LISA Simulator

1
Louis J. Rubbo, Neil J. Cornish, and Olivier
Poujade
http//www.physics.montana.edu/LISA/
Noise Simulation
Introduction
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.
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 (Sacc 9.0?10-30 m2/s4/Hz, Sps
1.0?10-22 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 (2?f)2 to arrive at the position noise.
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.
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.
The main features of The LISA Simulator are
? 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 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 LISA Simulator codes are open source software
written in the C programming language. We
encourage community involvement in developing
future releases of the Simulator.
Theory
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
AM Canum Venaticorum
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
CVns orbital frequency and proximity to the
Earth make it a good calibration binary for the
LISA observatory.
Properties of AM CVn
The finite speed of light leads to a
transcendental equation for the optical path
length
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
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.
Phase difference measured at spacecraft j at time
tj for a photon emitted from spacecraft i at time
ti
Michelson signal with spacecraft 1 acting as the
vertex craft
Low Frequency Comparison
Noiseless Michelson strain in the low frequency
limit (f lt f ? 10 mHz) 2

• Amplitude modulation, A(t)
• Frequency modulation, ?D(t)
• Phase modulation, ?P(t)

References
Top Left The noiseless Michelson strain spectral
densities produced in the low frequency limit and
by The LISA Simulator.
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/
Bottom Left The signal correlation between the
low frequency limit and The LISA Simulator for
noiseless detectors.
Support for this project was provided by the NASA
EPSCoR program through Cooperative Agreement
NCC5-579.