Subtraction of correlated noise in global networks of gravitational-wave interferometers Michael W. Coughlin,1 Nelson L. Christensen,2 Rosario De Rosa,3, 4 Irene Fiori,5 Mark Golkowski, 6 Melissa Guidry,7 Jan Harms,8 Jerzy Kubisz,9 Andrzej Kulak,10 Janusz Mlynarczyk,10 Federico Paoletti,11, 5 and Eric Thrane12 1Department of Physics, Harvard University, Cambridge, MA 02138, USA 2Physics and Astronomy, Carleton College, Northfield, MN 55057, USA 3INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy 4Universit`adi Napoli 'Federico II', Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy 5European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy 6Department of Electrical Engineering, University of Colorado Denver, Denver, CO 80204, USA 7Department of Physics, College of William and Mary, Williamsburg, VA 23185, USA 8INFN, Sezione di Firenze, Sesto Fiorentino, 50019, Italy 9Astronomical Observatory, Jagiellonian University, Krakow, Poland 10AGH University of Science and Technology, Department of Electronics, Krakow, Poland 11INFN, Sezione di Pisa, I-56127 Pisa, Italy 12School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia The recent discovery of merging black holes suggests that a stochastic gravitational-wave back- ground is within reach of the advanced detector network operating at design sensitivity. However, correlated magnetic noise from Schumann resonances threatens to contaminate observation of a stochastic background. In this paper, we report on the first effort to eliminate intercontinental correlated noise from Schumann resonances using Wiener filtering. Using magnetometers as prox- ies for gravitational-wave detectors, we demonstrate as much as a factor of two reduction in the coherence between magnetometers on different continents. While much work remains to be done, our results constitute a proof-of-principle and motivate follow-up studies with a dedicated array of magnetometers. PACS numbers: Introduction. A stochastic gravitational-wave back- generation detectors, additional magnetic environmental ground (SGWB) is a potential signal source for ground- correlations have also been identified [8, 9]. These cor- based, second-generation interferometric gravitational- relations would contaminate the gravitational-wave data wave detectors such as Advanced LIGO [1] and Advanced streams and thus inhibit the detection of the SGWB. Virgo [2]. An astrophysical SGWB could be produced Correlated noise produces a systematic error that cannot by objects such as compact binary coalescences, pulsars, be reduced by integration over time and therefore is a magnetars, or core-collapse supernovae. A cosmological fundamental limit for SGWB searches. background could be generated by various physical pro- Global electromagnetic fields such as the Schumann cesses in the early universe [3, 4]. Previous analyses have resonances are an example of environmental correlations achieved interesting constraints on these processes [3{5]. between interferometers. By inducing forces on magnets In particular, with the recent discovery of a binary black- or magnetically susceptible materials in the test-mass hole merger [6], there is a chance of observing a SGWB suspension system, these fields are predicted to induce from these systems [7]. correlated noise in the spatially separated gravitational- Typical searches for a SGWB cross-correlate data from wave detectors. arXiv:1606.01011v1 [gr-qc] 3 Jun 2016 two spatially-separated interferometers, where the de- Schumann resonances are due to the very small at- tector noise is assumed to be Gaussian, stationary, and tenuation of extremely low frequency (ELF) electromag- uncorrelated between the two interferometers and much netic waves in the Earth-ionosphere waveguide, which is larger than the signal. In the case where the noise is formed by the highly conducting Earth and the lower uncorrelated, the sensitivity of the search for the SGWB ionosphere. The ELF waves are reflected by the lower increases with time, tobs, and with signal-to-noise ratio ionospheric layers at altitudes smaller than the half wave- 1=2 (SNR) proportional to tobs . Even though the interfer- length, enabling propagation of transverse electromag- ometers are spatially separated, with Advanced LIGO netic waves similar to a low-loss transmission line. The consisting of detectors in Livingston, Louisiana and Han- attenuation increases with frequency reaching the max- ford, Washington, and Advanced Virgo in Cascina, Italy, imum at the waveguide cut-off frequency of about 1500 correlated noise between the detectors has been identi- Hz. In the lower part of the ELF range, the attenua- fied [8, 9]. Stationary noise lines, such as those from the tion rate is particularly small: at 10 Hz it is roughly 0.25 60 Hz power line and 1 Hz timing GPS noise, present at dB/1000 km [12] . This enables observation of strong both LIGO sites, were notched in previous data analyzed ELF electromagnetic field pulses (ELF transients) prop- [4, 5, 10, 11]. Due to the increased sensitivity of second agating around the world several times. 