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Synthetic LISA simulating time-delay interferometry in a model LISA - - PowerPoint PPT Presentation

Jan 13, 2024 132 likes •450 views

Synthetic LISA simulating time-delay interferometry in a model LISA (presenting) Michele Vallisneri lisa.jpl.nasa.gov (in absentia) John W. Armstrong LISA Science Office, Jet Propulsion Laboratory 12/17/2003 Why Synthetic LISA? Simulate

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SLIDE 1

Synthetic LISA

simulating time-delay interferometry in a model LISA

(presenting) Michele Vallisneri (in absentia) John W. Armstrong

LISA Science Office, Jet Propulsion Laboratory 12/17/2003

lisa.jpl.nasa.gov

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SLIDE 2

GWDAW 2003: Michele Vallisneri on Synthetic LISA 2 12/17/2003

Why Synthetic LISA?

  • Simulate LISA fundamental noises

at the level of science/technical requirements

  • Higher level than extended modeling (no spacecraft subsystems)
  • Lower level than data analysis tools (do time-domain simulation of TDI;

include removal of laser frequency fluctuations)

  • Provide streamlined module to filter GWs through TDI

responses, for use in developing data-analysis algorithms

  • Include full model of TDI

(motion of the LISA array, time- and direction-dependent armlengths, causal Doppler observables, 2nd-generation TDI observables)

  • Use directly or to validate (semi)analytic approximations
  • Make it friendly and fun to use
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SLIDE 3

GWDAW 2003: Michele Vallisneri on Synthetic LISA 3 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

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SLIDE 4

GWDAW 2003: Michele Vallisneri on Synthetic LISA 4 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

TDI

  • bservables
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SLIDE 5

GWDAW 2003: Michele Vallisneri on Synthetic LISA 5 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

  • geom. projection factor

photon propagation vector GW TT tensor GW buffeting of spacecraft s at emission (t-Ll) GW buffeting of spacecraft r at reception (t)

  • geom. projection factor

wavefront retard.; pi are spacecraft pos. Doppler shift due to GWs (Wahlquist-Estabrook response) measured for reception at spacecraft r and emission at spacecraft s (laser travels along arm l)

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SLIDE 6

GWDAW 2003: Michele Vallisneri on Synthetic LISA 6 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path shot noise at sc 1 fluctuations of laser 1* (reference) at reception (t) fluctuations of laser 3 at emission (t - L2) proof-mass 1* noise Doppler shift measured for reception at spacecraft 1 and emission at spacecraft 3 (laser travels along arm 2) Doppler shift measured between optical benches on spacecraft 1 fluctuations of lasers 1 and 1* proof-mass 1 noise

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SLIDE 7

GWDAW 2003: Michele Vallisneri on Synthetic LISA 7 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path theory rand+digital filter

Nyquist f: πf∆t = π/2

theory rand+digital filter

Nyquist f: πf∆t = π/2

LISA noises: 18 time series (6 proof mass + 6 optical path + 6 laser)

  • Assume Gaussian, f-2, f2, white
  • Generate in the time domain by applying digital filters to

uncorrelated white noise produced at fixed sampling time, then interpolate

  • For laser noise, use combination of Markov chain (exp(-∆t/λ)

correlation) and low-pass digital filter

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SLIDE 8

GWDAW 2003: Michele Vallisneri on Synthetic LISA 8 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA geometry

spacecraft positions → photon propagation → armlengths

1.One Solar orbit/yr; LISA triangle spins through 360°/orbit 2.Armlengths deviate from equilateral triangle at ~ 2% 3.Armlengths are time and direction dependent

Motion hinders noise suppression (1,2,3):

  • need accurate knowledge of

armlengths

  • high-order time delays needed

Motion improves sensitivity to GW (1):

  • to source position and polarization
  • makes it homogeneous in the sky

Motion complicates GW signals (1):

  • by changing orientation of LISA plane

(power spread through ~9 bins)

  • by Doppler-shifting incoming GW signals

(due to relative motion, dominates for f>10-3 Hz; bandwidth ~(ΩR/c)f)

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SLIDE 9

GWDAW 2003: Michele Vallisneri on Synthetic LISA 9 12/17/2003

The Synthetic LISA package

Implements the LISA block structure as a collection of C++ classes

Class LISA

Defines the LISA time-evolving geometry (positions of spacecraft, armlengths) OriginalLISA: static configuration with fixed (arbitrary) armlengths ModifiedLISA: stationary configuration, rotating with T=1yr; different cw and ccw armlengths CircularRotating: spacecraft on circular, inclined orbits; cw/ccw, time-evolving, causal armlengths EccentricInclined: spacecraft on eccentric, inclined orbits; cw/ccw, time-evolving, causal armlengths NoisyLISA (use with any LISA): adds white noise to armlengths used for TDI delays ...

