Searches for gravitational waves from known pulsars with S5 LIGO data

Harald Lück
Institut für Gravitationsphysik, Leibniz Universität Hannover and Max Planck Institute for Gravitational Physics (AlbertEinsteinInstitute)
ABSTRACT We present a search for gravitational waves from 116 known millisecond and
young pulsars using data from the fifth science run of the LIGO detectors. For
this search ephemerides overlapping the run period were obtained for all
pulsars using radio and Xray observations. We demonstrate an updated search
method that allows for small uncertainties in the pulsar phase parameters to be
included in the search. We report no signal detection from any of the targets
and therefore interpret our results as upper limits on the gravitational wave
signal strength. The most interesting limits are those for young pulsars. We
present updated limits on gravitational radiation from the Crab pulsar, where
the measured limit is now a factor of seven below the spindown limit. This
limits the power radiated via gravitational waves to be less than ~2% of the
available spindown power. For the Xray pulsar J05376910 we reach the
spindown limit under the assumption that any gravitational wave signal from it
stays phase locked to the Xray pulses over timing glitches, and for pulsars
J1913+1011 and J1952+3252 we are only a factor of a few above the spindown
limit. Of the recycled millisecond pulsars several of the measured upper limits
are only about an order of magnitude above their spindown limits. For these
our best (lowest) upper limit on gravitational wave amplitude is 2.3x10^26 for
J16037202 and our best (lowest) limit on the inferred pulsar ellipticity is
7.0x10^8 for J21243358.
 [Show abstract] [Hide abstract]
ABSTRACT: Rapidly spinning neutron stars in our Galactic neighborhood are promising sources of quasimonochromatic continuous gravitational waves observable by the current LIGO detectors. I describe a search done on the LIGO S5 data, looking for an isolated neutron star hypothesized to be at a distance of about 100 parsecs. This kind of search is computationally bound and is made possible by the implementation of barycentric resampling, which is described here as well. I also describe the work done at the Hanford LIGO site, while taking data for the Astrowatch program.08/2011;  SourceAvailable from: ArXiv[Show abstract] [Hide abstract]
ABSTRACT: In this dissertation, we review work presented in arXiv:0906.2015, arXiv:0907.1663, arXiv:1002.3132, arXiv:1003.2746, and arXiv:1007.2202 on the D1D5 system. We begin with some motivational material for black holes in string theory. In Chapter 2, we review the D1D5 system, including the gravity and CFT descriptions. In Chapter 3, we show how to perturbatively relax the decoupling limit in a general AdSCFT setting. This allows one to compute the emission out of the AdS/CFT into the asymptotic flat space. In Chapter 4, we apply that formalism to some particular geometries, and exactly reproduce the emission spectrum. These geometries are interpreted as fuzzball microstates of a black hole, and the emission as the microscopic analogue of the Hawking radiation. In Chapter 5, we discuss how to deform the D1D5 CFT off of its orbifold point. In particular, we present full offshell expressions for firstorder corrections to the CFT states. One can see how highenergy states can fragment into many lowerenergy states. In the conclusion, we discuss some opportunities for future work. Comment: PhD dissertation, 255 pages, 28 figures11/2010;
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arXiv:0909.3583v4 [astroph.HE] 26 Feb 2010
Searches for gravitational waves from known pulsars with S5
LIGO data
B. P. Abbott28, R. Abbott28, F. Acernese18ac, R. Adhikari28, P. Ajith2, B. Allen2,75,
G. Allen51, M. Alshourbagy20ab, R. S. Amin33, S. B. Anderson28, W. G. Anderson75,
