First Search for Gravitational Waves from Known Pulsars with Advanced LIGO
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The Astrophysical Journal,
839:12
(
19pp
)
, 2017 April 10
https:
//
doi.org
/
10.3847
/
1538-4357
/
aa677f
© 2017. The American Astronomical Society. All rights reserved.
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Annecy-le-Vieux de Physique des Particules
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University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
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Syracuse University, Syracuse, NY 13244, USA
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LIGO Hanford Observatory, Richland, WA 99352, USA
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Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29
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Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius, Italy
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Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
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CSIRO Astronomy and Space Science, Australia Telescope National Facility, Box 76 Epping, NSW, 1710, Australia
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International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia
Received 2017 January 26; revised 2017 March 15; accepted 2017 March 15; published 2017 April 7
Abstract
We present the result of searches for gravitational waves from 200 pulsars using data from the
fi
rst observing run of
the Advanced LIGO detectors. We
fi
nd no signi
fi
cant evidence for a gravitational-wave signal from any of these
pulsars, but we are able to set the most constraining upper limits yet on their gravitational-wave amplitudes and
ellipticities. For eight of these pulsars, our upper limits give bounds that are improvements over the indirect spin-
down limit values. For another 32, we are within a factor of 10 of the spin-down limit, and it is likely that some of
these will be reachable in future runs of the advanced detector. Taken as a whole, these new results improve on
previous limits by more than a factor of two.
Key words:
gravitational waves
–
pulsars: general
Supporting material:
machine-readable table
1. Introduction
The recent observations of gravitational waves from the
inspiral and merger of binary black holes herald the era of
gravitational-wave astronomy
(
Abbott et al.
2016b
,
2016c
)
.
Such cataclysmic, transient, and extragalatic events are not
however the only potential sources of observable gravitational
waves. Galactic neutron stars offer a more local, and
continuous, quasi-monochromatic source of gravitational
radiation. Although intrinsically far weaker than the transient
sources that have been observed, their continuous nature allows
their signals to be found buried deep in the noise by coherently
integrating over the long observing runs of the gravitational-
wave observatories.
The subset of known pulsars, identi
fi
ed through electro-
magnetic observations, provides an important possible source
of continuous gravitational waves. They are often timed with
exquisite precision, allowing th
eir rotational phase evolution,
sky location and, if required, binary orbital parameters to be
determined very accurately. In t
urn, these timings allow us to
carry out fully phase-coherent and computationally cheap
gravitational-wave searches over the length of our observa-
tion runs. A selection of kno
wn pulsars have already been
targeted using data from the
initial LIGO, Virgo, and
GEO 600 detectors
(
summarizedinAasietal.
2014
)
, setting
upper limits on their signal amplitudes, though without any
detections.
An important milestone is passed when this upper limit
falls below the so-called spin-down limit on gravitational
strain for the targeted pulsar. This spin-down limit is
determined by equating the power radiated through gravita-
tional-wave emission to the pulsar
’
s observed spin-down
luminosity
(
attributed to its loss in rotational kinetic energy
)
,
i.e.,aswouldbethecaseifitwerea
gravitar
(
Palomba
2005
;
Knispel & Allen
2008
)
, and determining the equivalent strain
expected at Earth.
154
It can be calculated
(
see, e.g., Aasi
et al.
2014
)
using
=
⎛
⎝
⎜
⎞
⎠
⎟
∣
̇
∣
()
h
GI f
cdf
5
2
,1
zz
0
sd
rot
32
rot
12
where
f
rot
and
̇
f
rot
are the pulsar
’
s frequency and
fi
rst frequency
derivative,
I
zz
is the principal moment of inertia
(
for which we
generally assume a canonical value of 10
38
kg m
2
)
, and
d
is the
pulsar
’
s distance. In previous searches, this limit has been
surpassed
(
i.e., a smaller limit on the strain amplitude has been
obtained
)
for two pulsars: PSR J0534
+
2200
(
the Crab pulsar;
Abbott et al.
2008
)
and PSR J0835
−
4510
(
the Vela pulsar;
Abadie et al.
2011
)
.
