White Dwarf White Dwarf background in the LISA data

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White Dwarf White Dwarf background in the LISA
data

• Andrzej Królak
• Albert Einstein Institute
• Golm
• on leave from
• Institute of Mathematics
• Warsaw

Joint work with J. Edlund, G. Nelemans and
M.Tinto
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WD-WD, WD-NS, NS-NS binaries with GW frequency
within LISA band are observed.These sources are
GUARANTEED
Distribution of WD binaries (Nelemans et al)
Total number of detatched binaries 208736473
Total number of interacting binaries 34291253
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Simulation of the background signal

• Background signal

uniformly distributed
Sources uniformly distributed in the Galactic disc
where H 2.5kpc, zo 200pc
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Time domain data
See also Cornish, Rubbo, Timpano 2005
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Cyclostationary random processes
Random process X(t) is cyclostationary if there
exists a period T such that EX(s) X(t)
C(s,t) C(s T, t T)
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Cyclostationary random processes cnd.

• Spectra of cyclostationary process

Let n(t) be a stationary process with spectral
density S(f) and variance
And let X(t) be a cyclostationary process
uncorrelated with n(t)
then
and
for k gt 0
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Autocorrelation function of the background signal
where
Ak 0 for k ? 0 when sources isotropically
distributed around the detector For a galactic
disc distribution Ak ? 0 for all k
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Harmonics of the sample variance of data least
squares fit
see also, Giampieri, Polnarev, 1997
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x v3/2 x 1/2
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(No Transcript)
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Analytic calculations vs. numerical estimates
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Data analysis problems
Stochastic signal
Interacting signals
Isolated signals
TDI
Long wavelength regime
Short wavelength regime
LISA motion long observation times network of
detectors