Download 1. Introduction

3rd Annual Report on GWA-WG2
Joint operation of antennas and network data analysis
L. Baggio1, M.A. Bizouard2, L. Bosi3, L. Brocco4, G. Cella5, E. Cuoco20, S. D`Antonio4, S.
Frasca4, G. Frossati 6, G. Guidi7, I.S. Heng8, A. Krolak9, F. Marion1, B. Mours1, A. Sintes10,
A. Ortolan11, A. Pai12, M.A. Papa12, A. Parameswaran12, I. Pinto13, G.A. Prodi14,
T. Regimbau15, E. Robinson18, J. Romano16, F. Salemi17, B.S. Sathyaprakash16, C. van den
Broeck16, A. Vecchio18, A.Vicerè7, M. Visco19, A.deWaard6, G.Woan8
1
CNRS/IN2P3/LAPP, Annecy, France and EGO, Cascina, Italy
2
LAL/IN2P3, Orsay, France
3
INFN and Università di Perugia, Italy
4
INFN Sezione di Roma1, Roma, Italy
5
INFN Sezione di Pisa, Italy
6
University of Leiden, The Netherlands
7
INFN and Universita di Firenze/Urbino, Firenze, Italy
8
University of Glasgow, Great Britain
9
Polish Academy of Sciences, Warsaw, Poland
10
Universitat de les Illes Balears, Palma de Mallorca, Spain
11
INFN Laboratori Nazionali di Legnaro, Italy
12
Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut, Golm, Germany
13
INFN and Università del Sannio, Benevento, Italy
14
INFN and University of Trento, Italy
15
CNRS/Observatoire de la Côte d'Azur, Nice, France
16
Cardiff University, Great Britain
17
INFN and University of Ferrara, Italy
18
University of Birmingham, Great Britain
19
CNR/IFSI and INFN Roma, Roma, Italy
20
EGO, Cascina, Italy
Coordinators: G.M. Guidi (INFN, Urbino University), I.S. Heng (Glasgow University)
1. Introduction
GWA-WG2 aims to promote discussion between European gravitational wave data analysts
and study network data analysis methodologies for gravitational wave searches, especially
those involving European detectors.
In March 2006, a new Implementation Plan was drawn up. The coordinators of WG2 drew up
an Implementation Plan based on a strategy that would
 provide support existing collaborations
 encourage the investigation and development of analyses not currently performed
 help build a scientific case for future generation detectors
In the next few paragraphs, an overview of these topics, their importance to the search for
gravitational waves and WG2 involvement in each area is provided.
Many members of WG2 are already involved in the joint analysis of data between different
detectors. The main joint analyses that involve WG2 members are LSC-Virgo, Virgo-bars and
IGEC2. LSC-Virgo is a trans-Atlantic involving data analysts from the LIGO Scientific
Collaboration (LSC), of which GEO is a member, and Virgo. Virgo-bars is a collaboration
between the European resonant-bar detectors, AURIGA, EXPLORER and NAUTILUS, and
Virgo. IGEC2 is a collaboration that brings together the resonant-bar detectors group from
across the world (ALLEGRO, AURIGA, EXPLORER and NAUTILUS).
In parallel with the support of existing joint analyses, WG2 also encourages the development
of new data analysis methods. Specifically, the use of coherent network analyses and joint
analyses using astronomical observations in electromagnetic spectrum are targeted as
emerging analyses that have the potential to make a big impact in the gravitational wave
community in the near future. Coherent network analyses for inspiral and burst searches take
into account the directional sensitivity of all gravitational wave detectors in the network. This
is vital for the LIGO-Virgo-GEO600 network since GEO600 and Virgo are not aligned to
each other and neither detector is aligned to the LIGO detectors. Another type of analysis
targeted in the Implementation Plan are searches for gravitational waves associated with
astronomical observations in the electromagnetic spectrum. Studies of gamma-ray bursts have
shown that sources of these bursts include merging neutron stars and supernova core
collapses. Therefore, gamma-ray burst observations can be used to trigger a search for
gravitational waves around the time of the burst. Similar searches can be performed using Xray and radio frequency observations. Glitches in the period of radio frequency pulses from a
rapidly rotating neutron star (pulsar) could be associated with a rearrangement of the crust in
the neutron star. This would cause the neutron star to oscillate and emit gravitational waves.
Attention has been also devoted to the current research for the developement of pipelines for
the search of GW from spinning compact objects and a workshop dedicated to this subject.
