mock data production, characteristics, and confusion background wg4 f2f – nice 09/01/10 tania...
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Mock Data Production, Characteristics, and Confusion Background
WG4 f2f – Nice 09/01/10Tania Regimbau
ET Mock Data
time series at the detector outputs E1, E2, E3
Noise : colored Gaussian noise based on ET-B sensitivity GW signal : extra galactic population of BNS
1 month of data on Atlas frames :
duration 2048 ssample rate 8192 Hz fL=10 Hz
Simulation Code (GW signal)
3
to0 ≤tc
0.., tcj ... tc
Ns ≤to0 +τmax
m1j , m
2j , z j
τj ( fmin
ET ; flso)
ψj ,α j ,δ j , ii ,ϕ c
j
F×j ,F+
j
if tcj −to
max <τ j
hj (t
ok ) =h+
j (tok)F+
j (tok) + h×
j (tok)F×
j (tok)
×Ns
Write parameters to file
Distributions
4
coalescence time (Poisson process):
masses: Gaussian distribution
redshift:
position in the sky: uniform distribution
polarization: uniform distribution
phase at the last stable orbit: uniform distribution
p(Δt) ∝exp(−Δt / λ) with λ=dRc
o
dz(z)dz
zmin
zmax∫⎡
⎣⎢⎢
⎤
⎦⎥⎥
−1
p(z) ∝
dRco
dz(z)
Coalescence Rate
5
dRc
dz(z) =&ρc
o(z)dVdz
(z) with &ρco(z) ∝
&ρ* (zf )
1+ zf
P(td)dtd∫
for:
SFR of Hopkins & Beacom 2006
H0=0.7, Ωm =0.3 and ΩΛ =0.7
⎧⎨⎪
⎩⎪
and (BNS):
&ρc
o(0) =1 Myr−1Mpc−3 *
P(td) ∝1 / td with td>20 Myr
⎧⎨⎪
⎩⎪
* ‘realistic’ rate from the LIGO rate paper
average time step
6
Luminosity Distance
Waveforms: Taylor T3 3.5 PPN
8
∝τ −1/4
Beam Functions
9
Detection Regimes
Resolved sources at close redshifts Sources separated by long stretches of silence
Popcorn background Sources start to overlap
Continuous stochastic backgroundSuperposition of unresolved sources
Defined by the duty cycle i.e the ratio between the average duration of the waveforms and the time interval between successive waveforms (also the average number of sources present at the detector)
Δ(z) = (1 + z ')τdRc
o
dz '0
z
∫ (z ')dz '
Signal Duration
11
fL (Hz) NS-NS (1.4+1.4) NS-BH (1.4+10)
40 (initial) 25 s 5.8 s
10 (Ad LIGO) 16.7 m 3.9 m
5 (Ad Virgo) 1.8 h 24.6 m
3 (possible ET) 6.9 h 1.6 h
1 (planned ET) 5.4 d 1.2 d
τ (day) ~5.4(
Mc−5/3
1.22Me
) fL−8/3
Duty Cycle
12
Evolution with zmax
13
Evolution with fL
14
Filter
15
Confusion Background NS-NS
16
1 10 100 10001E-27
1E-26
1E-25
1E-24
1E-23
1E-22
1E-21
ET ρ0=1 ρ0=0.01 ρ0=10
Sn(
f)1/
2 (H
z-1/2)
f (Hz)
no PN corrections, first harmonic in eccentricity
Stochastic analysis
∝νo4/3
νo (Hz)
CC statistic on 100000 s:
Pt estimate (100 Hz) = 7.4e-10Error = 3.5e-11
To continue with Craig’s talk…