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Searching for transient gravitational wavesfrom isolated neutron stars using STAMP
Stefanos Giampanis†
†University of Wisconsin - [email protected]
Abstract
Isolated (non-accreting) neutron stars (NSs) are ex-pected to emit continuous gravitational waves (GWs)via a number or mechanisms (non-axisymmetric dis-tortions, free precession, velocity perturbations in thestar’s fluid). Transient GWs from isolated NSs are alsoplausible via similar mechanisms. These include GWsdue to instabilities occurring at early stages in the NSsevolution, such as r-modes and bar-modes; GWs due tomagnetically induced deformations in young fast rotat-ing magnetars; and GWs associated with electromag-netic glitches. Depending on the process the durationof the GWs can vary from minutes to weeks and possi-bly months. STAMP, the Stochastic Transient AnalysisMulti-detector Pipeline, is a unique tool for searching forsuch signals in data from current and future generationgravitational wave detectors.
The STAMP Pipeline
STAMP, the “Stochastic Transient Analysis Multi-detector Pipeline” is a cross-correlation based multi-detector data analysis pipeline designed for detectinglong gravitational-wave transients [1]. STAMP usestime-frequency patterns in the cross-correlation powerbetween multiple detectors. These transients can spanany duration from seconds to weeks. STAMP does notassume a signal model but, instead, employes differentpattern-recognition techniques.
Secular bar mode instabilities
Newly formed rapidly rotating neutron stars (NSs) canbecome dynamically or secularly unstable via bar-mode(l = m = 2) instabilities driven by gravitational radia-tion. After the core collapse of a massive star or ac-cretion induced collapse of a white dwarf, the proto-NSsettles into an axisymmetric secularly unstable equilib-rium state if the ratio of its rotational energy T to thegravitational potential energy |W |, β = T/|W |, exceedsa threshold β > βsec � 0.14. The star is dynamicallyunstable if β > βdyn � 0.27. Dynamic instabilities haveextremely short growth times (O(ms)). Secular insta-bilities, on the other hand, are interesting GW sourcesfor STAMP. Depending on β, the NS’s mass, radius
and polytropic index, the growth time of a secularly un-stable bar mode can be approximately written as [2]τGW � 2× 10−5M−3
1.4R410(β−βsec)−5 s, for 0 < β−βsec � 1.
The larger β is the shorter the growth time of the insta-bility; hence the stronger the associated GW emission.The GW components can be expressed as [2, 5])
h+ = h[f (t); fmax,M,R] cosΦ(t)(1 + cos2 θ)/2 (1)h× = h[f (t); fmax,M,R] sinΦ(t) cos θ (2)
where M , R are the mass and radius of the NS, Φ isthe GW phase and θ is the angle between the rota-tion axis of the NS and the line of sight from earth.
0 50 100 150 200 250 300
!4
!2
0
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h [
stra
in]
t [sec]
0 100 200 3000
100
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z]
h+
hx
24.5 24.52 24.54 24.56 24.58 24.6 24.62 24.64 24.66 24.68 24.7!5
0
5x 10
!22
Figure 1: Example of a GW from a 1.4 solar mass NSat distance d = 80kpc, with a 20 km radius, polytropic in-dex n = 1 and θ = 300. The GW emission initially occursat 150 Hz and lasts O(100) sec. Top inset: frequencyevolution of GW.
time (s)
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z)
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R
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Figure 2: Example of STAMP’s SNR map using Fig. 1’ssynthetic waveform and noise similar to LIGO S5’s run.
r-mode instabilities
Like bar-modes the instability in r-modes is driven bygravitational radiation reaction (CFS instability); the GWemission mechanism is due to a time varying currentquadrupole; r-modes are (always) secularly unstable;the emitted GWs are quasi-sinusoidal at frequencies
fr �(l − 1)(l + 2)
l + 1ν
l=2=
4
3ν, (3)
where ν is the spin frequency of the NS. The growthtime of r-modes can vary over several orders of magni-tude and is very sensitive to temperature and the dissi-pative effects of viscosity. Owen et. al.[3] estimate aninitial linear growth phase ∼ 103 sec and a slowly vary-ing frequency ∼ 1kHz. After that initial phase the emit-ted GW (as the NS is spinning down due to gravitationalradiation) decreases in amplitude and frequency over amuch longer time.