The status of these searches has been reported during the 11th Gravitational Wave Data
Analysis Workshop (GWDAW11), Potsdam, December 2006 (htpp://gwdaw11.aei.mpg.de).
Several subjects that will be described below have been illustrated by members or
collaborators of WG2 in talks and posters.
There have been five phone-conferences and three meetings organised by WG2.
N5 – Table 1.1: Workshops/Meetings.
Date
Title/subject of meeting
/workshop
Location
Number of
attendees
20/02/06
Phono-conference
9
13/04/06
Phono-conference
6
20/04/06
Phono-conference
6
27/04/06
Working group 2 meeting
20/07/06
Phono-conference
24/09/06
Working group 2 workshop
on spinning compact objects
27/09/06
Phono-conference
Florence, Italy
19
14
Cardiff, UK
14
16
Website address
http://www.ego-gw.it/ILIASGW/N5-WP2_meetings.html
http://www.ego-gw.it/ILIASGW/N5-WP2_meetings.html
http://www.ego-gw.it/ILIASGW/N5-WP2_meetings.html
http://www.ego-gw.it/ILIASGW/N5-WP2_meetings.html
25/10/06
Working group 2 meeting
London, UK
14
http://www.ego-gw.it/ILIASGW/N5-WP2_meetings.html
2. Status of planned tasks
2.1. Study of the detector's compatibility and of the possible implementation of a
coherent data analysis for transient and chirp signals
As the GW detectors approach their project sensitivities, a deep study of coherent analysis
methods, which make use of the informations from the different detectors have become of
great importance. Based on the theoretical studies that have been developed over the last
decade, the effective implementation of these pipelines and the comparison with other
possible methods has been the subject of the ILIAS WG2 effort.
Two main implementations of coherent pipelines for transient unmodelled signals have been
examined. One can directly combine of the data streams from different detectors into a single
stream for analysis by a particular method or combine the outputs of the same method applied
separately to the different detector data streams.
The method for the first scenario was first outlined in J. Sylvestre Phys.Rev. D68 (2003)
102005. It was applied to one day of simulated data streams from LIGO and VIRGO
detectors, produced by the LIGO-VIRGO working group. The first results (see N.Leroy and
GM Guidi, Coherent Analysis for Burts Detection, presentation at WG2 Florence Meeting,
http://www.ego-gw.it/ILIAS-GW/N5-WP3-WP2-Florence.html) seem to indicate that, in the
actual implementation, the coherent method has a comparable detection efficiency and
source-sky reconstruction with two-fold coincidence detection methods already used to
analyse by the LSC-VIRGO working groups. Adding GEO data to the LSC-VIRGO network
will increase the sky resolution and the possibility to discriminate between real GW signals
and other spurious signals.
Time-series data from multiple detectors can also be linearly combined to form a null-stream,
which contains no trace of an incoming GW (see P.Ajith et al, Null-stream veto for for the
network analysis of GW bursts, presentation at WG2 Florence Meeting), thus allowing one to
discriminate between real GWs and spurious noise triggers. With the null-stream method, the
source position can be recontructed by probing the minimum of the null-stream power over
the sky regions previously inferred through the analysis of the time-delays between coincident
triggers.
The null-stream method has also been applied to construct bursts veto using known
instrumental couplings and applied to GEO S5 data (see P.Ajith et al: presentation at
GWDAW11). This application permits to distinguish instrumental glitches from gravitational
wave (GW) bursts. The strategy has been to make use of the transfer function from a detector
subs-ystem to the main detector output in order to have a phenomenological understanding of
their coupling and individuate a possible non-stationarity caused by an instrumental glitche.
Some preliminary investigations into the use of the coherent algorithm developed by a S.
Chatterji, P. Sutton, et al., called X-pipeline, to determine the source location of a burst
gravitational wave has also been performed by L. Porter and I.S. Heng. These injections used
the simulated data and signals generated for LSC-Virgo project 1b and studied the ability of
the LSC-Virgo network to reconstruct the location from which a burst gravitational wave
originated from. Core-collapse waveforms from the Dimmelmeier-Font-Mueller (DFM)
catalogue, gaussian pulses and sine-gaussian waveforms were injected into the simulated data.
The investigations showed that, for gravitational wave bursts with signal-to-noise ratios
greater than 10, the source location was determined for at least 50% of the DFM catalogue
waveforms. The source location could also be obtained for about 85% of the 1-millisecond
gaussian pulses. However, the source location could only be obtained for only about 25% of
the 4-millisecond gaussian pulses. This is because the signal-to-noise ratios for these signals
were smaller.
