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Observing Primordial Gravitational Waves Below the Binary-Black-Hole-Produced Stochastic Background

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Observing Primordial Gravitational Waves Below the Binary-Black-Hole-Produced Stochastic Background Digging Deeper: Observing Primordial Gravitational Waves below the Binary-Black-Hole-Produced Stochastic Background The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Regimbau, T. et al. “Digging Deeper: Observing Primordial Gravitational Waves below the Binary-Black-Hole-Produced Stochastic Background.” Physical Review Letters 118.15 (2017): n. pag. © 2017 American Physical Society As Published http://dx.doi.org/10.1103/PhysRevLett.118.151105 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/108853 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. week ending PRL 118, 151105 (2017) PHYSICAL REVIEW LETTERS 14 APRIL 2017 Digging Deeper: Observing Primordial Gravitational Waves below the Binary-Black-Hole-Produced Stochastic Background † ‡ T. Regimbau,1,* M. Evans,2 N. Christensen,1,3, E. Katsavounidis,2 B. Sathyaprakash,4, and S. Vitale2 1Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur, CS 34229, Nice cedex 4, France 2LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Physics and Astronomy, Carleton College, Northfield, Minnesota 55057, USA 4Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA and School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, United Kingdom (Received 25 November 2016; revised manuscript received 9 February 2017; published 14 April 2017) The merger rate of black hole binaries inferred from the detections in the first Advanced LIGO science run implies that a stochastic background produced by a cosmological population of mergers will likely mask the primordial gravitational wave background. Here we demonstrate that the next generation of ground-based detectors, such as the Einstein Telescope and Cosmic Explorer, will be able to observe binary black hole mergers throughout the Universe with sufficient efficiency that the confusion background can potentially be −13 subtracted to observe the primordial background at the level of ΩGW ≃ 10 after 5 years of observation. DOI: 10.1103/PhysRevLett.118.151105 Introduction.—According to various cosmological sce- detection suggests the existence of a population of black narios, we are bathed in a stochastic primordial gravita- holes with relatively large masses, that might have formed tional wave background (PGWB) produced in the very in low-metallicity stellar environments [24], either through early stages of the Universe. Proposed theoretical models the evolution of an isolated massive binary in a galaxy [25] include the amplification of vacuum fluctuations during or through mass segregation and dynamical interactions in inflation [1–3], pre-big bang models [4–6], cosmic (super) a dense globular system [26]. strings [7–10], or phase transitions [11–13]. The detection LIGO discoveries during the first observing run included of a primordial background would have a profound impact a high-confidence (> 5σ) detection of a second merger on our understanding of the evolution of the Universe, as it event GW151226 and a marginal event of lower signifi- represents a unique window on its first instants, up to the cance ð< 2σÞ LVT151012, both believed to be binary black limits of the Planck era, and on the physical laws that apply hole (BBH) mergers. GW151226 resulted from the merger at the highest energy scales. of black holes of mass m1 ¼ 14.2M⊙ and m2 ¼ 7.5M⊙ In addition to the PGWB, an astrophysical background is [27], and LVT151012 is believed to have resulted from the expected to result from the superposition of a large number of merger of black holes of mass m1 ¼ 23M⊙ and m2 ¼ unresolved sources since the beginning of stellar activity (see 13M⊙ [27]. These observations indicate that many more Ref. [14] for a review of different sources that could produce detections will occur in the future and have provided the an astrophysical background). The astrophysical background tightest constraints on the rate of such events [28]. potentially contains a wealth of information about the history Besides the loudest and closest events that can be detected and evolution of a population of point sources, but it is a individually by the Advanced LIGO–Advanced Virgo net- confusion noise background that is detrimental to the work, the population of undetected sources at larger redshift observation of the PGWB. In this Letter we show that at is expected to create a significant astrophysical background the sensitivity levels envisaged for third generation detectors [29]. The background from the population of binary neutron such as the Einstein Telescope (ET) [15] and Cosmic stars (BNSs) and BBHs has been investigated by many Explorer (CE) [16], it will be possible to detect most of authors in the past (see Refs. [14,30–35] for the most recent the