Young magnetars
Magnetars are NSs with high magnetic fields. Theirspin down and bright emission activity is believed tobe powered by their magnetic field. In the presenceof poloidal/toroidal magnetic fields the NS becomesoblate/prolate with an magnetically induced ellipticity�Q [6].
�Q ∼ k
�Bpole(G)
1016
�2× 10−4 (4)
k ∼ O(1) depends on the EOS, Bpole is the amplitudeof the dipolar surface magnetic field at the pole. In anaxisymmetric NS with a quadrupole ellipticity �Q if themagnetic axis does not coincide with the rotation axis,deviating by an angle α, the associated GW emissionoccurs at frequency ν, the NS spin frequency, if α issmall. The GW amplitude h0 is given by
h0 �4G
rc4(2πν)2I|�Q| sinα (5)
where r is the distance to the NS, c is the speed oflight and G is the Newton’s constant. Due to dissipa-tive processes α goes to zero as the rotation rate de-creases due to the NS spinning down emitting GWs.
This damping timescale can vary from months to yearsdepending on the magnetic field, induced ellipticity, ro-tational period and dissipation process. The transientGW can spend a significant portion of its lifetime withinthe frequency range of GW detector if the young NS isborn rotating at high frequencies (∼ 0.1− 1 kHz).
Transient GWs associated with NS “glitches”
Sudden spin-ups (more commonly referred to as“glitches”) are observed in the emitted EM spectrum ofseveral known NSs. A two fluid model, consisting of aninterior normal fluid, a superfluid and a crust is normallyemployed in phenomenological studies of the observedglitches [4]. Prix et. al. [7] assume a differentially ro-tating superfluid and crust and calculate the availablekinetic energy (“glitch” energy) when non-differential ro-tation is restored. The latter is hypothesized to occurat the time of a “glitch” while a differential rotation isbuilt up between two glitches. Whether the available“glitch” energy is transferred from the superfluid to thecrust exerting a strain onto it (hence an observed EM“glitch”) or is directly channeled in GW emission (via aninternal instability) remains a matter of study. Neverthe-less, the emitted GWs are of transient nature with dura-tion times comparable to observed relaxation times ofEM “glitches”. The GW signal is quasi-sinusoidal with awell-defined slowly varying frequency.
References
[1] E. Thrane et. al. arXiv:1012.2150v1
[2] D. Lai and S. Shapiro, APJ, 442, 259-272 (1995)
[3] B. Owen et. al. , Phys. Rev. D 58, 084020 (1998)
[4] A. G. Lyne, S. L. Shemar, and F. G. Smith, MNRAS315, 534-542 (2000)
[5] D. Lai, arXiv:astro-ph/0101042v1, (2001)
[6] L Gualtieri, R Ciolfi and V Ferrari,arXiv:1011.2778v1
[7] R. Prix, S. Giampanis, and C. Messenger,LIGO-P1100002
GWPAW, Milwaukee WI, January 26-29, 2011. LIGO-G1001137
• Isolated NSs as sources of transient GWs
• Intermediate duration (“long bursts”) GWs, O(s) - O(weeks)
• STAMP pipeline - Data analysis methods
NASA EM Followup of LIGO-Virgo Candidate EventsLindy Blackburn for the LIGO Scientific Collaboration and Virgo Collaboration
NASA Goddard Space Flight Center
We describe an offline, targeted search of archive data from several NASA high-energy EM instruments for prompt and afterglow EM
signals about the time of LIGO-Virgo GW events.
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4 CHAPTER 2. BAT INSTRUMENT
Figure 2.1: Idealized view of the Swift optical bench, including a cut-away view of the Burst Alert
Telescope (BAT). The main BAT structures are the coded aperture mask (top, shown as a randomly
filled grid, and the detector array (bottom). The narrow field instruments are mounted to the side
of the BAT.