Work has been performed to develop an algorithm to determine the sky location of signals
using the sky map outputs from X-pipeline. This work is ongoing.
The implementation of a coherent pipeline for chirp signals is also of great importance
because gravitational wave signals produced during the final inspiral stage of compact bodies
like NS or BH are a very promising source of detectable gravitational waves and have been
well modelled by theorists. Here too coherent analysis can increase the detection efficiency
and source sky-location, and thus the comparison of the results obtained through its
application with the ones obtained with a three- or two-fold coincident analysis is of the main
importance.
The first results presented by S Birindelli et al. (see Coherent and Coincidence Network
analysis for coalescing binaries, WG2 Florence Meeting; Testing coherent code for
coalescing binaries network analysis, WG2 London Meeting, http://www.ego-gw.it/ILIASGW/N5-WP2-London.html. See Poster presented at GWDAW11), based on the method
analysed by Pai et al, Phys.Rev. D64 (2001) 042004, indicate a gain up to the 25% in the
observable range of the detectors can be obtained in average with respect to a two- or three
fold analysis in the case of the LSC-VIRGO network. Since main problem for the application
of this coherent method is the computing resources required, a mixed-hierarchical approach
was used for the source sky-position reconstruction. This approach determines the two- or
three-fold time coincidence in the LSC-VIRGO network as a starting point. Through the
successive maximisation and fitting of the coherent network Likelyhood Function the sky
position’s coordinates determination was succesfully improved. This work points out that a
full coherent pipeline characterisation seems in fact very important.
A parallel work about parameter estimation is currently being undertaken using Monte Carlo
Markov Chains methods (see N. Christensen, Bayesian Parameter Estimation for Inspiral
Signals- Coherent Multi-Interferometer Study, WP2 Meeting, Florence). While the single
interferometer code is already working, the multi-interferometer “coherent” code, which
makes use of the coherent addition of signals, is under development: it searches - in addition
to the coalescing binaries masses, the coalescing time, the phase and the distance - for the sky
position parameters: polarization , angle of inclination of orbital plane , sky position RA
and dec. The method is being applied also to burst search, with sine-gaussian templates
hoping to catch the main characteristics of the unmodeled transient signals.
The code can currently manage signals from neutron star or black hole inspirals, which are
modeled to 3.5 post-Newtonian (PN) order in phase and to 2.5 PN order in amplitude (see C.
Röver, GWDAW11)
2.2. Develop infrastructure stochastic GW background search with GEO-VIRGO
data under LSC-VIRGO collaboration
The LSC-Virgo collaboration brings together gravitational wave scientists from both sides of
the Atlantic. At the moment, this collaboration is performing joint analyses for burst and
inspiral gravitational wave signals on small data sets. These analyses are mainly
methodological and aim to improve the understanding of the data analysts from the LSC and
Virgo on each others analysis methods as performed within their respective collaborations.
This work has now been expanded to include a joint search for stochastic gravitational waves.
Stochastic gravitational waves can be thought of as a gravitational wave equivalent of the
cosmic microwave background. Just like the cosmic microwave background, a stochastic
microwave background would also arise from the processes that happened after the Big Bag.
A stochastic gravitational wave background would also arise from a superposition of weak
gravitational waves emitted by distant neutron star mergers and supernovae.
Ideally, the best network of detectors for stochastic gravitational waves would be two aligned,
co-located gravitational wave detectors. However, two widely-spaced detectors are still
sensitive to a stochastic gravitational wave background provided the wavelength of the
gravitational wave is larger than twice the distance between the two detectors. Figure 2.1 plots
the stochastic sensitivity integrand for a white (flat as a function of frequency) stochastic
gravitational wave background for different LSC-Virgo detector pairs. The sensitivity
integrand folds in the design sensitivity of each detector as well as their respective
orientations to calculate the sensitivity of each detector to stochastic gravitational waves. The
GEO600-Virgo pair of detectors has similar sensitivities with the other pairs between about
250 Hz and 400 Hz. In fact, the GEO600-Virgo pair is about twice as sensitive as the other
pairs in some narrow frequency bands within this range.
Figure 2.1 Stochastic sensitivity integrand as a function of frequency.
