| The LISA Simulator software package is designed for use as an interface tool between source simulation and data analysis. The simulator takes as its input a gravitational wave strain, and returns as its output the simulated response of the LISA detector. The physics behind the simulator is described in a paper by N.J. Cornish & L.J. Rubbo, Phys. Rev. D67 022001, 2003 . The coordinate system and orbital model are described here. The format of the Simulator inputs and outputs, and instructions on how to compile and run the codes are given in the README that accompanies the source code. The current release of the LISA Simulator, Version 2.0, produces several output streams. The primary outputs are the X, Y and Z time delay interferometery (TDI) signals extracted from vertices 1, 2 and 3 of the LISA constellation. As a by-product of generating the TDI signals, the Simulator also outputs the Michelson signal from each vertex. The Simulator uses the TDI variables described in a paper by Cornish & Hellings, gr-qc/0306096 , which generalize the original TDI variables to account for the orbital motion of the detector. The Michelson and X-class variables are each produced in several forms: signal with noise; signal without noise; and noise without signal. The simulator has a modular design that allows the user to incorporate their own upgrades. For example, the subroutine that calculates the orbits of each spacecraft currently uses an approximation to the Keplarian orbits that is accurate to third order in the eccentricity. This subroutine could be replaced by a more accurate orbital model that incorporates the perturbations due to the Earth, Jupiter and other Solar system bodies. The LISA Simulator has a noise subroutine that models acceleration noise and shot noise on all six optical benches. The default noise root spectral densities are 3.0E-15 (m s^-2 Hz^-1/2) for the acceleration noise and 1.0E-11 (m Hz^-1/2) for the shot noise. The shot noise in each photo detector is drawn from an independent realization of a Gaussian random field (so the noise in each photo detector is treated as being uncorrelated). Similarly, the acceleration noise acting on each proof mass is drawn from an independent realization of a Gaussian random field, so that the component of the acceleration noise along each arm is treated as being uncorrelated. The acceleration noise is integrated twice to yield the position noise from the drag free system. The noise module does not include laser phase noise, as phase noise must be canceled on-board the spacecraft before the signals are telemetered down (see Section III A of the paper by Hellings, Phys. Rev. D With a little care, the LISA Simulator Michelson noise curves can be compared to Standard LISA Sensitivity curve. The default settings used in the LISA simulator noise module are identical to the default settings used by the Online Sensitivity Curve Generator with the "Laser shot noise" option for setting the noise floor. The Standard Sensitivity curve plots the effective strain spectral density, h_eff, which is defined as h_eff = sqrt(S_n/R), where S_n is the power spectral density of the noise and R is the LISA transfer function. In contrast, our curve shows a realization of h_f = sqrt(S_n). In the low frequency limit, R=3/5, while at high frequencies R drops as f^-2. However, this is not the sole reason for the difference. In order to convert the noise spectral density, which has units of meters per Hertz, into a strain spectral density, which has units of Hz^-1, one has to divide by some characteristic length. The sensitivity curve generator uses the average armlength L=5.0E9 meters, while we use the average optical path length 2L=1.0E10 meters. Thus, at low frequencies the two graphs differ by the overall factor of 2.0*sqrt(5/3), which gives a shift of 0.412 on a log10 scale. The graph below shows a realization of the Michelson noise for one year of observations. The number of samples was set at 2^23, so the graph terminates at a Nyquist frequency of 0.133 Hz.  The light green line is a Michelson noise realization, and the blue line shows the Michelson noise averaged across 128 frequency bins. The red line shows the Standard LISA Sensitivity curve, shifted down by a factor of 2.0*sqrt(5/3). Note that the curves agree at low frequencies, and diverge at high frequencies, as expected. The graph below shows the X-variable output of the LISA simulator for a single source. The source is the interacting white dwarf binary AM CVn, which emits gravitational waves with a frequency of 1.944 mHz. The red line is the Simulator response, the yellow line is the average noise, and the blue line is the analytic prediction for the average noise.  Below is the same graph, but zoomed in to the region where the signal is strongest.  Additional details about compiling and running the codes can be found in the README that comes with the source download. We welcome feedback and suggestions. |