2.4 The BAT Instrument
The BAT instrument is shown in Figure 2.1. The Burst Alert Telescope (BAT) makes the initial
detection of the gamma-ray burst (GRB), calculates a position for that burst, makes an on-board
decision if the burst is worth an NFI follow-up observation, and sends that position to the spacecraft
attitude control system, if it is worthy. It does all this within 10-30 sec of the initial trigger of
the burst. To do this for a large number of bursts (∼100 yr-1), BAT has a large FOV (1.4 sr
half-coded & 2.2 sr partially-coded). The only way to image such a large FOV is to use the coded-
aperture technique. The following sections describe the details of the design, the function of the
BAT instrument, and the data products that will be available to the world community.
2.4.1 Technical Description
The basic numbers describing the BAT instrument are listed in Table 2.1. The BAT instrument
consists of a detector plane of 32,768 CZT detector elements and front-end electronics, a coded
aperture mask located 1 m above the detector plane, a graded-Z fringe shield to reduce the instru-
mental background event rate and cosmic diffuse background, and a thermal radiator and control
system to keep the detector plane at a constant temperature. The control of the BAT instrument
is done through the Image Processor and it also does the on-board event processing (burst trigger
detection, burst location calculations, and burst figure-of-merit calculation). While searching for
bursts, BAT also accumulates a hard x-ray survey of the entire sky over the course of the mission.
The energy range of 15-150 keV in Table 2.1 describes the energy range over which the effective
area is more than 50% of the peak value. The range is governed at the lower end by the electronic
discriminator threshold, and at the upper end by increasing transparency of the lead tiles in the
LIGO-Virgo trigger time and sky location
FERMI GBM20 keV-40 MeV
65% FOV
RXTE ASM1-10 keV3% FOV
SWIFT BAT20 keV-150 keV
15% FOV
FERMI LAT20 MeV-300 GeV
20% FOV
LIGO-G1100001-v3 ! ! ! ! ! !!!
Low-latency Selection of Gravitational-wave Event Candidates for Wide-field Optical
Follow-up Observation!
! LIGO & Virgo have been recently operated as a multi-messenger event generator.
! Humans do final event event vetting and decision making regarding EM observing requests.
! This poster presents the EM follow-up infrastructure from event generation and focusing on the human vetting process.
Amber Stuver for the LSC and the Virgo Collaboration
Localization of gravitational wave sourceswith network of advanced detectors
M. Drago for the cWB group
Joint observations with GW detectors, electromagnetic(EM) telescopes or neutrino detectors can allow a multi-‐messenger investigation of the astrophysical source andmay improve the confidence of the first direct detection ofGWs.
We investigate the direction resolution of GW detectornetworks using Coherent Waveburst algorithm,considering simulated data of 2nd generationinterferometers: Advanced LIGO, Advanced Virgo, LargeCryogenic Gravitational Telescope and LIGO-‐Australia.
The major challenge is to establish unambiguousassociation between a GW signal and possible EMcounterpart
pointing to the GW candidate source, with an uncertaintywithin the EM instrument field of view (typically < fewsquare degrees)performing the sky localization in real time with low latencyto allow the observations of EM transients
arXiv: 0186522 [astro-‐ph.IM] 26 Jan 2011
Rapid Sky Localization from Partial Monte Carlo Markov Chains
B. Farr, V. Raymond, M. van der Sluys, I. Mandel, W. Farr, V. Kalogera, C. Röver, N. Christensen
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Sky Localization of NS-NS and NS-BH Inspirals
With GW Interferometer Networks.
• MCMC analysis of sky localization for astrophysical compact
binary populations using different networks (aLIGO, Virgo, LCGT,
AustralianLIGO).
• AustralianLIGO dramatically reduces sky errors (~ by a factor of 5).
• For specific trigger scenarios, 50% of NS-NSs are localized:
< 5 sq. deg. with networks including AustralianLIGO.
< 15 sq. deg. with only aLIGO+Virgo.