This means the analysis of data acquired by GEO600 and Virgo for a stochastic gravitational
wave background will, at the minimum, be an independent check. It also provides us with the
possibility of performing a directed, band-limited stochastic background search using these
two detectors.
In preparation for such an analysis, a team consisting of LSC and Virgo data analysts, which
included WG2 members G. Cella, E. Cuoco, T. Regimbau and E. Robinson, have been testing
their analysis code on common data sets to verify that they give consistent results (see
G.Cella, talk at the WG2-WG3 Florence workshop, and G.Cella et al., talk held at
GWDAW11). The first step was to verify that all three existing analysis codes (called
matapps, LALapps and NAP) are able to process data stored in LIGO and Virgo formats. In
addition to this, code to produce simulated stochastic background for injection into simulated
noise streams has been written. This code generates a simulated common data set used to test
the three analysis codes.
The code has been succesfully tested and the analysis of the LSC-Virgo Project1b simulated
data completed. The detection and simulation procedures have been extended to two different
non-flat spectra, astrophysically motivated, originated by the cumulative effects of magnetars
and double neutron star populations.
WG2 supported the partecipation of G. Cella to Stochastic GW background search with GEOVIRGO data under LSC-VIRGO collaboration, Nizza November 20-21 2006.
2.3. Support to the on-going joint data analysis searches Virgo-bars and IGECII
A large amount of work has been done in the Virgo-bars and IGEC2 collaborations, which
has eventually produced new upper limits. Both the analyses have been conducted taking into
account the Recommendation Report on the planning of joint observations, and proposals for
the related data exchange and analysis elaborated by the WG2 (see the Appendix to the
Report on WG2 Joint operation of antennas and network data analysis for the year 2005).
Virgo-bars working group has examined one day of coincident data acquired by the acoustic
bar detectors Auriga, Explorer and Nautilus and by Virgo interferometer in September 2005.
(see L. Baggio, Status and roadmap of bar and interferometer joint burst analyses, WG2
Meeting, Florence; F Salemi et al, VIRGO-bars joint data analysis, ILIAS Annual Meeting,
London; L Baggio et al, First joint search of GW waves by the Auriga - Explorer - Nautilus Virgo Collaboration, Virgo note VIR-NOT-FIR-1390-328, documet attached to this report; L
Baggio et al, talk held at GWDAW11 ).
The goal of the study is to assess interpreted confidence intervals on the flux of gravitational
waves (damped sinusoids with central frequency in the bandwith [850-950]Hz and damping
time from 1 to 30 ms) coming from the galactic center. The interpretation comes from
software injections which are used to compute the efficiency of detection for a source
population.
The main methodology is a coincidence search on trigger lists provided by each detector: the
coincident counts, divided by the efficiency and by the observation time, become observed
rates (or upper limits on rates).
However, a new approach is used in setting the magnitude thresholds for each detector. For
each template and each target amplitude, the thresholds are optimized in order to get the best
compromise between efficiency and false alarm rate. Thus the efficiency acts not just
passively at the end of the analysis to calibrate the results, but also actively during an
optimization phase. When the null hypothesis test is fulfilled, then the upper bound of the
confidence interval is used to set upper limit.
In order not to bias results by feedbacks on methods from looking at results, a blind analysis
procedure is adopted by adding a “secret” time offset to the detector times of the exchanged
data. The zero-lag analysis is eventually performed and the confidence intervals set according
to the confidence belt already used by IGEC1.
A test at 99% confidence level was performed: no excess of coincidences was found and the
null hypothesis is still holding. Thus the upper bound of the chosen confidence belt is our
quoted upper limit with a coverage of 95%.
The work is now being reviewed by the Virgo-bars working group in view of a possible
submission to a scientific journal.
As the 2-fold coincidence searches on which we have based the work have a high level of
accidental background, a claim of detection by a single observed double coincidence is not
possible: the study could be possibly extended by performing 3-fold coincidence searches
with the goal to be able to issue a claim at 99.5% confidence on a single observed triple.
During most of 2005, the IGEC2 has been the only network of gravitational wave detectors in
operation. Its first target in data analysis has been to perform a long term joint search for burst
gravitational waves. Up to now the search has been completed on 6 months of data, from May
20th to Nov. 15th 2005 (see GA Prodi, talk held at ILIAS Annual meeting in London, and G.