F. Antonucci21a, S. Aoudia42a, M. A. Arain63, M. Araya28, H. Armandula28, P. Armor75,
K. G. Arun25, Y. Aso28, S. Aston62, P. Astone21a, P. Aufmuth27, C. Aulbert2, S. Babak1,
P. Baker36, G. Ballardin11, S. Ballmer28, C. Barker29, D. Barker29, F. Barone18ac, B. Barr64,
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A. Brillet42a, M. Brinkmann2, V. Brisson25, C. Van Den Broeck8, A. F. Brooks28,
D. A. Brown52, A. Brummit46, G. Brunet31, R. Budzy´ nski44b, T. Bulik44cd, A. Bullington51,
H. J. Bulten40ab, A. Buonanno65, O. Burmeister2, D. Buskulic26, R. L. Byer51,
L. Cadonati66, G. Cagnoli16a, E. Calloni18ab, J. B. Camp38, E. Campagna16ac,
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S. Caride67, G. Castaldi71, S. Caudill33, M. Cavagli` a55, F. Cavalier25, R. Cavalieri11,
G. Cella20a, C. Cepeda28, E. Cesarini16c, T. Chalermsongsak28, E. Chalkley64,
P. Charlton77, E. ChassandeMottin4, S. Chatterji28, S. Chelkowski62, Y. Chen1,7,
A. Chincarini17, N. Christensen9, C. T. Y. Chung54, D. Clark51, J. Clark8, J. H. Clayton75,
F. Cleva42a, E. Coccia22ab, T. Cokelaer8, C. N. Colacino13,20, J. Colas11, A. Colla21ab,
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F. Piergiovanni16ac, V. Pierro71, M. Pietka44e, L. Pinard32, I. M. Pinto71, M. Pitkin64,
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C. M. Reed29, T. Reed34, T. Regimbau42a, H. Rehbein2, S. Reid64, D. H. Reitze63,
F. Ricci21ab, R. Riesen30, K. Riles67, B. Rivera29, P. Roberts3, N. A. Robertson28,64,
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J. Rollins10, J. D. Romano58, R. Romano18ac, J. H. Romie30, D. Rosi´ nska44gd, C. R¨ over2,
S. Rowan64, A. R¨ udiger2, P. Ruggi11, P. Russell28, K. Ryan29, S. Sakata39, F. Salemi43ab,
V. Sandberg29, V. Sannibale28, L. Santamar´ ıa1, S. Saraf48, P. Sarin31, B. Sassolas32,
B. S. Sathyaprakash8, S. Sato39, M. Satterthwaite5, P. R. Saulson52, R. Savage29, P. Savov7,
M. Scanlan34, R. Schilling2, R. Schnabel2, R. Schofield69, B. Schulz2, B. F. Schutz1,8,
P. Schwinberg29, J. Scott64, S. M. Scott5, A. C. Searle28, B. Sears28, F. Seifert2,
D. Sellers30, A. S. Sengupta28, D. Sentenac11, A. Sergeev23, B. Shapiro31, P. Shawhan65,
D. H. Shoemaker31, A. Sibley30, X. Siemens75, D. Sigg29, S. Sinha51, A. M. Sintes60,
B. J. J. Slagmolen5, J. Slutsky33, M. V. van der Sluys41, J. R. Smith52, M. R. Smith28,
N. D. Smith31, K. Somiya7, B. Sorazu64, A. Stein31, L. C. Stein31, S. Steplewski76,
A. Stochino28, R. Stone58, K. A. Strain64, S. Strigin37, A. Stroeer38, R. Sturani16ac,
A. L. Stuver30, T. Z. Summerscales3, K. X. Sun51, M. Sung33, P. J. Sutton8, B. Swinkels11,
G. P. Szokoly13, D. Talukder76, L. Tang58, D. B. Tanner63, S. P. Tarabrin37, J. R. Taylor2,
R. Taylor28, R. Terenzi22ac, J. Thacker30, K. A. Thorne30, K. S. Thorne7, A. Th¨ uring27,
K. V. Tokmakov64, A. Toncelli20ab, M. Tonelli20ab, C. Torres30, C. Torrie28, E. Tournefier26,
F. Travasso19ab, G. Traylor30, M. Trias60, J. Trummer26, D. Ugolini59, J. Ulmen51,
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A. G. Wiseman75, G. Woan64, R. Wooley30, J. Worden29, W. Wu63, I. Yakushin30,
H. Yamamoto28, Z. Yan74, S. Yoshida49, M. Yvert26, M. Zanolin12, J. Zhang67, L. Zhang28,
C. Zhao74, N. Zotov34, M. E. Zucker31, J. Zweizig28
The LIGO Scientific Collaboration & The Virgo Collaboration
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1AlbertEinsteinInstitut, MaxPlanckInstitut f¨ ur Gravitationsphysik, D14476 Golm, Germany
2AlbertEinsteinInstitut, MaxPlanckInstitut f¨ ur Gravitationsphysik, D30167 Hannover, Germany
3Andrews University, Berrien Springs, MI 49104 USA
4AstroParticule et Cosmologie (APC), CNRS: UMR7164IN2P3Observatoire de ParisUniversit´ e Denis
DiderotParis VII  CEA : DSM/IRFU
5Australian National University, Canberra, 0200, Australia
6California Institute of Technology, Pasadena, CA 91125, USA
7CaltechCaRT, Pasadena, CA 91125, USA
8Cardiff University, Cardiff, CF24 3AA, United Kingdom