Samaya Nissanke (JPL/Caltech), Neal Dalal (CITA), Daniel Holz (LANL),
Scott Hughes (MIT), Jon Sievers (CITA).Poster #28
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Summed Parallel Infinite Impulse Response (SPIIR) Filters For
Low-Latency Gravitational Wave DetectionShaun Hooper1, Linqing Wen1, David Blair1, Jing Luan2, Shin Kee Chung1 and Yanbei Chen2
1The University of Western Australia, 2California Institute of Technology
Prompt Optical Follow-Up
Time-Domain GW Detection Method
FIR yk =�k
j=−N bjxk−j Computationally expensiveIIR yk = a1yk−1 + b0xk Computationally cheap
Inspiral Waveform as a Summation of Sinusoids
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Shaun Hooper et. al SPIIR Filters For Low-Latency Gravitational Wave Detection (LIGO - G1100030) Mail: [email protected]
Compact binary coalescence searches withlow latency: why and how (P31, M1)
‣ Low-latency GW triggering will aid rapid EM followup
‣Techniques:‣principal component analysis‣ conditional SNR reconstruction‣multi-rate filtering‣ short FFTs‣ streaming architecture
P. Ajith, K. Cannon, B. Daudert, . Fotopoulos, M. Frei, C,. Hanna, S. Hooper, D. Keppel, A. Mercer, S. Privitera, A. Searle, L. Singer, A. Weinstein
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Burst search with gstreamer pipelinegstlal
GWPAW2011
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Coherently searching for perturbed black-hole ringdown signals with a network ofgravitational-wave detectors
Coherently searching for perturbed black-hole ringdown signals with a network ofgravitational-wave detectors
Dipongkar Talukder† and Sukanta Bose†
†Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814, USA
AbstractWe present results in Gaussian data from a template-based multi-detector coherent search for perturbed-black-hole ringdown signals. Like the past “coincidence” ringdown searches in LIGO data, our methodincorporates knowledge of the ringdown waveform in constructing the search templates. Additionally, it checks for consistency of signal amplitude and phase with the signals’ times-of-arrival at the detectors. Thelatter feature is common to both of our method and the Coherent WaveBurst algorithm, and can help bridge the gap in performance between the coincidence search and the coherent WaveBurst search for ringdownsignals. [LIGO Document Control Center Number: LIGO-G1100036-x0.]
Gravitational waves from perturbed blackholes
Several ground-based interferometric observatories, suchas LIGO and Virgo, have collected data so that as-tronomers can search for gravitational-wave (GW) signalsin them. One such signal is that arising from a perturbedblack hole, which can result from the coalescence of a com-pact binary. This signal is initially in the form of a super-position of quasi-normal modes. However, at late timesthe waveform, which is known as a ringdown, is expectedto be dominated by a single mode. The optimal methodfor searching such a signal buried in detector noise is tomatch-filter the detectors’ output with theoretically mod-eled waveforms. The coherent network statistic is optimalfor detecting these signals in stationary, Gaussian noise[1, 2]. But in real noise, which is non-Gaussian and non-stationary, additional discriminators of noise artifacts arerequired for obtaining a (near-)optimal statistic. Here, wedescribe a hierarchical method for coherently searchingringdown signals in a network of detectors that is aided bysuch discriminators.
The ringdown waveformThe central frequency and the decay time of the quasi-normal mode oscillation can be predicted with good accu-racy by black-hole perturbation theory. The plus and crosspolarizations of a ringdown waveform can be expressed interms of the central frequency f0 and the quality factor Qas
h+(t) =Ar(1 + cos2 ι) e−
πf0tQ cos(2πf0t) ,
h×(t) =Ar2 cos ι e−
πf0tQ sin(2πf0t) ,
where A is the amplitude, r is the distance from the sourceand ι is the inclination angle of the source. We considerhere only the dominant mode i.e, the most slowly dampedmode, l = m = 2. The strain produced in the detector isthen
h(t) = h+(t)F+(θ,φ,ψ) + h×(t)F×(θ,φ,ψ) ,
where F+,× are the detector antenna-pattern functions,with ψ being the wave-polarization angle and (θ,φ) beingthe sky-position of the source.
A search based on matched-filteringIn GW data analysis, the data from multiple detectorsis match-filtered with templates derived from theoreticalwaveforms to test the presence or absence of signals in thedata. Filtering the data s(t) with a template h0(t;µi) char-acterized by the source parameters µi yields the signal-to-noise ratio (SNR) statistic given by
ρ(h0) =�s, h0���h0, h0�
,
where �s, h0� denotes the noise-weighted scalar product ofthe data and the template. Far from the source, the ring-down template can be expressed as
h0(t) = e−πf0tQ cos(2πf0t− ϕ0) .
