Transcript Data Analysis for Gravitational Waves. I. Ground

International School of Relativistic Astrophysics:
John Archibald Wheeler
Data Analysis for Gravitational Waves
Bernard F Schutz
Albert Einstein Institute – Max Planck Institute for
Gravitational Physics, Golm, Germany
and
School of Physics and Astronomy, Cardiff University, Cardiff, UK
[email protected]
www.aei.mpg.de
Contents
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Introduction
Detecting signals with known waveforms
Detecting signals with unknown waveforms
Data analysis in the LSC
Including VIRGO and other detectors
Detecting with high sensitivity: LISA
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
2
Introduction
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
3
Role of Data Analysis
•
•
Aim of detector projects (LIGO, GEO, VIRGO, AURIGA, …) is to identify
signals and measure their parameters.
All GW detectors are linearly polarized and are sensitive to the phase of the
wave in their waveband.
– Measure h(t), time-dependence contains much information
•
•
Bar detectors have relatively small bandwidth (Δf/f ~ 0.1 or smaller),
interferometers have wide band (10 Hz < f < 2 kHz).
Ground-based GW detectors are noise-dominated even when signals are
present.
– Mean noise during 1 ms is around h ~ 10-21.
– Expected signal amplitudes for key sources, like coalescing binary neutron stars
and GW pulsars, is 10-23 or smaller.
•
•
Detectors operate in networks, providing both confidence and directional
informaton.
Data analysis is a key part of detection. The cleverness and sophistication of
detector hardware must be matched in quality by data analysis.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
4
Detector Noise
•
“Noise” refers to any random process that creates detector output.
– Can be intrinsic (e.g. photon shot noise) or external (e.g. ground vibration).
– Can be Gaussian (e.g. thermal noise) or non-Gaussian (e.g. laser intensity
fluctuations).
– Commissioning work includes minimizing non-Gaussian noise.
– All data analysis teams include specialists in detector characterization.
•
Additional disturbances in a data stream include:
– Interference: deterministic disturbances, e.g. EM field from power lines.
– Confusion: Overlapping signals or strong signals obscuring weaker ones.
LISA will have this problem, but not the ground-based detectors.
•
A detection against noise is a decision based on probability – There is no such thing as a perfect, absolutely certain measurement.
– When signal is weak, statements about confidence of detection must be
made with great care.
•
In the LSC at least one-third of the >400 scientists whose names go on
the papers are involved in data analysis and related activities.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
5
Statistical treatment of noise
•
•
Data is always sampled at a constant rate (e.g. 16kHz), so we will deal
with discrete data sets {xj , j = 0 .. }.
We will assume noise {nj} is
– Gaussian, i.e. pdf is the normal distribution
– Zero-mean: Enj = 0, where E is expectation value.
– Stationary, i.e. characteristics of noise independent of time
•
Usually work in Fourier domain, because process is stationary and because
FFT algorithm brings advantages for data processing.
•
Variance of noise in Fourier domain is called Spectral Noise Density S:
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
6
When we know what signal
we are looking for…
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
7
Statistical Detection of Known Signals
•
We suppose we are searching for a signal h = {hj} in a vector space X, and
that we understand our (Gaussian stationary) noise.
– Let p0(h) be the probability distribution function (pdf) for the pure noise, i.e. when
no signal is present.
– If we set a detection criterion such that we detect the signal if h is inside a region R
of X, then the chance that we will falsely identify a signal when it is not there is
called the false-alarm probability and is denoted by PF
– Let p1 be the pdf for noise plus the signal h. Then the corresponding detection
probability PD is
Bernard F Schutz
Albert Einstein Institute
06 June 2006
Erice: John Archibald Wheeler School
8
Frequentist and Bayesian Approaches
•
For frequentists, the usual wayof identifying signals is the NeymanPearson criterion for detection.
– We should test the likelihood ratio
•
While the theoretical
dispute between Bayesians
and
frequentists
has
often
– We then define the
detection
region R by
placing
a threshold k on Λ :
been heated, we have found
in the GW data analysis
For Bayesians, one begins also with the likelihood ratio of but takes
that prior
the practical
into account explicitly
knowledgedifferences
.
– One computes the
pdf from the
inposterior
the detection
of likelihood
signals of the signal Bk and
prior:



is
small.
pa | B   pa p B  a

k
prior
posterior
Bernard F Schutz
Albert Einstein Institute
06 June 2006
k

likelihood
Erice: John Archibald Wheeler School
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Matched Filtering
•
2s appropriate linear detection statistic is20s
All approaches show that the
the
matched filter. Its value should exceed some threshold.
