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Search for the Isotropic Stochastic Background Using Data from Advanced LIGO's Second Observing

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Search for the Isotropic Stochastic Background Using Data from Advanced LIGO's Second Observing Search for the isotropic stochastic background using data from Advanced LIGO's second observing run The LIGO Scientific Collaboration and The Virgo Collaboration (Dated: September 6, 2019) The stochastic gravitational-wave background is a superposition of sources that are either too weak or too numerous to detect individually. In this study we present the results from a cross- correlation analysis on data from Advanced LIGO's second observing run (O2), which we combine with the results of the first observing run (O1). We do not find evidence for a stochastic background, so we place upper limits on the normalized energy density in gravitational waves at the 95% credible 8 8 level of ΩGW < 6:0 10− for a frequency-independent (flat) background and ΩGW < 4:8 10− at 25 Hz for a background× of compact binary coalescences. The upper limit improves over× the O1 result by a factor of 2.8. Additionally, we place upper limits on the energy density in an isotropic background of scalar- and vector-polarized gravitational waves, and we discuss the implication of these results for models of compact binaries and cosmic string backgrounds. Finally, we present a conservative estimate of the correlated broadband noise due to the magnetic Schumann resonances in O2, based on magnetometer measurements at both the LIGO Hanford and LIGO Livingston observatories. We find that correlated noise is well below the O2 sensitivity. Introduction| A superposition of gravitational waves methodology, then describe the data and data quality from many astrophysical and cosmological sources cuts. As we do not find evidence for the stochastic back- creates a stochastic gravitational-wave background ground, we place upper limits on the possible amplitude (SGWB). Sources which may contribute to the stochas- of an isotropic stochastic background, as well as limits tic background include compact binary coalescences [1{ on the presence of alternative gravitational-wave polar- 8], core collapse supernovae [9{14], neutron stars [15{ izations. Upper limits on anisotropic stochastic back- 24], stellar core collapse [25, 26], cosmic strings [27{ grounds are given in a publication that is a companion 31], primordial black holes [32{34], superradiance of ax- to this one [70]. We then give updated forecasts of the ion clouds around black holes [35{38], and gravitational sensitivities of future stochastic searches and discuss the waves produced during inflation [39{47]. A particularly implications of our current results for the detection of the promising source is the stochastic background from com- stochastic background from compact binaries and cosmic pact binary coalescences, especially in light of the detec- strings. Finally, we present estimates of the correlated tions of one binary neutron star and ten binary black noise in the LIGO detectors due to magnetic Schumann hole mergers [48{55] by the Advanced LIGO Detector, resonances [71], and discuss mitigation strategies that are installed in the Laser Interferometer Gravitational-wave being pursued for future observing runs. Observatory (LIGO) [56], and by Advanced Virgo [57] so Method| The isotropic stochastic background can be far. Measurements of the rate of binary black hole and bi- described in terms of the energy density per logarithmic nary neutron star mergers imply that the stochastic back- frequency interval ground may be large enough to detect with the Advanced f dρGW LIGO-Virgo detector network [58, 59]. The stochastic ΩGW(f) = ; (1) background is expected to be dominated by compact ρc df binaries at redshifts inaccessible to direct searches for where dρGW is the energy density in gravitational waves gravitational-wave events [60]. Additionally, a detec- in the frequency interval from f to f + df, and ρc = tion of the stochastic background would enable a model- 2 2 3H0 c =(8πG) is the critical energy density required for a independent test of general relativity by discerning the spatially flat universe. Throughout this work we will use polarization of gravitational waves [61, 62]. Because gen- the value of the Hubble constant measured by the Planck eral relativity predicts only two tensor polarizations for 1 1 satellite, H0 = 67:9 kms− Mpc− [72]. gravitational waves, any detection of alternative polar- We use the optimal search for a stationary, Gaussian, izations would imply a modification to our current un- unpolarized, and isotropic stochastic background, which derstanding of gravity [63{65]. For recent reviews on is the cross-correlation search [66, 67, 73, 74] (however, relevant data analysis methods, see [66, 67]. see [75]). For two detectors, we define a cross-correlation ^ In this manuscript, we