9Carleton College, Northfield, MN 55057, USA
77Charles Sturt University, Wagga Wagga, NSW 2678, Australia
10Columbia University, New York, NY 10027, USA
11European Gravitational Observatory (EGO), I56021 Cascina (Pi), Italy
12EmbryRiddle Aeronautical University, Prescott, AZ 86301 USA
13E¨ otv¨ os University, ELTE 1053 Budapest, Hungary
14ESPCI, CNRS, F75005 Paris, France
15Hobart and William Smith Colleges, Geneva, NY 14456, USA
16INFN, Sezione di Firenze, I50019 Sesto Fiorentinoa; Universit` a degli Studi di Firenze, I50121b, Firenze;
Universit` a degli Studi di Urbino ’Carlo Bo’, I61029 Urbinoc, Italy
17INFN, Sezione di Genova; I16146 Genova, Italy
18INFN, sezione di Napolia; Universit` a di Napoli ’Federico II’bComplesso Universitario di Monte S.Angelo,
I80126 Napoli; Universit` a di Salerno, Fisciano, I84084 Salernoc, Italy
19INFN, Sezione di Perugiaa; Universit` a di Perugiab, I6123 Perugia,Italy
20INFN, Sezione di Pisaa; Universit` a di Pisab; I56127 Pisa; Universit` a di Siena, I53100 Sienac, Italy
21INFN, Sezione di Romaa; Universit` a ’La Sapienza’b, I00185 Roma, Italy
22INFN, Sezione di Roma Tor Vergataa; Universit` a di Roma Tor Vergatab, Istituto di Fisica dello Spazio
Interplanetario (IFSI) INAFc, I00133 Roma; Universit` a dell’Aquila, I67100 L’Aquilad, Italy
23Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
24InterUniversity Centre for Astronomy and Astrophysics, Pune  411007, India
25LAL, Universit´ e ParisSud, IN2P3/CNRS, F91898 Orsay, France
26Laboratoire d’AnnecyleVieux de Physique des Particules (LAPP), IN2P3/CNRS, Universit´ e de Savoie,
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F74941 AnnecyleVieux, France
27Leibniz Universit¨ at Hannover, D30167 Hannover, Germany
28LIGO  California Institute of Technology, Pasadena, CA 91125, USA
29LIGO  Hanford Observatory, Richland, WA 99352, USA
30LIGO  Livingston Observatory, Livingston, LA 70754, USA
31LIGO  Massachusetts Institute of Technology, Cambridge, MA 02139, USA
32Laboratoire des Mat´ eriaux Avanc´ es (LMA), IN2P3/CNRS, F69622 Villeurbanne, Lyon, France
33Louisiana State University, Baton Rouge, LA 70803, USA
34Louisiana Tech University, Ruston, LA 71272, USA
35Loyola University, New Orleans, LA 70118, USA
36Montana State University, Bozeman, MT 59717, USA
37Moscow State University, Moscow, 119992, Russia
38NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
39National Astronomical Observatory of Japan, Tokyo 1818588, Japan
40Nikhef, National Institute for Subatomic Physics, P.O. Box 41882, 1009 DB Amsterdam, The
Netherlandsa; VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlandsb
41Northwestern University, Evanston, IL 60208, USA
42Departement Artemis, Observatoire de la Cˆ ote d’Azur, CNRS, F06304 Nicea; Institut de Physique de
Rennes, CNRS, Universit´ e de Rennes 1, 35042 Rennesb; France
43INFN, Gruppo Collegato di Trentoaand Universit` a di Trentob, I38050 Povo, Trento, Italy; INFN,
Sezione di Padovacand Universit` a di Padovad, I35131 Padova, Italy
44IMPAN 00956 Warsawa; Warsaw Univ. 00681b; Astro. Obs. Warsaw Univ. 00478c; CAMKPAM
00716 Warsawd; Bialystok Univ. 15424e; IPJ 05400 SwierkOtwockf; Inst. of Astronomy 65265 Zielona
Gorag, Poland
45Rochester Institute of Technology, Rochester, NY 14623, USA
46Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom
47San Jose State University, San Jose, CA 95192, USA
48Sonoma State University, Rohnert Park, CA 94928, USA
49Southeastern Louisiana University, Hammond, LA 70402, USA
50Southern University and A&M College, Baton Rouge, LA 70813, USA
51Stanford University, Stanford, CA 94305, USA
52Syracuse University, Syracuse, NY 13244, USA
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S. B´ egin86,89, A. Corongiu82, N. D’Amico82,81, P. C. C. Freire78,90, J. W. T. Hessels85,79,
G. B. Hobbs80, M. Kramer87, A. G. Lyne87, R. N. Manchester80, F. E. Marshall88,