– In its simplest form one computes the inner product between the data {xj}
and the expected signal {hj}.
200s signal. Then we have
– To understand this, consider an expected sine-wave
– Matched filtering is a generalization of the Fourier transform. Like the FT it
improves if the signal duration is longer. Signal to noise ratio ~ Ncycles1/2
– Example: a 200 Hz signal buried in noise with 10 times the amplitude,
searched for in data sets of 2s, 20s, and 200s.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
10
Erice: John Archibald Wheeler School
Allowing for unknown time-of-arrival
•
In practice we do the search in the Fourier domain. By the Parseval theorem
•
This is desirable because we want to search for any arrival time τ, ie for an
arbitrarily shifted signal h(t-τ). Its Fourier transform is
– The detection statistic in the Fourier domain is then (if τ corresponds to timesample index j)
– This is just the Fourier transform and can be performed by the FFT algorithm. We
can therefore search over all arrival times with ~ NlogN operations rather than N2.
•
This also allows us to weight the filter when the noise is stationary but
colored. The square of the optimum signal-to-noise ratio (SNR) is
Bernard F Schutz
Albert Einstein Institute
06 June 2006
11
Erice: John Archibald Wheeler School
Signals belong to parametrized families
•
In practice our signal models h depend on parameters, such as the
masses of stars, the eccentricity of a binary, the spin rate of the neutron
star, the location of the signal on the sky. The likelihood depends on
parameters θn
•
The frequentist solution is to find the parameter values that maximize Λ:
Maximum Likelihood
Bernard F Schutz
Albert Einstein Institute
06 June 2006
12
Erice: John Archibald Wheeler School
Deterministic Signals: Coalescing Binaries
•
When a NS-NS, NS-BH, BH-BH system coalesces the signal is in principle known
(Will lectures). The inspiral is described by the post-Newtonian waveform.
Understanding the merger signal is the domain of numerical relativity. The
subsequent ringdown of the final black hole is also understood numerically.
Family depends
on m1, m2, s1, s2,
eccentricity (zero
for stellar systems),
phase at (say)
f = 100 Hz.
Chirp from
2 x 1.4 M
NS’s from
300Hz to
merger.
•
•
Searches are being done for masses from around 0.5 M to 20 M. Spins will
soon be included. Parameters are chosen with large overlap between nearby
templates, so that false dismissal is minimized.
Three or more detectors permit triangulation to find source location.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
13
Erice: John Archibald Wheeler School
Deterministic signals: GW pulsars
•
•
•
Neutron stars will radiate if they are asymmetric about spin axis. Could
be due to crust irregularity, solid core irregularity, free precession, …
Signal in rest frame of pulsar modelled as a slowly changing frequency.
Take f, df/dt, d2f/dt2 as parameters in a Taylor expansion.
But long data stretches are needed. For an amplitude of 10-26, we need
(10-21/10-26)2 ~ 1010 cycles to reach SNR ~ 1. For a 1 ms pulsar this is 4
months of data.
– Modulation by detector motion serious, angular resolution around λgw/ 1 AU ~
1 arcsecond (similar to radio pulsar resolution).
– Blind searches require searching ~1013 square
arcseconds on the sky!
detector
– This is the most compute-intensive of all the
searches, and its sensitivity is directly limited
Rorbit
by computer power. Einstein@Home is
dedicated to this.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
14
Erice: John Archibald Wheeler School
wave
When we don’t know what signal
we are looking for…
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Albert Einstein Institute
06 June 2006
15
Erice: John Archibald Wheeler School
Stochastic signals
•
Some signals are known to be totally random. Possible sources:
– Big Bang, inflation (Grishchuk talk), phase transitions in early universe
– Astrophysical sources, such as binaries, distant supernovae, …
•
•
If this random excitation is stronger than detector noise, and if detector noise is
understood or can be independently measured, then a stochastic background
can be identified (bolometric detection).
If two detectors with independent instrumental noise are available, their
outputs can be cross-correlated to look for a common noise.
Signal σ =2
Inst 1
σ =10
+
×
×
Inst 2
σ =10
Avg = -0.46
Bernard F Schutz
Albert Einstein Institute
06 June 2006
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+
Erice: John Archibald Wheeler School
Avg = 3.34
Working with separated detectors
•
•
Cross-correlation alone works only when
detectors have perfectly correlated signals,
which means they have to be in the same
place.