Class TDI(LISA,Wave)

Return time series of noise and GW TDI

  • bservables (builds causal yij’s; includes 1st-

and 2nd-generation observables) TDInoise: demonstrates laser-noise subtraction TDIsignal: causal, validated vs. LISA Simulator TDIfast: cached for multiple sources (Edlund)

Class Wave

Defines the position and time evolution of a GW source SimpleBinary: GW from a physical monochromatic binary SimpleMonochromatic: simpler parametrization InterpolateMemory: interpolate user-provided buffers for h+, hx ...

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SLIDE 10

GWDAW 2003: Michele Vallisneri on Synthetic LISA 10 12/17/2003

Class TDI(LISA,Wave)

Return time series of noise and GW TDI

  • bservables (builds causal yij’s; includes 1st-

and 2nd-generation observables) TDInoise: demonstrates laser-noise subtraction TDIsignal: causal, validated vs. LISA Simulator TDIfast: cached for multiple sources (Edlund)

Class Wave

Defines the position and time evolution of a GW source SimpleBinary: GW from a physical monochromatic binary SimpleMonochromatic: simpler parametrization InterpolateMemory: interpolate user-provided buffers for h+, hx ...

Class LISA

Defines the LISA time-evolving geometry (positions of spacecraft, armlengths) OriginalLISA: static configuration with fixed (arbitrary) armlengths ModifiedLISA: stationary configuration, rotating with T=1yr; different cw and ccw armlengths CircularRotating: spacecraft on circular, inclined orbits; cw/ccw, time-evolving, causal armlengths EccentricInclined: spacecraft on eccentric, inclined orbits; cw/ccw, time-evolving, causal armlengths NoisyLISA (use with any LISA): adds white noise to armlengths used for TDI delays ...

The Synthetic LISA package

...things to do with it right now!

Check the sensitivity of alternate LISA configurations

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SLIDE 11

GWDAW 2003: Michele Vallisneri on Synthetic LISA 11 12/17/2003

Class TDI(LISA,Wave)

Return time series of noise and GW TDI

  • bservables (builds causal yij’s; includes 1st-

and 2nd-generation observables) TDInoise: demonstrates laser-noise subtraction TDIsignal: causal, validated vs. LISA Simulator TDIfast: cached for multiple sources (Edlund)

Class Wave

Defines the position and time evolution of a GW source SimpleBinary: GW from a physical monochromatic binary SimpleMonochromatic: simpler parametrization InterpolateMemory: interpolate user-provided buffers for h+, hx ...

Class LISA

Defines the LISA time-evolving geometry (positions of spacecraft, armlengths) OriginalLISA: static configuration with fixed (arbitrary) armlengths ModifiedLISA: stationary configuration, rotating with T=1yr; different cw and ccw armlengths CircularRotating: spacecraft on circular, inclined orbits; cw/ccw, time-evolving, causal armlengths EccentricInclined: spacecraft on eccentric, inclined orbits; cw/ccw, time-evolving, causal armlengths NoisyLISA (use with any LISA): adds white noise to armlengths used for TDI delays ...

The Synthetic LISA package

...things to do with it right now!

Demonstrate laser-noise sub.:

  • 1st-generation TDI
  • modified TDI
  • 2nd-generation TDI
  • degradation of subtraction for

imperfect knowledge of arms

  • with armlocking
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SLIDE 12

GWDAW 2003: Michele Vallisneri on Synthetic LISA 12 12/17/2003

Class TDI(LISA,Wave)

Return time series of noise and GW TDI

  • bservables (builds causal yij’s; includes 1st-

and 2nd-generation observables) TDInoise: demonstrates laser-noise subtraction TDIsignal: causal, validated vs. LISA Simulator TDIfast: cached for multiple sources (Edlund)

Class Wave

Defines the position and time evolution of a GW source SimpleBinary: GW from a physical monochromatic binary SimpleMonochromatic: simpler parametrization InterpolateMemory: interpolate user-provided buffers for h+, hx ...

