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SynthLISA GWDAW

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Published on January 22, 2008

Author: Valentina

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Synthetic LISA simulating time-delay interferometry in a model LISA:  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 Why Synthetic LISA?:  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 A LISA block diagram (very high level!):  A LISA block diagram (very high level!) time-delayed combinations of yij and zij laser-noise and optical-bench-noise free 3 independent observables TDI observables A LISA block diagram (very high level!):  A LISA block diagram (very high level!) time-delayed combinations of yij and zij laser-noise and optical-bench-noise free 3 independent observables TDI observables time-delayed combinations of yij and zij laser-noise and optical-bench-noise free 3 independent observables TDI observables A LISA block diagram (very high level!):  A LISA block diagram (very high level!) Doppler yij Doppler zij inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations 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) A LISA block diagram (very high level!):  A LISA block diagram (very high level!) Doppler yij Doppler zij inter-spacecraft relative frequency fluctuations intra-spacecraft relative frequency fluctuations 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 A LISA block diagram (very high level!):  A LISA block diagram (very high level!) theory rand+digital filter Nyquist f: pfDt = p/2 theory rand+digital filter Nyquist f: pfDt = p/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(-Dt/l) correlation) and low-pass digital filter A LISA block diagram (very high level!):  A LISA block diagram (very high level!) One Solar orbit/yr; LISA triangle spins through 360°/orbit Armlengths deviate from equilateral triangle at ~ 2% 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 ~(WR/c)f) The Synthetic LISA package:  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 observables (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 ... The Synthetic LISA package:  Class TDI(LISA,Wave) Return time series of noise and GW TDI observables (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 The Synthetic LISA package:  Class TDI(LISA,Wave) Return time series of noise and GW TDI observables (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 The Synthetic LISA package:  Class TDI(LISA,Wave) Return time series of noise and GW TDI observables (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 Using Synthetic LISA:  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"); Example: unequal-arm 1st-gen. noises:  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 Example: noisyLISA subtraction:  Example: noisyLISA subtraction originallisa = lisaswig.OriginalLISA(16.6782,16.6782,16.6782) noisylisa = lisaswig.NoisyLISA(originallisa,1.0,measurement noise) originalnoise = 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 Example: monochromatic binary:  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. = p/2 ecliptic long. = 0 lat. = p/5 long. = p/3 f = 2 mHz T = 1 yr LISA array parameters # samples requested, sampling time Comparison with LISA Simulator:  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 Case study: S/Ns for extreme-mass ratio inspirals:  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 Summary!:  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) Synthetic LISA simulating time-delay interferometry in a model LISA:  Synthetic LISA simulating time-delay interferometry in a model LISA Michele Vallisneri Jet Propulsion Laboratory 12/12/2003 lisa.jpl.nasa.gov A LISA block diagram (very high level!):  A LISA block diagram (very high level!) 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 ~(WR/c)f) Motion improves sensitivity: to source position and polarization homogeneous in the sky Full model must include: Time dependence of arms Aberration A LISA block diagram (very high level!):  A LISA block diagram (very high level!) 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) = ay(tn) + n(ti) Resulting spectrum Sy(f) = Sn(f)/[4 sin2(pft)] for 1 (non-unit  cuts DC) theory rand+digital filter Nyquist f: pfDt = p/2 A LISA block diagram (very high level!):  A LISA block diagram (very high level!) 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(pft) Sn(f) A LISA block diagram (very high level!):  A LISA block diagram (very high level!) 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) A LISA block diagram (very high level!):  A LISA block diagram (very high level!) 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(-Dt/l) 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 A LISA block diagram (very high level!):  A LISA block diagram (very high level!) For the purpose of LISA detection, plane gravitational waves are completely specified by their ecliptic coordinates (l,b) 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 (l,b) defines the two GW polarizations The Synthetic LISA package:  Class TDI(LISA,Wave) Return time series of noise and GW TDI observables (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 Example: equal-arm 1st-gen. TDI noises:  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"); Example: equal-arm 1st-gen. TDI noises:  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"); Example: modified-TDI subtraction:  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 Example: realistic LISA noises:  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)

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