J. Middleditch83, A. Possenti82, S. M. Ransom84, I. H. Stairs86, and B. Stappers87
53The Pennsylvania State University, University Park, PA 16802, USA
54The University of Melbourne, Parkville VIC 3010, Australia
55The University of Mississippi, University, MS 38677, USA
56The University of Sheffield, Sheffield S10 2TN, United Kingdom
57The University of Texas at Austin, Austin, TX 78712, USA
58The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA
59Trinity University, San Antonio, TX 78212, USA
60Universitat de les Illes Balears, E07122 Palma de Mallorca, Spain
61University of Adelaide, Adelaide, SA 5005, Australia
62University of Birmingham, Birmingham, B15 2TT, United Kingdom
63University of Florida, Gainesville, FL 32611, USA
64University of Glasgow, Glasgow, G12 8QQ, United Kingdom
65University of Maryland, College Park, MD 20742 USA
66University of Massachusetts  Amherst, Amherst, MA 01003, USA
67University of Michigan, Ann Arbor, MI 48109, USA
68University of Minnesota, Minneapolis, MN 55455, USA
69University of Oregon, Eugene, OR 97403, USA
70University of Rochester, Rochester, NY 14627, USA
71University of Sannio at Benevento, I82100 Benevento, Italy
72University of Southampton, Southampton, SO17 1BJ, United Kingdom
73University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
74University of Western Australia, Crawley, WA 6009, Australia
75University of WisconsinMilwaukee, Milwaukee, WI 53201, USA
76Washington State University, Pullman, WA 99164, USA
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ABSTRACT
We present a search for gravitational waves from 116 known millisecond and
young pulsars using data from the fifth science run of the LIGO detectors. For
this search ephemerides overlapping the run period were obtained for all pulsars
using radio and Xray observations. We demonstrate an updated search method
that allows for small uncertainties in the pulsar phase parameters to be included
in the search. We report no signal detection from any of the targets and therefore
interpret our results as upper limits on the gravitational wave signal strength.
The most interesting limits are those for young pulsars. We present updated
limits on gravitational radiation from the Crab pulsar, where the measured limit
is now a factor of seven below the spindown limit. This limits the power radiated
via gravitational waves to be less than ∼2% of the available spindown power. For
the Xray pulsar J0537−6910 we reach the spindown limit under the assumption
that any gravitational wave signal from it stays phase locked to the Xray pulses
over timing glitches, and for pulsars J1913+1011 and J1952+3252 we are only
a factor of a few above the spindown limit. Of the recycled millisecond pulsars
78Arecibo Observatory, HC 3 Box 53995, Arecibo, Puerto Rico 00612, USA
79Astronomical Institute “Anton Pannekoek”, University of Amsterdam, 1098 SJ Amsterdam, The Nether
lands
80Australia Telescope National Facility, CSIRO, PO Box 76, Epping NSW 1710, Australia
81Dipartimento di Fisica Universit` a di Cagliari, Cittadella Universitaria, I09042 Monserrato, Italy
82INAF  Osservatorio Astronomico di Cagliari, Poggio dei Pini, 09012 Capoterra, Italy
83Modeling, Algorithms, and Informatics, CCS3, MS B265, Computer, Computational, and Statistical
Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
84National Radio Astronomy Observatory, Charlottesville, VA 22903, USA
85Netherlands Institute for Radio Astronomy (ASTRON), Postbus 2, 7990AA Dwingeloo, The Netherlands
86Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Van
couver, BC V6T 1Z1, Canada
87University of Manchester, Jodrell Bank Centre for Astrophysics AlanTuring Building, Oxford Road,
Manchester M13 9PL, UK
88NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
89D´ epartement de physique, de g´ enie physique et d’optique, Universit´ e Laval, Qu´ ebec, QC G1K 7P4,
Canada.