Class LISA

Defines the LISA time-evolving geometry (positions of spacecraft, armlengths) OriginalLISA: static configuration with fixed (arbitrary) armlengths ModifiedLISA: stationary configuration, rotating with T=1yr; different cw and ccw armlengths CircularRotating: spacecraft on circular, inclined orbits; cw/ccw, time-evolving, causal armlengths EccentricInclined: spacecraft on eccentric, inclined orbits; cw/ccw, time-evolving, causal armlengths NoisyLISA (use with any LISA): adds white noise to armlengths used for TDI delays ...

The Synthetic LISA package

...things to do with it right now!

Produce synthetic time series to test data- analysis algorithms

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SLIDE 13

GWDAW 2003: Michele Vallisneri on Synthetic LISA 13 12/17/2003

Using Synthetic LISA

The preferred interface to Synthetic LISA is through a simple script in the language Python.

This is a Python script! Import the Synthetic LISA library (lisaswig.py, _lisaswig.so) so we can use it Create a LISA (geometry) object; use static LISA, with equal arms Armlengths (s) Create a TDI object based on our chosen LISA Noise sampling time (s) Proof mass Sn × f2 (Hz-

1)

  • Opt. path Sn × f-2 (Hz-1) Laser Sn (Hz-1)

Laser correlation (s) Print X TDI noise to disk! File name # samples requested, sampling time TDI variables to print

#!/usr/bin/python import lisaswig; unequalarmlisa = lisaswig.ModifiedLISA(15.0,16.0,17.0); unequalarmnoise = lisaswig.TDInoise(unequalarmlisa, 1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,1.0); lisaswig.printtdi("noise-X.txt",unequalarmnoise,1048576,1.0,"X");

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SLIDE 14

GWDAW 2003: Michele Vallisneri on Synthetic LISA 14 12/17/2003

Example: unequal-arm 1st-gen. noises

... lisaswig.printtdi("noise-a.txt",unequalarmnoise,1048576,1.0,"a"); lisaswig.printtdi("noise-z.txt",unequalarmnoise,1048576,1.0,"z"); lisaswig.printtdi("noise-E.txt",unequalarmnoise,1048576,1.0,"E");

Note laser noise subtraction! 10-

25

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SLIDE 15

GWDAW 2003: Michele Vallisneri on Synthetic LISA 15 12/17/2003

Example: noisyLISA subtraction

  • riginallisa = lisaswig.OriginalLISA(16.6782,16.6782,16.6782)

noisylisa = lisaswig.NoisyLISA(originallisa,1.0,measurement noise)

  • riginalnoise = lisaswig.TDInoise(originallisa,

1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,0.1) noisynoise = lisaswig.TDInoise(noisylisa,originallisa, 1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,0.1)

measurement noise Sn (s2 Hz-

1)

Use different LISA for noise and TDI delays

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SLIDE 16

GWDAW 2003: Michele Vallisneri on Synthetic LISA 16 12/17/2003

Example: monochromatic binary

mylisa = lisaswig.CircularRotating(0.0,0.0,1.0) mybinary = lisaswig.SimpleBinary(frequency,initial phase,inclination,amplitude, ecliptic latitude,ecliptic longitude,polarization angle) mysignal = lisaswig.TDIsignal(mylisa,mybinary) lisaswig.printtdi("signal-X.txt",mysignal,secondsperyear/16.0,16.0,"X")

ecliptic lat. = π/2 ecliptic long. = 0

  • lat. = π/5
  • long. = π/3

f = 2 mHz T = 1 yr LISA array parameters # samples requested, sampling time

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SLIDE 17

GWDAW 2003: Michele Vallisneri on Synthetic LISA 17 12/17/2003

Comparison with LISA Simulator

Synthetic LISA LISA Simulator

TDI X (no noise), T = 1 yr

f = 1.94 mHz inc = 1.60 ecliptic lat. ≈ 0, long. = 0

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SLIDE 18

GWDAW 2003: Michele Vallisneri on Synthetic LISA 18 12/17/2003

Case study: S/Ns for extreme-mass ratio inspirals

Hughes- Glampedakis- Kennefick integrator (C++): output h+, hx (Python ) Synthetic LISA: generate A, E, T, X GW & noise time series Matlab: compute S/Ns

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SLIDE 19

GWDAW 2003: Michele Vallisneri on Synthetic LISA 19 12/17/2003

Summary!