For each template, triggers that have SNRs greater thana pre-defined threshold are retained. These triggers areused for determining coincidence across different detec-tors. This method is the so-called “coincidence multi-detector search” [3-5].
Data-find
Generate
bank of
templates
Generate
bank of
templates
Generate
bank of
templates
Generate
bank of
templates
Match-
filter data
Match-
filter data
Match-
filter data
Match-
filter data
Coincidence test: time,
waveform parametersDiscard (fail)
Candidate
event (pass)
Coherent stage:
phase and amplitude
consistency check
H1 H2 L1 V1
Figure 1: A schematic diagram of the coincidence and coherent stagesin the ringdown search pipeline.
Coherent statisticUnlike the coincident multi-detector search statistics thathave been employed so far, the coherent statistics are dif-ferent in the sense that they check for the consistency of thesignal amplitudes and phases in the different detectors withtheir different orientations and with the signal arrival timesin them [1, 2]. The coherent search statistic for two co-aligned detectors with different noise power spectral den-sity is the coherent SNR, given by
ρcoh =|C1 σ1 + C2 σ2|�
σ21 + σ22
,
∝�
(ρ1σ1)2 + (ρ2σ2)2 + 2(ρ1σ1)(ρ2σ2) cos(Φ1 − Φ2) ,
where σI is the template-norm and CI is the matched-filteroutput against a circular-polarization template in the Ith de-tector.For non-stationary artifacts, however, additional discrimi-nators are required. One such construct is the null-streamstatistic [6], which is
η =|C1/σ1 − C2/σ2|�
1/σ21 + 1/σ22
.
for two co-aligned detectors. For more detectors at differentsites and with different orientations, the above expressionwill involve antenna factors and time-delays.
101.25 101.26 101.27101
101.1
101.2
Coherent statistic
Coi
ncid
ence
sta
tistic
H1L1−doubles in double time
SlidesInjections
Figure 2: The scatter plot of coincidence and coherent statistic val-ues for injection triggers, denoted by red pluses, and background (orslide) triggers, represented by black asterisks. Here we present onlythe weak injections. All background triggers have been retained. Notethat there are more found injections that are louder than the loudestbackground trigger when the statistic used is the coherent one insteadof the coincidence one.
ResultsTo study the utility of the coherent statistics, we ran theringdown search pipeline (see Fig. 1) on the NINJA-2 (sim-ulated) data set for the 4km-long LIGO detectors in Han-ford (H1) and Livingston (L1) and for the duration of ap-proximately a week. A total of 226 signals were present inthe simulated data, of which 217 were found by the ring-down pipeline. A total of 143 background triggers, ob-tained through time-slide experiments, were found. Figure2 shows a scatter plot of the coincidence versus coherentstatistic for the found injection and slide triggers. In Fig. 3we compare efficiency of finding injection triggers using co-incidence and coherent searches. Note that only amplitudeconsistency is applied in this analysis.
10 20 30 40 50 60 70 80 90 1000
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foun
d lo
uder
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est b
ackg
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d
Efficiency of injection finding in the H1L1−doubles in double time
Coherent search Coincidence search
Figure 3: Here we compare the efficiencies of finding signals in H1-L1 using coincidence and coherent searches. All injection and back-ground triggers were found in (double) coincidence in H1 and L1. Notethat the average (vertical) error bar in each distance bin is 0.025.
DiscussionAs discussed above, we show that the coherent search per-forms better than the coincidence search at least in sta-tionary, Gaussian data. We expect its performance to beboosted for triple-site searches, where the phase consis-tency test can be applied. We will do so next [7], once thecoincidence stage of the three-site search has been imple-mented. There we plan to compare the performance of thecoherent ringdown search with that of the Coherent Wave-Burst [8].
AcknowledgementsWe thank Paul Baker, Sarah Caudill, Neil Cornish, JolienCreighton, Gregory Mendell and Fred Raab for helpful dis-cussions. This work was supported in part by NSF grantPHY-0855679.
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� Current (coincidence) search does not check for the consistency of the amplitudesand phases of the signals in the detectors due to a putative ringdown source withtheir observed time-delays.
� What happens to the performance of the search when these checks are applied?
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