90West Virginia University, Department of Physics, PO Box 6315, Morgantown, WV 26506, USA
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several of the measured upper limits are only about an order of magnitude above
their spindown limits. For these our best (lowest) upper limit on gravitational
wave amplitude is 2.3×10−26for J1603−7202 and our best (lowest) limit on the
inferred pulsar ellipticity is 7.0×10−8for J2124−3358.
Subject headings: gravitational waves  pulsars: general
1.Introduction
Within our Galaxy some of the best targets for gravitational wave searches in the sen
sitive frequency band of current interferometric gravitational wave detectors (∼40–2000Hz)
are millisecond and young pulsars. There are currently just over 200 known pulsars with
spin frequencies greater than 20Hz, which therefore are within this band. In this paper we
describe the latest results from the ongoing search for gravitational waves from these known
pulsars using data from the Laser Interferometric GravitationalWave Observatory (LIGO).
As this search looks for objects with known positions and spinevolutions it can use long
time spans of data in a fully coherent way to dig deeply into the detector noise. Here we use
data from the entire twoyear run of the three LIGO detectors, entitled Science Run 5 (S5),
during which the detectors reached their design sensitivities (Abbott et al. 2009b). This run
started on 2005 November 4 and ended on 2007 October 1. The detectors (the 4km and 2km
detectors at LIGO Hanford Observatory, H1 and H2, and the 4km detector at the LIGO Liv
ingston Observatory, L1) had duty factors of 78% for H1, 79% for H2, and 66% for L1. The
GEO600 detector also participated in S5 (Grote & the LIGO Scientific Collaboration 2008),
but at lower sensitivities that meant it was not able to enhance this search. The Virgo detec
tor also had data overlapping with S5 during Virgo Science Run 1 (VSR1) (Acernese et al.
2008). However this was also generally at a lower sensitivity than the LIGO detectors and
had an observation time of only about 4 months, meaning that no significant sensitivity
improvements could be made by including this data. Due to its multistage seismic isola
tion system Virgo does have better sensitivity than the LIGO detectors below about 40Hz,
opening the possibility of searching for more young pulsars, including the Vela pulsar. These
lower frequency searches will be explored more in the future.
This search assumes that the pulsars are triaxial stars emitting gravitational waves at
precisely twice their observed spin frequencies, i.e. the emission mechanism is an ℓ = m = 2
quadrupole, and that gravitational waves are phaselocked with the electromagnetic signal.
We use the socalled spindown limit on strain tensor amplitude hsd
for each pulsar in our analysis. This can be calculated, by assuming that the observed spin
down rate of a pulsar is entirely due to energy loss through gravitational radiation from an
0as a sensitivity target
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ℓ = m = 2 quadrupole, as
hsd
0= 8.06×10−19I38r−1
kpc(˙ ν/ν)1/2, (1)
where I38 is the pulsar’s principal moment of inertia (Izz) in units of 1038kgm2, rkpc is
the pulsar distance in kpc, ν is the spinfrequency in Hz, and ˙ ν is the spindown rate in
Hzs−1. Due to uncertainties in Izz and r, hsd
Part of this is due to the uncertainty in Izzwhich, though predicted to lie roughly in the
range 1–3×1038kgm2, has not been measured for any neutron star; and the best (though
still uncertain) prospect is star A of the double pulsar system J07373039 with 20 years’
more observation (Kramer & Wex 2009). Distance estimates based on dispersion measure
can also be wrong by a factor 2–3, as confirmed by recent parallax observations of the
double pulsar (Deller et al. 2009). For pulsars with measured braking indices, n = ν¨ ν/˙ ν2,
the assumption that spindown is dominated by gravitational wave emission is known to be
false (the braking index for quadrupolar gravitational wave emission should be 5, but all
measured n’s are less than 3) and a stricter indirect limit on gravitational wave emission can
be set. A phenomenological investigation of some young pulsars (Palomba 2000) indicates
that this limit is lower than hsd
Abbott et al. (2007) and Abbott et al. (2008) for more discussion of the uncertainties in
indirect limits. Recycled millisecond pulsars have intrinsically small spindowns, so for the
majority of pulsars in our search these spindown limits will be well below our current
sensitivities, making detection unlikely. However, our search also covers four young pulsars
with large spindown luminosities, and for these we can potentially beat or reach their spin
down limits using current data.
0 is typically uncertain by about a factor 2.