In this paper, we provide results from a search for
gravitational waves from 200 known pulsars using data from
the
fi
rst observing run
(
O1
)
of Advanced LIGO
(
aLIGO
)
.For
the LIGO Hanford Observatory
(
H1
)
and LIGO Livingston
Observatory
(
L1
)
,weuseddatastartingon2015September
11 at 01:25:03 UTC and 18:29:03 UTC, respectively, and
fi
nishing on 2016 January 19 at 17:07:59
UTC at both sites.
With duty factors of 60% and 51% for H1 and L1, this run
provided 78 days and 66 days of data respectively for
analysis. The estimated sensitivity of this search as a function
153
Deceased, 2016 March.
154
This is known to be a naïve limit. For several young pulsars where the
braking index
(
see Section
4
)
is measured
(
Lyne et al.
2015
; Archibald et al.
2016
)
, we know that it is not consistent with pure gravitational-wave emission,
and other energy-loss mechanisms can be dominant. Effects of this on spin-
down limit calculations are discussed in Palomba
(
2000
)
. Figures 9 and 10 of
Abdo et al.
(
2013
)
also show that for pulsars observed as
Fermi
gamma-ray
sources, a not insigni
fi
cant proportion of their spin-down luminosity is emitted
through gamma-rays.
5
The Astrophysical Journal,
839:12
(
19pp
)
, 2017 April 10
Abbott et al.
of source frequency is shown in Figure
1
.
155
We see that,
even with its comparatively sho
rt observation time, the O1
data provide a signi
fi
cant sensitivity improvement over the
previous runs, particularly at lower frequencies.
1.1. The Signal
We model the source as a rigidly rotating triaxial star,
generating a strain signal at the detector of
(
e.g., Jaranowski
et al.
1998
)
ady i f
ady i f
=+
+
+
́
⎡
⎣
⎢
()
(
)(
)
()
() ()]
()
ht
h
F t
t
Ft
t
1
2
,,, 1 cos cos
,,, cossin ,
2
D
D
0
2
where
h
0
is the gravitational-wave strain amplitude, and
+
F
D
and
́
F
D
are the antenna responses of observatory
D
to the
“
+
”
and
“
×
”
polarizations. These are dependent on the source sky
position
(
right ascension
α
and declination
δ
)
and polarization
angle
ψ
.
ι
is the inclination of the star
’
s rotation axis to the line
of sight, and
f
(
)
t
represents the evolution of the sinusoidal
signal phase with time.
This phase evolution is usefully represented as a Taylor
expansion, so that
å
ffp
d
=+
+
-+
=
+
()
()
()!
(())()
()
t
f
j
tT tt
2
j
1
,3
j
N
j
0
0
0
0
1
where
f
0
is the initial gravitational-wave phase at time epoch
T
0
, and
()
f
j
0
is the
j
th
time derivative of the gravitational-wave
frequency de
fi
ned at
T
0
.
d
()
tt
is the time delay from the
observatory to the solar system barycenter, and can also include
binary system barycentering corrections to put the observatory
and source in inertial frames. For the majority of pulsars,
expansions to
N
=
1 or 2 are all that are required, but for some
young sources, with signi
fi
cant timing noise, expansions to
higher orders may be used. For the case of a source rotating
around a principal axis of inertia and producing emission from
the
==
lm
2
(
spherical harmonic
)
mass quadrupole mode
(
e.g., a rigidly rotating star with a triaxial moment of inertia
ellipsoid
)
, the gravitational-wave frequencies and frequency
derivatives are all twice their rotational values, e.g.,
=
ff
2
ro
t
.
2. Pulsar Selection
To re
fl
ect the improved sensitivity of LIGO during O1, we
targeted pulsars with rotation frequencies,
f
rot
, greater than
about 10 Hz, but also included seven promising sources with
large spin-down luminosities
156
with
f
rot
just below 10 Hz. The
==
lm
2
quadrupolar emission frequencies of these targets
are therefore greater than
∼
20 Hz and within the band of good
sensitivity for the instruments. We did not impose an upper
limit on target frequency.