present a search for an isotropic statistic C(f) in every frequency bin stochastic background using data from Advanced LIGO's ? ^ 2 Re[~s1(f)~s2(f)] second observing run (O2). As in previous LIGO and C(f) = ; (2) T γT (f)S0(f) Virgo analyses, this search is based on cross-correlating the strain data between pairs of gravitational-wave de- wheres ~i(f) is the Fourier transform of the strain time tectors [68, 69]. We first review the stochastic search series in detector i = 1; 2 , T is the segment duration f g 2 used to compute the Fourier transform, and S0(f) is the also investigate several specific spectral indices predicted spectral shape for an ΩGW = const background given by for different gravitational-wave sources. In the frequency band probed by Advanced LIGO, the stochastic back- 2 3H0 ground from compact binaries is well approximated by S0(f) = : (3) 10π2f 3 a power law with α = 2=3 [77]. Slow roll inflation and cosmic string models can be described with α = 0 [78]. The quantity γ (f) is the normalized overlap reduction T Finally, following previous analyses [68], we use α = 3 as function for tensor (T) polarizations [73], which encodes an approximate value to stand in for a variety of astro- the geometry of the detectors and acts as a transfer func- physical models with positive slopes, such as unresolved tion between strain cross-power and Ω (f). Equation GW supernovae [11{14]. (2) has been normalized so that the expectation value of Data| We analyze data from Advanced LIGO's sec- C^(f) is equal to the energy density in each frequency bin ond observing run, which took place from 16:00:00 UTC C^(f) = ΩGW(f): (4) on 30 November, 2016 to 22:00:00 UTC on 25 August, h i 2017. We cross correlate the strain data measured by the In the limit where the gravitational-wave strain ampli- two Advanced LIGO detectors, located in Hanford, WA tude is small compared to instrumental noise, the vari- and Livingston, LA in the United States [56]. Linearly ance of C^(f) is approximately given by coupled noise has been removed from the strain time series at Hanford and Livingston using Wiener filtering 2 1 P1(f)P2(f) [79, 80], see also [81{83]. By comparing coherence spec- σ (f) 2 2 ; (5) ≈ 2T ∆f γT (f)S0 (f) tra and narrowband estimators formed with and without Wiener filtering, we additionally verified that this noise where P (f) are the one-sided noise power spectral den- 1;2 subtraction scheme does not introduce correlated arti- sities of the two detectors and ∆f is the frequency reso- facts into the Hanford and Livingston data. lution, which we take to be 1=32 Hz. Virgo does not have a significant impact on the sensi- An optimal estimator can be constructed for a model of tivity of the stochastic search in O2, because of the larger any spectral shape by taking a weighted combination of detector noise, the fact that less than one month of coin- the cross-correlation statistics across different frequency cident integration time is available, and because the over- bins f k lap reduction function is smaller for the Hanford-Virgo P 1 ^ 2 and Livingston-Virgo pairs than for Hanford-Livingston. ^ k w(fk)− C(fk)σ− (fk) Ωref = P 2 2 ; Therefore we do not include Virgo data in the O2 anal- w(fk)− σ− (fk) k ysis. 2 X 2 2 σΩ− = w(fk)− σ− (fk); (6) The raw strain data are recorded at 16,384 Hz. We k first downsample the strain time series to 4096 Hz, and where the optimal weights for spectral shape ΩGW(f) are apply a 16th-order high-pass Butterworth filter with knee given by frequency of 11 Hz to avoid spectral leakage from the noise power spectrum below 20 Hz. Next we apply a Ω (f ) w(f) = GW ref : (7) Fourier transform to segments with a duration of 192 s, ΩGW(f) using 50% overlapping Hann windows, then we coarse- grain six frequency bins to obtain a frequency resolution The broadband estimators are normalized so that of 1/32 Hz. As in [68], we observe in the band 20-1726 Ω^ = Ω (f ). By appropriate choices of the ref GW ref Hz. The maximum frequency of 1726 Hz is chosen to weightsh i w(f), one may construct an optimal search for avoid aliasing effects after downsampling the data. stochastic backgrounds with arbitrary spectral shapes, or Next, we apply a series of data quality cuts that re- for stochastic backgrounds with scalar and vector polar- move non-Gaussian features of the data. We remove izations. times when the detectors are known to be unsuitable Many models of the stochastic background can be ap- for science results [84] and times associated with known proximated as a power laws [74, 76], gravitational-wave events [55]. We also remove times f α where the noise is non-stationary, following the proce- ΩGW(f) = Ωref ; (8) dure described in the supplement of [69] (see also [68]). fref These cuts remove 16% of the coincident time which is with a spectral index α and an amplitude Ωref at a refer- in principle suitable for data analysis, leading to a coin- ence frequency fref .
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