Louis J. Rubbo, Neil J. Cornish, and Olivier Poujade Support for this project was provided by the NASA EPSCoR program through Cooperative Agreement NCC [1]“LISA Response Function”, N. J. Cornish & L. J. Rubbo, Phys. Rev. D 67, (2003) [2]“Angular Resolution of the LISA Gravitational Wave Detector”, C. Cutler, Phys. Rev. D 57, 7089 (1998) [3]LISA Pre-Phase A Report, P. L. Bender et. al. (1998) [4]Sensitivity Curves for Spaceborne Gravitational Wave Observatories, S. L. Larson, // The LISA Simulator is a virtual model of the proposed Laser Interferometer Space Antenna (LISA). The simulator software package is designed for use as an interface tool between source simulations 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 simulated output includes a realization of the dominant noise sources in the detector. This, combined with the response of the detector to the input gravitational wave, forms the complete output of the simulator.  Complete coverage of the LISA bandwidth (10 -5 Hz – 1 Hz).  Can handle any input waveform.  Includes all orbital modulations and path length variations.  Includes acceleration and photon shot noise.  Outputs the Michelson, Sagnac, and X signals. The main features of The LISA Simulator are: The LISA Simulator codes are open source software written in the C programming language. We encourage community involvement in developing future releases of the Simulator. The cataclysmic variable AM CVn is a binary system comprised of a low mass helium white dwarf that is transferring material to a more massive white dwarf by way of Roche lobe overflow. AM CVn’s orbital frequency and proximity to the Earth make it a good calibration binary for the LISA observatory. Primary mass0.5 M Sun Secondary mass0.033 M Sun Orbital period sec Orbital frequency0.972 mHz Distance100 pc Ecliptic-longitude170.39º Ecliptic-latitude37.44º Properties of AM CVn Shown below is the simulated response of the LISA detector to the gravitational waves emitted by AM CVn. The plot at the left shows where the signal sits in the full LISA band, while the plot on the right is a zoom in to the region of interest. Variation in the optical path length between spacecrafts i and j [1]: Phase difference measured at spacecraft j at time t j for a photon emitted from spacecraft i at time t i : Noiseless Michelson strain in the low frequency limit (f < f *  10 mHz) [2]: Bottom Left: The signal correlation between the low frequency limit and The LISA Simulator for noiseless detectors. Top Left: The noiseless Michelson strain spectral densities produced in the low frequency limit and by The LISA Simulator. Michelson signal with spacecraft #1 acting as the vertex craft: Amplitude modulation, A(t) Frequency modulation,  D (t) Phase modulation,  P (t) Technique The noise can be simulated in the time domain or the frequency domain. The contribution from each photo detector and each inertial sensor is modeled separately. The noise in each component is given as a realization of a Gaussian random process. The amplitudes are scaled by the noise spectral densities quoted in the LISA Pre- Phase A Report [3] (S acc = 9.0  m 2 /s 4 /Hz, S ps = 1.0  m 2 /Hz). In the time domain, the random walk in acceleration is integrated twice to yield the position noise, while in the frequency domain one only has to divide the Fourier coefficients by (2  f) 2 to arrive at the position noise. Comparison to the Standard LISA Noise Curve LISA ConstantsSource Constants GW SourceUnit Vectors Phase Times SignalNoise LISA Simulator Gaussian Dist. Random Number Response The LISA Simulator codes are written in a modular form allowing for ease in making upgrades and studies into particular areas of interest. The realization of the noise shown in the upper graph differs from the standard LISA noise curve shown to the right [4]. The main reason for the discrepancy is that the standard sensitivity curve plots the effective strain spectral density of the noise, which includes the LISA transfer function R(f), while the noise curve generated by The LISA Simulator plots the true noise spectral density. Sun Earth LISA GW Source xixi Gravitational Waveform The LISA Simulator LISA Response h + (t) h  (t) S(t) S(f) The remainder of the discrepancy can be traced to a factor of two difference in the definition of the strain. The Sensitivity Curve Generator scales the path length variations by the interferometer arm length L, while The LISA Simulator scales the path length variations by the optical path length 2L. The finite speed of light leads to a transcendental equation for the optical path length: