Transcript 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?
•
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
12/17/2003
GWDAW 2003: Michele Vallisneri on Synthetic LISA
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A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
LISA geometry
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
intra-spacecraft
relative frequency
fluctuations
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
3 independent observables
spacecraft positions
 photon propagation
 armlengths
12/17/2003
GWDAW 2003: Michele Vallisneri on Synthetic LISA
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A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
LISA geometry
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
intra-spacecraft
relative frequency
fluctuations
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
3 independent observables
spacecraft positions
 photon propagation
 armlengths
12/17/2003
GWDAW 2003: Michele Vallisneri on Synthetic LISA
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A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
TDI
observables
Doppler yij
inter-spacecraft
relative frequency
fluctuations
photon
propagation
vector
time-delayed
combinations
yij and
zij
GWofTT
tensor
laser freq. fluctuations,
(optical bench),
Doppler zij
laser-noise and opticalbench-noise free
Doppler
shift due
to GWs
proof mass,
optical
path
intra-spacecraft
(Wahlquist-Estabrook
3 independent observables
relative frequency
response) measured for
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
travelspropagation
along arm l)
 photon
(t-Ll) factor
(t)
wavefront retard.;
pi are spacecraft
geom. projection
 armlengths
pos.
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
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A LISA block diagram (very high level!)
fluctuations of laser
3 at emission (t - L2)
GW sources
Doppler shift measured for
reception
spacecraft
for planeatwaves,
work 1
and
emission
from
k, h+(t),athxspacecraft
(t) at
3
SSB
(laser travels along arm 2)
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
LISA geometry
proof-mass 1* noise
inter-spacecraft
relative frequency
fluctuations
time-delayed combinations
of yij and zij
Doppler zij
intra-spacecraft
relative frequency
fluctuations
proof-mass 1 noise
shot noise at sc 1
TDI
observables
Doppler yij
spacecraft positions
 photon propagation
 armlengths
fluctuations of lasers 1 and 1*
12/17/2003
fluctuations of laser 1*
(reference) at reception
(t)
laser-noise and opticalbench-noise free
3 independent observables
Doppler shift measured
between optical benches on
spacecraft 1
GWDAW 2003: Michele Vallisneri on Synthetic LISA
6
A LISA block diagram (very high level!)
for plane waves, work
from k, h+(t), hx(t) at
SSB
laser freq. fluctuations,
(optical bench),
proof mass, optical path
inter-spacecraft
relative frequency
fluctuations
Doppler zij
TDI
theory
observables
rand+digital
filter
time-delayed combinations
of yij and zij
laser-noise and opticalbench-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)
-2 2
•spacecraft
Assume Gaussian,
positions f , f , white
•Generate
in the time domain by applying digital filters to
photon propagation
uncorrelated
armlengths 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
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
12/17/2003
Nyquist f: pfDt = p/2
LISA noises
Doppler yij
Nyquist f: pfDt = p/2
GW sources
theory
rand+digital filter
A LISA block diagram (very high level!)
Motion complicates GW signals (1):
1. One Solar orbit/yr; LISA
•GW
by changing
orientation of LISA plane
sources
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
fromf>10
k, h-3+(t),
h
(t)
at
x
equilateral triangle at ~ 2%
Hz; bandwidth
~(WR/c)f)
SSB
3. Armlengths are time and
Motion improves sensitivity to GW
TDI
Doppler yij direction dependent
(1):
observables
LISA
• to
sourcenoises
position and polarization
inter-spacecraft
• makes it homogeneous in the relative
sky
time-delayed combinations
frequency
laser
freq.
fluctuations,
of yij and zij
Motion hinders noise suppression
fluctuations
(optical
Doppler zij
(1,2,3): bench),
laser-noise and opticalbench-noise free
proof
mass,
optical
path
• need accurate knowledge of
intra-spacecraft
3 independent observables
armlengths
relative frequency
• high-order time delays needed fluctuations
LISA geometry
spacecraft positions
 photon propagation
 armlengths
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
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The Synthetic LISA package
Implements the LISA block structure as a collection of C++ classes
Class LISA
Class Wave
Defines the LISA time-evolving geometry
(positions of spacecraft, armlengths)
Defines the position and time evolution of a
GW source
OriginalLISA: static configuration with fixed
(arbitrary) armlengths
ModifiedLISA: stationary configuration,
rotating with T=1yr; different cw and ccw
armlengths
SimpleBinary: GW from a physical
monochromatic binary
SimpleMonochromatic: simpler
parametrization
InterpolateMemory: interpolate user-provided
buffers for h+, hx
...