Vedovato, talk held at GWDAW11). The data analysis is based on a time coincidence search
between candidate events exchanged by the two groups operating the three INFN detectors
AURIGA, EXPLORER and NAUTILUS. The group operating the fourth operating detector,
ALLEGRO (LA, USA), was not able to exchange the required data according to the
scheduled plan of activities, so it has been agreed to use its data only for a posteriori studies.
The confidence of the results is objective thanks to the blind procedures adopted for the
search on the INFN detectors data, while any a posteriori investigations would contribute
conditional evidence with an unavoidable degree of subjectivity.
The most relevant differences with the first IGEC search on 1997-2000 data are:
- in the IGEC2 analysis most of the observation time is covered by a three-fold
coincidence search. Only the observation time in three fold coincidence among the
INFN bar detectors has been considered here;
- the current network data analysis has been tuned to allow the identification of a single
gw candidate with very high statistical confidence, allowing a false alarm rate of 1.0
per century. In addition, the background of accidental coincidences has been
investigated with higher accuracy, by resampling the experiment up to 20 millions
times with different pipelines and choices of the time shifts;
- the target signals has been extended also to templates showing some color in the
Fourier transform within the AURIGA bandwidth, in addition to the usual bursts of
ms duration;
- to take into account easily the statistical correlations among the multiple trials here
implemented, the trials has been merged together by an OR logic. In particular the
overall accidental background of the entire search is estimated from the union of the
accidental coincidences found in each trial.
The IGEC2 network analysis is not optimized for setting upper limits, but instead to identify
with a satisfactory confidence a single gravitational wave candidate. In fact the null
hypothesis (i.e. no signals present in the data) would be rejected if at least one triple
coincidence were found with a significance of 99.64% corresponding to a false claim rate of
1.005/ century over the 130.8 days of net three-fold observation time.
Figure 2.2 Histogram of the number of accidental coincidences found per each resampling of
the composite search (e.g. the union of three partially correlated trials). The histogram is in
agreement with a Poisson distribution with mean 0.00364 (chi2 = 0.06 with 1 degree of
freedom), which is taken as the reference distribution for the coincidences assuming that only
accidental coincidences are present. The false detection probability is 0.00363, corresponding
to 1.01 false alarms per century.
No triple coincidences has been found and therefore IGEC2 did not identify gravitational
wave candidates. The interpretation of the IGEC2 result in terms of upper limits would
require a measurement of the IGEC2 detection efficiency to some specific source models.
This has not been performed during the six months observations. However, thanks to the
VIRGO-bars activity, the detection efficiency has been measured on one sample day;
therefore, this analysis can directly benefit from the detailed information exchange and
discussions within WG2.
IGECII collaboration is now starting the analysis of 2006 data.
2.4. Support the activities of multilateral project between European and nonEuropean detectors
LSC-Virgo Working Group is a multilateral project between LSC and Virgo collaborations
aimed at performing a deep comparison between the analysis pipelines developed separately
in the two collaborations and assess the capability of performing a joint search. Several people
participating at the LSC-Virgo work are members of WG2, and this makes it easy for
exchanges between the groups. LIGO-Virgo simulated data sets has been in fact used for the
test of pipelines and new algorithms already presented in the previous sessions, i.e. the
coherent pipelines for transient and chirps signals, the MCMC coherent parameters’
estimation.
During the last months, after having concluded the joint analysis of one day long simulated
data set (see the preprint of the two articles which has been submitted to a scientific journal:
gr-qc/0701027 and gr-qc/0701026 at http://babbage.sissa.it), the efforts have been first
devoted to the characterisation of the search pipelines over non-coincident calibrated real data
from the GEO detector, the LIGO Hanford detector, and the Virgo detector.
The scope of this first exercise with real data has been to repeat the study previously
performed on 3 hours of simulated LIGO and Virgo data. The goal was to come to an
understanding of how both collaborations currently handle the details of real detector data
(such as lock segment, data quality, and veto information), to develop a common language for
describing the information, and to begin to develop the infrastructure to exchange them. The
inclusion of a number of burst and inspiral hardware injections has also permitted a simple
cross-validation study of search algorithms’ performance on real data. This has provided
confidence in the ability of the various search algorithms to handle non-stationarities of real
detector data and enabled comparisons of how they approach this task.
The results of these studies have been compared at a meeting of the LSC-Virgo working
group on 23 June, 2006 in Orsay, France ( http://virgo.web.lal.in2p3.fr/MEETINGS/LSCVirgo-2006/F2F-LSC-Virgo-June2006.html).