2 The main source of ELF waves in the Earth-ionosphere 0:015pT=Hz1=2 at 14 Hz [18]. These magnetometers can waveguide are negative cloud-to-ground (-CG) atmo- potentially be used to subtract correlated magnetic noise spheric discharges, in which the vertical component of in gravitational-wave detectors. In previous work [8, 9], the dipole moment dominates and effectively generates Thrane et al. estimated the effect of the correlated strain the electromagnetic waves. An individual -CG discharge the Schumann resonances would generate for second- is an impulse of current associated with the charge trans- generation gravitational-wave detectors and in particular fer of about 2.5 C in the plasma channel that has a their effect on SGWB searches. In addition to explor- length of 2 to 3 km and lasts for about 75µs. A typ- ing simple Wiener filter schemes using toy models for the ical dipole moment (charge moment) of a discharge is gravitational-wave detector strain and magnetometer sig- about 6 C km [13]. The spectrum of an impulse gen- nals, they show how to optimally detect a SGWB in the erated by -CG is practically flat up to the cut-off fre- presence of unmitigated correlated noise. In this paper, quency of the waveguide. On Earth, mainly in the trop- we carry out a demonstration of Wiener filtering with a ics, many thunderstorm cells are always active and pro- goal of reducing the coherence between widely separated duce about 50 -CG discharges per second. Since the magnetometers (serving as proxies for gravitational-wave vertical atmospheric discharges radiate electromagnetic detectors). For our study, we use data from ultra-high- waves in all directions, it leads to interference of waves sensitivity magnetometers, which have been deployed for propagating around the world. As a consequence, the geophysical analyses. Using these previously deployed spectrum of atmospheric noise exhibit resonances. The magnetometers, allows us access to instruments with su- solutions to the resonance field in a lossless spherical cav- perb sensitivity, located in very magnetically quiet loca- ity were obtained for the first time by W.O. Schumann tions. As shown in [9], this is a requirement for successful [14]. The predicted eigenfrequencies (10.6, 18.4, 26, 33.5 subtraction. Unfortunately, the available magnetometers Hz) turned out to be much higher than the observed fre- are not situated optimally to reproduce the subtraction quencies, which are close to 8, 14, 20, 26 Hz [15], because scheme we envision for LIGO/Virgo. Ideally, one would of the dispersive character of the attenuation introduced want at least one pair of perpendicular magnetometers by the ionosphere, which detunes the Earth-ionosphere for each gravitational-wave detector. This witness pair cavity [16]. The peaks of the Schumann resonances are should be far enough from the detector to avoid the lo- relatively wide. Their quality factors for the first three cal magnetic noise, but close enough that it measures a Schumann resonance modes are about 4, 5, and 6, re- similar Schumann field as would be present at the detec- spectively. Due to the attenuation the coherence time of tor. For this study, the witness sensors are very far away the field in the Earth-ionosphere cavity does not exceed from the proxy gravitational-wave sensors. Despite these 1 second. limitations, the work that follows is an important first The Schumann resonance background is a global field. step to realistic subtraction of correlated magnetic noise The amplitude distribution of the following resonance in gravitational-wave detectors. modes depends on the time of day and year [17]. The In the most-ideal scenario, magnetometers would be spectral density of the first resonance mode is about stationed near the gravitational-wave detectors, not di- 1.0 pT/Hz1=2 and is different for different observers be- rectly on-site so as to be directly affected by the local cause of their location relative to the world thunderstorm varying magnetic fields, but not so far away as to reduce centers. The daily and yearly changes in the ampli- the coherence of the magnetometers. This is likely to be tude are of several tens of percent and are related to within a few hundreds of meters of the gravitational-wave the changes of the distance from the active thunderstorm detectors. We can test aspects of this by using existing centers (source-observer effect) and the intensity