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…