Currently a second study is being performed using real coincident data from the GEO, LIGO,
and Virgo detectors. The purpose of this study is to develop and test the planned search
strategies for the full network of detectors in a way that is as close as possible to a real joint
astrophysical analysis.
The analysis is carried out over the frequency band of [800, 2000]Hz where all five
instruments display sensitivities within a factor of a few, and is adressing the research of
transient burst signals in this frequency range. Data quality, event-by-event vetoes studies are
performed in order to asses the background rates. An all-sky, all-times Monte Carlo is taking
place throught the injections of Sine Gaussian waveforms in a coincident way in the ITFs to
permit the tuning of the search pipeline and study the sensitivity of the different network
configurations that are possible with five detectors. The exercise will possibly include setting
an upper limit.
2.5. Develop new and/or extend joint searches indentified in study over previous 6
months
Development of searches for gravitational waves associated with pulsar glitches
and gamma-ray bursts
A search algorithm for gravitational wave emission from perturbed compact objects using
Bayesian inference has been developed by J. Clark and I.S. Heng (see J.Clark, talk held at
GWDAW11). Given some disruptive event, such as a pulsar glitch or soft gamma repeater
flare, the quasi-normal modes of the object in question (in these cases, a neutron star) are
excited. The oscillations are rapidly damped away by gravitational wave emission, leading to
a distinct 'ringdown' (i.e., a damped sinusoid) signal in gravitational wave interferometer data.
Efforts are focused on using Bayesian model selection to evaluate the relative probabilities of
various models describing gravitational wave interferometer data. This is achieved by
calculating the "evidence", defined as the likelihood, marginalised over all model parameters
and weighted by the joint prior for the parameters, for a variety of given models. The simplest
example is to compare the evidence for a ringdown waveform versus the evidence for white
noise. Assuming these are the only possibilities for the data, higher evidence for a ringdown
than for white noise would indicate a detection.
The method is currently being extended to demonstrate the potential of including a wider set
of models describing typical glitches in interferometer data to improve robustness. In
addition to this, the application of method to searches for gravitational waves from different
sources but with similar ringdown waveforms are also being investigated. Specifically, our
interest is in the black hole ringdown expected following the formation of a GRB. Here,
collaboration with experts in the field, such as A. Corsi, is vital to inform our choice of prior
and encompass an appropriate parameter space.
Furthermore, there are efforts to perform a search for possible gravitational wave signals
associated with gamma-ray bursts in Virgo data acquired during its current commissioning
phase, specifically the long GRB 050915a which was detected by the Swift satellite (see A.
Corsi, talk presented at ILIAS Annual meeting; A.Corsi, talk held at GWDAW11). The
approach here is to search for excess power around the time of the gamma-ray burst using a
wavelet-based analysis. This study is used as a prototype to define a methodology of analysis
and to evaluate up to which level VIRGO is able to constrain the GW output associated with a
typical long GRB, under the assumption that also the redshift lies in a range typical for long
GRBs.
New approach for the detection of stochastic backgrounds using Bayesian inference methods
are currently studies (see E. Robinson, poster at GWDAW11). The study addresses for the
moment the problem of detection of isotropic stochastic signals of arbitrary spectral shape by
applying it to a simple signal model using synthetic data sets.
Spinning Coalescing Binaries Workshop
One of the main problems currently being addressed in the search of gravitational waves from
the coalescence of compact objects like neutron starts and/or black holes, is the knowledge of
the exact temporal evolution of the signals and the implementation of detection pipelines
which are able to identify them. While for non-spinning stars the task can be accomplished by
standard matched filtering techniques over a bank of templates which reproduce, for the
expected range of stellar parameters, the signals, the situation is complicated for spinning
objects due to the large number of parameters for which a huge computing power is required.
This problem has been addressed at the Spinning Coalescing Binaries Workshop of the WG2
working group held on 14-15 September, 2006 in Cardiff, UK. The workshop has been
concentrated on source modelling and data analysis techniquess.
The dynamics of spinning compact binaries has been the subject of two presentations (G.
Faye, The dynamics of spinning compact binaries at the second-and-a-half post-Newtonian
approximation; L.A. Gergely, Spin and quadrupole moment effects in the post-Newtonian
dynamics of compact binaries ), which described new results on the computation of the spinorbit terms and its first Post-Newtonian correction and of spin-spin terms, quadrupole
moments and magnetic dipolar contributions, together with a possible explanation of the spinflip phenomenon. Detection improvement for earth-based interferometers and LISA coming
from the knowledge of these corrections were also examined.
