White Dwarf White Dwarf background in the LISA

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 Annecy 15 th December 2004

Data analysis problems Stochastic signal Interacting signals Isolated signals TDI Long wavelength regime Short wavelength regime LISA motion; long observation times; network of detectors Annecy 15 th December 2004

wd-wd, wd-ns, ns-ns binaries with GW frequency within LISA band are observed. These sources are GUARANTEED and the only ones that are guaranteed. Background signal and binary orientations uniformly distributed Sources uniformly distributed in the Galactic disc where H = 2. 5 kpc, zo = 200 pc Annecy 15 th December 2004

Distribution of WD binaries (Nelemans) Total number of detatched binaries Total number of interacting binaries Annecy 15 th December 2004 208736473 34291253

Cyclostationary random processes Random process X(t) is cyclostationary if there exists period T such that E[X(s) X(t)] = C(s, t) = C(s + T, t + T) Annecy 15 th December 2004

Cyclostationary random processes cnd. l 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 > 0 Annecy 15 th December 2004

Autocorrelation function of the background signal where Ak = 0 for k not zero 0 when sources isotropically distributed around the detector Ak not 0 for k not zero 0 for galactic distribution Annecy 15 th December 2004