CircularRotating: spacecraft on circular,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Class TDI(LISA,Wave)
EccentricInclined: spacecraft on eccentric,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Return time series of noise and GW TDI
observables (builds causal yij’s; includes 1stand 2nd-generation observables)
NoisyLISA (use with any LISA): adds white
noise to armlengths used for TDI delays
TDInoise: demonstrates laser-noise
subtraction
...
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TDIsignal: causal, validated vs. LISA
Simulator
TDIfast:
cached
for multiple sources (Edlund) 9
GWDAW 2003: Michele Vallisneri
on Synthetic
LISA
The Synthetic LISA package
...things to do with it right now!
Class LISA
Class Wave
Defines the LISA time-evolving geometry
(positions of spacecraft, armlengths)
Defines the position and time evolution of a
GW source
OriginalLISA: static configuration with fixed
(arbitrary) armlengths
ModifiedLISA: stationary configuration,
rotating with T=1yr; different cw and ccw
armlengths
SimpleBinary: GW from a physical
monochromatic binary
SimpleMonochromatic: simpler
parametrization
InterpolateMemory: interpolate user-provided
Check the sensitivity
buffers of
for h , h
...
CircularRotating: spacecraft
on circular, LISA
alternate
inclined orbits; cw/ccw, time-evolving,
configurations Class TDI(LISA,Wave)
causal armlengths
+
x
EccentricInclined: spacecraft on eccentric,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Return time series of noise and GW TDI
observables (builds causal yij’s; includes 1stand 2nd-generation observables)
NoisyLISA (use with any LISA): adds white
noise to armlengths used for TDI delays
TDInoise: demonstrates laser-noise
subtraction
...
12/17/2003
TDIsignal: causal, validated vs. LISA
Simulator
TDIfast:
cached
for multiple sources (Edlund)10
GWDAW 2003: Michele Vallisneri
on Synthetic
LISA
The Synthetic LISA package
...things to do with it right now!
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
Class Wave
Demonstrate
laser-noise
Defines the position and time evolution of a
GW source
sub.:
SimpleBinary: GW from a physical
1st-generation
TDI
monochromatic binary
modified
TDI
SimpleMonochromatic:
simpler
parametrization
2nd-generation TDI
InterpolateMemory: interpolate user-provided
degradation
buffers for h+,of
hx subtraction for
imperfect knowledge
... of arms
• with armlocking
•
•
•
•
Class TDI(LISA,Wave)
EccentricInclined: spacecraft on eccentric,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Return time series of noise and GW TDI
observables (builds causal yij’s; includes 1stand 2nd-generation observables)
NoisyLISA (use with any LISA): adds white
noise to armlengths used for TDI delays
TDInoise: demonstrates laser-noise
subtraction
...
12/17/2003
TDIsignal: causal, validated vs. LISA
Simulator
TDIfast:
cached
for multiple sources (Edlund)11
GWDAW 2003: Michele Vallisneri
on Synthetic
LISA
The Synthetic LISA package
...things to do with it right now!
Class LISA
Defines
the LISA time-evolving
geometry
Produce
synthetic
time
(positions of spacecraft, armlengths)
series to test dataOriginalLISA: static configuration with fixed
(arbitrary)
armlengths
analysis
algorithms
ModifiedLISA: stationary configuration,
rotating with T=1yr; different cw and ccw
armlengths
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
...
CircularRotating: spacecraft on circular,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Class TDI(LISA,Wave)
EccentricInclined: spacecraft on eccentric,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Return time series of noise and GW TDI
observables (builds causal yij’s; includes 1stand 2nd-generation observables)
NoisyLISA (use with any LISA): adds white
noise to armlengths used for TDI delays
TDInoise: demonstrates laser-noise
subtraction
...
12/17/2003
TDIsignal: causal, validated vs. LISA
Simulator
TDIfast:
cached
for multiple sources (Edlund)12
GWDAW 2003: Michele Vallisneri
on 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!
