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

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

A LISA block diagram (very high level!) GW sources for plane waves, work from k , h + (t), h x (t) at SSB TDI Doppler y ij LISA noises observables inter-spacecraft relative frequency time-delayed combinations laser freq. fluctuations, of y ij and z ij fluctuations Doppler z ij (optical bench), laser-noise and optical- proof mass, optical path bench-noise free intra-spacecraft 3 independent observables relative frequency fluctuations LISA geometry spacecraft positions → photon propagation → armlengths 3 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

A LISA block diagram (very high level!) GW sources for plane waves, work from k , h + (t), h x (t) at SSB TDI TDI Doppler y ij LISA noises observables observables inter-spacecraft relative frequency time-delayed combinations time-delayed combinations laser freq. fluctuations, of y ij and z ij of y ij and z ij fluctuations Doppler z ij (optical bench), laser-noise and optical- laser-noise and optical- proof mass, optical path bench-noise free bench-noise free intra-spacecraft 3 independent observables 3 independent observables relative frequency fluctuations LISA geometry spacecraft positions → photon propagation → armlengths 4 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

A LISA block diagram (very high level!) GW sources for plane waves, work from k , h + (t), h x (t) at SSB TDI Doppler y ij Doppler y ij LISA noises observables inter-spacecraft inter-spacecraft photon propagation vector relative frequency relative frequency time-delayed combinations laser freq. fluctuations, GW TT tensor of y ij and z ij fluctuations fluctuations Doppler z ij Doppler z ij (optical bench), laser-noise and optical- Doppler shift due to GWs proof mass, optical path bench-noise free intra-spacecraft intra-spacecraft (Wahlquist-Estabrook 3 independent observables relative frequency relative frequency response) measured for fluctuations fluctuations geom. projection factor reception at spacecraft r LISA geometry and emission at spacecraft GW buffeting of GW buffeting of s spacecraft positions spacecraft s at emission spacecraft r at reception (laser travels along arm l) → photon propagation (t-L l ) (t) geom. projection factor wavefront retard.; p i are spacecraft → armlengths pos. 5 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

A LISA block diagram (very high level!) fluctuations of laser fluctuations of laser 1* GW sources 3 at emission (t - L 2 ) (reference) at reception (t) Doppler shift measured for reception at spacecraft 1 for plane waves, work and emission at spacecraft from k , h + (t), h x (t) at proof-mass 1* noise shot noise at sc 1 3 SSB (laser travels along arm 2) TDI Doppler y ij Doppler y ij LISA noises observables inter-spacecraft inter-spacecraft relative frequency relative frequency time-delayed combinations laser freq. fluctuations, of y ij and z ij fluctuations fluctuations Doppler z ij Doppler z ij (optical bench), laser-noise and optical- proof mass, optical path bench-noise free intra-spacecraft intra-spacecraft 3 independent observables relative frequency relative frequency Doppler shift measured fluctuations fluctuations LISA geometry between optical benches on proof-mass 1 noise spacecraft 1 spacecraft positions → photon propagation → armlengths fluctuations of lasers 1 and 1* 6 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

A LISA block diagram (very high level!) theory GW sources rand+digital filter Nyquist f: π f ∆ t = π /2 for plane waves, work from k , h + (t), h x (t) at SSB TDI Doppler y ij theory LISA noises observables inter-spacecraft rand+digital filter Nyquist f: π f ∆ t = π /2 relative frequency time-delayed combinations laser freq. fluctuations, of y ij and z ij fluctuations Doppler z ij (optical bench), laser-noise and optical- proof mass, optical path bench-noise free intra-spacecraft 3 independent observables relative frequency fluctuations LISA noises : 18 time series (6 proof mass + 6 optical path + 6 LISA geometry laser) • Assume Gaussian, f -2 , f 2 , white spacecraft positions • Generate in the time domain by applying digital filters to → photon propagation uncorrelated white noise produced at fixed sampling time, → armlengths then interpolate • For laser noise, use combination of Markov chain (exp(- ∆ t/ λ ) correlation) and low-pass digital filter 7 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

A LISA block diagram (very high level!) Motion complicates GW signals (1) : 1.One Solar orbit/yr; LISA GW sources • by changing orientation of LISA plane triangle spins through (power spread through ~ 9 bins) 360°/orbit • by Doppler-shifting incoming GW signals for plane waves, work 2.Armlengths deviate from (due to relative motion, dominates for from k , h + (t), h x (t) at f>10 -3 Hz; bandwidth ~( Ω R/c)f) equilateral triangle at ~ 2% SSB 3.Armlengths are time and Motion improves sensitivity to GW TDI direction dependent Doppler y ij (1): LISA noises observables • to source position and polarization inter-spacecraft • makes it homogeneous in the sky relative frequency time-delayed combinations laser freq. fluctuations, of y ij and z ij Motion hinders noise suppression fluctuations Doppler z ij (optical bench), (1,2,3): laser-noise and optical- proof mass, optical path bench-noise free • need accurate knowledge of intra-spacecraft armlengths 3 independent observables relative frequency • high-order time delays needed fluctuations LISA geometry LISA geometry spacecraft positions spacecraft positions → photon propagation → photon propagation → armlengths → armlengths 8 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

The Synthetic LISA package Implements the LISA block structure as a collection of C++ classes Class Wave Class LISA Defines the position and time evolution of a Defines the LISA time-evolving geometry GW source (positions of spacecraft, armlengths) SimpleBinary : GW from a physical OriginalLISA : static configuration with fixed monochromatic binary (arbitrary) armlengths SimpleMonochromatic : simpler parametrization ModifiedLISA : stationary configuration, rotating with T=1yr; different cw and ccw InterpolateMemory : interpolate user-provided armlengths buffers for h + , h x ... CircularRotating : spacecraft on circular, inclined orbits; cw/ccw, time-evolving, Class TDI (LISA,Wave) causal armlengths EccentricInclined : spacecraft on eccentric, Return time series of noise and GW TDI inclined orbits; cw/ccw, time-evolving, observables (builds causal y ij ’s; includes 1st- and 2nd-generation observables) causal armlengths TDInoise : demonstrates laser-noise NoisyLISA (use with any LISA ): adds white subtraction noise to armlengths used for TDI delays TDIsignal : causal, validated vs. LISA ... Simulator TDIfast : cached for multiple sources (Edlund) 9 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003

The Synthetic LISA package ...things to do with it right now! Class Wave Class LISA Defines the position and time evolution of a Defines the LISA time-evolving geometry GW source (positions of spacecraft, armlengths) SimpleBinary : GW from a physical OriginalLISA : static configuration with fixed monochromatic binary (arbitrary) armlengths SimpleMonochromatic : simpler parametrization ModifiedLISA : stationary configuration, rotating with T=1yr; different cw and ccw InterpolateMemory : interpolate user-provided Check the sensitivity of armlengths buffers for h + , h x alternate LISA ... CircularRotating : spacecraft on circular, inclined orbits; cw/ccw, time-evolving, configurations Class TDI (LISA,Wave) causal armlengths EccentricInclined : spacecraft on eccentric, Return time series of noise and GW TDI inclined orbits; cw/ccw, time-evolving, observables (builds causal y ij ’s; includes 1st- and 2nd-generation observables) causal armlengths TDInoise : demonstrates laser-noise NoisyLISA (use with any LISA ): adds white subtraction noise to armlengths used for TDI delays TDIsignal : causal, validated vs. LISA ... Simulator TDIfast : cached for multiple sources (Edlund) 10 GWDAW 2003: Michele Vallisneri on Synthetic LISA 12/17/2003