0 by a factor 2.5 or more, depending on the pulsar. See
The LIGO band covers the fastest (highestν) known pulsars, and the quadrupole for
mula for strain tensor amplitude
h0= 4.2 × 10−26ν2
100I38ε−6r−1
kpc
(2)
indicates that these pulsars are the best gravitational wave emitters for a given equatorial
ellipticity ε = (Ixx− Iyy)/Izz(here ν100= ν/(100 Hz) and ε−6= ε/10−6). The pulsars with
high spindowns are almost all less than ∼ 104years old. Usually this is interpreted as greater
electromagnetic activity (including particle winds) in younger objects, but it could also mean
that they are more active in gravitational wave emission. This is plausible on theoretical
grounds too. Strong internal magnetic fields may cause significant ellipticities (Cutler 2002)
which would then decay as the field decays or otherwise changes (Goldreich & Reisenegger
1992). The initial crust may be asymmetric if it forms on a time scale on which the neutron
star is still perturbed by its violent formation and aftermath, including a possible lengthy
perturbation due to the fluid rmodes (Lindblom et al. 2000; Wu et al. 2001), and asymme
tries may slowly relax due to mechanisms such as viscoelastic creep. Also the fluid rmodes
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may remain unstable to gravitational wave emission for up to a few thousand years after
the neutron star’s birth, depending on its composition, viscosity, and initial spin frequency
(Owen et al. 1998; Bondarescu et al. 2009). Such rmodes are expected to have a gravita
tional wave frequency about 4/3 the spin frequency. However, we do not report on rmode
searches in this paper.
1.1.Previous analyses
The first search for gravitational waves from a known pulsar using LIGO and GEO600
data came from the first science run (S1) in 2002 September. This targeted just one pulsar
in the approximately one weeks worth of data – the then fastest known pulsar J1939+2134
(Abbott et al. 2004). Data from LIGO’s second science run (S2), which spanned from 2003
February to 2003 April, was used to search for 28 isolated pulsars (i.e. those not in binary
systems) (Abbott et al. 2005). The last search for gravitational waves from multiple known
pulsars using LIGO data combined data from the third and fourth science runs and had 78
targets, including isolated pulsars and those in binary systems (Abbott et al. 2007). The
best (lowest), 95% degreeofbelief, upper limit on gravitational wave amplitude obtained
from the search was h95%
0
= 2.6×10−25for J1603−7202, and the best (smallest) limit on
ellipticity was just under 10−6for J2124−3358. The data run used in this paper is almost
an order of magnitude longer, and has a best strain noise amplitude around a factor of two
smaller, than that used in the best previous search.
We have also previously searched the first nine months of S5 data for a signal from the
Crab pulsar (Abbott et al. 2008). That analysis used two methods to search for a signal:
one in which the signal was assumed to be precisely phaselocked with the electromagnetic
signal, and another which searched a small range of frequencies and frequency derivatives
around the electromagnetic parameters. The time span of data analysed was dictated by
a timing glitch in the pulsar on 2006 August 23, which was used as the end point of the
analysis. In that search the spindown limit for the Crab pulsar was beaten for the first
time (indeed it was the first time a spindown limit had been reached for any pulsar), with
a best limit of h95%
0
= 2.7×10−25, or slightly below onefifth of the spindown limit. This
allowed the total power radiated in gravitational waves to be constrained to less than 4%
of the spindown power. We have since discovered an error in the signal template used for
the search (Abbott et al. 2009a). We have reanalysed the data and find a new upper limit
based on the early S5 data alone at the higher value shown in Table 3, along with the smaller
upper limit based on the full S5 data.
For this analysis we have approximately 525 days of H1 data, 532 days of H2 data and
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437 days of L1 data. This is using all data flagged as science mode during the run (i.e. taken
when the detector is locked in its operating condition on the dark fringe of the interference
pattern, and relatively stable), except data one minute prior to loss of lock, during which
time it is often seen to become more noisy.
1.2. Electromagnetic observations
The radio pulsar parameters used for our searches are based on ongoing radio pulsar
monitoring programs, using data from the Jodrell Bank Observatory (JBO), the NRAO
100m Green Bank Telescope (GBT) and the Parkes radio telescope of the Australia Telescope
National Facility. We used radio data coincident with the S5 run as these would reliably
represent the pulsars’ actual phase evolution during our searches. We obtained data for 44
pulsars from JBO (including the Crab pulsar ephemeris, Lyne et al. (1993, 2009)), 39 pulsars
within the Terzan 5 and M28 globular clusters from GBT, and 47 from Parkes, including
pulsars timed as part of the Parkes Pulsar Timing Array (Manchester 2008). For 15 of these
pulsars there were observations from more than one site, making a total of 115 radio pulsars
in the analysis (see Table 1 for list of the pulsars, including the observatory and time span of
the observations). For the pulsars observed at JBO and Parkes we have obtained parameters
fit to data overlapping with the entire S5 run. For the majority of pulsars observed at GBT
the parameters have been fit to data overlapping approximately the first quarter of S5.