#!/usr/bin/python
import lisaswig;
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
unequalarmlisa = lisaswig.ModifiedLISA(15.0,16.0,17.0);
Armlengths (s)
Create a TDI object based on our chosen LISA
Laser correlation (s)
unequalarmnoise = lisaswig.TDInoise(unequalarmlisa,
1.0,2.5e-48,1.0,1.8e-37,1.0,1.1e-26,1.0);
Noise sampling time
(s)
Proof mass Sn  f2 (Hz- Opt. path Sn  f-2 (Hz-1) Laser Sn (Hz-1)
1)
lisaswig.printtdi("noise-X.txt",unequalarmnoise,1048576,1.0,"X");
TDI variables
to print
Print X TDI noise to disk!
File name # samples requested,
sampling time
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
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10-
Example: unequal-arm 1st-gen. noises
25
Note laser noise subtraction!
...
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");
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
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Example: noisyLISA subtraction
originallisa = lisaswig.OriginalLISA(16.6782,16.6782,16.6782)
noisylisa = lisaswig.NoisyLISA(originallisa,1.0,measurement noise)
measurement
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)
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
noise Sn (s2 Hz-1)
Use different
LISA for noise
and TDI
delays
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Example: monochromatic binary
f = 2 mHz
T = 1 yr
ecliptic lat. = p/2
ecliptic long. = 0
lat. = p/5
long. = p/3
mylisa = lisaswig.CircularRotating(0.0,0.0,1.0)
LISA array parameters
mybinary = lisaswig.SimpleBinary(frequency,initial phase,inclination,amplitude,
ecliptic latitude,ecliptic longitude,polarization angle)
# samples requested,
sampling time
mysignal = lisaswig.TDIsignal(mylisa,mybinary)
lisaswig.printtdi("signal-X.txt",mysignal,secondsperyear/16.0,16.0,"X")
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
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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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GWDAW 2003: Michele Vallisneri on Synthetic LISA
17
Case study: S/Ns
for extreme-mass ratio inspirals
HughesGlampedakisKennefick integrator
(C++): output h+, hx
12/17/2003
(Python
)
Synthetic LISA:
generate A, E, T, X GW
& noise time series
GWDAW 2003: Michele Vallisneri on Synthetic LISA
Matlab:
compute
S/Ns
18
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)
19
12/17/2003
GWDAW 2003: Michele Vallisneri on Synthetic 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!)
• One Solar orbit/yr, equilateral-triangle configuration kept to ~2%
• The
spins through 360°/orbit
GWtriangle
sources
• Motion complicates signals:
for •plane
waves, work
by changing
orientation of LISA plane (power spread through ~9 bins)
from
• k,
byhDoppler-shifting
incoming GW signals (due to relative motion;
+(t), hx(t) at
-3
SSB dominates for f>10 Hz; bandwidth ~(WR/c)f)
• Motion improves sensitivity:
TDI
Doppler yij
• to source position and polarization
observables
LISA
noises
• homogeneous in the sky inter-spacecraft
time-delayed combinations
•laser
Fullfreq.
model
must include: relative frequency
fluctuations,
of yij and zij
fluctuations
• Time
dependence of arms
(optical
bench),
Doppler zij
laser-noise and opticalbench-noise free
• Aberration
proof
mass, optical path
intra-spacecraft
3 independent observables
relative frequency
fluctuations
LISA geometry
spacecraft positions
 photon propagation
 armlengths
12/17/2003
GWDAW 2003: Michele Vallisneri on Synthetic LISA
21
A LISA block diagram (very high level!)
theory
rand+digital filter
GW sources
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
Nyquist f: pfDt = p/2
for plane waves, work
from k, h+(t), hx(t) at
SSB
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
intra-spacecraft
3 independent observables
relative frequency
fluctuations
Proof-mass Df/f noise: six time series
LISA geometry
• Assume Gaussian and red; baseline Sn  2.5 10-48 f-2 Hz-1
spacecraft positions
• Generate white noise n(ti) (independent Gaussian variates) at sampling
 photon propagation
interval Dt
 armlengths
• Filter through digital integrator: y(ti+1) = ay(tn) + n(ti)
• Resulting spectrum Sy(f) = Sn(f)/[4 sin2(pfDt)] for a1 (non-unit a cuts
DC)
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
22
A LISA block diagram (very high level!)
