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Louis J. Rubbo, Neil J. Cornish, and Olivier Poujade http://www.physics.montana.edu/LISA/ 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. Gravitational Waveform h+(t) The LISA Simulator h(t) S(t) LISA Response S(f) 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. The main features of The LISA Simulator are: Complete coverage of the LISA bandwidth (10-5 Hz – 1 Hz). Can handle any input waveform. 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 PrePhase A Report [3] (Sacc = 9.010-30 m2/s4/Hz, Sps = 1.010-22 m2/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 (2f)2 to arrive at the position noise. Comparison to the Standard LISA Noise Curve 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. Sn heff R Includes all orbital modulations and path length variations. Includes acceleration and photon shot noise. Outputs the Michelson, Sagnac, and X signals. 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. hSimulated Sn 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. LISA Constants The LISA Simulator codes are written in a modular form allowing for ease in making upgrades and studies into particular areas of interest. Variation in the optical path length between spacecrafts i and j [1]: 1 rˆij (ti ) rˆij (ti ) j ij (ti ) : h( )d 2 1 nˆ rˆij (ti ) i rˆij ( ) t ( ) nˆ x( ) LISA GW Source Source Constants Unit Vectors Signal Phase Times Noise Gaussian Dist. LISA Simulator Random Number GW Source Earth xi Response n̂ Sun The finite speed of light leads to a transcendental equation for the optical path length: ij (ti ) x j (ti ij (ti )) xi (ti ) rˆij (ti ) x j (ti ij (ti )) xi (ti ) ij (ti ) Phase difference measured at spacecraft j at time tj for a photon emitted from spacecraft i at time ti: a a ˆ ij (t j ) Ci (ti ) C j (t j ) ij (ti ) n (t j ) rij (ti ) nij (t j ) n ji (ti ) s ij ti t j ij 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. 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. Properties of AM CVn Primary mass 0.5 MSun Secondary mass 0.033 MSun Orbital period 1028.76 sec Orbital frequency 0.972 mHz Distance 100 pc Ecliptic-longitude 170.39º Ecliptic-latitude 37.44º (ti ) Michelson signal with spacecraft #1 acting as the vertex craft: S1 (t ) 12 (t 21 ) 21 (t ) 13 (t 31 ) 31 (t ) Noiseless Michelson strain in the low frequency limit (f < f* 10 mHz) [2]: s(t ) A(t )cos 2 ft D (t ) P (t ) • Amplitude modulation, A(t) • Frequency modulation, D(t) • Phase modulation, P(t) Top Left: The noiseless Michelson strain spectral densities produced in the low frequency limit and by The LISA Simulator. Bottom Left: The signal correlation between the low frequency limit and The LISA Simulator for noiseless detectors. [1] “LISA Response Function”, N. J. Cornish & L. J. Rubbo, Phys. Rev. D 67, 022001 (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, //http://www.srl.caltech.edu/%7Eshane/sensitivity/ Support for this project was provided by the NASA EPSCoR program through Cooperative Agreement NCC5-579.