Template bank construction for Buonnanno Chen Vallisneri (BCV) phenomenological
templates and its use in the search over real data (H. Takahashi, Template banks for spinning
black hole binaries; C. Van Den Broek, Searching for spinning binaries with BCV-spin
templates using the full metric; G. Jones, Searching for Spinning Binaries BH in LIGO S3
data ), and alternative detection algorithms (D. Brown, Implementation of the Physical
Templates Family for Spinning NS/BH Binaries searches; G.M. Guidi, Efficiency and
Clustering for NS-BH binaries) has been discussed in the Data Analysis section of the
workshop, together with the problem of the determination of coincidence triggers over a
network of interferometers (C. Robinson, Coincidence analysis using error ellipsoid; A
Sengupta, TrigScan, a clustering algorithm for inspiral search pipelines ).
The workshop has permitted an ample exchange of ideas. In addition to this, new possible
collaborations between different groups have been discussed.
2.6. Apply stochastic background search to GEO-VIRGO data exchanged under
LSC-VIRGO collaboration
The analysis of 24 hours of coincident real data from LSC-Virgo detectors has just begun.
This data set will be used to study the performance of the stochastic analysis algorithm on real
noise coming from the detectors. This work is ongoing.
2.7. Review and report results from existing joint searches, expecially Virgo-bars
and IGEC II
This task has been partly addressed in section 2.3 together with the description of the Virgobars and IGECII work. The results from existing joint searches have been indeed reported
several time in different conferences and/or workshop (WG2-WG3 Florence meeting, ILIAS
Annual meeting, GWDAW11), as indicated throughout this documents.
2.8. Preparation of the science case for future detectors.
Compact binary inspiral
Ground-based detectors will be able to observe the last stages of the inspiral of two compact
objects (neutron stars and/or black holes), where the motion is adiabatic in the sense that the
period of a single orbit is much smaller than the inspiral timescale. This regime is wellunderstood in the post-Newtonian approximation, where accurate waveforms have been
derived. Using the best available waveforms, the performance of EGO was compared with
that of Advanced LIGO, and a number of qualitative differences
were identified:
 At distances of a few hundred Mpc, EGO would be able to observe inspiral events
with total mass up to 1200 solar masses, or 3 times as high as Advanced LIGO. This
mass range comprises not only stellar mass binaries, but also binaries involving
intermediate mass black holes of the kind that may form in galactic nuclei and in
globular clusters.
 At these distances, EGO would be able to resolve individual component masses with
only a few percent uncertainty for systems with total mass up to ~500 solar masses.
By contrast, in Advanced LIGO these errors will be at best in the order of 10%, and
then only in a very limited mass interval. In this way, EGO would be able to
accurately ``map" the mass distribution of black holes.
 EGO would be able to establish even minor violations of the Kerr geometry outside a
rotating black hole, which could occur if the cosmic censorship conjecture fails to
hold, or if one or both components of a binary system are Boson stars (or still more
exotic objects).
 EGO would see inspiral events occurring throughout a significant part of the visible
Universe. Very conservative estimates indicate a detection rate of at least three orders
of magnitude higher than in Advanced LIGO. In the stellar mass regime, parameter
estimation with EGO at a luminosity distance of 15 Gpc would be as good as in
Advanced LIGO at a distance of only 1 Gpc. Given a network of detectors at the level
of EGO, distances could be determined from the gravitational wave signal. This would
allow us to study the evolution of the population of (massive) stars over cosmological
timescales by looking at the kind of black holes they produce.
 If one has multiple detectors one can also determine the sky position of an inspiral
event. This may allow the identification of the host galaxy (or of the host galaxy
cluster), which will have some definite redshift. With many such observations one
would be able to fit the luminosity distance as a function of redshift. The relation
between the two depends on several cosmological parameters (such as the Hubble
constant), which could be measured in this way.
 At the largest scales, galaxy clusters tend to be on the surfaces of ``bubbles"
surrounding ``voids". A network of EGO detectors would have the requisite distance
reach to check whether black hole binaries are similarly distributed, which may be of
interest to dark matter studies.
Spinning and precessing neutron stars.