GW sources
theory
rand+digital filter
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
Nyquist f: pfDt = p/2
for plane waves, work
from k, h+(t), hx(t) at
SSB
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
intra-spacecraft
3 independent observables
relative frequency
fluctuations
Optical
path
Df/f
noise: six time series
LISA geometry
• Assume Gaussian and blue; baseline Sn  1.8 10-37 f2 Hz-1
spacecraft positions
• Generate white noise n(ti) (independent Gaussian variates) at
 photon propagation
sampling interval Dt
 armlengths• Filter through digital differentiator: y(t ) = n(t ) - n(t )
i+1
i+1
i
2
• Resulting spectrum Sy(f) = 4 sin (pfDt) Sn(f)
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GWDAW 2003: Michele Vallisneri on Synthetic LISA
23
A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
theory
rand+digital filter
(sampling time = 1 s)
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
intra-spacecraft
relative frequency
fluctuations
Noise interpolation:
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
3 independent observables
LISA geometry
• 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
spacecraft positions
Fourier series resummation (but this requires the entire data train!)
 photon propagation
 armlengths• Simple linear interpolation between samples introduces some structure above
12/17/2003
the effective Nyquist frequency (of noise generation)
• Moral: generate noise (and sample TDI) comfortably above frequency of
interest
GWDAW 2003: Michele Vallisneri on Synthetic LISA
24
A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
LISA geometry
spacecraft positions
 photon propagation
 armlengths
12/17/2003
Laser Df/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)
TDI
Doppler
y
ij noise at fixed sampling
• Generating white
observables
inter-spacecraft
interval and then interpolating overestimates
time-delayed
combinations
relative
frequency (imposing lax
this correlation
requirements
on
of
y
and
z
ij
ij
fluctuations
armlength-measurement
error)
Doppler zij
laser-noise and optical•intra-spacecraft
It is also possible to generate
exp(-Dt/l)
bench-noise
free
correlated noise at arbitrary3 times
using
an
independent
observables
relative frequency
unequal-timestep Markov process (Ornsteinfluctuations
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
GWDAW 2003: Michele Vallisneri on Synthetic LISA
25
A LISA block diagram (very high level!)
GW sources
for plane waves, work
from k, h+(t), hx(t) at
SSB
LISA noises
laser freq. fluctuations,
(optical bench),
proof mass, optical path
Doppler yij
inter-spacecraft
relative frequency
fluctuations
Doppler zij
TDI
observables
time-delayed combinations
of yij and zij
laser-noise and opticalbench-noise free
intra-spacecraft
3 independent observables
relative frequency
fluctuations
LISA geometry
For the purpose of LISA detection, plane gravitational waves are
completely specified by their ecliptic coordinates (l,b) and by their h+(t) and
spacecraft positions
hx(t) time series at the solar system baricenter
 photon propagation
 armlengths• Retardation to the LISA spacecraft is trivial given the plane-wave
structure
12/17/2003
• A conventional rotation angle (l,b) defines the two GW polarizations
GWDAW 2003: Michele Vallisneri on Synthetic LISA
26
The Synthetic LISA package
...things to do with it right now!
Class LISA
Defines
the LISA time-evolving
geometry
Generate
synthetic
(positions of spacecraft, armlengths)
galactic-WD confusion
OriginalLISA: static configuration with fixed
(arbitrary)
armlengths
backgrounds
ModifiedLISA: stationary configuration,
rotating with T=1yr; different cw and ccw
armlengths
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
...
CircularRotating: spacecraft on circular,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Class TDI(LISA,Wave)
EccentricInclined: spacecraft on eccentric,
inclined orbits; cw/ccw, time-evolving,
causal armlengths
Return time series of noise and GW TDI
observables (builds causal yij’s; includes 1stand 2nd-generation observables)
NoisyLISA (use with any LISA): adds white
noise to armlengths used for TDI delays
TDInoise: demonstrates laser-noise
subtraction
...
12/17/2003
TDIsignal: causal, validated vs. LISA
Simulator
TDIfast:
cached
for multiple GW sources (Jeff)
27
GWDAW 2003: Michele Vallisneri
on Synthetic
LISA
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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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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Example: modified-TDI subtraction
modifiedlisa = lisaswig.ModifiedLISA(16.6782,16.6782,16.6782)
Use different
LISA for noise
and TDI
delays
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");
modified
obs
correctednoise = lisaswig.TDInoise(modifiedlisa,
TDI
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");
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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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