Uploaded July 2022 | Updated September 2026, 1 hour ago
The LISA measurements of galactic binaries can be reasonably well approximated using tri-linear representations. For a single signal, the tri-linear approximations of one of the TDI variables are of the form
X(t)≈∑j∑if(t)A(t,j,i)e(j)k0(i). (1)
The three-dimensional array A only depends on the LISA geometry and the spacecraft orbits. On the other hand, the source parameters of the gravitational waves (GW) are encoded in f(t), e and k0. In the case of galactic binaries the function f(t) reduces to a mildly chirping complex exponential function. The vector k0 represents the direction of propagation and the complex vector e contains information about the polarisation, the initial phase, the inclination and the amplitude.
Using the example of the LISA Data Challenge (LDC) data set 1-3, we show how approximation (1) simplifies the estimation of the source parameters. The data domain is divided into narrow frequency bands, and within each band the source parameters are estimated in a two-part process: Firstly, representations of the form (1) are estimated from the available narrow-band data using an alternating least squares algorithm. Secondly, the actual source parameters are extracted from the estimates of f(t), e and k0. This technique exploits the fact that in the tri-linear approximation the contributions from the LISA geometry are separated from those of the astrophysical objects.
Authors: Franziska Riegger, Fredrik Andersson, Johan Robertsson
Presenter: Franziska Riegger
The LISA measurements of galactic binaries can be reasonably well approximated using tri-linear representations. For a single signal, the tri-linear approximations of one of the TDI variables are of the form
X(t)≈∑j∑if(t)A(t,j,i)e(j)k0(i). (1)
The three-dimensional array A only depends on the LISA geometry and the spacecraft orbits. On the other hand, the source parameters of the gravitational waves (GW) are encoded in f(t), e and k0. In the case of galactic binaries the function f(t) reduces to a mildly chirping complex exponential function. The vector k0 represents the direction of propagation and the complex vector e contains information about the polarisation, the initial phase, the inclination and the amplitude.
Using the example of the LISA Data Challenge (LDC) data set 1-3, we show how approximation (1) simplifies the estimation of the source parameters. The data domain is divided into narrow frequency bands, and within each band the source parameters are estimated in a two-part process: Firstly, representations of the form (1) are estimated from the available narrow-band data using an alternating least squares algorithm. Secondly, the actual source parameters are extracted from the estimates of f(t), e and k0. This technique exploits the fact that in the tri-linear approximation the contributions from the LISA geometry are separated from those of the astrophysical objects.
Authors: Franziska Riegger, Fredrik Andersson, Johan Robertsson
Presenter: Franziska Riegger