Pulsars generally exhibit timing noise on long time scales. Over tens of years this can
cause correlations in the pulse time of arrivals which can give systematic errors in the pa
rameter fits produced, by the standard pulsar timing package TEMPO91, of order 2–10 times
the regular errors that TEMPO assigns to each parameter (Verbiest et al. 2008), depending
on the amplitude of the noise. For our pulsars, with relatively short observation periods
of around two years, the longterm timing noise variations should be largely folded in to
the parameter fitting, leaving approximately white uncorrelated residuals. Also millisecond
pulsars, in general, have intrinsically low levels of timing noise, showing comparatively white
residuals. This should mean that the errors produced by TEMPO are approximately the
true 1σ errors on the fitted values.
The regular pulse timing observations of the Crab pulsar (Lyne et al. 1993, 2009) in
dicate that the 2006 August 23 glitch was the only glitch during the S5 run. One other
radio pulsar, J1952+3252, was observed to glitch during the run (see §5.1.3.) Independent
ephemerides are available before and after each glitch.
91http://www.atnf.csiro.au/research/pulsar/tempo/
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We include one pulsar in our analysis that is not observed as a radio pulsar. This is
PSRJ0537−6910 in the Large Magellanic Cloud, for which only Xray timings currently exist.
Data for this source come from dedicated time on the Rossi Xray Timing Explorer (RXTE)
(Middleditch et al. 2006), giving ephemerides covering the whole of S5. These ephemerides
comprise seven interglitch segments, each of which produces phasestable timing solutions.
The segments are separated by times when the pulsar was observed to glitch. Due to the
complexity of the pulsar behaviour near glitches, which is not reflected in the simple model
used to predict pulse times of arrival, sometimes up to ∼ 30 days around them are not
covered by the ephemerides.
2. Gravitational wave search method
The details of the search method are discussed in Dupuis & Woan (2005) and Abbott et al.
(2007), but we will briefly review them here. Data from the gravitational wave detectors are
heterodyned using twice the known electromagnetic phase evolution of each pulsar, which
removes this rapidly varying component of the signal, leaving only the daily varying ampli
tude modulation caused by each detector’s antenna response. Once heterodyned the (now
complex) data are lowpass filtered at 0.25Hz, and then heavily downsampled, by averaging,
from the original sample rate of 16384Hz to 1/60Hz. Using these downsampled data (Bk,
where k represents the kthsample) we perform parameter estimation over the signal model
yk(a) given the unknown signal parameters a. This is done by calculating the posterior
probability distribution (Abbott et al. 2007)
p(a{Bk}) ∝
M
?
j
?
n
?
k
(ℜ{Bk} − ℜ{yk(a)})2+ (ℑ{Bk} − ℑ{yk(a)})2
?−mj
× p(a), (3)
where the first term on the right hand side is the likelihood (marginalised over the data
variance, giving a Student’stlike distribution), p(a) is the prior distribution for a, M is
the number of data segments into which the Bks have been cut (we assume stationarity of
the data during each segment), mjis the number of data points in the jth segment (with a
maximum value of 30, i.e. we only assume stationarity for periods less than, or equal to, 30
minutes in length), and n =?j
KolmogorovSmirnov tests performed to assess these in previous analyses).
j=1mj. The assumption of Gaussianity and stationarity of
the segments holds well for this analysis (see §4.5 of Dupuis (2004) for examples of χ2and
We have previously (Abbott et al. 2004, 2005, 2007) performed parameter estimation
over the four unknown gravitational wave signal parameters of amplitude h0, initial phase φ0,
cosine of the orientation angle cosι, and polarisation angle ψ, giving a = {h0,φ0,cosι,ψ}.
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Priors on each parameter are set to be uniform over their allowed ranges, with the upper end
of the range for h0set empirically from the noise level of the data. We choose a uniform prior
on h0for consistency with our previous analyses (Dupuis & Woan 2005; Abbott et al. 2004,
2005, 2007) and to facilitate straightforward comparison of sensitivity. Extensive trials with
software injections have shown this to be a very reasonable choice, returning a conservative
(i.e. high) upper limit consistent with the data and any possible signal.