Real detectors are separated and have
different orientations.
Well
correlated
responses
– Correlation better for waves arriving from
some directions than from others.
– Correlation improves for longer wavelengths
•
Analysis is done in Fourier domain to allow:
– Weighting for colored noise
– Weighting for frequency response of
correlation – optimum filter
Bernard F Schutz
Albert Einstein Institute
06 June 2006
17
Erice: John Archibald Wheeler School
Poorly
correlated
responses
Unmodeled burst signals
•
•
•
•
Some signals are difficult to model (e.g. from gravitational collapse) or
unexpected. Harder to improve SNR when you have little information.
Teams do various power-based tests, looking for excess power in a
range of spectrum, or excess power in time-series, or excess power in
a cluster in a time-frequency or wavelet diagram.
Two or more detectors are required for confidence.
Three detectors allow a redundancy test, called the null stream veto.
– Since a GW is determined by two functions of time (two polarizations), if its
source direction is known then three detectors have redundancy.
– There is then a null stream, a linear combination which has no signal.
– If a signal is suspected, the null stream should look like typical noise. If it
does not, then signal can be vetoed.
– Four detectors can test for non-GR signal model, such as scalar polarization.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
18
Erice: John Archibald Wheeler School
Data analysis in the
Bernard F Schutz
Albert Einstein Institute
06 June 2006
19
Erice: John Archibald Wheeler School
•
LIGO Scientific Collaboration
All data from 4 interferometers (3 LIGO + GEO) pooled for analysis.
– LSC has done joint analysis with TAMA (Japan) and Allegro (bar detector).
•
•
Self-governing organization distinct from LIGO but reporting to LIGO.
Any group may join by signing MOU, periodically updated and reviewed
– Group commits to useful work on detector development or data analysis.
– Group promises to abide by data release and publication rules.
– Members entitled to appear in author list of collaboration-wide papers.
•
LSC coordinates
–
–
–
–
–
•
Development of Advanced LIGO detector (cooperation with GEO)
Operation of detectors
Data analysis and publication
Current spokesman: Peter Saulson (Syracuse University)
Current data analysis coordinator: Maria Alessandra Papa (AEI Potsdam)
Science runs S1 – S4 led to published upper limits with instruments still in
commissioning.
– Analysis run by 4 teams: pulsars, inspiral, stochastic, bursts.
•
LIGO has now reached design sensitivity and S5 has been going for 8 months.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
20
Erice: John Archibald Wheeler School
How an analysis team works
•
Analysis teams consist of typically 15-20 active members, many others who
contribute at particular times.
– Each team has a theorist and an experimentalist as co-chairs.
•
•
•
•
•
•
LSC members required to spend at least 50% of research time on LSC work,
and to spend time doing shift-work at the detectors.
Teams are international, meet weekly by telephone conference, hold about 4
face-to-face meetings per year in association with LSC meetings.
Teams write and document code, document their analysis methods. All
software and documentation is in open-source repositories.
Code is reviewed in detail, line-by-line, by a team of LSC members from
outside the analysis team. Code reviews typically involve an extra telephone
conference each week.
Results papers are written jointly, using cvs repositories, and when ready are
also externally reviewed in detail before being presented to LSC. All statistical
statements, tests, conclusions must be justified. More telephone conferences.
Paper is finally presented to LSC, open for comment from all members for
some weeks before being placed on gr-qc and submitted for publication.
Conference presentations are given by LSC-wide telecon before going public.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
21
Erice: John Archibald Wheeler School
Binary neutron stars S5 search
●
Sensitivity of search given in terms of
the horizon distance: distance to
1.4+1.4 M optimally oriented &
located binary at SNR=8
• First three months of S5 data is analyzed.
S2 Horizon Distance
1.5 Mpc
Bernard F Schutz
Albert Einstein Institute
06 June 2006
22
Erice: John Archibald Wheeler School
Primordial black holes
S2 Observational Result
Rate per MW halo per year
Phys. Rev. D. 72, 082002 ( 2005)
Rate < 63 per year per
Milky-Way-like halo
• This is a MACHO search: small binary
objects. No known astrophysical
formation mechanism.