sources, giving hope that the confusion background can papers), who suggested that Advanced LIGO and Advanced be subtracted from the data, enabling the study of a PGWB. Virgo had a realistic chance of detecting this background This problem is similar to the one investigated in after a few years of operation with the standard cross- Refs. [17,18] in the context of the Big Bang Observer. correlation method, even if this background is nor continuous On September 14, 2015, Advanced LIGO [19–21] (no overlap of the sources) or Gaussian [36]. directly detected gravitational waves (GWs) from the In Ref. [29] the LIGO and Virgo Collaborations calcu- collision of two stellar-mass black holes at a redshift of lated the contribution to the stochastic background from z ∼ 0.1 (GW150914) [22,23]. The inferred component BBHs with the same masses as GW150914. Taking into masses of m1 ¼ 36 M⊙ and m2 ¼ 29 M⊙ are larger than account the statistical uncertainty in the rate, they found those of candidate black holes in x-ray binaries inferred that the stochastic signal could be detected, in the most from reliable dynamical measurements [24]. This first optimistic case, even before the design sensitivity of the 0031-9007=17=118(15)=151105(6) 151105-1 © 2017 American Physical Society week ending PRL 118, 151105 (2017) PHYSICAL REVIEW LETTERS 14 APRIL 2017 instruments is reached, but more likely after a few years of where RfðzÞ is the massive binary formation rate, PðtdÞ is the their operation at design sensitivity. It was also shown that distribution of the time delay td between the formation of lower mass systems that are too faint to be detected the massive progenitors and their merger, zf is the redshift at individually could add a significant contribution to the the formation time tf ¼ tðzÞ − td,andtðzÞ is the age of the background. Following this first Letter, other authors have Universe at merger. The value of Rm at z ¼ 0 corresponds to investigated the implication of GW150914 for the con- the local rate estimated from the first LIGO observation fusion background, including models of metallicity evo- þ138 −3 −1 run [27],whichis99−70 Gpc yr for model A and lution with redshift and mass distributions [37,38], and þ43 −3 −1 30−21 Gpc yr for model B. arrived at the same conclusion: the background from BBHs R ðzÞ is likely to be higher than previously expected and may We assume that f follows the cosmic star formation dominate over the primordial background. rate and we use the recent model of Ref. [41], based on the In this Letter, we use Monte Carlo simulations to calculate gamma-ray burst rate of Ref. [42] and on the normalization the confusion background from BBHs observed by networks described in Refs. [43,44]. We also assume that black holes of 30M of ground-based detectors. We study the potential reduction ⊙ or larger can only be formed below the metallicity Z ¼ Z =2 in the level of this background as more BBH signals are threshold c ⊙ [24,29]. The metallicity is drawn from detected, and can be subtracted from the data, because of the alog10-normal distribution with a standard deviation of 0.5 improved sensitivity of ET [15] and CE [16] compared to around the mean at each redshift [45] calculated from the advanced detectors. We show that the confusion background mean metallicity-redshift relation of Ref. [46], rescaled of astrophysically produced GWs can be significantly upwards by a factor of 3 to account for local observations reduced, paving the way to observe the primordial back- [41,47]. We further assume that the time delay distribution Pðt Þ∝tα α¼−1 t >t – ground. We do not investigate subtraction techniques in follows d d,with for d min [48 55], where t ¼ 50 106 detail, nor the residual resulting from the subtraction, but min × years is the minimum delay time for a assume that the signals can be removed with high enough massive binary to evolve until coalescence (see, e.g., t accuracy to search for an underlying stochastic gravitational Ref. [56]), and a maximum time delay max equal to the wave background of a different origin. Hubble time. ˆ Simulation of a population.—In order to calculate the (3) The location in the sky Ω, the cosine of the orientation ι, total contribution of BBHs to the confusion background, we the polarization ψ, and the phase of the signal at coalescence consider the fiducial model of Ref. [29] and generate ϕ0 were drawn from uniform distributions. an extra-galactic population of BBHs using the (iv) For each BBH, we determine if its resultant GW Monte Carlo procedure described in Refs. [36,39,40] and emission is detectable in a given detector network. The summarized below. signal-to-noise ratio (SNR) ρA detected by matched filter- (1) The intrinsic masses m1, m2 (in the source frame) are ing with an optimum filter in the ideal case of Gaussian selected from one of the two astrophysical distributions noise, in a detector labeled A,is Z considered in Ref.
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