  • Synthetic LISA is the package I would have wanted to

download and use, had I not written it

  • Synthetic LISA simulates LISA fundamental noises and

GW response at the level of science/technical requirements

  • Synthetic LISA includes a full model of the LISA science

process (2nd-generation TDI, laser-noise subtraction)

  • Synthetic LISA’s modular design allows easy interfacing to

extended modeling and data-analysis applications

  • Synthetic LISA is user-friendly and extensible (C++,

Python, other scripting languages)

  • Synthetic LISA is planned for open-source release in

Jan/Feb (NASA permitting)

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SLIDE 20

Synthetic LISA

simulating time-delay interferometry in a model LISA Michele Vallisneri

Jet Propulsion Laboratory 12/12/2003

lisa.jpl.nasa.gov

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SLIDE 21

GWDAW 2003: Michele Vallisneri on Synthetic LISA 21 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA geometry

spacecraft positions → photon propagation → armlengths

  • One Solar orbit/yr, equilateral-triangle configuration kept to ~2%
  • The triangle spins through 360°/orbit
  • Motion complicates signals:
  • by changing orientation of LISA plane (power spread through ~9 bins)
  • by Doppler-shifting incoming GW signals (due to relative motion;

dominates for f>10-3 Hz; bandwidth ~(ΩR/c)f)

  • Motion improves sensitivity:
  • to source position and polarization
  • homogeneous in the sky
  • Full model must include:
  • Time dependence of arms
  • Aberration
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SLIDE 22

GWDAW 2003: Michele Vallisneri on Synthetic LISA 22 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path Proof-mass ∆f/f noise: six time series

  • Assume Gaussian and red; baseline Sn ≈ 2.5 10-48 f-2 Hz-1
  • Generate white noise n(ti) (independent Gaussian variates) at sampling

interval ∆t

  • Filter through digital integrator: y(ti+1) = αy(tn) + n(ti)
  • Resulting spectrum Sy(f) = Sn(f)/[4 sin2(πf∆t)] for α→1 (non-unit α cuts

DC) theory rand+digital filter

Nyquist f: πf∆t = π/2

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SLIDE 23

GWDAW 2003: Michele Vallisneri on Synthetic LISA 23 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path Optical path ∆f/f noise: six time series

  • Assume Gaussian and blue; baseline Sn ≈ 1.8 10-37 f2 Hz-1
  • Generate white noise n(ti) (independent Gaussian variates) at

sampling interval ∆t

  • Filter through digital differentiator: y(ti+1) = n(ti+1) - n(ti)
  • Resulting spectrum Sy(f) = 4 sin2(πf∆t) Sn(f)

theory rand+digital filter

Nyquist f: πf∆t = π/2

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SLIDE 24

GWDAW 2003: Michele Vallisneri on Synthetic LISA 24 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

Noise interpolation:

  • The TDI observables operate on noise values at times specified to 30 ns
  • If noise is band limited, the exact time structure can be reconstructed by

Fourier series resummation (but this requires the entire data train!)

  • Simple linear interpolation between samples introduces some structure above

the effective Nyquist frequency (of noise generation)

  • Moral: generate noise (and sample TDI) comfortably above frequency of

interest

theory rand+digital filter (sampling time = 1 s)

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SLIDE 25

GWDAW 2003: Michele Vallisneri on Synthetic LISA 25 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

Laser ∆f/f noise: six time series

  • Assume Gaussian and white, band-limited

between 1 Hz and 10 Hz, Sn ≈ 1.1 10-26 Hz-1

  • To understand TDI laser-frequency-noise

subtraction, it is crucial to model correctly the short-time correlation structure of the noise: residual n(t) ≈ n(t + L est. error.) - n(t)

  • Generating white noise at fixed sampling

interval and then interpolating overestimates this correlation (imposing lax requirements on armlength-measurement error)

  • It is also possible to generate exp(-∆t/λ)

correlated noise at arbitrary times using an unequal-timestep Markov process (Ornstein- Uhlenbeck process); this underestimates the real laser-noise correlation (imposing exacting requirements on armlength-measurement error)

  • A good balance can probably be found by

producing noise with a Markov chain, followed by a digital filter

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SLIDE 26

GWDAW 2003: Michele Vallisneri on Synthetic LISA 26 12/17/2003

A LISA block diagram (very high level!)