• S3 search complete
– Under internal review
– 0.09 yr of data
– 1 Milky-Way like halo for 0.5+0.5 M
• S4 search complete
– Under internal review
– 0.05 yr of data
– 3 Milky-Way like halos for 0.5+0.5 M
• S5 analysis getting under way
Total mass
Bernard F Schutz
Albert Einstein Institute
06 June 2006
23
Erice: John Archibald Wheeler School
Binary black holes
S2 Observational Result
Log| cum. no. of events |
Phys. Rev. D. 73, 062001 (2006)
• S3 search complete
– Under internal review
– 0.09 yr of data
– 5 Milky-Way like galaxies for
5+5 M
• S4 search complete
Rate < 38 per year per
Milky-Way-like galaxy
– Under internal review
– 0.05 yr of data
– 150 Milky-Way like galaxies
for 5+5 M
signal-to-noise ratio squared
Bernard F Schutz
Albert Einstein Institute
06 June 2006
24
Erice: John Archibald Wheeler School
Binary black holes S5 search
• 3 months of S5 analyzed
• Horizon distance (detector
sensitivity) versus mass for BBH
binary neutron star
horizon distance
Average over run
1 sigma variation
binary black hole
Bernard F Schutz
Albert Einstein Institute
horizon distance
06 June 2006
25
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Image: R. Powell
Radiation from rotating neutron stars
“Mountain” on neutron star
Accreting neutron star
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Albert Einstein Institute
06 June 2006
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Wobbling neutron star
R-modes
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Pointing at known neutron stars
•
•
Targeted search of GWs from
known isolated radio pulsars
S1 analysis: upper-limit (95%
confidence) on PSR J1939+2134:
h0 < 1.4 x 10-22 (e < 2.9 x 10-4)
Phys Rev D 69, 082004 (2004)
•
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Albert Einstein Institute
06 June 2006
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S2 analysis: 28 pulsars (all the ones
above 50 Hz for which search
parameters are “exactly” known)
Erice: John Archibald Wheeler School
28 pulsars targeted for S2
B0021-72C
B0021-72D
B0021-72F
B0021-72G
B0021-72L
B0021-72M
B0021-72N
B0531+21 (Crab)
B1516+02A
B1820-30A
B1821-24
B1937+21 (S1)
B1951+32
B0030+0451
J0711-6830
J1024-0719
J1629-6902
J1721-2457
J1730-2304
J1744-1134
J1748-2446C
J1910-5959B
J1910-5959C
J1910-5959D
J1910-5959E
J1913+1011
J2124-3358
J2322+2057
There are 38 known isolated radio pulsars with fGW > 50 Hz, including PSR
J1939+2134 (used in S1) and the Crab pulsar
• Timing information for 28 pulsars:
– Radio observations collected over S2/S3 for 18 of these (Michael Kramer)
ATNF catalogue used for 10 others
•
The remaining 10 pulsars have not been included in the analysis because
of outdated spin parameters (would require more that one template)
Bernard F Schutz
Albert Einstein Institute
06 June 2006
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Erice: John Archibald Wheeler School
S2 results
16 2G I zz f 0
h0 
e
4
c
R
2
Best upper-limits:
J1910 – 5959D:
h0 = 1.7 x 10-24
J2124 – 3358:
e = 4.5 x 10-6
Crab: a factor ~ 30
from spin-down
limit
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Albert Einstein Institute
06 June 2006
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Dots: UL on h0
Squares: UL on e
Red and magenta
refer to PSRs with
no info on fdot
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S5 results on pulsars
• 32 known isolated, 44 in
binaries, 30 in globular
clusters
Lowest ellipticity upper limit:
PSR J2124-3358
(fgw = 405.6Hz, r = 0.25kpc)
ellipticity = 4.0x10-7
Bernard F Schutz
Albert Einstein Institute
06 June 2006
30
Erice: John Archibald Wheeler School
Einstein@Home
• Matched-filtering for continuous
GWs
• All-sky, all-frequency search
– computationally limited
• Aiming at detection, not upper
limits
• Public outreach distributed
computing
To participate, sign up at
http://www.physics2005.org
Bernard F Schutz
Albert Einstein Institute
06 June 2006
31
• Results: S3 showed no
evidence of pulsar, S5 ongoing.