We have obtained timings for 200 known pulsars in this
band. Timing was performed using the 42 ft telescope and
Lovell telescope at Jodrell Bank
(
UK
)
, the 26 m telescope at
Hartebeesthoek
(
South Africa
)
, the Parkes radio telescope
(
Australia
)
, the Nançay Decimetric Radio Telescope
(
France
)
,
the Arecibo Observatory
(
Puerto Rico
)
and the
Fermi
Large
Area Telescope
(
LAT
)
. Of these, 122 have been targeted in
previous campaigns
(
Aasi et al.
2014
)
, while 78 are new to this
search.
For the vast majority of these, we have obtained timing
solutions using pulse time-of-arrival
(
TOA
)
observations that
spanned the O1 run. For those pulsars whose TOAs did not
span O1, we still expect them to maintain very good coherence
when extrapolated to the O1 time. The
TEMPO
157
or
TEMPO
2
(
Hobbs et al.
2006
)
pulsar timing codes were used to produce
these solutions, which provide us with precise information on
the parameters de
fi
ning each pulsars phase evolution, including
their sky location and any binary system orbital dynamics if
applicable.
158
2.1. High-value Targets
We identi
fi
ed 11 sources
(
Table
1
)
for which we could either
improve upon, or closely approach, the spin-down limit based
on Equation
(
1
)
. These are all young pulsars at the lower end of
our sensitive frequency band and include the Crab and Vela
pulsars for which the spin-down limit had already been
surpassed
(
Abbott et al.
2008
; Abadie et al.
2011
; Aasi
et al.
2014
)
.
3. Analyses
Following Aasi et al.
(
2014
)
, we used three largely
independent methods for carrying out the search for the
11 high-value targets: the time-domain-based
Bayesian
(
Dupuis
& Woan
2005
)
and
/
-
statistic
(
Jaranowski & Królak
2010
)
methods, and the frequency-domain-based
5n
-vector method
(
Astone et al.
2010
,
2012
)
. For the other 189 targets only the
Bayesian
method was applied.
We refer the reader to Aasi et al.
(
2014
)
and references
therein for more detailed descriptions of these methods.
Generally, the methods were not modi
fi
ed for O1, although
there have been some signi
fi
cant improvements to the
Bayesian
method, which are described in Appendix
A
.
In addition, the results from the
n
5
-vector method used an
earlier data release, with a slightly different instrumental
calibration
(
Abbott et al.
2016a
)
, than that used for the two
other methods. The calibrations applied differ, however, by less
than 3% in amplitude and less than 3
◦
in phase for all high-
value sources.
For one high-value target, PSR J1302
−
6350, the
5n
-vector
method was not used. This pulsar is in a binary system, which
is not currently handled by this method. PSR J0205
+
6449
underwent a glitch on MJD 57345
(
2015 November 19
)
,
causing the rotation frequency to increase by
~ ́
-
8.3 10
6
Hz.
Because of the uncertain relation between the gravitational-
wave and electromagnetic signal phases over a glitch, we
analyzed both the pre-and-post-glitch periods independently
and combined these incoherently to give the
fi
nal result. To the
best of our knowledge, none of our other sources glitched
during the course of O1.
155
The sensitivity is taken as
¢
S
1
0.8
n
, where
¢
S
n
is the harmonic mean of the
observation-time-weighted one-sided power spectral densities,
S
T
n
, for H1
and L1
(
see
https:
//
dcc.ligo.org
/
LIGO-G1600150
/
public
and
https:
//
dcc.
ligo.org
/
LIGO-G1600151
/
public
, respectively
)
. The factor of 10.8 gives the
95% credible upper limit on gravitational-wave strain amplitude averaged over
orientation angles assuming Gaussian noise
(
Dupuis & Woan
2005
)
.
156
PSRs J0908
−
4913, J1418
−
6058, J1709
−
4429, J1826
−
1334, J1845
−
0743, J1853
−
0004, and J2129
+
1210A.
157
http:
//
tempo.sourceforge.net
158
Of the 200 pulsars, 119 are in binary systems.
6
The Astrophysical Journal,
839:12
(
19pp
)
, 2017 April 10
Abbott et al.