LISA geometry

spacecraft positions → photon propagation → armlengths

LISA noises

laser freq. fluctuations, (optical bench), proof mass, optical path

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB

time-delayed combinations

  • f yij and zij

laser-noise and optical- bench-noise free 3 independent observables

TDI

  • bservables

Doppler yij Doppler zij

inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations

GW sources

for plane waves, work from k, h+(t), hx(t) at SSB For the purpose of LISA detection, plane gravitational waves are completely specified by their ecliptic coordinates (λ,β) and by their h+(t) and hx(t) time series at the solar system baricenter

  • Retardation to the LISA spacecraft is trivial given the plane-wave

structure

  • A conventional rotation angle ψ(λ,β) defines the two GW polarizations
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SLIDE 27

GWDAW 2003: Michele Vallisneri on Synthetic LISA 27 12/17/2003

Class TDI(LISA,Wave)

Return time series of noise and GW TDI

  • bservables (builds causal yij’s; includes 1st-

and 2nd-generation observables) TDInoise: demonstrates laser-noise subtraction TDIsignal: causal, validated vs. LISA Simulator TDIfast: cached for multiple GW sources (Jeff)

Class Wave

Defines the position and time evolution of a GW source SimpleBinary: GW from a physical monochromatic binary SimpleMonochromatic: simpler parametrization InterpolateMemory: interpolate user-provided buffers for h+, hx ...

Class LISA

Defines the LISA time-evolving geometry (positions of spacecraft, armlengths) OriginalLISA: static configuration with fixed (arbitrary) armlengths ModifiedLISA: stationary configuration, rotating with T=1yr; different cw and ccw armlengths CircularRotating: spacecraft on circular, inclined orbits; cw/ccw, time-evolving, causal armlengths EccentricInclined: spacecraft on eccentric, inclined orbits; cw/ccw, time-evolving, causal armlengths NoisyLISA (use with any LISA): adds white noise to armlengths used for TDI delays ...

The Synthetic LISA package

...things to do with it right now!

Generate synthetic galactic-WD confusion backgrounds

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SLIDE 28

GWDAW 2003: Michele Vallisneri on Synthetic LISA 28 12/17/2003

Example: equal-arm 1st-gen. TDI noises

equalarmlisa = lisaswig.OriginalLISA(16.6782,16.6782,16.6782); equalarmnoise = lisaswig.TDInoise(equalarmlisa, 1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,1.0); lisaswig.printtdi("noise-X.txt",equalarmnoise,1048576,1.0,"X");

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SLIDE 29

GWDAW 2003: Michele Vallisneri on Synthetic LISA 29 12/17/2003

Example: equal-arm 1st-gen. TDI noises

... lisaswig.printtdi("noise-a.txt",equalarmnoise,1048576,1.0,"z"); lisaswig.printtdi("noise-z.txt",equalarmnoise,1048576,1.0,"z"); lisaswig.printtdi("noise-E.txt",equalarmnoise,1048576,1.0,"E");

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SLIDE 30

GWDAW 2003: Michele Vallisneri on Synthetic LISA 30 12/17/2003

Example: modified-TDI subtraction

modifiedlisa = lisaswig.ModifiedLISA(16.6782,16.6782,16.6782) modifiednoise = lisaswig.TDInoise(equalarmlisa,modifiedlisa, 1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,1.0e-6) lisaswig.printtdi("noise-Xm.txt",modifiednoise,samples,1.0,"X"); correctednoise = lisaswig.TDInoise(modifiedlisa, 1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,1.0e-6) lisaswig.printtdi("noise-Xmc.txt",correctednoise,samples,1.0,"Xm");

Use different LISA for noise and TDI delays modified TDI obs

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SLIDE 31

GWDAW 2003: Michele Vallisneri on Synthetic LISA 31 12/17/2003

Example: realistic LISA noises

For 1 yr of integration, including galactic-WD confusion noise

“short LISA” (L = 1.66x106 km) baseline LISA (L = 1.66x106 km)