  16
 / 2
Upper limit to the Galactic event rate
N
T
•Ｎ： Upper limit to the average number of events
over certain threshold
•Ｔ： Length of data [hours]

• : Detection efficiency
Galactic event simulation
We perform Galactic event simulation to estimate detection efficiency
Assume binary neutron stars distribution in our Galaxy
dN  e
 R2 / 2 R02  Z / hz
e
RdRdZ
Mass : distribute uniformly between
R0  4.8 kpc
hz  1 kpc
1 2M
•Give a time during DT6
•Determine mass, position, inclination angle, phase by
random numbers
•Give a test signal into real data
•Search
•Make event lists and estimate detection efficiency
Galactic event detection efficiency
 /  2  16
  0.23
Upper limit to the event rate: Poisson statistics
•Threshold (  /  2  16 )
•Expected number of fake events over threshold：Nbg=0.1
•Observed number of events over threshold: Nobs=0
Assuming Poisson distribution for the number of real/fake events
over the threshold,
we obtain upper limit to the expected number of real events from
e
( x  N bg ) n

n!
n 0
 1  CL
n
n  N obs
( N bg )
 N bg
e

n!
n 0
 ( x  N bg )
n  N obs
N=2.3 (C.L.=90%)
Upper limit to the Galactic event rate
threshold=16 (～S/N=11)
(fake event rate=0.8/year)
Efficiency   0.23
•We also obtain upper limit to the average number of events
over threshold by standard Poisson statistics analysis
N=2.3 (C.L.=90%)
•Observation time T＝1039 hours
N
 0.0095 [1/ hour] (C. L.  90%)
T
c.f.
Caltech 40m : 0.5/hour
Allen et al. Phys. Rev. Lett. 83, 1498 (1999).
(C.L.=90%)
DT7 analysis
TAMA DT7: 2002.8.31 ～ 2002.9.2
Best Sensitivity:
3.3 1021 / Hz
DT7 event lists
23.7 hours data
These results will be used for TAMA-LIGO coincidence analysis.

2
chi square
Divide frequency region into bins.
Test whether the contribution to  from each
bins agree with that expected from chirp signal
F
  (s, h) Gz
H
2
f2
f1
fmin
 
2
*
df
S (f)
n
3  4 5
2
1
~
~
s ( f )h ( f )
f3
f4

f5 
1
i
IJ
K
2
(



)
i
i
2
 i 2  (  i   i )2 ,  i   i
fmax
Variation of Noise power (1 minute average)
TAMA DT6 all 8/1～9/20/2001


f
4
df
  f min

S
(
f
)
n


f max
7 / 3
1/ 2
f min  100Hz, f max  2500Hz
[1.09minutes]
Variation of Noise power (1 minute average)
LISM DT6 9/3 ～9/17/2001
f max

f 7 / 3 
 4  f min df

S
(
f
)
n


1/ 2
f min  100Hz, f max  2500Hz
[1.09minutes]
TAMA data analysis activity
•Binary inspiral search : one step search (Tagoshi, Tatsumi,Takahashi)
TAMA-LISM coincidence
(Takahashi,Tagoshi,Tatsumi)
two step search (Tagoshi, Tanaka)
•Binary inspiral search using Wavelet: (Kanda)
•Continuous wave from known pulsar: (Soida, Ando)
•Burst wave search: (Ando)
•Noise veto analysis: (Kanda)
•Calibration: (Tatsumi, Telada,…)
•Interferometer online diagnostic: (Ando,…)
•BH ringdown search, Stochastic background search, etc. will be done.
•Two new post-docs (Tsunesasa(NAOJ),Nakano(Osaka))

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