Using a uniformly spaced grid on this fourdimensional parameter space the posterior is
calculated at each point. To obtain a posterior for each individual parameter we marginalise
over the three others. Using the marginalised posterior on h0 we can set an upper limit
by calculating the value that, integrating up from zero, bounds the required cumulative
probability (which we have taken as 95%). We also combine the data from multiple detectors
to give a joint posterior. To do this we simply take the product of the likelihoods for each
detector and multiply this joint likelihood by the prior. This is possible due to the phase
coherence between detectors. Again we can marginalise to produce posteriors for individual
parameters.
Below, in §2.1, we discuss exploring and expanding this parameter space to more di
mensions using a Markov chain Monte Carlo (MCMC) technique.
2.1. MCMC parameter search
When high resolutions are needed it can be computationally time consuming to calculate
the posterior over an entire grid as described above, and redundant areas of parameter space
with very little probability are explored for a disproportionately large amount of time. A
more efficient way to carry out such a search is with a Markov chain Monte Carlo (MCMC)
technique, in which the parameter space is explored more efficiently and without spending
much time in the areas with very low probability densities.
An MCMC integration explores the parameter space by stepping from one position
in parameter space to another, comparing the posterior probability of the two points and
using a simple algorithm to determine whether the step should be accepted. If accepted
it moves to that new position and repeats; if it is rejected it stays at the current position
and repeats. Each iteration of the chain, whether it stays in the same position or not, is
recorded and the amount of time the chain spends in a particular part of parameter space is
directly proportional to the posterior probability density there. The new points are drawn
randomly from a specific proposal distribution, often given by a multivariate Gaussian with
a mean set as the current position, and a predefined covariance. For an efficient MCMC the
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proposal distribution should reflect the underlying posterior it is sampling, but any proposal
(that does not explicitly exclude the posterior), given enough time, will sample the posterior
and deliver an accurate result. We use the MetropolisHastings (MH) algorithm to set the
acceptance/rejection ratio. Given a current position aiMH accepts the new position ai+1
with probability
?
where p(ad) is the posterior value at a given data d, and q(ab) is the proposal distribution
defining how we choose position a given a current position b. In our case we have symmet
ric proposal distributions, so q(ai+1a)/q(aiai+1) = 1 and therefore only the ratio of the
posteriors is needed.
α(ai+1ai) = min1,p(ai+1d)
p(aid)
q(aiai+1)
q(ai+1ai)
?
, (4)
A welltuned MCMC will efficiently explore the parameter space and generate chains
that, in histogram form, give the marginalised posterior distribution for each parameter.
Defining a good set of proposal distributions for the parameters in a has been done experi
mentally assuming that they are uncorrelated and therefore have independent distributions.
(There are in fact correlations between the h0and cosι parameters and the φ0and ψ pa
rameters, but in our studies these do not significantly alter the efficiency from assuming
independent proposals.) The posterior distributions of these parameters will also generally
not be Gaussian, especially in low SNR cases (which is the regime in which we expect to
be), but a Gaussian proposal is easiest to implement and again does not appear to sig
nificantly affect the chain efficiency. We find that, for the angular parameters, Gaussian
proposal distributions with standard deviations of an eighth the allowed parameter range
(i.e. σφ0= π/4rad, σcosι= 1/4 and σψ= π/16rad) provide a good exploration of the pa
rameter space (as determined from the ratio of accepted to rejected jumps in the chain) for
low SNR signals. We have performed many simulations comparing the output of the MCMC
and gridbased searches, both on simulated noise and simulated signals, and both codes give
results consistent to within a few percent. In these tests we find that the computational
speed of the MCMC code is about three times faster than the gridbased code, although this
can vary by tuning the codes.
An MCMC integration may take time to converge on the bulk of the probability distri
bution to be sampled, especially if the chains start a long way in parameter space from the
majority of the posterior probability. Chains are therefore allowed a burnin phase, during
which the positions in the chain are not recorded. For low SNR signals, where the signal
amplitude is close to zero and the posteriors are reasonably broad, this burnin time can be
short. To aid the convergence we use simulated annealing in which a temperature parame
ter is used to flatten the posterior during burnin to help the chain explore the space more
quickly. We do however use techniques to assess whether our chains have converged (see
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