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S5 incoherent searches
preliminary
.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
32
Erice: John Archibald Wheeler School
LIGO Results on W0h1002
LIGO run
H-L
H1-H2
< 44
(H2-L1)
Cross-correlated
instrumental noise
found
S2
unpublished
< 0.035
(H1-L1)
Cross-correlated
instrumental noise
found
S3
In PRL
< 8.4e-4
(H1-L1)
Trying to account for
instrumental noise in
bounding W
S1
PRD 69(2004)
Frequency Range
Obs. Time
40-314 Hz
64 hours
(08/23/02 –
09/09/02)
50-300 Hz
387 hours
(02/14/03 –
04/14/03)
69-156 Hz
218 hrs)
(10/31/03 –
01/09/04)
447 hrs (H1-L1)
510 hrs (H1-H2)
(02/22/05 –
03/24/05)
S4
Starting
Analysis
Bernard F Schutz
Albert Einstein Institute
06 June 2006
33
Erice: John Archibald Wheeler School
Bursts Analysis: Targets
Precise nature of gravitational-wave
burst (GWB) signals typically
unknown or poorly modeled.
– Can’t base such a broad search
on having precise waveforms.
– Search for generic GWBs of
duration ~1ms-1s, frequency
~100-4000Hz.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
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A1B1G1
A3B3G1
A4B1G2
1
–20
– core-collapse supernovae
– merging, perturbed, or
accreting black holes
– gamma-ray burst engines
– cosmic string cusps
– others
1.5
Amplitude [x 10 ]
Catastrophic events involving solarmass compact objects can
produce transient “bursts” of
gravitational radiation in the
LIGO frequency band:
0.5
0
–0.5
Gravitational w ave form s
from s te llar–core collaps e
(10k pc from the earth)
–1
–1.5
0
10
20
30
Time [msec]
possible supernova waveforms
T. Zwerger & E. Muller, Astron.
Astrophys. 320 209 (1997)
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40
50
The future: including VIRGO,
further expanding the network
Bernard F Schutz
Albert Einstein Institute
06 June 2006
35
Erice: John Archibald Wheeler School
VIRGO-LSC joint analysis
•
An MOU is under negotiation among VIRGO, the LSC, and GEO. It will
provide for
– Joint data analysis teams working on all data.
– Joint publications.
– Coordination of observing runs.
•
•
•
•
Joint data analysis begins when VIRGO finishes commissioning, we
hope by end 2006.
As detectors are upgraded (minor and major upgrades) data analysis
will continue for a decade or more.
Japanese building cooled detector, can expect that this will join
network when it is ready (several years yet).
Other ground-based plans in Australia may lead to a further detector.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
36
Erice: John Archibald Wheeler School
Networks of detectors
•
•
Networks of detectors can be highly heterogeneous. For optimum
analysis one should regard them as a single detector system.
Present methods for analysis for short-duration signals (inspirals,
bursts) apply thresholds to detector or filter outputs separately.
Candidate events must be in coincidence.
– High-amplitude events dominated by non-Gaussian (instrumental) noise
– Threshold/coincidence method eliminates most of these.
– Method not optimum.
•
Optimum method is “coherent detection”, essentially adding data
together before selecting by threshold.
– Simple to see that this is optimum for two co-located detectors.
– With separated detectors, do this for each possible source location.
– Data must be weighted for detector sensitivity and orientation, shifted
appropriately in time.
– Still a subject of research, not yet implemented in LSC.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
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Erice: John Archibald Wheeler School
Data Analysis
with high sensitivity:
LISA
Bernard F Schutz
Albert Einstein Institute
06 June 2006
38
Erice: John Archibald Wheeler School
LISA Project
•
•
•
•
Scientific leadership is provided by the LIST (LISA International Science
Team), co-chaired by Tom Prince (JPL) and Karsten Danzmann (AEI
Hannover).
Data analysis has not been as thoroughly studied as the hardware, but
efforts underway to ensure that the analysis system is ready on time.
Data analysis planning is overseen by LIST Working Group 1B (cochaired by Neil Cornish and Bernard Schutz), but most activity is
coordinated by ESA and NASA in their separate communities.
Structures not yet mature.
LISA Pathfinder coming soon, will give us experience of how to handle
“housekeeping” data, but will not produce GW data.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
39
Erice: John Archibald Wheeler School
Similarities with ground-based sources
•
•
•
LISA sources have many similarities with ground-based
sources.
Inspiralling supermassive black-hole binaries emit signals
identical with those at high frequencies, rescaled by the mass.