Spinning neutron stars (NS) with any sort of departure from sphericity are candidate sources
of gravitational waves. A simple model in which a spinning NS has an equatorial ellipticity of
 ≈ 1-b/a, where a and b are the semi-major and semi-minor axes, respectively, emits
gravitational waves of amplitude proportional to  and at twice the spin frequency. EGO will
be able to detect all milli-second neutron stars of ellipticity as small as 10-8 anywhere in the
galaxy with a large signal-to-noise ratio. Some of the closer systems will be detectable even if
their ellipticity is O(10-10). On a standard NS this is equivalent to a ``mountain'' of size
smaller than the tenth of a m. It would be remarkable to survey the entire galaxy for neutron
stars with such a small departure from sphericity.
Low-mass X-ray binaries in which the accretion torque seems to be balanced by the radiation
reaction produced by the emission of gravitational waves are potential sources for advanced
detectors. While advanced LIGO will have to tune itself to a narrow-band mode to observe
LMXBs, EGO could watch the entire frequency band of 100 Hz to a kHz with in broad-band
mode but with the same sensitivity as advanced LIGO. Using signal-recycling techniques
EGO will be able to dig deeper for LMXBs.
As neutron stars lose rotational kinetic energy through electromagnetic radiation, they lose
ellipticity. This can cause a breaking of the crust, leading to the formation of small
``mountains" on the surface. The associated triaxiality will induce a precessing motion, with a
precession frequency that is typically much smaller than the rotation frequency. To leading
order, the gravitational wave spectrum will then contain the following spectral lines:
 A main line at twice the rotational frequency; if the star is not precessing then only
this line will be present.
 With precession, there will be a second line at approximately the rotation frequency,
as well as a third line appearing as a sidelobe to the first one.
If all three lines are visible, in principle one would be able to measure the neutron star's
precession angle, its oblateness, and its deviation from axisymmetry due to ``mountains",
which would yield information on the structure of the crust. Together with the precession
damping timescale one could infer how the crust interacts with the superfluid interior and get
a better understanding of the latter's equation of state.
In an Advanced LIGO detector equipped with a signal recycling mirror at the output, in a
narrow frequency interval one can have a strain sensitivity as low as 10-24 Hz-1/2, tunable
between 500 Hz and 1000 Hz. A few months' integration time could then reveal all three
spectral lines for sources at a distance up to ~10 kpc, but only if the precession angle is near
the physical upper limit. Even considering uncertainties in the damping timescale, the number
of such sources will be very low.
With third generation detectors the situation would be different. If one can have a tunable
narrowband sensitivity of 10-25 Hz-1/2 in the same frequency range as Advanced LIGO, the
above spectrum may be visible for sources as far as the center of the galaxy, with reasonable
precession angles. A further improvement to 10-26 Hz-1/2 might allow visibility of the three
spectral lines for sources in neighboring galaxies.
Stochastic Background
A set of two or more co-located inteferometers with the same sensitivity as EGO will be able
to detect a stochastic background of gravitational waves. For instance, currently we are
considering a configuration of an equilateral triangle for EGO. Such a configuration can be
used to construct three co-located EGOs. The sensitivity of such a configuration will be
sensitive to a background of gravitational waves of density at the level of GW = 2 10-11, a
factor of 15 better than advanced LIGO.
Figure 2.3 The projected sensitivity of a future generation detector (labelled EGO). Also
plotted are the expected signal strengths for a variety of sources.
3. Conclusions
GWA-WG2 is an active organisation which has brought together European gravitational wave
data analysts and theorists to discuss important issues in the gravitational wave field through
the organisation of meetings, workshops and phone-conferences. WG2 has provided some
support to existing collaborations for the joint data analysis projects that involve data acquired
by European gravitational wave detectors. WG2 has also targeted emerging issues in
gravitational wave data analysis and provided travel support to European scientists to build
collaborations in these areas. All Tasks listed in the Implementation Plan have been
performed.
4. List of publications and conference proceedings
L Baggio et al.
First joint search of GW waves by the Auriga - Explorer - Nautilus - Virgo
Collaboration, Virgo note VIR-NOT-FIR-1390-328 (2006)
P. Ajith, M. Hewitson and I. S. Heng
Null-stream veto for two collocated detectors: implementation issues
Classical and Quantum Gravity 23 19 S741-S749 (2006)
F Beauville et al
Detailed comparison of LIGO and Virgo Inspiral Pipelines in Preparation for a Joint
Search, gr-qc/0701027 (2006)
F Beauville et al
A comparison of methods for gravitational wave burst searches from LIGO and Virgo
gr-qc/0701026 (2006)