Supplement–Upper Limits on the Stochastic Gravitational-Wave Background from
Advanced LIGO’s First Observing Run
In this supplement we describe in more detail how the
data in the main text are analyzed. Data used in the
analysis are from times when both detectors are in a
low-noise observing mode. We exclude certain times and
frequencies based on auxiliary channels that established
them as instrumental effects within the detectors.
We remove times due to known instrumental artifacts,
such as radio frequency (RF) glitching and electronics
saturations [1], or due to simulated signals (referred to
as hardware injections) generated by coherently moving
the interferometer mirrors [2]. We also exclude segments
associated with detections of gravitational waves. Data
are also excluded when the detectors’ noise power spectra
vary by more than 20% over the course of three 192s seg-
ments. This cut is performed to remove non-stationary
noise, and has been used in previous analyses [3]. A ded-
icated study has verified that removing variations of 20%
provides a close-to-optimal balance between the false pos-
itive and false negative rates. The total live time with all
vetoes applied, for 192s segments, is 29.85 days. These
cuts remove 35% of the time-series data.
We exclude frequencies known to be associated with in-
strumental artifacts, such as vibrations of the test mass
suspensions and calibration lines. We also remove fre-
quencies that are known to be instrumentally correlated
between the two LIGO detectors. As an example, we
detected a comb-like structure (a series of lines evenly
spaced in frequency) at half Hz frequencies with 1 Hz
separation. This structure was coherent between the
two sites and subsequently observed in auxiliary chan-
nels. The contributing frequency bins were not included
in the analysis. The frequency domain cuts remove 21%
of the observing band within each segment.
To verify the data analysis cuts described above, we
introduce an artificial time shift of 1 s between the two
sites. This effectively blinds the analysis by removing cor-
relations due to a broadband gravitational-wave signal,
while maintaining instrumental correlations with coher-
ence times greater than 1 s. This method also allows us
to identify additional instrumental artifacts that are not
identified using the cuts above, without biasing our anal-
ysis of the data. Upon studying the time-shifted data
with the analysis cuts described above, we find no excess
correlation, which is consistent with statistical expecta-
tions of uncorrelated Gaussian noise.
As a test of the detectors and the analysis pipeline,
we simulate a strong stochastic signal both by a hard-
ware injection and by a software injection (made by
adding a coherent signal to the data streams). The in-
jected background signals were isotropic and Gaussian,
with an amplitude of Ω
0
= 8
.
7
×
10
−
5
and a duration
of 600 s. Both types of injections were successfully re-
covered within 1
σ
uncertainty: the hardware injection
measured (8
.
8
±
0
.
6)
×
10
−
5
and the software injection
measured (9
.
0
±
0
.
6)
×
10
−
5
.
Finally, we study the possibility of correlated noise be-
tween H1 and L1 so that we may be confident that the
systematic error in our measurements is negligible. After
accounting for narrowband correlation detector artifacts
arising from digital systems, we estimate the contamina-
tion from the environment. Previous investigations have
identified geophysical Schumann resonances as the most
likely source of correlated environmental noise [4, 5]. Ex-
citations in the spherical shell cavity formed between the
surface of the Earth and the ionosphere cause magnetic
fields to be correlated over great distances, comparable to
the separation between H1 and L1. The magnetic fields,
in turn, can couple mechanically to the test mass through
the suspension system or electronically [5]. In order to
ascertain the systematic error from environmental corre-
lated noise, we construct a correlated noise budget. We
employ a number of conservative assumptions in order to
estimate the worst-case-scenario contamination.
The first step is to measure the frequency-dependent
coupling of the detector to ambient magnetic fields us-
ing external coils as an actuator [4, 5]. It is not prac-
tical to induce fields that act on the entire detector si-
multaneously, so we measure the coupling at each test
mass.
Next, we use magnetometers to measure the
magnetic coherence between the two sites. Using the
method described in [4, 5], we combine the magnetic
cross-power spectra and the coupling functions to esti-
mate the worst-case correlated noise from Schumann res-
10
2
10
−14
10
−12
10
−10
10
−8
10
−6
10
−4
10
−2
10
0
Frequency (Hz)
Ω
GW
O1 PI Curve
Correlated Noise Budget
FIG. 1. We show the O1 power-law integrated curve (PI
curve) along with the correlated noise budget as described
in the text. The noise budget falling below the O1 PI curve
indicates that correlated noise does not affect the O1 analysis.
2
onances Ω
noise
(
f
). Our conservative noise budget for O1
corresponds to the solid black curve in Figure 1. This
curve is obtained by fitting a power law to the magnetic
noise budget. We compare the noise budget to the power-
law integrated energy density spectrum (dashed black
curve) [6], which represent the statistical uncertainty of
the stochastic search. During O1, the correlated noise is
sufficiently low as to be ignored, contributing much less
than one sigma. (If the correlated noise estimate was sig-
nificant, the noise budget would be comparable to or in
excess of the dashed curve in the region of
∼
20-30 Hz.)
Work is ongoing to monitor and mitigate correlated noise
for future.
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et al.
,
https://dcc.ligo.org/LIGO-P1600285/
public
.
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et al.
, Physical Review Letters
113
, 231101 (2014).
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87
, 123009 (2013).
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fler, Phys. Rev. D
90
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, 124032
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