Binary star systems in the Galaxy emit signals very like those of
GW pulsars:
– Slowly-changing frequency (orbit decay raises f in this case)
– Modulation by motion of LISA (less severe due to longer
wavelength)
– Differences: higher harmonics present if orbit is eccentric,
interactions between stars may lead to other effects.
•
•
EMRI signals unlike any ground-based source, but experience
with blind GW pulsar searches will help us to handle searching
the extremely large parameter space of these signals.
LISA data stream much smaller than ground-based. Easier to
do analysis.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
40
Erice: John Archibald Wheeler School
LISA as a network of detectors
•
LISA is really three detectors.
– Each vertex produces an interferometric signal.
– For long wavelengths (λ > arm-length) these signals
are correlated, and a null stream (linear combination
with zero GW signal) can be formed.
– For short wavelengths these signals have distinct
forms. Still possible to form null stream for signals
from any particular direction, as for ground-based
networks.
•
•
LISA has extensive on-board processing to remove
frequency noise. Will return three data streams,
called TDI signals. (TDI = time-delay interferometry)
As LISA orbits, its antenna pattern rotates. From the
induced amplitude and phase modulation it can
determine directions to sources.
– Additional information at short wavelengths from timedelays between TDI streams.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
41
Erice: John Archibald Wheeler School
High-SNR GW Observing
• LISA observations will have high SNR, up to 104 in amplitude.
• For many sources, LISA will face signal confusion
– Binaries in the Galaxy
below ~1 mHz blend into a “binary sea” that cannot be
-10
W

10
resolved: toogwmany sources per frequency bin.
– Above 1 mHz, EMRI capture signals are visible out to z ~ 0.5; more distant
capture events provide the main background against which detection must
take place. Olber’s Paradox avoided only by high-z cutoff in sources.
– Resolvable binary systems above 1 mHz must be separated from nonstochastic EMRI interference.
– Transient signals, such as from SMBH binary coalescence, must be separated
from binary and EMRI background.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
42
Erice: John Archibald Wheeler School
Approach to LISA data analysis
• Requirement is to resolve overlapping signals. This involves not just
detecting them but also measuring all parameters needed to remove
them from the data stream.
• Main data-analysis approach will be iterative:
– Solve for strong sources approximately, subtract them.
– Solve for next strongest, subtract, go back to strongest and remove their
residuals better.
– Binary orbital parameters improve with time, so their signals can be subtracted
better after 2nd year. So transient events (black hole mergers) in first year also
improve after 2 years.
• Data products: source detections and parameters, cleaned-up data
streams, full data streams.
• Highly integrated analysis system required, but no decisions yet by
agencies on how or where this analysis will be done, what proprietary
data rights the scientists will have, etc.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
43
Erice: John Archibald Wheeler School
Challenges of LISA data analysis
• Confusion challenge
– Source identification not unique. Must use intelligent principles to identify “best”
identifications. How to guarantee that iterative scheme finds the globally “best”
solution? What is the right search method?
• Network challenge
– LISA actually has 3 interferometer signals, optimum combinations depend on
source location and polarisation. Modulation complicates this.
• Computational challenge
– Parameter space for EMRIs is huge. Even with anticipated improvements in
computing, a hierarchical search will be needed. Not clear how to do this against
a background of weaker EMRIs.
• Theory challenge
– Some signal templates not yet known well enough, including EMRIs and BH
merger waveforms.
• Organizational challenge
– There is no legacy analysis system: it must be designed in scientific community
but be highly integrated.
Bernard F Schutz
Albert Einstein Institute
06 June 2006
44
Erice: John Archibald Wheeler School
What is happening now
• Hardware
– LPF being built, lessons learned applied to LISA design.
– Astrium Friedrichshafen is doing the formulation study for ESA
• Data analysis
– ESA has formed a Data Analysis Study Team to coordinate work of more than 50
institutions in Europe.
– JPL has held meetings of US scientists to distribute work.
– ESA (ESTEC) and NASA (JPL) will run independent but coordinated efforts
developing algorithms in the community.
– In Europe, groups must be funded by national agencies (PPARC). In the US, the
NASA budget restrictions leave little room for funding data analysis development.
– LIST provides overall coordination, issues mock data challenges.
• Mock Data Challenges: first will be released at LISA Symposium this month.
Periodic releases, increasing in complexity, as stimulus to community and as
demonstration of competence.
• Conclusion
– Many opportunities for key contributions, leadership!
Bernard F Schutz
Albert Einstein Institute
06 June 2006
45
Erice: John Archibald Wheeler School